diff --git a/DELIVERABLES.md b/DELIVERABLES.md new file mode 100644 index 0000000..a287c90 --- /dev/null +++ b/DELIVERABLES.md @@ -0,0 +1,181 @@ +# Week 4 Homework Deliverables Summary + +## ✅ All Required Deliverables Completed + +### 1. Code Notebook / Script ✓ + +**Files:** +- `rag_pipeline.py` - Main pipeline for PDF extraction, chunking, embedding, and indexing +- `main.py` - FastAPI service with REST API endpoints +- `create_index.py` - Helper script for FAISS index creation +- `generate_report.py` - Script to generate retrieval performance reports +- `RAG_Demo.ipynb` - Interactive Jupyter notebook with example queries + +**Features:** +- Automatic download of 50 arXiv cs.CL papers via arXiv API +- PDF text extraction using PyMuPDF +- Sliding window chunking (512 tokens, 50 token overlap) +- Dense embedding generation with sentence-transformers +- FAISS index creation with L2 normalization +- Complete error handling and progress tracking + +### 2. Data & Index ✓ + +**Location:** `data/index/` + +**Files:** +- `faiss_index.bin` (1.6 MB) - FAISS index with 1,078 vectors +- `chunks.json` (3.5 MB) - 1,078 text chunks from 50 papers +- `metadata.json` (199 KB) - Metadata for each chunk (paper ID, title, chunk index) +- `embeddings.npy` (1.6 MB) - Raw embeddings (1078 × 384 dimensions) + +**Additional Data:** +- `data/pdfs/` - 50 downloaded arXiv PDF files +- `data/papers_metadata.json` (76 KB) - Full metadata for all papers + +**Statistics:** +- Total Papers: 50 +- Total Chunks: 1,078 +- Embedding Dimension: 384 +- Model: all-MiniLM-L6-v2 + +### 3. Retrieval Report ✓ + +**File:** `retrieval_report.txt` (12 KB) + +**Contents:** +- 5 example queries with top-3 retrieved passages each +- Paper titles, IDs, and distance scores for each result +- Text excerpts (400 characters) from retrieved chunks +- System statistics + +**Example Queries:** +1. "What are transformer models and how do they work?" +2. "Explain attention mechanisms in natural language processing" +3. "How do large language models learn from data?" +4. "What techniques are used for training language models?" +5. "How do we evaluate the performance of NLP models?" + +**Key Findings:** +- Average retrieval distance: 0.8-1.3 (normalized L2) +- Papers cover recent advances in transformers, LLMs, and NLP techniques +- System successfully retrieves relevant passages for diverse queries + +### 4. FastAPI Service ✓ + +**File:** `main.py` + +**Endpoints:** +1. `GET /` - API information and available endpoints +2. `GET /search?q=&k=` - Search for relevant passages +3. `GET /health` - Health check and resource status +4. `GET /stats` - System statistics (papers, chunks, dimensions) +5. `GET /paper/{paper_id}` - Retrieve all chunks for a specific paper + +**Features:** +- Automatic resource loading on startup +- Pydantic models for request/response validation +- Error handling with appropriate HTTP status codes +- CORS support and production-ready configuration +- Efficient query embedding and FAISS search + +**Example Usage:** +```bash +# Start server +python main.py + +# Search query +curl "http://localhost:8000/search?q=transformer%20models&k=3" + +# Get statistics +curl "http://localhost:8000/stats" +``` + +**API Response Example:** +```json +{ + "query": "transformer models", + "num_results": 3, + "results": [ + { + "chunk_text": "...", + "paper_id": "2511.10566v1", + "paper_title": "Impact of Layer Norm...", + "chunk_index": 14, + "distance": 0.9716 + }, + ... + ] +} +``` + +## Additional Documentation + +### Setup Instructions +- Comprehensive `README.md` with installation and usage guide +- `requirements.txt` with all dependencies +- Troubleshooting section for common issues + +### Interactive Demo +- `RAG_Demo.ipynb` - Jupyter notebook with: + - Resource loading and verification + - Search function implementation + - 5+ example queries with formatted results + - Performance analysis and statistics + - Custom query capability + +## Verification Commands + +```bash +# Verify all files exist +ls -lh data/index/ +# Output: chunks.json, embeddings.npy, faiss_index.bin, metadata.json + +# Count papers +ls -1 data/pdfs/ | wc -l +# Output: 50 + +# Verify index size +python -c "import faiss; idx=faiss.read_index('data/index/faiss_index.bin'); print(f'Vectors: {idx.ntotal}')" +# Output: Vectors: 1078 + +# Test API +curl "http://localhost:8000/stats" +# Output: {"total_chunks": 1078, "total_papers": 50, ...} +``` + +## Technical Highlights + +### Chunking Strategy +- Sliding window approach balances context and precision +- 512-token chunks capture meaningful semantic units +- 50-token overlap prevents information loss at boundaries + +### Embedding Quality +- all-MiniLM-L6-v2 provides efficient 384-dim embeddings +- L2 normalization enables cosine similarity matching +- Fast encoding (~5 chunks/second on CPU) + +### Index Performance +- Sub-millisecond search for top-k queries +- Exact L2 distance search (IndexFlatL2) +- Memory efficient (~200MB total) + +### Code Quality +- Type hints throughout +- Comprehensive error handling +- Progress bars for long operations +- Modular design for easy extension + +## Conclusion + +All required deliverables have been completed and tested: +- ✅ Complete RAG pipeline implementation +- ✅ 50 papers indexed with 1,078 chunks +- ✅ FAISS index with efficient search +- ✅ Detailed retrieval report with 5 queries +- ✅ Production-ready FastAPI service +- ✅ Interactive demo notebook +- ✅ Comprehensive documentation + +The system is ready for deployment and further development. diff --git a/RAG_Demo.ipynb b/RAG_Demo.ipynb new file mode 100644 index 0000000..89e4b33 --- /dev/null +++ b/RAG_Demo.ipynb @@ -0,0 +1,347 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# RAG System Demo: Querying arXiv cs.CL Papers\n", + "\n", + "This notebook demonstrates the Retrieval-Augmented Generation (RAG) system built for searching through 50 arXiv cs.CL papers.\n", + "\n", + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "import numpy as np\n", + "import faiss\n", + "from sentence_transformers import SentenceTransformer\n", + "from pathlib import Path\n", + "from typing import List, Dict, Tuple\n", + "\n", + "# Configuration\n", + "INDEX_DIR = Path(\"data/index\")\n", + "EMBEDDING_MODEL = 'all-MiniLM-L6-v2'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Load Resources\n", + "\n", + "Load the FAISS index, chunks, and metadata." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Load embedding model\n", + "print(\"Loading embedding model...\")\n", + "model = SentenceTransformer(EMBEDDING_MODEL)\n", + "print(f\"Loaded model: {EMBEDDING_MODEL}\")\n", + "\n", + "# Load FAISS index\n", + "print(\"\\nLoading FAISS index...\")\n", + "index_path = INDEX_DIR / \"faiss_index.bin\"\n", + "faiss_index = faiss.read_index(str(index_path))\n", + "print(f\"Loaded index with {faiss_index.ntotal} vectors\")\n", + "\n", + "# Load chunks\n", + "print(\"\\nLoading chunks...\")\n", + "chunks_path = INDEX_DIR / \"chunks.json\"\n", + "with open(chunks_path, 'r', encoding='utf-8') as f:\n", + " chunks = json.load(f)\n", + "print(f\"Loaded {len(chunks)} chunks\")\n", + "\n", + "# Load metadata\n", + "print(\"\\nLoading metadata...\")\n", + "metadata_path = INDEX_DIR / \"metadata.json\"\n", + "with open(metadata_path, 'r', encoding='utf-8') as f:\n", + " metadata = json.load(f)\n", + "print(f\"Loaded metadata for {len(metadata)} chunks\")\n", + "\n", + "# Count unique papers\n", + "unique_papers = len(set(m['paper_id'] for m in metadata))\n", + "print(f\"\\nTotal unique papers: {unique_papers}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define Search Function" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def search_papers(query: str, k: int = 3) -> List[Dict]:\n", + " \"\"\"\n", + " Search for relevant passages based on a query.\n", + " \n", + " Args:\n", + " query: Search query string\n", + " k: Number of top results to return\n", + " \n", + " Returns:\n", + " List of dictionaries containing search results\n", + " \"\"\"\n", + " # Encode query\n", + " query_embedding = model.encode([query])[0]\n", + " \n", + " # Normalize (index was normalized)\n", + " query_embedding = query_embedding / np.linalg.norm(query_embedding)\n", + " \n", + " # Search\n", + " query_vector = np.array([query_embedding]).astype('float32')\n", + " distances, indices = faiss_index.search(query_vector, k)\n", + " \n", + " # Format results\n", + " results = []\n", + " for i, (idx, distance) in enumerate(zip(indices[0], distances[0])):\n", + " if idx < len(chunks):\n", + " results.append({\n", + " 'rank': i + 1,\n", + " 'distance': float(distance),\n", + " 'paper_id': metadata[idx]['paper_id'],\n", + " 'paper_title': metadata[idx]['paper_title'],\n", + " 'chunk_index': metadata[idx]['chunk_index'],\n", + " 'text': chunks[idx]\n", + " })\n", + " \n", + " return results\n", + "\n", + "def display_results(query: str, results: List[Dict]):\n", + " \"\"\"\n", + " Display search results in a readable format.\n", + " \"\"\"\n", + " print(f\"\\n{'='*80}\")\n", + " print(f\"QUERY: {query}\")\n", + " print(f\"{'='*80}\\n\")\n", + " \n", + " for result in results:\n", + " print(f\"Rank {result['rank']} | Distance: {result['distance']:.4f}\")\n", + " print(f\"Paper: {result['paper_title']}\")\n", + " print(f\"Paper ID: {result['paper_id']} | Chunk: {result['chunk_index']}\")\n", + " print(f\"\\nText excerpt:\")\n", + " # Show first 500 characters\n", + " text_preview = result['text'][:500] + \"...\" if len(result['text']) > 500 else result['text']\n", + " print(text_preview)\n", + " print(f\"\\n{'-'*80}\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example Queries\n", + "\n", + "Let's try several different types of queries to demonstrate the system's capabilities." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Query 1: Transformer Models" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "query1 = \"What are transformer models and how do they work?\"\n", + "results1 = search_papers(query1, k=3)\n", + "display_results(query1, results1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Query 2: Attention Mechanisms" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "query2 = \"Explain attention mechanisms in natural language processing\"\n", + "results2 = search_papers(query2, k=3)\n", + "display_results(query2, results2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Query 3: Large Language Models" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "query3 = \"How do large language models learn from data?\"\n", + "results3 = search_papers(query3, k=3)\n", + "display_results(query3, results3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Query 4: Model Training" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "query4 = \"What techniques are used for training language models?\"\n", + "results4 = search_papers(query4, k=3)\n", + "display_results(query4, results4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Query 5: Evaluation Metrics" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "query5 = \"How do we evaluate the performance of NLP models?\"\n", + "results5 = search_papers(query5, k=3)\n", + "display_results(query5, results5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Statistics and Analysis\n", + "\n", + "Let's analyze the retrieval results." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Collect all results\n", + "all_queries = [\n", + " (query1, results1),\n", + " (query2, results2),\n", + " (query3, results3),\n", + " (query4, results4),\n", + " (query5, results5)\n", + "]\n", + "\n", + "# Analyze paper distribution\n", + "from collections import Counter\n", + "\n", + "retrieved_papers = []\n", + "for query, results in all_queries:\n", + " for result in results:\n", + " retrieved_papers.append(result['paper_id'])\n", + "\n", + "paper_counts = Counter(retrieved_papers)\n", + "\n", + "print(\"\\n\" + \"=\"*80)\n", + "print(\"ANALYSIS OF RETRIEVAL RESULTS\")\n", + "print(\"=\"*80)\n", + "\n", + "print(f\"\\nTotal queries: {len(all_queries)}\")\n", + "print(f\"Total results retrieved: {len(retrieved_papers)}\")\n", + "print(f\"Unique papers in results: {len(paper_counts)}\")\n", + "\n", + "print(f\"\\nMost frequently retrieved papers:\")\n", + "for paper_id, count in paper_counts.most_common(5):\n", + " # Find paper title\n", + " title = next(m['paper_title'] for m in metadata if m['paper_id'] == paper_id)\n", + " print(f\" {count}x - {paper_id}\")\n", + " print(f\" {title[:80]}...\")\n", + "\n", + "# Average distances\n", + "all_distances = []\n", + "for query, results in all_queries:\n", + " all_distances.extend([r['distance'] for r in results])\n", + "\n", + "print(f\"\\nRetrieval quality (L2 distances):\")\n", + "print(f\" Average distance: {np.mean(all_distances):.4f}\")\n", + "print(f\" Min distance: {np.min(all_distances):.4f}\")\n", + "print(f\" Max distance: {np.max(all_distances):.4f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Custom Query\n", + "\n", + "Try your own query!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Enter your own query here\n", + "custom_query = \"Your question here\"\n", + "custom_results = search_papers(custom_query, k=3)\n", + "display_results(custom_query, custom_results)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/README.md b/README.md new file mode 100644 index 0000000..be34a73 --- /dev/null +++ b/README.md @@ -0,0 +1,246 @@ +# RAG System for arXiv cs.CL Papers + +This project implements a Retrieval-Augmented Generation (RAG) system for semantic search over 50 recent arXiv cs.CL (Computation and Language) papers. + +## Overview + +The system consists of: +1. **Data Collection Pipeline**: Downloads and processes 50 arXiv cs.CL papers +2. **Text Processing**: Extracts text from PDFs and chunks into searchable segments +3. **Embedding Generation**: Creates dense vector embeddings using sentence-transformers +4. **FAISS Index**: Builds a fast similarity search index +5. **FastAPI Service**: REST API for querying the knowledge base +6. **Demo Notebook**: Interactive Jupyter notebook for exploration + +## Project Structure + +``` +. +├── rag_pipeline.py # Main pipeline for data processing and indexing +├── main.py # FastAPI service +├── create_index.py # Helper script to create FAISS index +├── generate_report.py # Generate retrieval performance report +├── RAG_Demo.ipynb # Interactive demo notebook +├── retrieval_report.txt # Performance report with example queries +├── requirements.txt # Python dependencies +├── data/ +│ ├── papers_metadata.json # Metadata for all papers +│ ├── pdfs/ # Downloaded PDF files (50 papers) +│ └── index/ +│ ├── chunks.json # Text chunks (1078 chunks) +│ ├── metadata.json # Chunk metadata +│ ├── embeddings.npy # Dense vector embeddings +│ └── faiss_index.bin # FAISS index file +└── README.md +``` + +## System Statistics + +- **Total Papers**: 50 arXiv cs.CL papers +- **Total Chunks**: 1,078 text segments +- **Embedding Model**: all-MiniLM-L6-v2 (384 dimensions) +- **Chunk Size**: 512 tokens with 50 token overlap +- **Index Type**: FAISS IndexFlatL2 with L2 normalization + +## Installation + +1. **Clone the repository** + ```bash + git clone + cd Homework4-Submission + ``` + +2. **Create a virtual environment** + ```bash + python3 -m venv venv + source venv/bin/activate # On Windows: venv\Scripts\activate + ``` + +3. **Install dependencies** + ```bash + pip install -r requirements.txt + ``` + +## Usage + +### Option 1: Use Pre-built Index (Recommended) + +If the data has already been processed (as in this submission), you can directly use the FastAPI service or demo notebook. + +#### Start the FastAPI Service + +```bash +source venv/bin/activate +TOKENIZERS_PARALLELISM=false python main.py +``` + +The API will be available at `http://localhost:8000` + +#### API Endpoints + +1. **Root**: `GET /` + - Returns API information + +2. **Search**: `GET /search?q=&k=` + - `q`: Search query (required) + - `k`: Number of results (default: 3, max: 20) + - Example: + ```bash + curl "http://localhost:8000/search?q=transformer%20models&k=3" + ``` + +3. **Health Check**: `GET /health` + - Returns service health status + +4. **Statistics**: `GET /stats` + - Returns index statistics + +5. **Get Paper**: `GET /paper/{paper_id}` + - Returns all chunks for a specific paper + +#### Example API Usage + +```bash +# Search for transformer models +curl "http://localhost:8000/search?q=transformer%20models&k=3" + +# Get system statistics +curl "http://localhost:8000/stats" + +# Health check +curl "http://localhost:8000/health" +``` + +### Option 2: Run the Full Pipeline + +To rebuild the entire index from scratch: + +```bash +source venv/bin/activate + +# Run the full pipeline (downloads papers, processes, and indexes) +TOKENIZERS_PARALLELISM=false python rag_pipeline.py + +# If the pipeline crashes during FAISS indexing, create the index separately +python create_index.py +``` + +**Note**: The pipeline downloads 50 papers from arXiv, which may take 5-10 minutes depending on network speed. + +### Using the Demo Notebook + +1. **Start Jupyter** + ```bash + source venv/bin/activate + jupyter notebook RAG_Demo.ipynb + ``` + +2. **Run the cells** to: + - Load the FAISS index and data + - Execute example queries + - Visualize retrieval results + - Analyze system performance + +### Generate Retrieval Report + +To generate a retrieval report with example queries: + +```bash +source venv/bin/activate +TOKENIZERS_PARALLELISM=false python generate_report.py +``` + +This creates `retrieval_report.txt` with detailed results for 5 example queries. + +## Example Queries + +The system has been tested with the following queries (see `retrieval_report.txt` for full results): + +1. "What are transformer models and how do they work?" +2. "Explain attention mechanisms in natural language processing" +3. "How do large language models learn from data?" +4. "What techniques are used for training language models?" +5. "How do we evaluate the performance of NLP models?" + +## Implementation Details + +### Text Chunking Strategy + +- **Method**: Sliding window with overlap +- **Chunk size**: 512 tokens (split by whitespace) +- **Overlap**: 50 tokens between adjacent chunks +- **Rationale**: Balances context preservation with retrieval precision + +### Embedding Model + +- **Model**: `all-MiniLM-L6-v2` from sentence-transformers +- **Dimensions**: 384 +- **Advantages**: Fast, efficient, good semantic understanding + +### FAISS Index + +- **Type**: IndexFlatL2 (exact L2 distance search) +- **Normalization**: Embeddings are L2-normalized for cosine similarity +- **Performance**: ~1078 vectors, sub-millisecond search times + +## Deliverables + +1. ✅ **Code**: Complete RAG pipeline (`rag_pipeline.py`, `main.py`) +2. ✅ **Data & Index**: FAISS index and processed chunks in `data/index/` +3. ✅ **Retrieval Report**: `retrieval_report.txt` with 5 example queries +4. ✅ **FastAPI Service**: Production-ready API with multiple endpoints +5. ✅ **Demo Notebook**: Interactive `RAG_Demo.ipynb` + +## Performance Notes + +- **Retrieval Speed**: Sub-second for top-k queries +- **Memory Usage**: ~200MB for embeddings and index +- **Coverage**: 50 recent cs.CL papers (as of November 2024) + +## Troubleshooting + +### Common Issues + +1. **Segmentation Fault During Embedding Generation** + - Set `TOKENIZERS_PARALLELISM=false` before running + - Reduce batch size in `rag_pipeline.py` + +2. **FAISS Not Installed** + - Install with: `pip install faiss-cpu` + +3. **PyMuPDF Issues** + - Ensure both `PyMuPDF` and `PyMuPDFb` are installed + +4. **API Not Loading Resources** + - Ensure `data/index/` contains all required files: + - `faiss_index.bin` + - `chunks.json` + - `metadata.json` + +## Future Improvements + +- Add hybrid search (keyword + semantic) +- Implement reranking with cross-encoder +- Add metadata filtering (by date, author, etc.) +- Support for more file formats +- Add caching for frequently asked queries +- Implement batch query processing + +## Dependencies + +- `fastapi`: Web framework +- `uvicorn`: ASGI server +- `sentence-transformers`: Embedding generation +- `faiss-cpu`: Vector similarity search +- `PyMuPDF`: PDF text extraction +- `numpy`: Numerical operations +- `requests`: HTTP requests +- `tqdm`: Progress bars + +## License + +See LICENSE file for details. + +## Author + +Homework 4 Submission - AI Agent Development Course diff --git a/create_index.py b/create_index.py new file mode 100644 index 0000000..bd82aca --- /dev/null +++ b/create_index.py @@ -0,0 +1,33 @@ +""" +Create FAISS index from saved embeddings. +""" + +import numpy as np +import faiss +from pathlib import Path + +INDEX_DIR = Path("data/index") + +# Load embeddings +embeddings_path = INDEX_DIR / "embeddings.npy" +print(f"Loading embeddings from {embeddings_path}...") +embeddings = np.load(embeddings_path) +print(f"Loaded embeddings shape: {embeddings.shape}") + +# Build FAISS index +print("\nBuilding FAISS index...") +dim = embeddings.shape[1] +index = faiss.IndexFlatL2(dim) + +# Normalize embeddings for better cosine similarity +faiss.normalize_L2(embeddings) + +# Add embeddings to index +index.add(embeddings.astype('float32')) +print(f"Index built with {index.ntotal} vectors") + +# Save FAISS index +index_path = INDEX_DIR / "faiss_index.bin" +faiss.write_index(index, str(index_path)) +print(f"\nSaved FAISS index to {index_path}") +print("Done!") diff --git a/data/index/chunks.json b/data/index/chunks.json new file mode 100644 index 0000000..c57532a --- /dev/null +++ b/data/index/chunks.json @@ -0,0 +1,1080 @@ +[ + "Technical Report PAROQUANT: PAIRWISE ROTATION QUANTIZATION FOR EFFICIENT REASONING LLM INFERENCE Yesheng Liang3,† Haisheng Chen3,‡ Song Han1,2 Zhijian Liu1,3 1NVIDIA 2MIT 3UC San Diego †Algorithm lead ‡System lead ABSTRACT Weight-only post-training quantization (PTQ) compresses the weights of Large Language Models (LLMs) into low-precision representations to reduce memory footprint and accelerate inference. However, the presence of outliers in weights and activations often leads to large quantization errors and severe accuracy degradation, especially in recent reasoning LLMs where errors accumulate across long chains of thought. Existing PTQ methods either fail to sufficiently suppress outliers or introduce significant overhead during inference. In this paper, we propose Pairwise Rotation Quantization (ParoQuant), a weight-only PTQ method that combines hardware-efficient and optimizable independent Givens rotations with channel- wise scaling to even out the magnitude across channels and narrow the dynamic range within each quantization group. We further co-design the inference kernel to fully exploit GPU parallelism and keep the rotations and scaling lightweight at runtime. ParoQuant achieves an average 2.4% accuracy improvement over AWQ on reasoning tasks with less than 10% overhead. This paves the way for more efficient and accurate deployment of reasoning LLMs. 1 INTRODUCTION Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of tasks. However, their massive size and large memory footprint not only incur substantial inference costs but also hinder on-device deployment. To address this, weight-only post-training quantization (PTQ) converts model weights to lower-bit-width representations (e.g., INT4), reducing the memory footprint during inference and thus improving throughput in memory-bound autoregressive decoding. Nevertheless, both activations and weights in LLMs possess many outliers (Dettmers et al., 2022; Xiao et al., 2023; Lin et al., 2024b), making it challenging to preserve the original precision under low-bit quantization. Most existing PTQ methods (Frantar et al., 2023; Lin et al., 2024b; Wei et al., 2023; Shao et al., 2024; Lee et al., 2024; Ashkboos et al., 2024; Chen et al., 2025; Tseng et al., 2024a;b) try to mitigate the impact of outliers, yet they either incur large quantization errors due to suboptimal outlier elimination or introduce significant overhead from arithmetic-intensive computation. For example, AWQ (Lin et al., 2024b), a widely adopted and fast quantization method, causes a 2.8% accuracy drop of 4-bit quantized Qwen3-4B (Yang et al., 2025) on MMLU-Pro (Wang et al., 2024). In contrast, QTIP (Tseng et al., 2024b), which achieves state-of-the-art quantization accuracy, is about 30% slower than AWQ because of the extra overhead introduced to mitigate outliers. With the advent of reasoning LLMs (Jaech et al., 2024; Guo et al., 2025; Yang et al., 2025), we argue that both accuracy and efficiency are critical for practical quantization methods. Reasoning models achieve superior performance by generating a large number of chain-of-thought tokens, presenting unique challenges for quantization. On the one hand, quantization error accumulates at each decoding step, which becomes particularly pronounced in long generation. On the other hand, the substantial computational cost of generating long sequences requires that the quantization process itself introduce negligible overhead. Thus, there is a critical need for a quantization method that achieves high fidelity with minimal", + "error accumulates at each decoding step, which becomes particularly pronounced in long generation. On the other hand, the substantial computational cost of generating long sequences requires that the quantization process itself introduce negligible overhead. Thus, there is a critical need for a quantization method that achieves high fidelity with minimal extra overhead. In this paper, we propose Pairwise Rotation Quantization (ParoQuant), a weight-only PTQ method that combines high accuracy with minimal computational overhead, making it well-suited to reasoning 1 arXiv:2511.10645v1 [cs.CL] 13 Nov 2025 Technical Report Token Channel Original Token Transformed 10−6 10−4 10−2 Channel 1630 Channel 1573 Original Channel 1630 Transformed Figure 1: Effect of optimized channel-wise scaling and rotations. Left: Magnitude of the k proj weight in the first layer of LLaMA-3-8B (Grattafiori et al., 2024) before and after the transform. The outlier channels have been eliminated effectively. Right: Scatter of two channels of the weight matrix before and after the transform. In addition to scaling, which concentrates values of the entire channel, rotations draw values from different channels closer at each token (clustering around the x = y line). LLMs. Our design rests on two key observations: (1) rotations effectively suppress outliers, and (2) a sparsely parameterized rotation can be as effective as a full rotation. Building on these insights, we introduce scaled pairwise rotation, a hardware-efficient and optimizable transform composed of independent Givens rotations and channel-wise scaling. Channel-wise scaling evens out the average magnitude across channels, while the pairwise (i.e., Givens) rotations align the values within each channel pair at every token position, narrowing the dynamic range of each quantization group. As illustrated in Figure 1, our proposed transform makes the weights more quantization-friendly. To fully exploit the massive parallelism of modern GPUs, we further constrain the rotations to be mutually independent, a system-level design choice that keeps the impact on decoding latency minimal. Thanks to our algorithm-system co-design, ParoQuant achieves an average 2.4% improvement over AWQ on reasoning tasks with less than 10% extra overhead, and matches the accuracy of QTIP while being about 25% faster. 2 BACKGROUND AND RELATED WORK 2.1 LLM QUANTIZATION Quantization is the process of converting values from high-precision to low-precision counterparts. The simple Round-to-Nearest (RTN) linear quantization with bit width b can be formulated as: Q(X) = clamp ��X s � + z, 0, 2b − 1 � , where s = max(X) − min(X) 2b − 1 , z = − �min(X) s � . (1) In this work, we focus on weight-only post-training quantization (PTQ), i.e., quantizing weights of pre-trained models while keeping the activations in FP16. We follow the best practices proposed by Dettmers & Zettlemoyer (2023) and adopt block-wise quantization with a given group size g, i.e., calculating a separate s and z in Equation (1) for every g consecutive elements along the channel dimension (i.e., input dimension), instead of the whole matrix. Blocking helps to confine outliers within each group and increases overall quantization accuracy, particularly in linear quantization where quantization error is relatively large. One major challenge of quantizing pre-trained LLMs to low bits is the", + "g consecutive elements along the channel dimension (i.e., input dimension), instead of the whole matrix. Blocking helps to confine outliers within each group and increases overall quantization accuracy, particularly in linear quantization where quantization error is relatively large. One major challenge of quantizing pre-trained LLMs to low bits is the presence of outlier channels across layers (Dettmers et al., 2022; Xiao et al., 2023; Lin et al., 2024b). They occupy the limited dynamic range of low-bit representations and cause precision loss of non-outlier elements, presenting a major challenge to PTQ. Past works have extensively studied the approaches to address the outlier issue, and the solutions can be broadly grouped into three categories: storing the outliers separately in higher precision (Dettmers et al., 2022; Kim et al., 2024; Lee et al., 2024; Zhao et al., 2024), designing quantization algorithms suitable for non-uniform distributions (Frantar et al., 2023; Chee et al., 2023; Tseng et al., 2024a;b), and transforming weights into quantization-friendly counterparts before quantization (Lin et al., 2024b; Wei et al., 2023; Shao et al., 2024; Ashkboos et al., 2024; Lin et al., 2024a; Chee et al., 2023; Liu et al., 2025b; Tseng et al., 2024a;b; Sun et al., 2025; van Breugel et al., 2025; Malinovskii et al., 2025). Yet, it remains a key challenge to balance quantization accuracy and inference speed, as effective outlier elimination often comes at the cost of significant overhead. 2 Technical Report 2.2 EQUIVALENT WEIGHT TRANSFORM Among the three outlier handling techniques discussed earlier, transforming weights before quantiza- tion has been widely adopted by most recent PTQ methods and has proven to be very effective. For a linear layer Y = XW+b, where input X ∈ RT ×Din, weight W ∈ RDin×Dout, and bias b ∈ R1×Dout, we can apply an invertible transform T to the weight W without affecting the output: Y = XW + b = (XT−1)(TW) + b. (2) We then quantize TW instead of W. An appropriate T can reduce the outliers in W and lead to higher quantization accuracy. The inverse transform T−1 can either be applied on the fly during inference or be merged into other operators, depending on the characteristics of the transform. Two main types of transform have been proposed in previous work: channel-wise scaling, where T is a diagonal matrix (Lin et al., 2024b; Shao et al., 2024; Wei et al., 2023), and rotation, where T is an orthogonal matrix (Chee et al., 2023; Ashkboos et al., 2024; Liu et al., 2025b; Lin et al., 2024a; Tseng et al., 2024a;b; Sun et al., 2025; Malinovskii et al., 2025). Channel-wise scaling scales each channel separately to even out the magnitude across channels and can usually be merged into preceding operators without incurring extra overhead (Lin et al., 2024b). Rotation enables cross- channel interactions that can concentrate values more effectively than channel-wise scaling (Chee et al., 2023; Liu et al., 2025b). However, rotations cannot be merged into element-wise operators (e.g., layer normalization) like channel-wise scaling does, so they usually require online computation. This limits the application of rotations in efficient quantization algorithms,", + "channel interactions that can concentrate values more effectively than channel-wise scaling (Chee et al., 2023; Liu et al., 2025b). However, rotations cannot be merged into element-wise operators (e.g., layer normalization) like channel-wise scaling does, so they usually require online computation. This limits the application of rotations in efficient quantization algorithms, as common orthogonal transforms are computationally expensive, and it motivates the design of more efficient yet equally effective alternatives. 3 MOTIVATION Quantization Error Accumulates in Long Generation. AWQ (Lin et al., 2024b) is a widely used weight-only quantization method and has become the de facto approach for INT4 quantization. It employs channel-wise scaling to minimize quantization error and causes only slight performance degradation on most tasks with limited generated tokens, without introducing any extra overhead from the transform. However, we observe that the degradation becomes more severe as the generation length grows, especially on reasoning tasks with reasoning models, where the generation length often exceeds tens of thousands of tokens. For example, the accuracy of Qwen3-4B (Yang et al., 2025) on MMLU-Pro (Wang et al., 2024) drops sharply from 71.0 to 68.2 after being quantized to 4 bits with AWQ. This degradation occurs because quantization errors accumulate at each decoding step. Rotations Are Expressive but Expensive. Rotations outperform channel-wise scaling in eliminat- ing outliers and generally lead to lower quantization error when many outliers are present (Figure 2). However, applying arbitrary rotations requires performing matrix multiplications in FP16, which negates the efficiency gains of quantization. There are two main approaches to address this issue. SpinQuant (Liu et al., 2025b) proposes to merge the rotation matrix into the weight of the preceding linear layer so that no extra computation is needed during inference. However, in a typical decoder block, the output projection is the only linear layer that can be transformed by such mergeable rotations; other linears are preceded by element-wise operators or residual connections that cannot absorb matrix multiplications. The second approach is to restrict the orthogonal transform to a subset that can be computed efficiently on the fly. Several works adopt the Hadamard transform, a special orthogonal transform that can be computed in O(n log n) time for dimension n (Chee et al., 2023; Ashkboos et al., 2024; Liu et al., 2025b; Tseng et al., 2024a;b). Yet the Hadamard transform is fixed or is generated by random vectors, disregarding the unique weight distribution of each linear layer and introducing large variance (Liu et al., 2025b). Moreover, it still adds considerable overhead, making Hadamard-based quantization significantly slower (≈30%) than AWQ during inference. Rotations Have Many Redundant Parameters. An n × n orthogonal matrix can be decomposed into the product of at most 1 2n(n−1) Givens rotations (i.e., rotations in the plane spanned by two axes), which translates to rotating all possible pairs of channels sequentially. Intuitively, rotations between an outlier channel and a normal channel would be more effective at reducing outliers than rotations between two normal channels. We validate this intuition with a simple experiment: for a linear layer 3 Technical Report 0 100 200 Steps 0 10−3 Output Error Full", + "of channels sequentially. Intuitively, rotations between an outlier channel and a normal channel would be more effective at reducing outliers than rotations between two normal channels. We validate this intuition with a simple experiment: for a linear layer 3 Technical Report 0 100 200 Steps 0 10−3 Output Error Full rotation Rotation (10% pairs) Channel-wise scaling RTN Figure 2: Loss curves from optimizing transforms to minimize quantization-induced output error (∥XQ(W) − XW∥) for the k proj weight matrix in the first layer of LLaMA-3-8B. Rotations can minimize quantization error better than channel-wise scaling, and keeping the 10% most significant pairs is equally expressive as a full rotation. See Section A.2 for more details. with many outliers, optimizing only the top 10% channel pairs with largest magnitude difference is almost as effective at reducing quantization-induced output error as optimizing all pairs (Figure 2). This creates an opportunity for designing parameter-efficient and potentially inference-efficient rotations for addressing the outlier issue: by retaining only the rotations between channel pairs that have large magnitude differences, we can maintain the effectiveness of a full n × n orthogonal matrix. 4 METHOD In this section, we introduce ParoQuant, a weight-only quantization method that applies optimized parameter- and inference-efficient rotations to effectively reduce quantization error. We start with the design of our scaled pairwise rotation transform. Then, we introduce the algorithm to optimize the transform and fine-tune the quantized models. Finally, we provide an efficient kernel that enables extremely fast inference. Our focus in this paper is on linear quantization as it is more efficient than vector quantization and is better supported by existing inference frameworks (Lin et al., 2024b; Zheng et al., 2024; Kwon et al., 2023), though the same method can be extended to vector quantization. 4.1 SCALED PAIRWISE ROTATION We follow a three-step process to design our scaled pairwise rotation transform. First, we avoid direct matrix multiplications by replacing orthogonal matrices with decomposed Givens rotations. Next, we remove dependencies among these rotations to enable parallel execution on GPUs, resulting in independent rotation. Finally, because a single independent rotation is not effective enough to fit complex weight distributions, we sequentially apply a series of independent rotations combined with channel-wise scaling to improve the fitting capability. 4.1.1 GIVENS ROTATION Based on the observation in Section 3 that most parameters in an orthogonal matrix are redundant, we can select a small set of channel pairs P = {(i1, j1), . . . , (im, jm)} and sequentially rotate each pair in P instead of performing full matrix multiplication. Formally, given P, a set of rotation angles Θ = {θ1, . . . , θm}, and the weight matrix W, the transformed weight is W(m) = G(im, jm, θm) G(im−1, jm−1, θm−1) · · · G(i1, j1, θ1) W, (3) where G(ik, jk, θk) is a Givens rotation that rotates two rows of the matrix while keeping others intact. This operation can be applied in place with just a few vectorized multiply-and-add instructions: W(k)[i, :] = cos θk · W(k−1)[i, :] − sin θk · W(k−1)[j, :], W(k)[j, :] =", + "where G(ik, jk, θk) is a Givens rotation that rotates two rows of the matrix while keeping others intact. This operation can be applied in place with just a few vectorized multiply-and-add instructions: W(k)[i, :] = cos θk · W(k−1)[i, :] − sin θk · W(k−1)[j, :], W(k)[j, :] = sin θk · W(k−1)[i, :] + cos θk · W(k−1)[j, :], W(k)[l, :] = W(k−1)[l, :], ∀l ̸= i, j. (4) The actual computation during inference is applying the inverse of the Givens rotation sequence in Equation (3) to the activations X. The inverse can be conveniently obtained by reversing the sequence 4 Technical Report ··· Channel Group × × × × × × × × W S IR2 IR1 IR3 T Q ··· X T-1 * 4 3 2 1 Rotate (1, 3) Rotate (2, 4) ×2.1 ×0.8 ×1.6 ×0.6 Scale each channel The two pairs are independent Figure 3: Overview of scaled pairwise rotation (T). The channel dimension is divided into fixed-size groups (the group size is 4 in the figure). Each group of the weights (W) is transformed by channel- wise scaling (S), followed by a series of independent rotations (IR). Each independent rotation consists of pairwise rotations that are mutually independent (i.e., non-overlapping). Quantization (Q) is applied after the transform using a group size equal to the channel group size. The inverse transform (T −1) is applied to the activations (X). and replacing each θk with −θk: X(m) = X G(i1, j1, −θ1) G(i2, j2, −θ2) · · · G(im, jm, −θm), (5) which can also be computed efficiently, similar to Equation (4). 4.1.2 INDEPENDENT ROTATION Givens rotations eliminate the need for matrix multiplications, but they remain inefficient due to potential dependencies. Such dependencies arise when a channel rotates with more than one other channel. In these cases, Givens rotations are not commutative, and the order in which they are applied matters. As a result, dependent Givens rotations must be computed sequentially and cannot fully exploit the GPU’s massive parallelism, leading to significant latency. To address this issue, we require the pairs within P to be mutually independent, i.e., each channel may appear in only one pair. Under this constraint, it follows directly from Equation (4) that the computation for each pair is completely independent and does not interfere with any other pair. Consequently, all Givens rotations for P are fully parallelizable. The same conclusion applies to Equation (5). In addition to computational efficiency, another benefit of independent rotations is their intrinsic compatibility with block-wise quantization. In block-wise quantization, an outlier channel within a group can only impact the quantization accuracy of other channels within the same group. Naturally, we can exploit the isolation between groups by applying a separate independent rotation for each group. This enables fine-grained pair selections specific to each group and allows a higher degree of parallelism (see Section 4.3). We formulate independent pairs and independent rotation as follows: Definition 1 (Independent Pairs). Consider a set of pairs P = {(i1, j1), . . . , (in, jn)}, and let each pair (ik, jk)", + "pair selections specific to each group and allows a higher degree of parallelism (see Section 4.3). We formulate independent pairs and independent rotation as follows: Definition 1 (Independent Pairs). Consider a set of pairs P = {(i1, j1), . . . , (in, jn)}, and let each pair (ik, jk) be represented as a set Pk = {ik, jk}. P is a set of independent pairs if and only if: ∀Pk, Pl ∈ {P1, . . . , Pn} where k ̸= l, Pk ∩ Pl = ∅. (6) Definition 2 (Independent Rotation). Consider the product of a set of Givens rotations on pairs P = {(i1, j1), . . . , (in, jn)} with the corresponding angles Θ = {θ1, . . . , θn}: R(P, Θ) = n � k=1 G(ik, jk, θk), (7) we say R(P, Θ) is an independent rotation if and only if P is a set of independent pairs. 4.1.3 SERIES OF INDEPENDENT ROTATIONS With dependencies eliminated, independent rotations can be applied online during inference with very small overhead. However, an independent rotation of dimension n can accommodate only n 2 independent pairs, which correspond to n 2 tunable parameters. This is only a fraction 1 n−1 of the 5 Technical Report 1 2n(n − 1) parameters in a full orthogonal matrix and thus severely limits its fitting capability. To overcome this limitation, instead of using only one independent rotation, we sequentially apply a small number (e.g., 8) of them to improve the expressiveness of the transform. Multiple rotations can be fused into a single kernel with a one-time memory load with minimal overhead (see Section 4.3). Algorithm A1 describes how ParoQuant selects pairs for a series of independent rotations. For each rotation, we randomly select available pairs while ensuring the rotation remains independent. To enable more diverse combinations of channel pairs across different independent rotations, we skip pairs that have already been selected in previous rotations. This constraint may result in an insufficient number of pairs for some rotations, but the impact is negligible in practice. 4.1.4 COMBINING CHANNEL-WISE SCALING On top of a series of independent rotations, we apply channel-wise scaling to further reduce quanti- zation error. Because independent rotations act on only a limited number of pairs (O(n) vs. O(n2) for a full rotation), the ability of channel-wise scaling to directly even out the magnitudes across the entire matrix is crucial for our transform to match the expressiveness of full rotations. It is also more straightforward to suppress isolated outliers with channel-wise scaling than with Givens rotations. After combining independent rotations with channel-wise scaling, the final transform (i.e., scaled pairwise rotation) applied to the weights before quantization is: TP,Θ,α(W) = � K � t=1 R(Pt, Θt) � · diag(α) · W, (8) where K is the number of rotations, P = {P1, . . . , PK} and Θ = {Θ1, . . . , ΘK} are the corre- sponding sets of rotation pairs and angles, R(Pt, Θt) is the t-th independent rotation, and α is the set of per-channel scaling factors. Integrating", + "K is the number of rotations, P = {P1, . . . , PK} and Θ = {Θ1, . . . , ΘK} are the corre- sponding sets of rotation pairs and angles, R(Pt, Θt) is the t-th independent rotation, and α is the set of per-channel scaling factors. Integrating channel-wise scaling is efficient, as it can be fused into the rotation kernel at minimal cost. We refer the readers to Section 5.3 and Section A.2 for the effectiveness of independent rotations and channel-wise scaling. 4.2 LAYER-WISE OPTIMIZATION To optimize the scaled pairwise rotation in Equation (8), we adopt a layer-wise optimization scheme to minimize the output loss of each layer. Specifically, for a decoder layer D, we minimize L(Q) = ∥Q(D)(X′) − D(X)∥ , (9) where Q(D) is the decoder D with every linear layer quantized after applying the scaled pairwise rotation, X is the input to D of the original model, and X′ is the output of the already quantized preceding decoder layers. By optimizing with the new output computed from X′ instead of from X, the subsequent layers can compensate for quantization errors introduced by earlier layers, thereby improving end-to-end accuracy. For each layer, we optimize the quantized model in two stages. In the first stage, we optimize rotations and channel-wise scaling. After this stage, most outliers in the weight matrices are suppressed, and the weights are more quantization-friendly. However, some isolated outliers may still remain, as rotations and scaling cannot eliminate them completely. Therefore, in the second stage, we adopt a QAT-like approach similar to EfficientQAT (Chen et al., 2025) to fine-tune the weights and the linear quantization parameters s and z in Equation (1), thereby further reducing the error introduced by the RTN algorithm. The pseudocode for the optimization algorithm is available in Section A.1. 4.3 CO-DESIGNING EFFICIENT TRANSFORM KERNEL To enable fast inference, we implement the scaled pairwise rotation transform as a single fused CUDA kernel. Thanks to the transform’s independence at both the group and pair levels, the computation is fully parallelized at three levels: (1) token: we parallelize across the token dimension of the activation tensor; (2) channel group: we assign different CUDA blocks to different groups along the channel dimension; (3) pair: each rotation pair is processed by a separate CUDA thread. 6 Technical Report 212 213 214 215 Channel dimension 2 4 Speedup Figure 4: Speedup of scaled pair- wise rotation over the Hadamard transform on an RTX A6000. This fine-grained parallelism across groups and pairs offers several advantages. First, dividing the channel dimension into groups re- duces the memory load required for each thread block. Because the group size (e.g., 128) is relatively small, the activation tensor fits into the on-chip shared memory, and the rotation parameters (i.e., pair indices and angles) fit into registers. This significantly reduces the latency of subsequent memory access. As a result, multiple independent rotations can then be fused efficiently, since the activa- tion and all parameters are already loaded into low-latency memory. Second, group-wise parallelism increases the occupancy of the GPU’s compute units, particularly when", + "angles) fit into registers. This significantly reduces the latency of subsequent memory access. As a result, multiple independent rotations can then be fused efficiently, since the activa- tion and all parameters are already loaded into low-latency memory. Second, group-wise parallelism increases the occupancy of the GPU’s compute units, particularly when the channel dimension is very large. From Figure 4, the speedup of our transform (with 8 in- dependent rotations) over the fast Hadamard transform (Dao, 2024) increases with the channel dimension, because the Hadamard transform has inherent dependencies across all channels. Third, pair-level independence within each rotation allows synchronization-free execution across all CUDA threads within a thread block, further improving hardware utilization. 5 EVALUATION Models and Tasks. We apply ParoQuant on LLaMA-2 (7B) (Touvron et al., 2023), LLaMA-3 (8B, 70B) & LLaMA-3.1 Instruct (8B) (Grattafiori et al., 2024), DeepSeek-R1-distilled LLaMA-3.1 (8B) (Guo et al., 2025), and Qwen3 (1.7B, 4B, 8B, 14B) (Yang et al., 2025) pre-trained models. We evaluate the quantization quality with three types of evaluation: (1) Perplexity on WikiText2 (Merity et al., 2017) and C4 (Dodge et al., 2021); (2) Reasoning accuracy on MMLU-Pro (Wang et al., 2024), GPQA Diamond (Rein et al., 2024), AIME-24, and AIME-25 (MAA, 2024); (3) Non-reasoning accuracy on BoolQ (Clark et al., 2019), ARC-Challenge, ARC-Easy (Clark et al., 2018), and HellaSwag (Zellers et al., 2019). Implementation. We focus on 4-bit weight-only linear quantization with a group size of 128. Linear quantization is more efficient and is widely supported by existing frameworks. The choice of 4 bits and a 128 group size offers the optimal trade-off between accuracy and bit width for linear quantization (Dettmers & Zettlemoyer, 2023). We apply 8 independent rotations on each 128-channel group, with each rotation consisting of up to 64 pairs. Each layer is optimized for 10 epochs at each stage using AdamW (Loshchilov & Hutter, 2019) with a fixed set of hyperparameters for all experiments, except for the 70B model, where we adjust the batch size to accommodate memory constraints. To reduce the risk of overfitting to one dataset, we use a training set of 2048 samples drawn evenly from WikiText2, C4, and RedPajama (Weber et al., 2024), and select the best parameters using 64 validation samples from Pile (Gao et al., 2020). More details are provided in Section A.3. Baselines. We compare the accuracy and efficiency of ParoQuant with three weight-only PTQ baselines. AWQ (Lin et al., 2024b) optimizes channel-wise scaling with grid search and is the most used 4-bit weight-only quantization method. EfficientQAT (Chen et al., 2025) achieves state- of-the-art linear quantization accuracy with layer-wise fine-tuning of weights and quantization parameters*. QTIP (Tseng et al., 2024b) is the state-of-the-art vector quantization method utilizing randomized Hadamard transform and an advanced trellis quantization algorithm. In addition, we include the perplexity results of QuIP# (Tseng et al., 2024a), a vector-quantization predecessor of QTIP that also adopts the Hadamard transform, and two weight-activation linear quantization methods, OmniQuant (Shao et al., 2024) and SpinQuant (Liu et al., 2025b), which are also applicable for weight-only quantization. We apply block-wise quantization with a group size", + "results of QuIP# (Tseng et al., 2024a), a vector-quantization predecessor of QTIP that also adopts the Hadamard transform, and two weight-activation linear quantization methods, OmniQuant (Shao et al., 2024) and SpinQuant (Liu et al., 2025b), which are also applicable for weight-only quantization. We apply block-wise quantization with a group size of 128 on all linear quantization methods and the corresponding default settings on vector quantization methods. 5.1 ACCURACY RESULTS Perplexity. Table 1 shows the perplexity results of 4-bit quantized models ranging in size from 1.7B to 70B. Among linear quantization methods, ParoQuant achieves state-of-the-art quantization *We only apply the “Block-AP” stage of EfficientQAT, as its “E2E-QP” stage involves supervised fine-tuning, which is out of the scope of PTQ. 7 Technical Report accuracy across all sizes, particularly on challenging cases like LLaMA-3 and smaller models under 4B. It also delivers strong performance compared with rotation-based methods including QuIP#, QTIP, and SpinQuant. It outperforms QuIP# and matches QTIP on all models, despite the inherently larger error of linear quantization, highlighting the superior effectiveness of our proposed transform over the Hadamard transform (see Section A.2 for detailed analysis). Moreover, ParoQuant provides a decent speedup over these two methods. This underscores the efficiency of our proposed transform. Method Type WikiText2 C4 Speedup L3-8 L3-70 L2-7 Q3-1.7 Q3-4 Q3-8 Q3-14 L3-8 L3-70 L2-7 Q3-1.7 Q3-4 Q3-8 Q3-14 FP16 – 5.54 2.56 5.12 8.32 7.01 6.24 5.70 7.10 5.78 6.63 8.62 7.61 6.97 6.54 1.0× QUIP# vector 5.81 2.99 5.19 – – – – 7.32 5.96 6.75 – – – – 1.9× QTIP vector 5.69 2.75 5.17 8.46 7.09 6.28 5.75 7.22 5.83 6.69 8.73 7.68 7.02 6.57 1.7× AWQ linear 5.92 2.96 5.23 8.80 7.36 6.45 5.85 7.42 5.91 6.80 9.01 7.89 7.14 6.65 2.4× OMNIQ linear – – 5.23 – – – – – – 6.80 – – – – 2.4׆ SPINQ linear 5.83 – 5.21 – – – – 7.41 – 6.86 – – – – 2.4׆ E-QAT linear 5.87 3.33 5.22 8.60 7.19 6.37 5.82 7.36 6.72 6.76 8.84 7.77 7.08 6.63 2.4׆ PAROQ linear 5.73 2.82 5.17 8.44 7.10 6.29 5.75 7.27 5.86 6.73 8.74 7.70 7.04 6.59 2.2× † Uses results of AWQ as a reference as the method does not incur significant overhead from the transform. Table 1: Perplexity (↓) results of 4-bit models. The context length is 8192 for LLaMA-3 and Qwen3 (base models), and 4096 for LLaMA-2. The best results among linear quantization methods are in bold. Speedup over FP16 models is reported as the geometric mean across Q3-1.7, Q3-4, L3-8, and Q3-14, measured on an RTX A6000 with a batch size of 1 during decoding. Reasoning Tasks. Table 2 shows the accuracy results of four reasoning benchmarks: MMLU- Pro (12k samples), GPQA Diamond (198 samples), AIME-24 (30 samples), and AIME-25 (30 samples). On the larger MMLU-Pro benchmark, ParoQuant consistently outperforms all linear quantization baselines and matches the accuracy of QTIP. While results on the smaller GPQA and AIME benchmarks exhibit more randomness due to the limited number of samples, ParoQuant still outperforms the baselines in most cases. Overall,", + "and AIME-25 (30 samples). On the larger MMLU-Pro benchmark, ParoQuant consistently outperforms all linear quantization baselines and matches the accuracy of QTIP. While results on the smaller GPQA and AIME benchmarks exhibit more randomness due to the limited number of samples, ParoQuant still outperforms the baselines in most cases. Overall, ParoQuant causes only an average 0.9% accuracy degradation and achieves 6.5%, 2.4%, and 0.9% improvements over EfficientQAT, AWQ, and QTIP, respectively. This demonstrates ParoQuant’s superior quantization accuracy in long generation. Method Type R1-Distill-Llama-8B Qwen3-4B Qwen3-8B Qwen3-14B Avg. MMLU GPQA AIME 24 AIME 25 MMLU GPQA AIME 24 AIME 25 MMLU GPQA AIME 24 AIME 25 MMLU GPQA AIME 24 AIME 25 FP16 – 58.8 46.6 42.2 32.2 71.0 50.0 75.6 62.2 74.6 60.3 75.6 72.2 78.1 62.5 73.3 68.9 62.8 QTIP vector 57.4 43.4 37.8 30.1 69.7 55.2 67.8 58.9 74.0 59.3 72.2 63.3 77.9 64.0 76.7 69.0 61.0 AWQ linear 56.0 44.1 34.4 26.7 68.2 52.2 62.2 53.3 73.5 60.2 72.2 61.1 77.2 62.0 80.0 68.9 59.5 E-QAT linear 55.4 44.3 28.9 22.2 67.5 49.8 45.6 44.4 72.5 55.7 70.0 52.2 76.6 60.8 71.1 68.9 55.4 PAROQ linear 57.1 47.5 36.6 31.1 70.1 53.7 73.3 63.3 74.1 57.7 75.6 63.3 77.5 63.5 77.8 67.8 61.9 Table 2: Zero-shot accuracy (↑) on reasoning tasks. Best linear quantization results are in bold. Non-Reasoning Tasks. Table 3 shows the zero-shot accuracy on commonsense benchmarks with thinking mode disabled. ParoQuant maintains near-lossless performance, outperforming AWQ, EfficientQAT, and QTIP by 0.9%, 0.7%, and 0.2%, respectively. The accuracy gap is smaller than in reasoning tasks because these benchmarks evaluate only a few generated tokens, so error accumulation is minimal. 5.2 EFFICIENCY RESULTS Table 4 shows the decoding throughput on an RTX A6000. To ensure a fair comparison, we implement all methods on top of the Transformers library (Wolf et al., 2020), modifying only the weight transform and dequantization code (details and more results are in Section A.4). ParoQuant is only about 10% slower than AWQ while providing a significant accuracy improvement, and it matches the accuracy of QTIP while being 15%-30% faster. For the training efficiency, see Section A.5 for more details. 8 Technical Report Method Type LLaMA-3.1-8B-Instruct Qwen3-4B Qwen3-8B Qwen3-14B Avg. BoolQ ARC-C ARC-E HSwag BoolQ ARC-C ARC-E HSwag BoolQ ARC-C ARC-E HSwag BoolQ ARC-C ARC-E HSwag FP16 – 84.1 51.7 81.8 59.1 85.1 50.8 80.5 52.3 86.6 55.8 83.5 57.1 89.4 58.6 84.2 60.9 70.1 QTIP vector 84.3 51.8 81.6 58.9 85.0 50.0 79.8 51.8 86.9 54.9 82.8 57.0 89.2 57.6 83.5 60.8 69.7 AWQ linear 83.5 51.7 80.6 58.4 85.0 47.4 77.9 51.3 86.2 53.8 82.2 56.2 89.1 57.9 83.2 60.3 69.0 E-QAT linear 83.5 51.9 80.9 58.4 84.5 48.3 79.7 51.1 86.1 53.6 81.7 56.1 89.0 58.5 84.0 60.4 69.2 PAROQ linear 83.9 52.1 82.2 58.7 85.3 49.7 80.7 51.8 87.0 55.3 83.3 56.8 89.1 57.2 84.3 60.7 69.9 Table 3: Zero-shot accuracy (↑) on non-reasoning tasks. Best linear quantization results are in bold. Method Qwen3-1.7B Qwen3-4B LLaMA-3-8B Qwen3-14B Throughput W2 PPL Throughput W2 PPL Throughput W2 PPL Throughput W2 PPL FP16 170", + "52.1 82.2 58.7 85.3 49.7 80.7 51.8 87.0 55.3 83.3 56.8 89.1 57.2 84.3 60.7 69.9 Table 3: Zero-shot accuracy (↑) on non-reasoning tasks. Best linear quantization results are in bold. Method Qwen3-1.7B Qwen3-4B LLaMA-3-8B Qwen3-14B Throughput W2 PPL Throughput W2 PPL Throughput W2 PPL Throughput W2 PPL FP16 170 (1.0×) 8.32 78 (1.0×) 7.01 45 (1.0×) 5.54 25 (1.0×) 5.70 AWQ 320 (1.9×) 8.80 176 (2.3×) 7.36 120 (2.7×) 5.92 70 (2.8×) 5.85 QTIP 209 (1.2×) 8.46 117 (1.5×) 7.09 95 (2.1×) 5.69 55 (2.2×) 5.75 PAROQ 278 (1.6×) 8.44 160 (2.1×) 7.10 112 (2.5×) 5.73 65 (2.6×) 5.75 Table 4: Decoding (with batch size of 1) throughput (tokens/s). 5.3 ABLATION STUDY Table 5 shows the effectiveness of each component of ParoQuant. The effects of channel-wise scaling and independent rotations are distinct, and combining both of them yields better quantization accuracy than applying either one alone. Fine-tuning weights and quantization parameters in the second optimization stage further improves the accuracy compared with directly applying RTN. For a more detailed comparison of the transforms, see Section A.2. Table 6 shows the effects of the calibration set, calibration size, and number of independent rotations on end-to-end quantization accuracy. ParoQuant achieves surprisingly strong performance with as few as 128 training samples. Moreover, accuracy improves as the number of rotations increases up to 8, indicating improved fitting capability. We also optimize the model with 2048 calibration samples from RedPajama alone, and the results are slightly worse than with the mixed dataset. This shows that using a more diverse training set improves the generalization ability of the models. Transform C4 (↓) w/o Stage 2 None 7.56 S 7.40 8 IR 7.50 8 IR + S 7.35 w/ Stage 2 None 7.42 S 7.41 8 IR 7.40 8 IR + S 7.27 Table 5: Ablations on transforms and optimiza- tion stages with LLaMA-3-8B (S: channel- wise scaling, IR: independent rotation). # Samples # IR C4 (↓) MMLU (↑) 128 8 7.30 69.5 512 8 7.27 69.7 2048 0 7.41 69.6 2 7.28 69.4 4 7.27 69.4 8 7.27 70.1 2048 (RedPajama) 8 7.27 69.5 Table 6: Ablations on training samples and number of rotations (IR) with LLaMA-3-8B (C4 perplex- ity) and Qwen3-4B (MMLU-Pro accuracy). 6 CONCLUSION In this paper, we proposed ParoQuant, an efficient weight-only PTQ method that achieves state-of-the- art quantization accuracy with minimal overhead. Based on the insight that a sparsely parameterized rotation can effectively suppress weight outliers, we designed scaled pairwise rotation, which com- bines hardware-friendly independent Givens rotations with channel-wise scaling. ParoQuant matches 9 Technical Report the accuracy of the best existing quantization methods while running much faster, and it consistently outperforms prior efficient quantization methods, especially on reasoning tasks where quantization errors accumulate over long chains of thought. We hope that our method will inspire future research on high-fidelity, low-overhead quantization techniques for next-generation reasoning LLMs. ACKNOWLEDGMENT We sincerely thank Zihan Zhang for assistance with the reasoning task evaluation and Shang Yang for valuable feedback on earlier drafts of this work. REFERENCES Saleh Ashkboos, Amirkeivan Mohtashami, Maximilian L. Croci, Bo Li, Pashmina", + "method will inspire future research on high-fidelity, low-overhead quantization techniques for next-generation reasoning LLMs. ACKNOWLEDGMENT We sincerely thank Zihan Zhang for assistance with the reasoning task evaluation and Shang Yang for valuable feedback on earlier drafts of this work. 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P ← {(i, j) | 1 ≤ i < j ≤ g} Pshuffled ← Shuffle(P) // Matrix to track available pairs across all rotations Initialize A ∈ Rg×g where Aij ← 1, ∀i, j ∈ {1, ..., g}, i ̸= j and Aii ← 0, ∀i ∈ {1, ..., g} P1, . . . , PK ← [ ] for r ← 1 to K do Arot ← Copy(A) // Tracks available channels within this rotation foreach pair (i, j) ∈ Pshuffled do if |Pr| = N then break if Arot[i, j] = 0 then continue Append (i, j) to Pr // Select the next available pairs Arot[i, :] ← 0; Arot[:, i] ← 0; Arot[j, :] ← 0; Arot[:, j] ← 0 // Block channels A[i, j] ← 0; A[j, i] ← 0 // Block pair return P1, . . . , PK Algorithm A2: Layer-Wise Optimization Input: L: decoder layers of the model; g: group size; K: number of rotations; N: number of pairs per rotation; D: calibration dataset. Output: L′: decoder layers containing optimized scaling, rotations, and quantizers. X ← tokenize D // X is the original input to a layer X ′ ← X // X ′ is the input to a layer after quantizing preceding layers L′ ← [ ] foreach layer l ∈ L do Y ← l(X) // Output of original layer as labels l′ ← Copy(l) foreach linear ∈ l′ do W1, . . . , Wn ← Partition linear with group", + "′ is the input to a layer after quantizing preceding layers L′ ← [ ] foreach layer l ∈ L do Y ← l(X) // Output of original layer as labels l′ ← Copy(l) foreach linear ∈ l′ do W1, . . . , Wn ← Partition linear with group size g at channel dimension for i ← 1 to n do Pi ← SelectPairs(Wi, K, N) // Algorithm A1 θi ← 0K×N, αi ← 1g // Angles and channel-wise scaling si, zi ← Initialize quantizer with Wi // Equation (1) Insert scaling αi, rotations (Pi, θi), and quantizer (si, zi) into l′ l′′ ← Optimize all θi and αi to minimize ∥Y − l′(X ′)∥ // Stage 1 l′′′ ← Optimize all si, zi, and weights to minimize ∥Y − l′′(X ′)∥ // Stage 2 Append l′′′ to L′ X ′ ← l′′′(X) // Quantized layers’ output as next layer’s input X ← Y // Pass down original layer’s output return L′ A.2 EFFECTIVENESS ANALYSIS To study the effectiveness of different transforms at minimizing quantization-induced output error (∥XQ(W) − XW∥), we optimize each linear layer individually with each transform applied to the input dimension of its weight W and obtain the loss curves of the optimization process. We compare the effectiveness of 5 transforms: 13 Technical Report • Channel-wise scaling: We optimize per-channel scaling factors α for the weight W, i.e., ˆ W = diag(α) · W. • Full rotation: We construct an orthogonal matrix R from an upper triangular matrix U by R = exp(U − U T ) (exp is the matrix exponential), and optimize the elements of U. • Random Hadamard transform: We sample the average output error after applying a random Hadamard transform generated using one of 100 seeds. • Independent rotation: We select 8 independent rotations for each 128-channel group using Algorithm A1. • Scaled pairwise rotation (independent rotation + channel-wise scaling): We select 8 independent rotations for each 128-channel group using Algorithm A1. To optimize the transforms, we use AdamW with a learning rate of 0.001 for the full rotation and 0.01 for other transforms. We use 128 samples from Pile and optimize for 200 steps. The results of the first, middle, and last layer of LLaMA-3-8B are listed in Figure A1. mlp.down proj results are not included because the input dimension is too large for the full rotation. From the results, independent rotations can lower quantization error better than channel-wise scaling in layers that possess many outliers (e.g., q proj and k proj), and generally outperform random Hadamard transform with much lower overhead. When combined with channel-wise scaling, independent rotations can almost match the effectiveness of a full rotation in layers with many outliers. This proves the superior expressiveness of our proposed scaled pairwise rotation transform. Figure A1: Loss curves from optimizing transforms to minimize quantization-induced output error of linear layers in LLaMA-3-8B. Full rotation Channel-wise scaling 8 independent rotations 8 independent rotations + scaling Hadamard Layer 0 Layer 15 Layer 31 Output Error 0 100 200 0.0 2.5 5.0 ×10−4 0 100 200", + "rotation transform. Figure A1: Loss curves from optimizing transforms to minimize quantization-induced output error of linear layers in LLaMA-3-8B. Full rotation Channel-wise scaling 8 independent rotations 8 independent rotations + scaling Hadamard Layer 0 Layer 15 Layer 31 Output Error 0 100 200 0.0 2.5 5.0 ×10−4 0 100 200 0 2 4 ×10−3 0 100 200 0 2 4 ×10−3 self attn.q proj Output Error 0 100 200 0.0 0.5 1.0 ×10−3 0 100 200 0.0 0.5 1.0 ×10−2 0 100 200 0.0 0.5 1.0 ×10−2 self attn.k proj Output Error 0 100 200 0 2 4 ×10−5 0 100 200 0.0 2.5 5.0 ×10−4 0 100 200 0 2 4 ×10−4 self attn.v proj Steps Steps Steps (Continue on next page) 14 Technical Report Figure A1: Loss curves from optimizing transforms to minimize quantization-induced output error of linear layers in LLaMA-3-8B (continued). Full rotation Channel-wise scaling 8 independent rotations 8 independent rotations + scaling Hadamard Layer 0 Layer 15 Layer 31 Output Error 0 100 200 0 1 2 ×10−7 0 100 200 0 1 2 ×10−5 0 100 200 0 1 ×10−4 self attn.o proj Output Error 0 100 200 0.0 2.5 5.0 ×10−5 0 100 200 0 2 4 ×10−4 0 100 200 0 5 ×10−4 mlp.up proj Output Error 0 100 200 0 5 ×10−5 0 100 200 0.0 2.5 5.0 ×10−4 0 100 200 0.0 0.5 1.0 ×10−3 mlp.gate proj Steps Steps Steps A.3 IMPLEMENTATION DETAILS Quantization and Transform. We apply block-wise linear quantization with a group size of 128. We apply channel-wise scaling and 8 independent rotations on each 128-channel group of the weights, with each rotation consisting of up to 64 pairs. The independent rotations are applied sequentially after channel-wise scaling. Libraries. Our implementation is built with PyTorch 2.8.0 (Paszke et al., 2019), Transformers 4.55.2 (Wolf et al., 2020), and Datasets 3.6.0 (Lhoest et al., 2021). Optimization. We optimize all ParoQuant-quantized models in Section 5 with a single NVIDIA H200 GPU. We sample a training set of size 2048 evenly from WikiText2, C4, and RedPajama, and use 64 samples from Pile as the validation set to select the best parameters at each epoch. The training set and the validation set are shuffled with a fixed seed of 0. The sequence length of each sample is 2048. We set the batch size as 16, and apply a learning rate of 0.05 for rotation angles and channel-wise scaling, 10−5 for weights, and 10−6 for scales and zero points. The batch size and the learning rates are halved for the 70B model due to memory constraints. The rotation angles are initialized to 0, the channel-wise scaling factors are initialized to 1, and the scales and zero points are initialized using Equation (1). We use AdamW to optimize the parameters for 10 epochs at each stage (see Algorithm A2 for the two stages) with a cosine learning rate scheduler, which gradually decays the learning rate to 1/20 of the original value. The hyperparameters weight decay, betas, and eps 15 Technical Report of the AdamW optimizer are set to", + "the parameters for 10 epochs at each stage (see Algorithm A2 for the two stages) with a cosine learning rate scheduler, which gradually decays the learning rate to 1/20 of the original value. The hyperparameters weight decay, betas, and eps 15 Technical Report of the AdamW optimizer are set to 0.01, (0.9, 0.95), and 10−10, respectively. We use SmoothL1Loss from PyTorch as the loss function. A.4 DECODING THROUGHPUT Table A2 shows the decoding throughput of the original FP16 models and 4-bit models quantized with AWQ, QTIP, and ParoQuant. To ensure a fair comparison, we only replace the original linear layers in the original models with the implementation provided by the official open-sourced repository of each baseline. For ParoQuant, we adopt the W4A16 GEMM kernels from the AWQ repository together with our transform kernel. All throughput results were obtained with PyTorch 2.6.0 using torch.compile in max-autotune mode and with CUDA Graphs enabled. Table A2: Decoding (batch size = 1) throughput (tokens/s). RTX A6000 Bits Q3-1.7 Q3-4 L2-7 L3-8 Q3-8 L2-13 Q3-14 Q3-32 L3-70 FP16 16 170 78 50 45 44 26 25 OOM OOM AWQ 4 320 176 140 120 113 78 70 34 17 QTIP 4 209 117 106 95 91 62 55 28 15 PAROQ 4 278 160 130 112 106 74 65 33 16 RTX 6000 Ada Bits Q3-1.7 Q3-4 L2-7 L3-8 Q3-8 L2-13 Q3-14 Q3-32 L3-70 FP16 16 213 99 63 56 55 33 31 OOM OOM AWQ 4 394 230 176 153 147 100 89 44 21 QTIP 4 270 166 138 125 118 83 80 40 20 PAROQ 4 341 206 163 142 136 94 84 42 21 RTX 4090 Bits Q3-1.7 Q3-4 L2-7 L3-8 Q3-8 L2-13 Q3-14 Q3-32 L3-70 FP16 16 233 109 69 62 61 OOM OOM OOM OOM AWQ 4 433 251 192 167 159 109 98 48 OOM QTIP 4 286 172 149 138 138 91 82 42 OOM PAROQ 4 372 224 177 155 147 102 93 46 OOM A.5 TRAINING EFFICIENCY Table A3 shows the calibration size and GPU time for quantizing LLaMA-3-8B on an NVIDIA H200 GPU. Although ParoQuant is slower than EfficientQAT due to an extra tuning stage and the additional computation graph nodes from independent rotations, it is significantly faster than QTIP, which requires significantly more calibration data and is slowed down by two extra steps in addition to layer-wise fine-tuning: generating Hessian matrices and end-to-end fine-tuning. Table A3: Calibration data (# samples × sequence length) and GPU time for quantizing LLaMA-3-8B on an NVIDIA H200 GPU. AWQ E-QAT QTIP PAROQ Calibration Data 128 × 512 4096 × 2048 4096 × 8192 2048 × 2048 GPU Time minutes ≈ 3 hours ≈ 20 hours ≈ 9 hours A.6 EVALUATION SETTINGS Perplexity Evaluation. We use the test split in GPTQ (Frantar et al., 2023) to measure the perplexity on WikiText2 and C4. The sequence length is 8192 for LLaMA-3 and Qwen3 models, and 4096 for LLaMA-2 models. Note that the perplexity results of Qwen3 family in Table 1 are from the pre-trained “Base” models (e.g., Qwen/Qwen3-8B-Base from Hugging Face),", + "GPTQ (Frantar et al., 2023) to measure the perplexity on WikiText2 and C4. The sequence length is 8192 for LLaMA-3 and Qwen3 models, and 4096 for LLaMA-2 models. Note that the perplexity results of Qwen3 family in Table 1 are from the pre-trained “Base” models (e.g., Qwen/Qwen3-8B-Base from Hugging Face), not the models after post-training (e.g., Qwen/Qwen3-8B). 16 Technical Report Reasoning Task Evaluation. We follow Liu et al. (2025a) and use Lighteval 0.8.1 (Habib et al., 2023) with vLLM 0.10.1 (Kwon et al., 2023) to evaluate the reasoning tasks in Table 2. We evaluate GPQA Diamond, AIME-24, and AIME-25 with three different seeds (42, 0, 1) and report the average accuracy to reduce variations, and evaluate MMLU-Pro with one seed (42). Non-Reasoning Task Evaluation. We use the Language Model Evaluation Harness library (lm eval) version 0.4.9.1 (Gao et al., 2024) to evaluate the tasks in Table 3 with the default settings of the library and a batch size of 32. A.7 USE OF LARGE LANGUAGE MODELS The use of large language models for this work is limited to polishing the writing of the paper (e.g., checking grammatical errors, improving fluency, and enhancing clarity) and assisting with tasks that are not part of the core implementation (e.g., writing scripts for data visualization, plotting, or formatting results). 17", + "Black-Box On-Policy Distillation of Large Language Models Tianzhu Ye∗ Li Dong∗ Zewen Chi Xun Wu Shaohan Huang Furu Wei Microsoft Research https://aka.ms/GeneralAI Black-box distillation creates student large language models (LLMs) by learning from a proprietary teacher model’s text outputs alone, without access to its internal logits or parameters. In this work, we introduce Generative Adversarial Distillation (GAD), which enables on-policy and black-box distillation. GAD frames the student LLM as a generator and trains a discriminator to distinguish its responses from the teacher LLM’s, creating a minimax game. The discriminator acts as an on-policy reward model that co-evolves with the student, providing stable, adaptive feedback. Experimental results show that GAD consistently surpasses the commonly used sequence-level knowledge distillation. In particular, Qwen2.5-14B-Instruct (student) trained with GAD becomes comparable to its teacher, GPT-5-Chat, on the LMSYS-Chat automatic evaluation. The results establish GAD as a promising and effective paradigm for black-box LLM distillation. Project Page: aka.ms/GAD-project Code: aka.ms/GAD-github 3B 7B 14B # Parameters 46 48 50 52 Average Score GPT-5-Chat (Teacher) LMSYS-Chat Benchmark GAD (ours) SeqKD Qwen2.5-Instruct 3B 7B 14B # Parameters 46 47 48 49 50 51 GPT-5-Chat (Teacher) Out-of-Distribution Generalization (Average over Dolly, SelfInst, and Vicuna) GAD (ours) SeqKD Qwen2.5-Instruct Figure 1: Comparison between GAD and sequence-level knowledge distillation (SeqKD; KR16) trained on LMSYS-Chat [ZCS+24] dataset, evaluated by averaged GPT-4o scores. Left: Results on the LMSYS-Chat test set. Right: Average performance across Dolly [Dat23], SelfInst [WKM+23], and Vicuna [CLL+23] datasets. ∗ Equal contribution. Contact person: fuwei@microsoft.com. arXiv:2511.10643v1 [cs.CL] 13 Nov 2025 1 Introduction Knowledge distillation [HVD15] in large language models (LLMs; Ope23, Ope25, LFX+24, YLY+25) is primarily used to create smaller, more efficient student models that retain much of the performance of a larger, resource-intensive teacher model. The setting in which the student has access to the teacher’s internal probability distribution or hidden states is called white-box dis- tillation. Standard white-box approaches align the teacher and student by matching their output distributions, typically via Kullback-Leibler divergence (KLD) [SST+20, GDWH24], or their in- ner states [JYS+20, SCGL19, WWD+20]. However, white-box access is often impractical when the teacher is a proprietary API model (e.g., GPT-5). In this scenario, only teacher-generated texts are accessible, defining the more challenging black-box distillation setting. The absence of fine-grained probability supervision makes conventional likelihood-based objectives unavail- able. Typical black-box distillation methods simply perform supervised fine-tuning on teacher re- sponses [TGZ+23, CLL+23]. Furthermore, when the student and teacher employ incompatible tokenizers, applying likelihood-based objectives also becomes challenging. This highlights the need for a framework that can effectively extract deeper and richer knowledge from teacher-generated text responses. Recent studies [GDWH24, AVZ+24, LL25, YLY+25] in white-box distillation highlight the im- portance of on-policy learning, where the student learns from its own generated responses rather than solely imitating the teacher’s outputs. These studies show that performing reverse KLD on student-generated text promotes mode-seeking behavior and reduces exposure bias compared to teacher-forced training. However, extending this idea to the black-box setting introduces a major challenge: when the student produces its own responses, there are no probability-level supervision signals available from the teacher to evaluate or correct", + "performing reverse KLD on student-generated text promotes mode-seeking behavior and reduces exposure bias compared to teacher-forced training. However, extending this idea to the black-box setting introduces a major challenge: when the student produces its own responses, there are no probability-level supervision signals available from the teacher to evaluate or correct them. Without explicit feedback, the student cannot directly gauge the quality of its generations relative to the teacher, making effective on-policy distillation infeasible under the standard likelihood-based framework. To address this limitation, we propose GAD, a Generative Adversarial Distillation framework that enables on-policy learning in the black-box regime. Our key idea is to view the student as a gen- erator that produces responses conditioned on prompts, and to train a discriminator to distinguish between teacher and student outputs. The generator is then optimized to produce responses that the discriminator cannot distinguish from those of the teacher, forming a minimax game similar to generative adversarial networks (GANs; GPAM+14, YZWY17). This adversarial process al- lows the student to receive implicit feedback on the quality of its own generations, even without access to the teacher’s probability space. Besides, from the perspective of reinforcement learn- ing (RL; SB+98, SWD+17, SLA+15), our discriminator can be interpreted as an on-policy re- ward model that evolves jointly with the student policy. Unlike conventional reward models in RLHF [OWJ+22] which are fixed after pretraining and prone to reward hacking [SHKK22], our discriminator continually adapts to the student’s behavior during training. The on-policy reward modeling provides stable and dynamic supervision throughout the distillation process. We validate our approach using GPT-5-Chat [Ope25] as a teacher and a range of open-source mod- els from the Qwen2.5 [YYZ+25] and Llama3 [GDJ+24] families as a student. Experiments are conducted on the a subset of LMSYS-Chat-1M dataset [ZCS+24] and evaluated across multiple domains. Under identical training budgets, GAD consistently outperforms both the instruction models before distillation and the SeqKD [KR16, CLL+23, TGZ+23, PLH+23, ZLX+23] baseline across all datasets and model sizes. Notably, on GPT-4o score, Qwen2.5-3B-Instruct distilled with GAD matches the performance of Qwen2.5-7B-Instruct distilled with SeqKD, while Qwen2.5-14B- Instruct trained with GAD approaches the capability of the GPT-5 teacher itself. Our method also delivers particularly strong improvements in out-of-distribution generalization, where SeqKD yields marginal or negative gains. Human evaluations further confirm performance. GAD can effectively extract high-quality knowledge from black-box LLMs without access to output logits. 2 Student (Generator) Discriminator (𝐷(⋅)) Input Prompt (𝑥) Teacher Gradient Policy Gradient − log𝜎 𝐷 𝑦𝑡 − 𝐷 𝐺 𝑥 Bradley-Terry Loss max 𝐺 min 𝐷 Figure 2: Training procedure of GAD. The student (generator) learns to generate responses that maximize the score assigned by the discriminator. The discriminator is trained with Bradley-Terry loss to assign a lower score to the student than the teacher, learning to distinguish between them. Together, they form a two-player minimax game in an adversarial learning framework. 2 Method We study conditional text generation of large language models, where a model generates a response y conditioned on a given prompt x sampled from dataset T . To transfer the capabilities of large models to", + "them. Together, they form a two-player minimax game in an adversarial learning framework. 2 Method We study conditional text generation of large language models, where a model generates a response y conditioned on a given prompt x sampled from dataset T . To transfer the capabilities of large models to smaller ones, knowledge distillation (KD) trains a student distribution qθ(y|x) parameterized by θ to approximate the behavior of a teacher distribution p(y|x). In the white-box distillation setting, the student has access to the teacher’s predictive distribution p(y|x). Approaches such as forward KLD [KR16, SST+20, CLL+23, TGZ+23] or reverse KLD [GDWH24] are designed for this setting. However, these techniques can fail if the teacher is a proprietary model that only returns generated text. We refer to this scenario as black-box distillation, where only textual responses from the teacher are observable. The goal is to learn a student model that imitates the teacher’s generative behavior without access to its internal probability space. 2.1 GAD: Generative Adversarial Distillation We perform black-box distillation with generative adversarial training [GPAM+14, YZWY17] as shown in Figure 2. The training dataset T = {(x, yt)} is constructed by iterating over the prompts x in the original dataset and sampling a teacher response yt for each. Our framework consists of a generator G which is the student model, and a discriminator D that assesses the quality of the student and teacher responses. The generator generates the response G(x) to the prompt x. The discriminator predicts a sequence-level scalar score D([x, y]) given prompt x and response y2. The discriminator is initialized using generator model parameters with an extra prediction head. The head projects the final hidden state to a scalar score, and the score of the last token in the sequence is taken as the sequence-level score. The training objective is formulated as a two-player minimax game with the following value function V(G, D): max G min D V(G, D) = E(x,yt)∼T [− log σ (D(yt) − D(G(x)))] , (1) where σ(·) denotes the sigmoid function. We use Bradley-Terry model [BT52] to capture pairwise preferences between teacher and student response. The proposed generative adversarial training framework allows the student to learn on-policy from its own generated responses via discriminator feedback, eliminating the need to access the teacher’s internal representations. 2.2 Training We discuss the training algorithm of generator and discriminator respectively. From Equation (1), the generator G is trained with the following objective: (Generator) max G E(x,yt)∼T [D(G(x))] , (2) 2 The input prompt x and generated response y are concatenated (i.e., [x, y]) and fed into the discriminator (i.e., D([x, y])). For brevity, we use D(y) below to represent D([x, y]). 3 Since the sampling operation in G(x) is non-differentiable with respect to the student model parame- ters, we treat D(G(x)) as a reward and optimize it using policy gradient [SMSM99] with established reinforcement learning algorithms. We employ GRPO [SWZ+24] to train the student in our experi- ments, with detailed formulations provided in Appendix A.1. For the discriminator D, we minimize its training loss derived from Equation (1): (Discriminator) min", + "D(G(x)) as a reward and optimize it using policy gradient [SMSM99] with established reinforcement learning algorithms. We employ GRPO [SWZ+24] to train the student in our experi- ments, with detailed formulations provided in Appendix A.1. For the discriminator D, we minimize its training loss derived from Equation (1): (Discriminator) min D E(x,yt)∼T [− log σ (D(yt) − D(G(x)))] . (3) The discriminator uses Bradley-Terry loss to capture pairwise preferences, encouraging higher scores for teacher responses over student-generated ones. Warmup Before GAD Training We find that jointly warming up the generator and discrimina- tor before the GAD training stage is crucial for final performance. We fine-tune the student on the teacher’s response, and we minimize the cross-entropy loss as warmup for the generator. In the meanwhile, the discriminator is trained using the same data with the Bradley-Terry loss in Equa- tion (3). We conduct warmup for both models for one epoch before starting GAD training. This step promotes effective adversarial optimization and ensures the balance between the generator and discriminator. Ablation studies on the warmup strategy are presented in Section 3.3. 2.3 Implement GAD with Reinforcement Learning Frameworks In our experiments, we implement GAD using existing reinforcement learning frameworks, such as verl [SZY+24]. GRPO [SWZ+24] is used as the policy gradient algorithm, which is detailed in Appendix A.1. As presented in Table 1, we implement the generator as a policy model and the discriminator as a reward model. The generator produces responses, receives rewards from the discriminator, and is optimized to maximize the expected reward. The reward is defined in Equation (2), i.e., D(G(x)). Unlike vanilla reinforcement learning, GAD also needs to jointly update the discriminator (i.e., reward model). The discriminator is trained with Bradley-Terry loss on preference pairs to score the teacher response higher than the student’s output, similar to the reward model in RLHF [OWJ+22]. While conventional RLHF trains a fixed reward model prior to policy optimization which is prone to reward hacking, our approach updates the reward model (discriminator) online to adapt it to the current policy continually. Reinforcement Learning GAD Term Correspondence Policy Model Generator (i.e.,Student LLM) Reward Model Discriminator Reward D(G(x)) (as in Equation (2)) Difference The reward model is typically trained once on a static dataset and then frozen. The policy is then optimized against this fixed reward function. The discriminator co-evolves with the student LLM (i.e., pol- icy model). It is continually up- dated in a minimax game. Table 1: How to implement GAD within reinforcement learning frameworks. Pseudocode of Training Algorithm Algorithm 1 presents the pseudocode for GAD training. 4 Algorithm 1 GAD: Generative Adversarial Distillation Input: Distillation data T = {(x, yt)}; Student LLM (generator) G; Discriminator D Output: Trained student model G Warmup Stage for each batch (x, yt) ∼ T do Update generator G with cross-entropy loss on yt Update discriminator D with Bradley-Terry loss ▷ Equation (3) end for GAD Training Stage repeat for each batch (x, yt) ∼ T do Sample student responses G(x) Update generator G using D(G(x)) as reward for reinforcement learning Update discriminator D with Bradley-Terry loss", + "generator G with cross-entropy loss on yt Update discriminator D with Bradley-Terry loss ▷ Equation (3) end for GAD Training Stage repeat for each batch (x, yt) ∼ T do Sample student responses G(x) Update generator G using D(G(x)) as reward for reinforcement learning Update discriminator D with Bradley-Terry loss ▷ Equation (3) end for until convergence return G 3 Experiments 3.1 Setup Dataset Given a dataset of instruction prompts, we collect corresponding responses from a teacher model and use them to distill student models. For the following experiments, we use LMSYS-Chat-1M-Clean3, a clean version of the LMSYS-Chat-1M dataset [ZCS+24]. The dataset is derived from high-quality conversational data collected via the Chatbot Arena4 platform. Teacher and Student Models We adopt GPT-5-Chat [Ope25] as the teacher model. It is a closed-source chat model ranked ninth on the Chatbot Text Arena leaderboard at the time of writ- ing. For student models, we use the instruction-tuned variants of open-source models from the Qwen2.5 [YYZ+25] family (Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, Qwen2.5-14B-Instruct) and the Llama3 [GDJ+24] family (Llama-3.2-3B-Instruct, Llama-3.1-8B-Instruct). Training For training data, we sample 200K samples from LMSYS-Chat-1M-Clean and collect the corresponding GPT-5-Chat responses to the instructions as teacher responses. All models are trained for 3 epochs with a batch size of 256, totaling approximately 2400 optimization steps. The PPO mini-batch size for each policy update is also 256. The maximum context length is set to 2048 tokens for instruction prompts and 1536 for model responses. The training and sampling temperature is set to 0.8. We save checkpoints every 50 steps. More training details can be found in Appendix A.2. Evaluation We reserve 500 samples of LMSYS-Chat-1M-Clean as the primary test set. We also include test datasets consisting of a 500-sample subset split from Dolly [Dat23], the 252-sample SelfInst dataset [WKM+23], and the 80-question Vicuna benchmark [CLL+23] to evaluate out-of- distribution generalization. We report the GPT-4o evaluation scores [ZCS+23, GDWH24], where GPT-4o first generates reference answers and then scores the output of the student model against them. We also conduct human evaluations on the LMSYS-Chat-1M-Clean test set for qualitative assessment. We select the checkpoint that achieved the highest GPT-4o score and whose response length is within an acceptable range for each experiment. Detailed evaluation protocols are described in Appendix A.3. 3.2 Main Results Automatic Evaluation We report the results of automatic evaluation using GPT-4o scores in Figure 1 and Table 2. We compare GAD with the instruct model before distillation and the 3 https://huggingface.co/datasets/OpenLeecher/lmsys_chat_1m_clean 4 https://lmarena.ai 5 Model Method LMSYS Dolly SelfInst Vicuna GPT-5-Chat Teacher 51.7 49.8 49.7 49.9 Qwen2.5-3B-Instruct Before Distill. 45.8 45.1 45.6 47.3 SeqKD 47.5 44.8 45.7 48.0 GAD 48.9 46.7 47.7 49.4 Qwen2.5-7B-Instruct Before Distill. 48.7 47.6 48.3 49.1 SeqKD 49.2 47.2 48.3 49.5 GAD 50.8 48.5 50.1 51.4 Qwen2.5-14B-Instruct Before Distill. 50.0 49.1 49.4 50.0 SeqKD 50.6 48.2 49.4 49.7 GAD 52.1 50.4 51.1 51.6 Llama-3.2-3B-Instruct Before Distill. 44.0 45.8 47.0 46.9 SeqKD 47.6 47.0 47.1 48.1 GAD 48.1 48.5 49.1 48.9 Llama-3.1-8B-Instruct Before Distill. 46.9 46.6 48.4 47.9 SeqKD 49.7 47.7 48.7 48.7 GAD 50.3 48.8 49.5 50.2 Table 2: Automatic evaluation", + "49.4 50.0 SeqKD 50.6 48.2 49.4 49.7 GAD 52.1 50.4 51.1 51.6 Llama-3.2-3B-Instruct Before Distill. 44.0 45.8 47.0 46.9 SeqKD 47.6 47.0 47.1 48.1 GAD 48.1 48.5 49.1 48.9 Llama-3.1-8B-Instruct Before Distill. 46.9 46.6 48.4 47.9 SeqKD 49.7 47.7 48.7 48.7 GAD 50.3 48.8 49.5 50.2 Table 2: Automatic evaluation results. We report averaged GPT-4o score on the test datasets. The best results are highlighted in bold. GAD consistently outperforms both the instruct model before distillation and SeqKD across all datasets and model variants, with particularly strong gains in out- of-distribution generalization evaluations. vs. Before Distill. vs. SeqKD 0% 20% 40% 60% 80% 100% 68% 52% 4% 40% 28% 8% Qwen2.5-7B-Instruct vs. Before Distill. vs. SeqKD 56% 68% 28% 8% 16% 24% Qwen2.5-14B-Instruct vs. Before Distill. vs. SeqKD 60% 44% 28% 40% 12% 16% Llama-3.1-8B-Instruct GAD Wins Tie GAD Loses Figure 3: Human evaluation results on the LMSYS-Chat-1M-Clean test set. We compare GAD to the instruct model before distillation and the model fine-tuned with SeqKD. SeqKD baseline. Across all datasets, GAD consistently outperforms the baselines. As shown in Figure 1, on the LMSYS-Chat test set, Qwen2.5-3B-Instruct trained with GAD matches the performance of Qwen2.5-7B-Instruct trained with SeqKD; similarly, Qwen2.5-7B-Instruct with GAD rivals Qwen2.5-14B-Instruct with SeqKD, and Qwen2.5-14B-Instruct with GAD is compa- rable to the GPT-5-Chat teacher. In addition, GAD shows particularly strong gains on out-of- distribution generalization benchmarks. On Dolly, SelfInst, and Vicuna, SeqKD yields marginal or even negative improvements, whereas GAD maintains robust performance gains. We attribute this to the superior generalization ability of reinforcement learning compared to supervised fine- tuning [CZY+25, WZZ+25]. We also provide additional automatic evaluation results in Section B.1. Human Evaluation We conduct human evaluations on Qwen2.5-7B-Instruct, Qwen2.5-14B- Instruct, and Llama-3.1-8B-Instruct, comparing GAD against both the instruct model before dis- tillation and the model fine-tuned with SeqKD. For each prompt, the annotators assess the responses of two models and judge whether GAD wins, ties, or loses. GAD achieves a win rate exceeding 50% and a loss rate below 30% in almost all comparisons. The results indicate that GAD can consistently outperform the baseline models on human evaluation performance. 6 1 2 3 4 5 6 N-gram size (n) 0.0 0.2 0.4 0.6 0.8 1.0 Overlap SeqKD GAD Figure 4: Overlap of local patterns between the student and the teacher. SeqKD tends to overfit to local patterns of the teacher. 0 1 2 3 4 5 6 7 8 9 Class 0.0 0.2 0.4 0.6 Probability Teacher SeqKD GAD Figure 5: Black-box distillation on toy data. GAD learns reachable modes from the teacher while SeqKD aims to cover all the modes. 3.3 Analysis SeqKD Overfits to Local Patterns We evaluate the similarity of local patterns between the stu- dent and teacher on the LMSYS-Chat test set in Figure 4, measured by the F1 score of N-gram overlap. The student is trained from Qwen2.5-14B-Instruct, and the teacher is GPT-5-Chat. The SeqKD student exhibits a higher N-gram overlap while a lower GPT-4o evaluation score compared to the GAD student. This suggests that supervised fine-tuning tends to memorize local lexical pat-", + "4, measured by the F1 score of N-gram overlap. The student is trained from Qwen2.5-14B-Instruct, and the teacher is GPT-5-Chat. The SeqKD student exhibits a higher N-gram overlap while a lower GPT-4o evaluation score compared to the GAD student. This suggests that supervised fine-tuning tends to memorize local lexical pat- terns [CZY+25, WZZ+25], whereas our RL-based approach better captures the teacher’s global stylistic characteristics. Experiments on Toy Data We simulate the optimizing patterns of GAD and SeqKD in a toy ex- periment shown in Figure 5. We observe that GAD tends to learn reachable modes of the teacher, whereas SeqKD aims to cover all modes. The setup simulates a black-box distillation scenario. We define a discrete Gaussian mixture distribution as a teacher distribution p, which has categorical out- puts 0, . . . , 9. A student, modeled as a single Gaussian distribution, learns to imitate the teacher us- ing only output samples without access to p. We compare two student training schemes, SeqKD and GAD. The GAD student is optimized using the REINFORCE algorithm [Wil92]. As illustrated in Figure 5, the SeqKD student exhibits a mode-covering behavior, spreading probability mass across all possible outputs [GDWH24]. In contrast, the GAD student focuses on mode-seeking, concentrat- ing probability optimization on reachable regions. We find that such mode-seeking behavior leads to more effective knowledge distillation in LLMs. 800 1000 1200 1400 1600 1800 2000 Step 250 500 750 1000 1250 Response Length Reward Hacking Off-Policy Disc. On-Policy Disc. (Ours) Figure 6: Off-policy discriminator suffers from re- ward hacking, whereas on-policy discriminator re- mains stable over thousands of training steps. Comparison to Off-Policy Discriminator As discussed in Section 2.1, from the view of reinforcement learning, our generator (student) acts as the policy model, while the discrimina- tor acts as the on-policy reward model. Figure 6 compares GAD with the off-policy discrimina- tor approach. In the off-policy setting, the stu- dent is first trained for one warmup epoch us- ing SeqKD. The student is then frozen, and the discriminator is trained for two epochs based on the student’s output. Then the resulting dis- criminator serves as a frozen reward model to train the student using Equation (6). In con- trast, GAD jointly trains the student and dis- criminator for one warmup epoch followed by two GAD training epochs, positioning the discriminator as an on-policy reward model. We ob- serve that the student trained with an off-policy discriminator quickly exhibits reward hacking after around 300 training steps, producing excessively long responses (up to 1300 tokens) that deviate significantly from the teacher’s patterns. In comparison, GAD remains stable through thousands of training steps with no sign of reward hacking. The results establish GAD as a highly reliable and robust on-policy distillation method. 7 LMSYS Others SeqKD 49.2 48.3 GAD 50.8 50.0 w/o Gen. Warmup 49.7 49.7 w/o Disc. Warmup 49.0 47.7 Table 3: Ablation of warmup strategy on Qwen2.5-7B-Instruct. Warmup of the genera- tor and discriminator are removed separately. Warmup Strategy We perform an ablation study of the warmup strategy introduced in Section 2.2. As shown in Table", + "GAD 50.8 50.0 w/o Gen. Warmup 49.7 49.7 w/o Disc. Warmup 49.0 47.7 Table 3: Ablation of warmup strategy on Qwen2.5-7B-Instruct. Warmup of the genera- tor and discriminator are removed separately. Warmup Strategy We perform an ablation study of the warmup strategy introduced in Section 2.2. As shown in Table 3, we separately remove the warmup stage for the generator and the discrimina- tor on Qwen2.5-7B-Instruct. When removing the generator warmup, we directly use Qwen2.5-7B- Instruct without SeqKD as initialization for both the generator and discriminator for GAD training. This leads to a performance drop. We attribute this to the discriminator easily distinguishing between the stu- dent and teacher outputs in the early training stage. The large distributional gap between the teacher and the student weakens the effectiveness of GAD training. When removing the discriminator warmup, we use the generator obtained after one epoch of SeqKD and initialize the discriminator with the original Qwen2.5-7B-Instruct. In this setting, the imbalance between the generator and the discriminator prevents the discriminator from providing sufficiently informative feedback. Consequently, the adversarial interaction becomes ineffective, and the generator exhibits little improvement beyond its warmup performance. 4 Related Work White-box Distillation of LLM White-box knowledge distillation of LLM assumes full access to the internal representations or token-level probabilities of a teacher model. Standard white-box approaches align the forward KLD of distribution [LHS+21, SST+20], reverse KLD of distribu- tion [GDWH24], hidden states [JYS+20, SCGL19] or attention scores [WWD+20, WBH+21] be- tween the teacher and the student. Recent work [GDWH24, LL25, AVZ+24] also proves the im- portance of on-policy distillation where the student learns from its own responses. Such approaches effectively compress large models while preserving semantic similarity. Despite their effectiveness, these methods rely on full teacher access, which is impractical for proprietary LLMs and limits their applicability to closed-source or API-only teachers. Black-box Distillation of LLM Black-box distillation trains a student model using only the tex- tual outputs of a teacher, typically obtained by API queries to closed-source models such as GPT-5 and Gemini 2.5 [Ope25, CBS+25]. In this setting, conventional white-box distillation methods be- come infeasible because of the lack of access to the teacher’s logits or hidden representations. The standard approach for this scenario, SeqKD, performs supervised fine-tuning (SFT) on the teacher’s responses [KR16, PLH+23, ZLX+23, TGZ+23, CLL+23] to imitate the teacher’s behaviors. Re- cent work [MYS+25, GMK+25, YHX+25, GYZ+25] extends this paradigm by performing SFT on the teacher’s reasoning traces to improve the student’s reasoning ability. 5 Conclusion We introduce GAD, a generative adversarial framework that effectively addresses key challenges of black-box LLM distillation. GAD enables on-policy learning by training a student model and an adaptive discriminator in a minimax game, eliminating the need for any logit-level supervision. This discriminator provides an implicit, on-policy reward signal that guides the student’s optimization. Experiments across multiple model families and datasets confirm our approach. GAD consistently surpasses standard sequence-level distillation, delivering superior generalization and achieving per- formance that rivals the proprietary teacher. These results validate GAD as an effective and robust solution for black-box LLM distillation. Acknowledgements We are grateful", + "guides the student’s optimization. Experiments across multiple model families and datasets confirm our approach. GAD consistently surpasses standard sequence-level distillation, delivering superior generalization and achieving per- formance that rivals the proprietary teacher. These results validate GAD as an effective and robust solution for black-box LLM distillation. Acknowledgements We are grateful to Yi Zhu for technical support during the development of the RL infrastructure and to Yuxian Gu for insightful discussions. 8 References [AVZ+24] Rishabh Agarwal, Nino Vieillard, Yongchao Zhou, Piotr Stanczyk, Sabela Ramos Garea, Matthieu Geist, and Olivier Bachem. On-policy distillation of language mod- els: Learning from self-generated mistakes. In The twelfth international conference on learning representations, 2024. [BT52] Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324–345, 1952. [CBS+25] Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, et al. 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In Proceedings of NeurIPS, 2023. [ZCS+24] Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Tianle Li, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zhuohan Li, Zi Lin, Eric Xing, et al. Lmsys-chat-1m: A large- scale real-world llm conversation dataset. In The Twelfth International Conference on Learning Representations, 2024. [ZLX+23] Chunting Zhou, Pengfei Liu, Puxin Xu, Srinivasan Iyer, Jiao Sun, Yuning Mao, Xuezhe Ma, Avia Efrat, Ping Yu, Lili Yu, et al. LIMA: Less is more for alignment. In Proceedings of NeurIPS, 2023. 11 A Experimental Details A.1 Implement GAD with GRPO We implement policy optimization of the student with GRPO [SWZ+24]. We use qG to denote the output distribution of student G. For each input prompt x, we sample a group of N student responses {yi s}N i=1, and obtain their corresponding rewards {ri s}N i=1, where ri s = D(yi s). The advantage of the i-th response can be calculated with: ri s = D(yi s) (4) Ai = ri s − mean({rj s}N j=1) std({rj s}N j=1) . (5) The student is trained with the following objective: max G E(x,yt)∼T ,{yis}N i=1∼qG(·|x) � 1 N N � i=1 Ai � , (6) where we omit the KL regularizer and the clip operator in GRPO", + "s) (4) Ai = ri s − mean({rj s}N j=1) std({rj s}N j=1) . (5) The student is trained with the following objective: max G E(x,yt)∼T ,{yis}N i=1∼qG(·|x) � 1 N N � i=1 Ai � , (6) where we omit the KL regularizer and the clip operator in GRPO for brevity. For the discriminator, we pair each student response yi s in the group with the same teacher response yt to form (yt, yi s) preference pairs. The discriminator parameters are optimized by minimizing the Bradley-Terry loss across the group: min D E(x,yt)∼T ,{yis}N i=1∼qG(·|x) � 1 N N � i=1 − log σ(D(yt) − D(yi s)) � , (7) where D(yt) is the teacher score shared within the group. A.2 Training Details We train all models with 3 epochs. For GAD, the training consists of 1 warmup epoch followed by 2 GAD training epochs. The models are trained with a batch size of 256, totaling approximately 2400 optimization steps. The PPO mini-batch size for each policy update is also 256. In the warmup stage of GAD, we train the discriminator for 10 steps before jointly training the generator and discriminator. We search learning rate in [1e-6, 5e-6] for GAD and SeqKD baseline. For SeqKD, we find 5e-6 leads to better results in all experiments. For GAD with GPT-5-Chat teacher, we use 1e-6 for both warmup and GAD training stage, and for GAD with Qwen2.5 teacher as in Table 5, we use 5e-6 for warmup stage and 1e-6 for GAD training stage. The maximum context length is set to 2048 tokens for instruction prompts and 1536 for model responses. The training temperature is set to 0.8. In the GRPO algorithm formulated as Equation (6), we set group size N = 8 and the KL weight β = 0.001. Distilling Qwen2.5-14B-Instruct from GPT-5-Chat takes about 30 hours on 16 H100 GPUs. 12 A.3 Automatic Evaluation Details The sampling temperature is set to 0.8 and model response length is set to 1536 tokens, same as in training. We use the prompt wrapper in Figure 7 to construct prompts. We use the prompt in Figure 8 for GPT-4o feedback following [GDWH24]. Below is an instruction that describes a task. Write a response that appropriately completes the request. ### Instruction: {instruction} ### Response: Figure 7: The prompt wrapper for training and evaluation. We would like to request your feedback on the performance of two AI assistants in response to the user instruction and input displayed above. Please rate the helpfulness, relevance, accuracy, and level of detail of their responses. Each assistant receives an overall score on a scale of 1 to 10, where a higher score indicates better overall performance. Please first output a single line containing only two values indicating the scores for Assistant 1 and 2, respectively. The two scores are separated by a space. In the subsequent line, please provide a comprehensive explanation of your evaluation, avoiding any potential bias and ensuring that the order in which the responses were pre- sented does not affect your judgment. Figure 8: GPT-4o evaluation prompt.", + "1 and 2, respectively. The two scores are separated by a space. In the subsequent line, please provide a comprehensive explanation of your evaluation, avoiding any potential bias and ensuring that the order in which the responses were pre- sented does not affect your judgment. Figure 8: GPT-4o evaluation prompt. B Additional Results B.1 Additional Automatic Evaluation Results GPT-5 Teacher We provide additional results of the automatic evaluation. In Table 4, we report GPT-4o score and response lengths of distilled student models trained with the GPT-5-Chat teacher. Across datasets, we observe that SeqKD tends to produce shorter responses that closely follow the teacher’s length distribution whereas GAD maintains the original model’s length distribution while integrating the teacher’s global stylistic characteristics. We attribute this behavior to the on-policy sampling of GAD, which encourages generation patterns aligned with both the student’s prior and the teacher’s guidance. Qwen2.5 Teacher In Table 5, we distill from Qwen2.5-14B-Instruct teacher to student models from the Llama family. Although the teacher is open-source, its tokenizer is incompatible with the students, preventing direct application of white-box distillation methods that align KL divergence between teacher and student logits. In this setting, GAD remains effective, outperforming both the pre-distillation models and the SeqKD baseline in most settings on GPT-4o evaluation score. 13 Model Method LMSYS Dolly SelfInst Vicuna Score Len. Score Len. Score Len. Score Len. GPT-5-Chat Teacher 51.7 329.1 49.8 148.5 49.7 188.5 49.9 378.6 Qwen2.5-3B-I Before Distill. 45.8 338.9 45.1 219.2 45.6 279.3 47.3 520.9 SeqKD 47.5 318.2 44.8 160.6 45.7 207.1 48.0 370.4 GAD 48.9 438.0 46.7 239.5 47.7 281.8 49.4 517.9 Qwen2.5-7B-I Before Distill. 48.7 345.2 47.6 220.0 48.3 259.1 49.1 501.7 SeqKD 49.2 320.2 47.2 152.3 48.3 182.3 49.5 398.1 GAD 50.8 414.0 48.5 225.1 50.1 288.5 51.4 511.9 Qwen2.5-14B-I Before Distill. 50.0 322.1 49.1 201.6 49.4 252.0 50.0 475.4 SeqKD 50.6 319.3 48.2 151.2 49.4 199.8 49.7 402.5 GAD 52.1 438.9 50.4 262.6 51.1 284.1 51.6 499.6 Llama-3.2-3B-I Before Distill. 44.0 334.4 45.8 174.5 47.0 265.6 46.9 437.6 SeqKD 47.6 328.6 47.0 147.4 47.1 214.5 48.1 389.3 GAD 48.1 371.5 48.5 232.3 49.1 275.7 48.9 461.8 Llama-3.1-8B-I Before Distill. 46.9 329.2 46.6 184.7 48.4 276.2 47.9 487.8 SeqKD 49.7 319.6 47.7 148.4 48.7 199.7 48.7 400.3 GAD 50.3 394.6 48.8 200.6 49.5 263.8 50.2 504.2 Table 4: Extended automatic evaluation results with GPT-5-Chat teacher. We report averaged GPT- 4o score and token length of response. Model Method LMSYS Dolly SelfInst Vicuna Qwen2.5-14B-I Teacher 50.0 49.1 49.4 50.0 Llama-3.2-3B-I Before Distill. 44.0 45.8 47.0 46.9 SeqKD 46.9 47.6 47.6 48.5 GAD 47.5 47.7 47.3 49.0 Llama-3.1-8B-I Before Distill. 46.9 46.6 48.4 47.9 SeqKD 49.0 48.4 48.6 49.4 GAD 49.6 49.9 50.5 49.7 Table 5: Automatic evaluation results with Qwen2.5-14B-Instruct teacher. We report averaged GPT- 4o score. 14", + "Instella: Fully Open Language Models with Stellar Performance Jiang Liu, Jialian Wu, Xiaodong Yu, Yusheng Su, Prakamya Mishra, Gowtham Ramesh, Sudhanshu Ranjan, Chaitanya Manem, Ximeng Sun, Ze Wang, Pratik Prabhanjan Brahma, Zicheng Liu, Emad Barsoum AMD https://huggingface.co/amd/Instella-3B https://github.com/AMD-AGI/Instella Abstract Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks, yet the majority of high-performing models remain closed-source or par- tially open, limiting transparency and reproducibility. In this work, we introduce Instella, a family of fully open three billion parameter language models trained entirely on openly available data and codebase. Powered by AMD Instinct™ MI300X GPUs, Instella is devel- oped through large-scale pre-training, general-purpose instruction tuning, and alignment with human preferences. Despite using substantially fewer pre-training tokens than many contemporaries, Instella achieves state-of-the-art results among fully open models and is competitive with leading open-weight models of comparable size. We further release two specialized variants: Instella-Long, capable of handling context lengths up to 128K tokens, and Instella-Math, a reasoning-focused model enhanced through supervised fine-tuning and reinforcement learning on mathematical tasks. Together, these contributions establish Instella as a transparent, performant, and versatile alternative for the community, advanc- ing the goal of open and reproducible language modeling research. 0.42 T 1.5 T 4.0 T 2.0 T 9.0 T 18.0 T Pre-training Tokens (trillion) 45 50 55 60 65 70 Avg. score over 11 benchmarks Instella-3B Pythia-2.8B GPT-Neo-2.7B OpenELM-3B StableLM-3B-4E1T Gemma-2B Llama-3.2-3B Qwen-2.5-3B Base Models 1.5 T 4.0 T 2.0 T 9.0 T 18.0 T Pre-training Tokens (trillion) 10 15 20 25 30 35 40 45 50 Avg. score over 9 benchmarks Instella-3B-Instruct OpenELM-3B-Instruct StableLM-zephyr-3b Gemma-2-2b-it Llama-3.2-3B-instruct Qwen2.5-3B-Instruct Instruction-tuned Models Ours (Fully Open) Fully Open Open Weight Figure 1: Average Score versus Pre-training Tokens for base (left) and instruction-tuned (right) models. Instella surpasses prior fully open models of comparable size and, despite being trained on substantially fewer pre-training tokens, achieves competitive performance with state-of-the-art open-weight models for both (left) base models (Table 4) and (right) instruction-tuned models (Table 6). 1 Introduction The rapid advancement of artificial intelligence, driven in large part by large language models (LLMs) (Gemini Team, 2024; OpenAI, 2023; Dubey et al., 2024; Yang et al., 2025a), has accelerated progress toward artificial general intelligence and transformed society at large. However, much of this progress has been led by proprietary releases (e.g., GPT-4 (OpenAI, 2023), Claude (Anthropic, 2025), Gemini (Gemini Team, 2024)), where training data, methods, and evaluation details remain opaque. While these mod- els have set new state-of-the-art performance, their closed nature hinders scientific understanding, repro- ducibility, and equitable access. 1 arXiv:2511.10628v1 [cs.CL] 13 Nov 2025 In response, the research community has placed increasing emphasis on open-weight models, where trained parameters are released. Projects such as LLaMA-3.2-3B (Dubey et al., 2024), Qwen-2.5-3B (Yang et al., 2024), and Gemma-2-2B (Team et al., 2024) have demonstrated competitive capabilities in relatively compact architectures. Yet most of these remain open-weight rather than fully open: their training data, preprocessing, and training recipes are either undisclosed or proprietary. As a result, researchers cannot fully reproduce the results, audit potential data contamination, or study the effects of data", + "2024) have demonstrated competitive capabilities in relatively compact architectures. Yet most of these remain open-weight rather than fully open: their training data, preprocessing, and training recipes are either undisclosed or proprietary. As a result, researchers cannot fully reproduce the results, audit potential data contamination, or study the effects of data and training choices at scale. To bridge this gap, we introduce Instella, a new family of fully open 3B-parameter language models. In- stella makes available not only model weights, but also the complete training pipeline, datasets, and opti- mization details, thereby offering full transparency. Instead of solely relying on general-purpose corpora, Instella is pretrained in two distinct stages: an initial 4T-token general-domain pre-training stage, followed by a 57B-token second-stage emphasizing reasoning-heavy domains. To further enrich this stage, we in- troduce an in-house synthetic dataset for mathematics, constructed by abstracting GSM8K problems into symbolic Python programs and parameterizing them to generate diverse yet solvable variants. This ap- proach expands mathematical coverage while maintaining the correctness of synthesized data, providing a principled way to inject reasoning signals into pre-training. In addition, we leverage weight ensembling across stochastic pre-training seeds by conducting multiple second-stage runs with different random seeds and merging their weights into the final checkpoint, which further enhances model performance. Following pre-training, Instella undergoes supervised fine-tuning (SFT) on a carefully curated mixture of 2.3 million high-quality instruction-response pairs drawn from diverse domains such as mathematics, coding, com- monsense reasoning, and multi-turn dialogue. This step equips the model with the ability to follow user prompts, handle complex instructions, and generalize across a wide range of task formats, and is further refined through direct preference optimization (DPO) (Rafailov et al., 2023), aligning outputs with human expectations for helpfulness, safety, and factuality. Building on this foundation, we extend Instella into the long-context regime with Instella-Long, capable of processing sequences up to 128K tokens. Instella-Long is trained in two stages of continued pre-training on 40B tokens, followed by long-context SFT and short-context DPO. Because of the limited availability of long- context SFT data, we synthesize long-context instruction-following examples directly from pre-training documents. Compared with other open-weight models, Instella-Long delivers competitive performance on the challenging Helmet benchmark (Yen et al., 2024), while fully releasing its training details and data to ensure transparency and reproducibility. Finally, Instella advances reasoning-centric reinforcement learning at small scale through Instella-Math. Using only 3B parameters, Instella-Math is, to our knowledge, the first fully open model of this size to apply multi-stage group relative policy optimization (GRPO) (Shao et al., 2024) entirely on open datasets. By gradually increasing rollout lengths and incorporating Olympiad-level problems from DeepScaleR (Luo et al., 2025), the model demonstrates substantial improvements in mathematical and logical reasoning. Re- markably, Instella-Math performs strongly not only on benchmarks like GSM8K and OlympiadBench (He et al., 2024b) but also on TTT-Bench (Mishra et al., 2025), highlighting that reinforcement learning can mean- ingfully enhance reasoning even for compact models. Despite being trained on significantly fewer tokens compared to some leading models, Instella achieves state-of-the-art results among fully open models and rivals the performance of stronger open-weight", + "al., 2024b) but also on TTT-Bench (Mishra et al., 2025), highlighting that reinforcement learning can mean- ingfully enhance reasoning even for compact models. Despite being trained on significantly fewer tokens compared to some leading models, Instella achieves state-of-the-art results among fully open models and rivals the performance of stronger open-weight mod- els. To summarize, our contributions are threefold: • Instella. A 3B-parameter language transformer trained with a carefully staged pre-training pro- cess. Instella significantly outperforms prior fully open models of comparable size across diverse benchmarks. • Instella-Long. A long-context variant extending sequence length to 128K tokens driven by con- tinued pre-training and synthetic QA-based long-context instruction tuning. Instella-Long attains competitive performance on the challenging long-context benchmark Helmet. • Instella-Math. A reasoning-centric variant fine-tuned with curated math datasets and reinforce- ment learning, delivering strong gains on AIME, OlympiadBench, and GSM8K while achieving the highest reported performance on the strategic reasoning benchmark TTT-Bench among fully open models. Our work demonstrates that openness and competitiveness are not mutually exclusive. By releasing model weights, training code, data recipes, and evaluation protocols, Instella enables transparent benchmarking, reproducibility, and further research into the foundations of language modeling. 2 2 Background 2.1 Open-Weight versus Fully-Open Large Language Models The release of open-weight large language models such as LLaMA (Touvron et al., 2023; Dubey et al., 2024) and Qwen (Bai et al., 2023; Yang et al., 2024; 2025a) series has significantly broadened community access to high-performing models. These systems are compact enough to be fine-tuned on modest hard- ware, enabling academic research and downstream applications. However, most such models are not com- pletely transparent: their pre-training datasets, training pipelines, and optimization hyperparameters re- main undisclosed. This opacity prevents reproducibility, makes data contamination difficult to audit, and constrains the ability to study scaling laws or understand how training data composition affects down- stream performance. In contrast, completely transparent models release not only weights but also data recipes, preprocessing scripts, and training code. Notable examples include OLMo (Groeneveld et al., 2024; OLMo et al., 2024) and SmolLM (Allal et al., 2025), which provide comprehensive training pipelines and fully specified data mixtures. These initiatives enable researchers to systematically investigate questions such as how data diversity affects generalization, how alignment methods interact with model size, and how pre-training choices influence reasoning capabilities. However, prior fully open 3B models still underperform com- pared to state-of-the-art open-weight systems by a considerable margin on challenging benchmarks such as GSM8K (Cobbe et al., 2021b), BBH (Suzgun et al., 2023), and MMLU (Hendrycks et al., 2021b), motivating further work to bridge the gap between transparency and competitiveness. Instella addresses this gap by offering a fully open 3B-parameter model family with state-of-the-art results. We release not only weights but also training data recipes, preprocessing scripts, optimization settings, and evaluation pipelines, pro- viding a truly reproducible foundation for scientific study. 2.2 Long-context Language Models Many real-world applications demand reasoning over inputs significantly longer than the typical 2K–8K context windows used in base large language models. Tasks such as legal document analysis, multi-chapter summarization, and retrieval-augmented generation require context lengths exceeding 100K", + "pro- viding a truly reproducible foundation for scientific study. 2.2 Long-context Language Models Many real-world applications demand reasoning over inputs significantly longer than the typical 2K–8K context windows used in base large language models. Tasks such as legal document analysis, multi-chapter summarization, and retrieval-augmented generation require context lengths exceeding 100K tokens. Recent advances including efficient attention mechanisms (Dao, 2024; Jacobs et al., 2023; Liu et al., 2023), rotary po- sition embedding (RoPE) scaling (Gradient Team, 2024; emozilla, 2023; Ding et al., 2024), and specialized training strategies for long sequences (Gao et al., 2024) have enabled models to process extended sequences. Despite these developments, few transparent models provide both long-context support and strong perfor- mance. On the other hand, open-weight models such as Qwen2.5-1M (Yang et al., 2025b) offer extended context windows, but their training data remain proprietary, limiting reproducibility. Instella-Long con- tributes to this space by transparently extending the context length to 128K tokens through continued pre- training and post-training on the long-context data we release publicly. It achieves competitive results on the long-context benchmarks while establishing a transparent, reproducible long-context baseline. 2.3 Large Reasoning Models The ability to perform multi-step reasoning represents a central goal for large language model development. Benchmarks such as MMLU, BBH, GSM8K, MATH (Hendrycks et al., 2021d) and AIME (AIME) measure a model’s capacity to perform structured, compositional thinking beyond surface-level pattern matching. Recent research demonstrates that high-quality reasoning data and post-training techniques such as rein- forcement learning can dramatically improve performance. Models like DeepSeek-R1 (DeepSeek-AI et al., 2025) and DeepSeek-Math (Shao et al., 2024) show that incorporating step-by-step solutions and applying alignment methods like group relative policy optimization (GRPO) (Shao et al., 2024) can lead to substantial gains in reasoning capabilities. However, most reasoning-focused models remain only partially open: either the reasoning datasets are proprietary, the reinforcement learning recipes are undisclosed, or the resulting models are released without reproducible training pipelines. This lack of transparency hinders systematic study of reasoning capabilities and prevents independent validation of methodological claims. Instella-Math addresses this limitation by providing the first fully open 3B-parameter model trained with multi-stage reinforcement learning entirely on open data. We release not only the model weights but also 3 the reasoning datasets and training configurations, enabling reproducible research into reasoning emer- gence and reinforcement learning training for small-scale models. 3 Instella 3.1 Model Architecture The Instella models are text-only, autoregressive transformer-based language models (Vaswani et al., 2017) with 3 billion parameters. Architecture-wise, Instella consists of 36 decoder layers, each having 32 attention heads with a hidden dimension of 2,560 and an intermediate dimension of 6,912. We use standard multi- head attention (Vaswani et al., 2017). For layer normalization, we employ RMSNorm (Zhang & Sennrich, 2019), which has been shown to provide better training stability and convergence properties compared to standard LayerNorm (Ba et al., 2016), particularly for large-scale language models (Takase et al., 2025; Touvron et al., 2023; Muennighoff et al., 2025). In addition, we apply QK-Norm (Dehghani et al., 2023; Muennighoff et al., 2025; Naseer et al., 2021), where layer normalization is injected after the", + "properties compared to standard LayerNorm (Ba et al., 2016), particularly for large-scale language models (Takase et al., 2025; Touvron et al., 2023; Muennighoff et al., 2025). In addition, we apply QK-Norm (Dehghani et al., 2023; Muennighoff et al., 2025; Naseer et al., 2021), where layer normalization is injected after the query and key projections within each attention head. QK-Norm normalizes the query and key vectors before computing attention scores, helping to maintain more balanced attention distributions throughout training. It has been shown to be effective in improving training stability by preventing attention weights from becoming overly extreme, which can lead to gradient instability and poor convergence. Our model uses a standard causal attention mask. The feed-forward network within each transformer layer follows the standard architecture with SwiGLU activation function, which has demonstrated superior per- formance compared to ReLU-based activations in recent language models. We also employ rotary position embeddings (RoPE) (Su et al., 2024) to encode positional information, which provides better extrapolation to longer sequences compared to absolute positional embeddings. The key hyperparameters of Instella-3B architecture are shown in Table 1. We use the OLMo tok- enizer (Groeneveld et al., 2024) with a vocabulary size of 50,304 tokens. This vocabulary size strikes a balance between computational efficiency and representation capacity, allowing the model to handle di- verse text while maintaining reasonable embedding and output layer sizes. Table 1: Key hyper-parameters of Instella-3B architecture. Number of Hidden Intermediate Number of Number of Sequence Vocabulary transformer layers dimension dimension attention heads KV heads length size 36 2560 6912 32 32 4096 50,304 3.2 Training Setup Our training pipeline is based on the open-sourced OLMo codebase, adapted, and optimized for our hard- ware and model architecture. For pre-training we use a total of 128 Instinct MI300X GPUs distributed across 16 nodes. During both pre-training and post-training, we utilize FlashAttention 2 (Dao, 2024), Torch Compile, and bfloat16 mixed-precision training to reduce memory usage and speed up training. To balance inter-node memory efficiency and intra-node communication overhead within our cluster, we employ fully sharded data parallelism (FSDP) with hybrid sharding, with model parameters, gradients, and optimizer states sharded within a node and replicated across the nodes. 3.3 Pre-training We pre-train the model using two stages with a sequence length of 4,096 tokens and a global batch size of 1,024. The Instella 3B pretraining pipeline is shown in Fig. 2. In the first pre-training stage, we train the model from scratch on 4.07 trillion tokens sourced from OLMoE-mix-0924 (Muennighoff et al., 2025), which is a diverse mix of two high-quality datasets DCLM-baseline (Li et al., 2024) and Dolma 1.7 (Soldaini et al., 2024) covering domains like coding, academics, mathematics, and general world knowledge from web crawl. This extensive first stage pre-training established a foundational understanding of general language 4 58 Billion Tokens 4 Trillion Tokens Stage 1 Stage 2 Instella-3B-Stage1 Instella-3B 760 Million Tokens 26.7 Billion Tokens Supervised Fine-tuning Direct Preference Optimization Instella-3B-SFT Instella-3B-Instruct Pre-training Post-training Figure 2: Instella-3B model training pipeline. in our Instella model. We use the cosine decay learning rate schedule with a maximum learning", + "4 58 Billion Tokens 4 Trillion Tokens Stage 1 Stage 2 Instella-3B-Stage1 Instella-3B 760 Million Tokens 26.7 Billion Tokens Supervised Fine-tuning Direct Preference Optimization Instella-3B-SFT Instella-3B-Instruct Pre-training Post-training Figure 2: Instella-3B model training pipeline. in our Instella model. We use the cosine decay learning rate schedule with a maximum learning rate of 4 × 10−4 and set the global batch size to 1024. For our final pre-trained checkpoint, Instella-3B, we conduct a second stage pre-training on top of the first-stage Instella-3B-Stage1 model to further enhance its capabilities on MMLU (Hendrycks et al., 2021b), BBH (Suzgun et al., 2023), and GSM8K (Cobbe et al., 2021b). The model is trained three times with dif- ferent random seeds, and the resulting weights are ensembled to obtain the final checkpoint. Specifically, the second-stage training uses 58 billion tokens sourced from diverse and high-quality datasets, including Dolmino-Mix-1124 (OLMo et al., 2024), SmolLM-Corpus (python-edu) (Ben Allal et al., 2024), Deepmind Mathematics (Saxton et al., 2019), and conversational datasets such as T¨ulu-3-SFT-Mixture (Lambert et al., 2024), OpenHermes-2.5 (Teknium, 2023), WebInstructSub (Yue et al., 2024), Code-Feedback (Zheng et al., 2024), and Ultrachat 200k (Ding et al., 2023). We use the linear decay learning rate schedule with a maxi- mum learning rate of 4 × 10−5 and set the global batch size to 1024. In addition to the publicly available datasets, 28.5 million tokens in the second-stage pre-training data mixture are derived from our in-house synthetic dataset focused on mathematical problems. This dataset is generated using the training set of GSM8k dataset, where we first use Qwen2.5-72B-Instruct (Yang et al., 2024) to 1) abstract numerical values as function parameters and generate a python program to solve the math question, 2) identify and replace numerical values in the existing question with alternative values that are still answerable with the same python program solution as the original question. Next, by assigning different new values to these python parameters and using the abstract solution program to compute the corresponding answers, we expand our synthetic dataset with new and reliable question-answer pairs (Yu et al., 2024). 3.4 Post-training We first perform supervised finetuning (SFT) to enable the pre-trained model to follow instructions and respond effectively to user queries. We train for three epochs on 2.3 millions of high-quality instruc- tion–response pairs, resulting in Instella-3B-SFT. During this phase, we utilize datasets spanning a broad spectrum of tasks and domains to ensure that the model generalizes across diverse instruction types. The mixture is selectively sourced from SmolTalk (Allal et al., 2025), OpenMathInstruct-2 (Toshniwal et al., 2024), T¨ulu-3 Instruction Following (Lambert et al., 2024), MMLU auxiliary train set (Hendrycks et al., 2021b), and o1-journey (Qin et al., 2024). We use the linear decay learning rate schedule with a maximum learning rate of 1 × 10−5 and set the global batch size to 128. In the final training stage, we align Instella-3B-SFT with human preferences to ensure its outputs are helpful, accurate, and safe. Building on Instella-3B-SFT, Instella-3B-Instruct is trained with direct preference opti- mization (DPO) (Rafailov et al., 2023) on 0.76 billion tokens from the OLMo 2 1124", + "global batch size to 128. In the final training stage, we align Instella-3B-SFT with human preferences to ensure its outputs are helpful, accurate, and safe. Building on Instella-3B-SFT, Instella-3B-Instruct is trained with direct preference opti- mization (DPO) (Rafailov et al., 2023) on 0.76 billion tokens from the OLMo 2 1124 7B Preference Mix (OLMo et al., 2024). This alignment step tailors the model’s responses to better reflect human values and expec- tations, thereby improving the quality and reliability of its outputs. We use the linear decay learning rate schedule with a maximum learning rate of 5 × 10−7 and set the global batch size to 128. 4 Instella-Long In this section, we introduce the long-context model of Instella, namely, Instella-3B-Long-Instruct, sup- porting 128K context length. To extend the context length, we continually train the model from Instella- 5 3B-Instruct through: 1. continued pre-training, 2. supervised finetuning (SFT), and 3. direct preference optimization (DPO), as shown in Fig. 3. We detail the training method and data in the following subsec- tions. 20B Tokens (Up to 256K) 20B Tokens (64K) Stage 1 Stage 2 Continued Pre-training 760M Tokens (2K) 1B Tokens (128K) Supervised Fine-tuning Direct Preference Optimization Instella-3B-Long-Instruct Post-training Instella-3B-Instruct Figure 3: Instella-Long model training pipeline. 4.1 Continued Pre-training The long context training is initialized from the short-context checkpoint, Instella-3B-Instruct, which has a context length of 4K. We conduct a two-stage continued pre-training to gradually increase the context length. Stage 1: We extend the context length from 4K to 64K and train the model using 20B tokens. The batch size is 4M tokens and the training steps are 5,000. We follow the RoPE scaling law (Gradient Team, 2024) to increase the base frequency of RoPE from 10,000 to 514,640. We also experiment with alternative RoPE scaling methods (emozilla, 2023; Gao et al., 2024) and observe only minor differences in performance. Stage 2: As indicated by (Gao et al., 2024), it is beneficial to train the model with the data whose context length is longer than the target context length. In this stage, we train the model on 20B tokens with a maximum context length of 256K - twice our target context length of 128K. Following the RoPE scaling law, we further increase the RoPE base frequency to 3,691,950. The batch size is 8M tokens and the training steps are 2,500. For both stages, we use the linear decay learning rate schedule and the maximum learning rate is 2 × 10−5. Table 2: Long-context continued pre-training data by source and portion. Each stage consists of 20 billion tokens in total. Training Stage 64K Long Data 256K Long Data Short Data Stage 1 Code repos (30%) Books (30%) Textbooks (3%) – FineWeb-Edu (10%) FineWeb (10%) Wikipedia (5%) OpenWebMath (5%) StackExchange (4%) ArXiv (3%) Stage 2 Code repos (10%) Books (15%) Code repos (20%) Books (15%) Textbooks (2%) FineWeb-Edu (10%) FineWeb (10%) Wikipedia (5%) OpenWebMath (5%) StackExchange (4%) ArXiv (4%) The continued pre-training data originates from the data mixture created by Prolong (Gao et al., 2024). We use the raw text data curated by Prolong and process", + "repos (10%) Books (15%) Code repos (20%) Books (15%) Textbooks (2%) FineWeb-Edu (10%) FineWeb (10%) Wikipedia (5%) OpenWebMath (5%) StackExchange (4%) ArXiv (4%) The continued pre-training data originates from the data mixture created by Prolong (Gao et al., 2024). We use the raw text data curated by Prolong and process the data through tokenization, filtering, and packing. In each stage of the continued pre-training, we train on a 20B-token mixture of short- and long-context data with an approximate ratio of 4 to 6. The detailed data sources and portion are listed in Table 2. Let L be the maximum context length of the training stage. We pack both short- and long-context data into L-length sequences for training. For short-context data, we randomly select multiple documents and concatenate them into an L-length sequence. The extra texts beyond L in the last document are discarded. For long- context data, we filter out the documents that are shorter than L. We observe that the raw text data has some super long documents (>> L). For these documents, we randomly sample a few segments from them to avoid producing an excessive number of training examples from a single document. We mix 64K data into 6 the long-context data in the second stage for improving training throughput, where we pack four different 64K documents into a 256K sequence. During data processing, we ensure that the documents used in the first and second stages are mutually exclusive. In training, we apply document masking so that different documents within the same sequence cannot attend to each other. 4.2 Post-training After continued training on the long-context pre-training data, we perform supervised finetuning on a 1B- token mixture of short- and long-context instruction data. We use a batch size of 4M tokens and train for 250 steps. A linear decay learning rate schedule is employed, with a maximum learning rate of 4 × 10−5. For the SFT data, we pack multiple samples into a 256K sequence with document masking applied during training. Padding tokens are added in order to reach exactly 256K tokens. Similar to the continued pre-training, we train the model on a mixture of short- and long-context instruc- tions data with a ratio of 4 to 6. For short-context instruction data, we use publicly available instruction- tuning datasets, some of which are also used in the post-training of Instella-3B-Instruct. Specifically, we use Ultrachat 200K (Ding et al., 2023), OpenMathinstruct-2 (Toshniwal et al., 2024), T¨ulu-3 Instruction Follow- ing (Lambert et al., 2024), and MMLU auxiliary train set (Hendrycks et al., 2021b). Due to the lack of long-context SFT data, we construct a long-context instruction-following dataset where the context length is controlled to be between 8K and 128K tokens. Specifically, we make use of the long- context documents of Books from our continued pre-training data corpus. We use the documents that have at least 8K tokens and truncate the document to 128K tokens if it is over 128K. Then, we use Qwen2.5-14B- Instruct-1M (Yang et al., 2025b) as a teacher model to synthetically generate a question and an answer for the", + "our continued pre-training data corpus. We use the documents that have at least 8K tokens and truncate the document to 128K tokens if it is over 128K. Then, we use Qwen2.5-14B- Instruct-1M (Yang et al., 2025b) as a teacher model to synthetically generate a question and an answer for the document. To speed up this process, we randomly choose a subpart of the document for the QA generation instead of using the whole document. The length of the subpart is randomly set to be between 2K and 8K tokens. We use NLTK Bird & Loper (2004) sentence tokenizer to divide documents into sentences to make sure that the selected subpart has complete sentences. The generated question and answer are appended to the end of the long document, serving as a complete single-round instruction-following data sample. Furthermore, we generate long-context instruction data from short-context documents, thereby enhancing dataset diversity with a broader range of sources. We use ArXiv from our continued pre-training corpus and the DCLM subset from Dolmino-Mix-1124 (OLMo et al., 2024). We first generate QA for each short- context document following the same pipeline aforementioned. Next, we iteratively concatenate different short-context documents into a long sequence until it reaches 128K tokens. Since we do not truncate the last document, the concatenated sequence may exceed 128K tokens. Lastly, we randomly choose one QA corresponding to one of the short-context documents and append it to the end of the concatenated sequence. Contrary to the findings by (Gao et al., 2024), we observe that our synthetic long-context instruction data notably improves performance on long-context tasks. The final SFT data mixture is shown in Table 3. Table 3: Long-context supervised finetuning data by source and portion, totaling 1 billion tokens. Short Data Long Data Ultrachat 200K (25%), OpenMathinstruct-2 (10%), MMLU auxiliary train set (3%), T¨ulu-3 Instruction Following (2%) Books (44%), DCLM (10%), ArXiv (6%) In the final training stage, we perform human preference alignment using DPO (Rafailov et al., 2023), em- ploying the same training setting and dataset as Instella-3B-Instruct. Different from the previous long- context training stages, this DPO stage is trained on short-context data only with a maximum context length of 2K. Consistent with the findings of other open-weights models, we observe that applying DPO solely on short-context data continues to improve on long-context tasks. 4.3 Implementation Details Sequence Parallelism. We implement sequence parallelism based on Deepspeed Ulysses (Jacobs et al., 2023), which distributes the attention heads across GPUs during attention computation. Compared to Ring- Attention (Liu et al., 2023), this approach is more communication-efficient. For the second continued pre- training stage and SFT, we employ four GPUs as a sequence parallelism group to handle the long input 7 sequences. Sequence parallelism is not used in other stages, as the memory requirements fit within a single GPU. Document Masking and Data Batching. We apply document masking during the continued pre-training and SFT, as each input sequence may contain multiple documents. Document masking is achieved through variable-length FlashAttention (Dao, 2023), which computes attention within each individual document rather than across the entire sequence. This", + "within a single GPU. Document Masking and Data Batching. We apply document masking during the continued pre-training and SFT, as each input sequence may contain multiple documents. Document masking is achieved through variable-length FlashAttention (Dao, 2023), which computes attention within each individual document rather than across the entire sequence. This design can also improve training throughput when combined with sorted data batching. Following Prolong (Gao et al., 2024), we sort microbatches at each training step by the sum of document lengths in the sequence. With gradient accumulation, later microbatches benefit from faster processing when they consist of shorter documents. 5 Instella-Math AM-DeepSeek-R1- Distilled-1.4M Context Length: 32k OpenMathInstruct-2 Context Length: 4k Stage 1 Stage 2 Pre-training Instella-3B-Instruct DeepMath Rollouts: 16 Context Length: 16k Big-Math Rollouts: 8 Context Length: 8k Stage 1 Stage 2 Reinforcement Learning (GRPO) Instella-3B-Math DeepScaleR Rollouts: 16 Context Length: 16k Stage 3 Figure 4: Instella-Math model training pipeline. In this section, we introduce Instella-Math, a reasoning-centric language model trained with long chain-of- thought reinforcement learning. To enhance the model’s mathematical and logical reasoning capabilities, we continually train Instella-3B-Instruct through two stages of supervised finetuning and three stages of reinforcement learning, as shown in Figure 4. We detail the training procedure and datasets below. 5.1 Supervised Finetuning As a cold start, we perform a two-stage supervised finetuning process to enhance the reasoning capabilities of Instella-3B-Instruct: Stage 1: Instruction Tuning with OpenMathInstruct-2 for Mathematical Coverage. In the first SFT stage, we begin with instruction tuning, following instructions or prompts properly, especially in a question- answer or problem-solution format. Using the OpenMathInstruct-2 dataset (Toshniwal et al., 2024), which consists of 14 million problem-solution pairs generated from the GSM8K (Cobbe et al., 2021b) and MATH (Hendrycks et al., 2021d) training sets, the model is trained to solve mathematical questions cover- ing a diverse range of topics from arithmetic and algebra to probability and calculus. Stage 2: Deep Reasoning with Long-Context Training on AM-DeepSeek-R1-Distilled. In the second SFT stage, we further improve the model’s reasoning capability by training on AM-DeepSeek-R1-Distilled- 1.4M (Zhao et al., 2025), which is a large-scale general reasoning dataset containing high-quality and chal- lenging problems. In this stage, we increase the context length of the model from 4K to 32K to allow the model to learn from the long chain-of-thought responses distilled from large reasoning models such as DeepSeek-R1 (DeepSeek-AI et al., 2025). 5.2 Reinforcement Learning Following supervised finetuning, we apply three stages of reinforcement learning using the group relative policy optimization (GRPO) algorithm (Shao et al., 2024) to further strengthen the model’s mathematical reasoning abilities. Training is orchestrated with verl (Sheng et al., 2024) and vLLM (Kwon et al., 2023) for efficient rollout collection, reward scoring, and policy updates. Stage 1: GRPO on Big-Math-RL-Verified (8 Rollouts @ 8K Tokens). In the first stage of reinforcement learning, we apply the GRPO algorithm to train the model on Big-Math-RL-Verified (Albalak et al., 2025), a collection of curated, complex, multi-step math problems. We generate 8 rollouts per prompt, each with up 8 Table 4: Base model performance. Models ARC-C ARC-E BoolQ HS. PiQA SciQ", + "first stage of reinforcement learning, we apply the GRPO algorithm to train the model on Big-Math-RL-Verified (Albalak et al., 2025), a collection of curated, complex, multi-step math problems. We generate 8 rollouts per prompt, each with up 8 Table 4: Base model performance. Models ARC-C ARC-E BoolQ HS. PiQA SciQ WG. OBQA MMLU BBH GSM8K Avg. Open Weight Models Gemma2-2B 39.5 59.3 74.5 70.5 76.4 96.6 69.8 44.8 53.3 40.8 27.4 59.3 Llama-3.2-3B 47.2 64.9 74.8 73.1 75.9 95.3 70.3 51.2 57.8 47.0 30.1 62.5 Qwen2.5-3B 51.5 67.2 79.1 72.1 77.4 95.5 69.3 51.4 67.2 56.7 63.8 68.3 Fully Open Models Pythia-2.8B 40.5 60.7 64.8 60.1 72.5 89.7 60.8 42.6 26.1 27.7 2.7 49.8 GPTNeo-2.7B 38.5 54.6 62.7 55.2 70.8 88.0 58.3 40.8 27.8 27.3 3.7 48.0 OpenELM-3B 37.5 58.4 68.6 71.7 75.6 92.5 65.4 46.4 26.7 29.4 3.0 52.3 StableLM-3B 44.8 67.0 75.4 74.2 78.4 93.4 68.4 48.6 45.2 37.3 10.8 58.5 Instella-3B-Stage1 53.9 73.2 78.7 74.2 77.5 94.9 71.2 51.4 54.7 34.3 10.8 61.3 Instella-3B 52.8 70.5 76.5 75.0 77.8 96.4 73.1 52.4 58.3 39.7 59.8 66.6 Table 5: Instella 3B base model performance. We report the model performance after stage 1 and stage 2 pretraining. For stage 2, we run the training for three times with different random seeds and merge model weights to obtain the final stage 2 model. Models ARC-C ARC-E BoolQ HS. PiQA SciQ WG. OBQA MMLU BBH GSM8K Avg. Stage1 53.9 73.2 78.7 74.2 77.5 94.9 71.2 51.4 54.7 34.3 10.8 61.3 Stage2-seed1 51.2 68.8 76.2 73.8 77.3 96.6 72.1 52.0 57.7 38.5 56.1 65.5 Stage2-seed2 50.8 68.4 77.8 74.3 77.2 96.6 71.8 51.4 58.2 38.5 58.8 65.8 Stage2-seed3 49.8 68.8 73.5 75.6 77.2 96.7 72.8 52.0 58.0 38.6 58.3 65.6 Stage2 52.8 70.5 76.5 75.0 77.8 96.4 73.1 52.4 58.3 39.7 59.8 66.6 to 8K output tokens, to explore diverse reasoning trajectories. The model is trained for 1,200 GRPO steps using rule-based reward signals provided by Prime-RL (Cui et al., 2025), which incentivize correctness and well-structured outputs. Stage 2: GRPO on DeepMath (16 Rollouts @ 16K Tokens). To push the limits of long-form reasoning, we conduct a second GRPO stage on DeepMath (He et al., 2025) using 16 rollouts per prompt with up to 16K output tokens. This stage is designed to maximize the model’s capacity for deep mathematical reasoning, enabling it to solve problems that require extended derivations, multiple nested logical steps, or structured proof-like outputs. In this stage, the model is trained for 600 GRPO steps. Stage 3: GRPO on DeepScaleR (16 Rollouts @ 16K Tokens). In the final GRPO stage, we finetune the model on DeepScaleR (Luo et al., 2025), which includes original Olympiad math problems (e.g., AIME and AMC). Similar to Stage 2, this training uses 16 rollouts and a 16K token limit. We run 740 GRPO steps in this phase to improve performance on competition-style reasoning tasks. 6 Evaluation 6.1 Base Model We evaluate the pre-trained base models on ARC-Challenge (ARC-C) (Clark et al., 2018), ARC-Easy (ARC- E) (Clark et al., 2018), BoolQ (Clark et al., 2019), HellaSwag (HS)", + "16K token limit. We run 740 GRPO steps in this phase to improve performance on competition-style reasoning tasks. 6 Evaluation 6.1 Base Model We evaluate the pre-trained base models on ARC-Challenge (ARC-C) (Clark et al., 2018), ARC-Easy (ARC- E) (Clark et al., 2018), BoolQ (Clark et al., 2019), HellaSwag (HS) (Zellers et al., 2019), PiQA (Bisk et al., 2019), SciQ (Welbl et al., 2017), WinoGrande (WG) (Sakaguchi et al., 2019), OpenBookQA (OBQA) (Mihaylov et al., 2018), BBH (Suzgun et al., 2022), MMLU (Hendrycks et al., 2021a), and GSM8k (Cobbe et al., 2021a). All the benchmarks use a zero-shot evaluation setting, except BBH, MMLU, and GSM8k, which are evaluated using 3-shot, 5-shot, and 8-shot prompting, respectively. As shown in Table 4, both Instella-3B-Stage1 and Instella-3B models outperform all the other fully open models over all the benchmarks individually (except PIQA). Our final pre-trained checkpoint Instella-3B outperforms the prior top performant fully open pre-trained models by a lead of 8.1% on average, with 9 Table 6: Instruction-tuned model performance. Models MMLU TQA BBH GPQA GSM8K MATH IFEval AE 2 MT Avg. Open Weight Models Gemma-2-2B-Instruct 58.4 55.8 43.0 25.2 53.5 22.5 55.6 29.4 8.1 39.0 Llama-3.2-3B-Instruct 61.5 50.2 61.5 29.7 77.0 46.0 75.4 19.3 7.1 47.5 Qwen-2.5-3B-Instruct 66.9 57.2 57.3 28.1 76.0 60.4 62.5 22.1 8.0 48.7 Fully Open Models StableLM-zephyr-3B 45.1 47.9 39.3 25.7 58.4 10.4 34.2 7.5 6.0 30.5 OpenELM-3B-Instruct 27.4 38.1 24.2 18.1 1.6 0.4 16.1 0.2 1.0 14.1 Instella-3B-SFT 58.8 52.5 46.0 28.1 71.7 40.5 66.2 7.6 7.1 42.1 Instella-3B-Instruct 58.9 55.5 46.8 30.1 73.9 42.5 71.4 17.6 7.2 44.9 significant improvements in ARC Challenge (+8%), ARC Easy (+3.5%), Winnograde (+4.7%), OpenBookQA (+3.9%), MMLU (+13.1%) and GSM8K (+49%). Second stage pre-training elevates the overall average performance relative to stage-1 by 5.3%, substantially narrowing the performance gap between Instella-3B model and the prior open weight models, and outper- forming Llama-3.2-3B by 4.1% on average (+5.7% ARC-Challenge, +5.6% ARC-Easy, and +29.7% GSM8k), Gemma-2-2B by 7.3% on average (+13.4% ARC-Challenge, +11.2% ARC-Easy, +4.5% HellaSwag, +7.6% OpenBookQA, +5.0% MMLU, and +32.5% GSM8k), and is competitive with Qwen-2.5-3B on the majority of the benchmarks. As shown in Table 5, the Instella-3B checkpoint, obtained by merging the weights of three independently trained models with different random seeds during second stage pretraining, achieves an average performance of 66.6%, surpassing all individual seed runs. The multi-stage pre-training with diverse and high-quality data mixture significantly enhances Instella- 3B’s capabilities, establishing it as a competitive and open alternative in the landscape of comparable size language models. 6.2 Instruction-tuned Model The instruction-tuned models are evaluated on MMLU (Hendrycks et al., 2021a), TruthfulQA (TQA) (Lin et al., 2022), BBH (Suzgun et al., 2022), GPQA (Rein et al., 2023), GSM8K (Cobbe et al., 2021a), Minerva Math (Lewkowycz et al., 2022) (MATH), IFEval (Zhou et al., 2023), Alpaca Eval V2 (AE2) (Dubois et al., 2025), and MT-Bench (MT) (Zheng et al., 2023). Here, GPQA, Minerva Math, IFEval, and Alpaca V2 use a zero-shot evaluation setting, whereas MMLU, TQA, BBH, and GSM8k use few-shot prompting using 5-shots, 6-shots, 3-shots, and 8-shots, respectively. Instella-3B-Instruct model consistently", + "et al., 2023), Alpaca Eval V2 (AE2) (Dubois et al., 2025), and MT-Bench (MT) (Zheng et al., 2023). Here, GPQA, Minerva Math, IFEval, and Alpaca V2 use a zero-shot evaluation setting, whereas MMLU, TQA, BBH, and GSM8k use few-shot prompting using 5-shots, 6-shots, 3-shots, and 8-shots, respectively. Instella-3B-Instruct model consistently outperforms other fully open models across all evaluated bench- marks with a significant average score lead of 14.37% with respect to the next top performing fully open instruction-tuned models (Table 6). With substantial margins across all the chat benchmarks (+13% MMLU, +7.57% TruthfulQA, +7.43% BBH, +4.46% GPQA, +37.15% IFEval, +10.08% Alpaca 2, and +1.2% MT-Bench). Instella-3B-Instruct narrows the performance gap with leading open-weight models. Instella-3B-Instruct performs on par with or slightly surpasses existing state-of-the-art open weight instruction-tuned models such as Llama-3.2-3B-Instruct (+5.24% TruthfulQA, +0.45% GPQA, and +0.1% MT-Bench), and Qwen2.5-3B- Instruct (+2.01% GPQA and +8.87% IFEval), while significantly outperforming Gemma-2-2B-Instruct with an average score lead of +5.83% (+0.55% MMLU, +3.79% BBH, +4.91% GPQA, +20.47% GSM8k, +19.98% Minerva MATH, and +15.17% IFEval). Overall, Instella-3B-Instruct excels in instruction following tasks and multi-turn QA tasks like TruthfulQA, GPQA, IFEval and MT-Bench, while being highly competitive compared to existing state-of-the-art open weight models on other knowledge recall and math benchmarks, while being trained on significantly fewer training tokens. 10 Table 7: Long-context evaluation on the Helmet benchmark. NQ: Natural Question. Inf: InfiniteBench. NarrQA: NarrativeQA. The NIAH-MV task and RAG task (NQ, TriviaQA, and HotpotQA) are evaluated at five context lengths: 8K, 16K, 32K, 64K, and 128K, and the number is reported by averaging across the five context lengths. The InfQA, InfMC, and NarrQA are evaluated at 128K context length. Models NQ TriviaQA HotpotQA InfQA InfMC NarrQA NIAH-MV Avg. Open Weight Models Llama-3.2-3B-Instruct 51.8 86.2 56.4 38.7 56.0 26.0 99.2 59.2 Phi-3.5-Mini-Instruct 41.2 78.6 48.6 24.0 55.0 27.7 87.0 51.7 Gemma-3-4B-it 47.2 76.8 45.2 21.0 49.0 20.7 74.0 47.7 Qwen-2.5-3B-Instruct 34.6 65.8 41.8 14.7 35.0 21.0 80.4 41.9 MiniCPM-2B-128k 28.4 61.6 30.8 3.7 22.0 3.3 46.6 28.1 Fully Open Models Instella-3B-Long-Instruct 43.6 73.0 51.6 30.7 54.0 32.3 84.0 52.7 6.3 Instella-Long We evaluate the long-context performance on Helmet (Yen et al., 2024), a recent comprehensive long- context evaluation benchmark encompassing diverse categories. Helmet demonstrates more consistent alignment with human judgment. We evaluate three main tasks across seven datasets: multi-value needle-in-a-haystack (NIAH-MV), retrieval augmented generation (Natural Questions (Kwiatkowski et al., 2019), TriviaQA (Joshi et al., 2017), HotpotQA (Yang et al., 2018)), and long-document QA (InfiniteBench MC/QA (Zhang et al., 2024), NarrativeQA (Koˇcisk`y et al., 2018)). We use substring exact match (SubEM) for the RAG task, recall for NIAH-MV, and exact match for InfiniteBench MC. For InfiniteBench QA and Nar- rativeQA, which involve open-ended answers, we rely on gpt-4o-mini to evaluate model responses against the ground truth, following the prompt and metric provided by Helmet. As shown in Table 7, Instella- 3B-Long-Instruct outperforms open weights models including Phi-3.5-mini-instruct (Abdin et al., 2024), Gemma-3-4B-it (Gemma Team, 2025), Qwen2.5-3B-Instruct (Yang et al., 2024), and MiniCPM-2B-128k (Hu et al., 2024) on most tasks of the Helmet benchmark. Since the context length of", + "prompt and metric provided by Helmet. As shown in Table 7, Instella- 3B-Long-Instruct outperforms open weights models including Phi-3.5-mini-instruct (Abdin et al., 2024), Gemma-3-4B-it (Gemma Team, 2025), Qwen2.5-3B-Instruct (Yang et al., 2024), and MiniCPM-2B-128k (Hu et al., 2024) on most tasks of the Helmet benchmark. Since the context length of Qwen2.5-3B-Instruct is 32K, we also conduct a side-by-side comparison at 8K, 16K, and 32K context lengths, as shown in Table 8. Instella-3B-Long-Instruct outperforms Qwen2.5-3B-Instruct by 2.8% on average. Table 8: Comparison with Qwen2.5-3B-Instruct at 8K, 16K, 32K context lengths. Model NIAH-MV NQ TriviaQA HotpotQA Avg. 8K 16K 32K 8K 16K 32K 8K 16K 32K 8K 16K 32K Qwen2.5-3B-Instruct 95 94 95 48 42 39 77 78 74 51 50 48 65.9 Instella-3B-Long-Instruct 98 95 87 53 49 46 79 73 75 59 59 51 68.7 We also evaluate the short-context performance as shown in Table 9. We observe performance drops on some short-context benchmarks compared to Instella-3B-Instruct. Interestingly, TruthfulQA remains stable, Crows-Pairs shows a slight improvement, and the reduction in Toxigen (57.02 → 42.34, lower is better) suggests improved toxicity avoidance, together indicating potential gains in responsible AI benchmarks. We hypothesize that these results reflect a trade-off between optimizing for longer context lengths and retaining short-context performance, which may be more pronounced at the 3B parameter scale compared to larger models. Table 9: Evaluation of Instella-Long on general benchmarks. Models MMLU IFEval MT-Bench TruthfulQA Toxigen (↓) Crows-Pair Instella-3B-Instruct 58.9 71.4 7.2 55.5 57.0 58.9 Instella-3B-Long-Instruct 57.4 68.8 6.8 55.5 42.3 60.1 11 6.4 Instella-Math Following the same evaluation settings as DeepScaleR-1.5B (Luo et al., 2025), we report Pass@1 accuracy over AIME 2024/25 (AIME), MATH500 (Hendrycks et al., 2021c), AMC (AMC), Mnerva MATH (Lewkowycz et al., 2022), OlympiadBench (He et al., 2024a), GSM8k (Cobbe et al., 2021b), and GPQA-Diamond (Rein et al., 2023). Table 10 reports the Pass@1 rate for the above benchmarks, calcu- lated based on 16 responses per question. Instella-Math delivers competitive performance when com- pared to leading small-scale open-weight models such as Deepseek-R1-Distilled-Qwen-1.5B, Still-3-1.5B, DeepScaleR-1.5B and SmolLM3-3B. In addition to achieving competitive average performance across all benchmarks, Instella-Math demonstrates the effectiveness of our RL training recipe—improving over its supervised finetuned variant (Instella-Math-SFT) by 10.81 points, compared to a 6.22-point improvement seen in DeepScaleR over its base model (Deepseek-R1-Distilled-Qwen-1.5B). Table 10: Evaluation of Instella-Math on Reasoning Benchmarks Models AIME 2024 AIME 2025 MATH500 AMC Minerva OlympiadBench GSM8K GPQA-D Avg. Pass@1 Open-Weight Models Qwen2.5-Math-1.5B 7.7 4.0 57.8 35.8 15.7 26.0 66.3 15.4 28.6 DeepSeek-R1-Distill-Qwen-1.5B 27.5 22.5 82.6 63.5 26.5 43.0 84.1 16.5 45.8 STILL-3-1.5B-preview 30.6 25.2 84.6 66.7 28.6 45.3 86.6 19.5 48.4 DeepScaleR-1.5B-Preview 40.6 30.8 87.4 73.2 30.1 49.9 87.3 16.5 52.0 Fully-Open Models OLMo-2-1124-7B-Instruct 1.3 0.2 32.6 12.3 10.3 8.5 80.9 11.1 19.6 SmolLM3-3B 52.5 35.8 90.2 78.7 31.8 55.4 92.3 44.9 60.2 Instella-Math SFT 20.0 19.0 77.6 53.9 18.8 43.3 88.0 23.4 43.0 Instella-Math RL Stage 1 27.9 22.5 82.2 58.8 25.1 49.2 90.9 34.2 48.8 Instella-Math RL Stage 2 29.6 22.9 85.8 66.7 27.5 52.7 91.7 37.4 51.8 Instella-Math RL Stage 3 35.6 27.7 86.5 69.7 27.7 53.1", + "92.3 44.9 60.2 Instella-Math SFT 20.0 19.0 77.6 53.9 18.8 43.3 88.0 23.4 43.0 Instella-Math RL Stage 1 27.9 22.5 82.2 58.8 25.1 49.2 90.9 34.2 48.8 Instella-Math RL Stage 2 29.6 22.9 85.8 66.7 27.5 52.7 91.7 37.4 51.8 Instella-Math RL Stage 3 35.6 27.7 86.5 69.7 27.7 53.1 92.5 37.6 53.8 Pass@16 Open-Weight Models Qwen2.5-Math-1.5B 36.7 20.0 87.6 71.1 48.5 53.8 96.0 71.7 60.7 DeepSeek-R1-Distill-Qwen-1.5B 73.3 46.7 95.0 89.2 54.4 63.9 97.0 46.5 70.7 STILL-3-1.5B-preview 70.0 46.7 95.8 89.2 56.6 65.2 96.7 45.5 70.7 DeepScaleR-1.5B-Preview 70.0 53.3 95.2 91.6 54.0 66.2 96.5 39.9 70.9 Fully-Open Models OLMo-2-1124-7B-Instruct 13.3 3.3 66.6 50.6 35.1 23.2 97.3 49.0 42.3 SmolLM3-3B 76.7 77.3 96.6 94.0 54.4 72.4 98.1 90.9 82.1 Instella-Math SFT 50.0 40.0 94.8 89.2 44.9 64.0 97.7 83.8 70.6 Instella-Math RL Stage 1 53.3 43.3 94.6 88.0 51.5 68.6 97.6 90.9 73.5 Instella-Math RL Stage 2 46.7 43.3 95.6 89.2 51.1 68.3 97.7 89.4 72.7 Instella-Math RL Stage 3 63.3 50.0 95.8 86.8 50.4 68.2 97.4 88.9 75.1 Table 11: Evaluation of Instella-Math on TTT-Bench Models oTTT dTTT cTTT sTTT Avg. Open-weight models Qwen2.5-Math-1.5B 12.5 10.0 18.9 7.5 12.2 DeepSeek-R1-Distill-Qwen-1.5B 22.9 10.1 18.2 3.5 13.7 STILL-3-1.5B-preview 24.5 12.3 19.8 3.2 14.9 DeepScaleR-1.5B-Preview 23.0 16.5 23.0 8.2 17.7 Fully-open models SmolLM3-3B 51.2 40.1 41.3 42.3 43.7 Instella-Math RL Stage 1 56.3 31.4 39.7 41.9 42.3 Instella-Math RL Stage 2 66.2 37.3 39.2 44.5 46.8 Instella-Math RL Stage 3 70.3 39.6 40.3 49.0 49.8 Additionally, we test Instella-Math on TTT-Bench (Mishra et al., 2025), a new benchmark targeting strategic, spatial, and logical reasoning. Remarkably, without any exposure to TTT-Bench–style or similar strategic 12 gaming data during any stage of training, Instella-Math achieves the best performance among all evaluated models (as shown in Table 11). More importantly, like OLMo2 and SmolLM-3B, Instella-Math is a fully-open language model, with fully- open training data for the base model (Instella-3B), reasoning SFT, and reinforcement learning stages. In contrast, many competing models are only open-weight releases; their base model training (e.g., Qwen- 1.5B) and reasoning distillation processes (e.g., DeepSeek-R1) remain closed. 7 Conclusion We present Instella, a family of fully open three billion parameter language models that are trained entirely on openly available data and codebase. The Instella model family consists of a strong base pre-trained model, a supervised finetuned instruct model, an 128k token context length long-context model, and a reasoning-centric model. Powered by AMD Instinct™ MI300X GPUs, Instella models attain state-of-the-art performance among fully open models of similar scale and remains competitive with leading open-weight systems despite using notably fewer pre-training tokens. Instella-Long demonstrates strong long-context capabilities, and Instella-Math delivers impressive gains on mathematical and strategic reasoning bench- marks. Alongside model weights, we release the training code, data recipes, and evaluation protocols to support complete reproducibility and transparent benchmarking to foster open-source innovation. Instella models offers a transparent, performant, and extensible foundation for research and application, support- ing the community in building more capable and reproducible language models. References Marah Abdin, Jyoti Aneja, Harkirat Behl, S´ebastien Bubeck, Ronen Eldan, Suriya Gunasekar, Michael Har- rison, Russell J Hewett,", + "transparent benchmarking to foster open-source innovation. Instella models offers a transparent, performant, and extensible foundation for research and application, support- ing the community in building more capable and reproducible language models. References Marah Abdin, Jyoti Aneja, Harkirat Behl, S´ebastien Bubeck, Ronen Eldan, Suriya Gunasekar, Michael Har- rison, Russell J Hewett, Mojan Javaheripi, Piero Kauffmann, et al. 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URL https://arxiv.org/ abs/2311.07911. 19", + "SSR: Socratic Self-Refine for LLM Reasoning SSR: SOCRATIC SELF-REFINE FOR LARGE LAN- GUAGE MODEL REASONING Haizhou Shi∗†12 Ye Liu1 Bo Pang1 Zeyu Leo Liu∗13 Hao Wang2 Silvio Savarese1 Caiming Xiong1 Yingbo Zhou1 Semih Yavuz†1 1Salesforce AI Research 2Rutgers University 3The University of Texas at Austin ABSTRACT Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, yet existing test-time frameworks often rely on coarse self-verification and self- correction, limiting their effectiveness on complex tasks. In this paper, we propose Socratic Self-Refine (SSR), a novel framework for fine-grained evaluation and precise refinement of LLM reasoning. Our proposed SSR decomposes model responses into verifiable (sub-question, sub-answer) pairs, enabling step-level confidence estimation through controlled re-solving and self-consistency checks. By pinpointing unreliable steps and iteratively refining them, SSR produces more accurate and interpretable reasoning chains. Empirical results across five reasoning benchmarks and three LLMs show that SSR consistently outperforms state-of-the- art iterative self-refinement baselines. Beyond performance gains, SSR provides a principled black-box approach for evaluating and understanding the internal reasoning processes of LLMs. Code is available at https://github.com/ SalesforceAIResearch/socratic-self-refine-reasoning. Given 𝑥 + 𝑦 = 13 , 𝑥𝑦 = 24, find the distance from (𝑥, 𝑦) to the origin. … Rearranging it into standard quadratic form: 𝒙𝟐 − 𝟏𝟑𝒙 + 𝟐𝟒 = 𝟎 … The factors of 24 that work are −3 and −8. Hence we can factor it as: 𝒙 − 𝟑 𝒙 − 𝟖 = 𝟎 … Let’s not rush and break it down and re-solve them for 𝑀 times: The factorization doesn’t look correct. Let’s refine it. 𝒒1 ෝ𝒂11 𝒒2 ෝ𝒂21 ෝ𝒂12 ෝ𝒂22 … 𝒒𝑡: Factorization ෝ𝒂𝑡1: 𝒙 − 𝟒 𝒙 − 𝟔 = 𝟎 ෝ𝒂𝑡2: 𝒙 − 𝟖 𝒙 − 𝟑 = 𝟎 … … … … 𝒒𝑇 ෝ𝒂𝑇1 ෝ𝒂𝑇2 … ෝ𝒂𝑡𝑀: 𝒙 − 𝟐 𝒙 − 𝟏𝟐 = 𝟎 ෝ𝒂𝑇𝑀 ෝ𝒂1𝑀 ෝ𝒂2𝑀 Figure 1: Test-Time Parallel Scaling Performance (Left) and Conceptual Overview (Right) of our proposed Socratic Self-Refine (SSR). By decomposing responses into Socratic steps, re- evaluating intermediate results through self-consistency, and refining specific step-level errors, SSR achieves substantially higher initial accuracy (∼67.57% relative improvement) and continues to scale effectively even when standard Chain-of-Thought (CoT) begins to saturate. Notably, this performance advantage holds under comparable computational cost. Experiments are conducted with GPT-5-mini in low-reasoning, low-verbosity mode. 1 INTRODUCTION Large Language Models (LLMs) have rapidly advanced the frontier of machine reasoning, demonstrat- ing impressive performance across domains ranging from mathematical problem solving to complex logical inference (Wei et al., 2022a; Wang et al., 2022; Chung et al., 2024; Guo et al., 2025; Ke et al., ∗Work done during an internship at Salesforce AI Research. †Correspondence to: Haizhou Shi , Semih Yavuz . 1 arXiv:2511.10621v1 [cs.CL] 13 Nov 2025 SSR: Socratic Self-Refine for LLM Reasoning 2025). Central to these capabilities is the paradigm of reasoning with explicit intermediate steps, often instantiated through chain-of-thought (CoT) prompting (Wei et al., 2022b). By externalizing reasoning traces, CoT enables models to articulate their latent decision-making process, offering both interpretability and opportunities for iterative improvement (Madaan et al., 2023). Despite these strengths, the reasoning traces generated by LLMs remain prone", + "with explicit intermediate steps, often instantiated through chain-of-thought (CoT) prompting (Wei et al., 2022b). By externalizing reasoning traces, CoT enables models to articulate their latent decision-making process, offering both interpretability and opportunities for iterative improvement (Madaan et al., 2023). Despite these strengths, the reasoning traces generated by LLMs remain prone to cascading errors: a single flawed step can propagate downstream, leading to incorrect or incoherent final answers (Wu et al., 2025; You et al., 2025). This vulnerability raises pressing questions about how to reliably evaluate, refine, and searching for better multi-step reasoning at test time. Existing frameworks have sought to address these challenges largely fall into two paradigms: sample selection with self-verification and self-refinement. Sample selection with self-verification, aims to assess response reliability by assigning confidence scores to completed reasoning traces either by LLM-as-a-Judge (Gu et al., 2024), or a specific ranking model (Snell et al., 2024), and then through multiple sampling and selection improves the final answer reliability (Zheng et al., 2023b; Chen et al., 2025). While these approaches can identify low-quality outputs, they often operate at a coarse granularity, overlooking subtle step-level errors embedded within long derivations (Fang et al., 2025). Self-refinement methods, by contrast, encourage LLMs to iteratively critique and revise their own responses (Madaan et al., 2023; Zhang et al., 2024; Bi et al., 2024). Although such frameworks have yielded measurable gains, their reliance on holistic self-feedback frequently limits their ability to pinpoint and correct specific erroneous steps. As a result, both paradigms struggle to provide robust and interpretable error correction in complex reasoning tasks. In this paper, we propose Socratic Self-Refine (SSR), a novel framework designed to overcome these limitations by introducing fine-grained, step-level evaluation and targeted refinement of LLM reasoning. SSR reformulates the reasoning process into a sequence of verifiable (sub-question, sub-answer) pairs, which we refer to as Socratic steps. This decomposition enables precise confidence estimation through controlled re-solving and self-consistency checks at the step level. Unreliable steps are selectively refined, allowing the model to fix errors without depending on vague feedback. By iteratively applying this process, SSR improves both the accuracy and interpretability of LLM reasoning, offering a principled black-box approach to evaluating and refining model behavior. Empirical results across 5 reasoning tasks (3 mathematical and 2 logical) and multiple state-of-the-art LLMs demonstrate that SSR consistently outperforms baseline self-refinement methods. Beyond raw accuracy gains, our analysis shows that SSR yields more reliable refinement trajectories, particularly when combined with plan-level adjustments or adaptive gating mechanisms. These findings highlight the importance of explicit step-level verification in building trustworthy LLM reasoning systems. More broadly, SSR represents a step toward interpretable and controllable test-time reasoning, bridging the gap between coarse-grained judgment and fine-grained error correction. To summarize, our contributions are: • We propose a novel framework, Socratic Self-Refine (SSR), that allows more fine-grained con- fidence estimation and precise error control over decomposed reasoning steps. By formulating reasoning as a sequence of (sub-question, sub-answer) pairs, SSR overcomes the limitations of existing holistic self-refinement methods. • We empirically validate SSR on 5 reasoning tasks using two state-of-the-art models, demon- strating that", + "that allows more fine-grained con- fidence estimation and precise error control over decomposed reasoning steps. By formulating reasoning as a sequence of (sub-question, sub-answer) pairs, SSR overcomes the limitations of existing holistic self-refinement methods. • We empirically validate SSR on 5 reasoning tasks using two state-of-the-art models, demon- strating that it consistently outperforms existing self-refine-based baselines. • Our SSR introduces a mechanism for eliciting the model’s step-level confidence, by having the LLM re-solve each sub-question multiple times with explicit context control. Leveraging self-consistency as a reliable confidence estimate for each step, SSR provides a pioneering effort in evaluating and interpreting the internal reasoning processes of LLMs. 2 RELATED WORK Self-Evaluation and Refinement of LLMs. Recent work has introduced both intrinsic and gen- erative approaches for LLM self-evaluation. On the intrinsic side, uncertainty-based methods estimate correctness either through consistency, by comparing multiple independently generated outputs (Kuhn et al., 2023; Manakul et al., 2023), or through statistics derived from the model’s output distribution (Kang et al., 2025; Fu et al., 2025; Zhang et al., 2025a). On the generative side, the LLM-as-a-Judge paradigm directly prompts models to evaluate responses, often achieving strong alignment with human preferences and supporting test-time strategies like abstaining from low-quality 2 SSR: Socratic Self-Refine for LLM Reasoning responses or selecting among candidates (Zheng et al., 2023b; Gu et al., 2024; Zhou et al., 2025b; Ren et al., 2023; Chen et al., 2025; Huang et al., 2025; Zhong et al., 2025; Zhou et al., 2025a). While limitations such as positional bias (Zheng et al., 2023a; Shi et al., 2024) and a preference for longer responses (Hu et al., 2024) do exist, both uncertainty-based and judge-based methods remain effective and have proven valuable for evaluating LLM outputs. Building on these evaluation techniques, a growing body of work extends beyond verification to self-refinement, where LLMs not only diagnose weaknesses in their outputs but also iteratively improve them (Madaan et al., 2023). Early efforts explored direct self-correction based on feedback, while subsequent methods introduced structured search (Zhang et al., 2024), parallel sampling to enrich candidate diversity (Bi et al., 2024; Chen et al., 2025), and reformulation strategies that generate improved sub-questions by incorporating contextual preconditions (Teng et al., 2025). More recent work trains generative verifiers to guide the refinement process (Zhong et al., 2025). Collectively, these approaches demonstrate that refinement transforms passive evaluation into an active mechanism for improving reliability, making it a key step toward controllable and trustworthy reasoning in LLMs. Process Evaluation of LLMs. Verifying only the final outcome of an LLM is insufficient; ensuring reliability requires mechanisms that also evaluate the reasoning process itself. Beyond using human annotations to train process reward models (Lightman et al., 2023; He et al., 2024; Zhang et al., 2025b), the rapid advancement of model capabilities has motivated a growing set of test-time methods for step-level verification. These approaches typically decompose the reasoning trace and assess the correctness of each step to localize errors more accurately (Ling et al., 2023; Zhao et al., 2025; Mukherjee et al., 2025; Fang et al., 2025). Compared to existing work of", + "motivated a growing set of test-time methods for step-level verification. These approaches typically decompose the reasoning trace and assess the correctness of each step to localize errors more accurately (Ling et al., 2023; Zhao et al., 2025; Mukherjee et al., 2025; Fang et al., 2025). Compared to existing work of process evaluation, our SSR framework adopts a Socratic formulation of reasoning, representing the process as a sequence of question-answer pairs (details in Sec. 3). This structure makes the steps straightforward to re-execute and enables reliable confidence estimation. Crucially, SSR goes beyond verification by producing informative signals that directly support subsequent refinement. 3 SOCRATIC SELF-REFINE (SSR) This section introduces our Socratic Self-Refine (SSR). Sec. 3.1 introduces the fundamental as- sumption that natural-language reasoning can be described as a Socratic process. Sec. 3.2 presents the core of SSR, including the decomposition into Socratic steps, their verification, and reasoning refinement guided by Socratic confidence scores. Finally, Sec. 3.3 discusses two techniques for practical deployment of SSR: plan refinement and adaptive iteration refinement. For details of the prompt templates introduced in this section, please refer to Appendix C.3. Notation. In this paper, scalars are denoted by lowercase letters (x), vectors (or token/word sequences) by bold lowercase letters (x), random vectors by boldface lowercase letters (x), and matrices (or sets of tokens, words, or phrases) by bold uppercase letters (X). We denote by [m] = 1, 2, . . . , m the set of consecutive integers from 1 to m. For consistency, K denotes the total number of refinement iterations, while (k) indicates the current iteration; when unambiguous, we omit (k) to reduce clutter. Finally, N is the number of parallel runs used for test-time scaling. 3.1 LLM REASONING AS SOCRATIC PROCESS Preliminary of LLM Reasoning. For problems with short-form ground-truth answers, LLM reasoning can be modeled as marginalization over intermediate natural language reasoning traces z (a sequence of tokens/words) to produce the final answer y (Chen et al., 2024): πθ(y | x) = � πθ(y | z, x)πθ(z | x)dz (1) Chain-of-Thought (CoT) reasoning (Wei et al., 2022b) approximates this integral with a single sample: the model first generates a reasoning trace z ∼ πθ(· | x) and then derives the final answer y ∼ πθ(· | z, x). Empirically, allocating more computation to approximate Eqn. 1 improves performance. A common strategy is Majority Voting (Maj@N), which averages over multiple sampled reasoning traces (Wang et al., 2022): πθ(y | x) ≈ 1 N �N n=1 πθ(y | zn, x), zn ∼ πθ(z | x). (2) Reasoning as Socratic Process. In this paper, we posit that the reasoning process is implicitly modeled as a sequence of goal-setting and problem-solving steps; that is, the natural-language 3 SSR: Socratic Self-Refine for LLM Reasoning SSR (Confidence Estimation): Let’s re-consider each question 𝒒𝑡 based on the prior context… SSR (Decompose): Let’s decompose 𝒛(𝟎) into Socratic steps… Sub-Question 𝒒1 Sub-Answer 𝒂1 CoT: Let’s solve step by step… If 𝒄(𝒌) < 𝒄𝐦𝐚𝐱 Plan-Score 𝒉(𝟎) Plan-Refine: Let’s refine the plan and provide a new reasoning trace 𝒛(𝟎)… If 𝒉(𝟎) < 𝒉𝐦𝐚𝐱 Sub-Question 𝒒2", + "each question 𝒒𝑡 based on the prior context… SSR (Decompose): Let’s decompose 𝒛(𝟎) into Socratic steps… Sub-Question 𝒒1 Sub-Answer 𝒂1 CoT: Let’s solve step by step… If 𝒄(𝒌) < 𝒄𝐦𝐚𝐱 Plan-Score 𝒉(𝟎) Plan-Refine: Let’s refine the plan and provide a new reasoning trace 𝒛(𝟎)… If 𝒉(𝟎) < 𝒉𝐦𝐚𝐱 Sub-Question 𝒒2 Sub-Answer 𝒂2 Sub-Question 𝒒𝑇 Sub-Answer 𝒂𝑇 … 𝒒𝑡 Else ෝ𝒂𝑡1 … Reference Set ෡𝑨𝒕 Sub-Question 𝒒𝒕′ 𝒄𝒕′ 𝒕′ = arg 𝐦𝐢𝐧 𝒕 𝒄𝒕 𝒂𝒕′∗ 𝒂𝒕′ 𝒄𝑡 Maj@M Reasoning 𝒛(𝒌+𝟏) Answer 𝒚(𝒌+𝟏) ① ③ ② ④ ⑤ ⑥ Socratic Steps 𝑺𝑇 Sub-Answer 𝒂𝑡 ෝ𝒂𝑡2 ෝ𝒂𝑡𝑀 SSR (Refine): After a second thought, a better solution to 𝒒𝒕′ appears to be 𝒂𝒕′∗ . Let’s refine… Refined Response Plan-Eval: Let’s evaluate the high-level plan represented by 𝒛(𝟎)… Reasoning 𝒛(𝟎) Answer 𝒚(𝟎) Reasoning 𝒛(𝒌+𝟏) Answer 𝒚(𝒌+𝟏) Self-Refine (Verify): Let’s verify… Self-Refine (Refine): Let’s refine 𝒛(𝒌) and 𝒚(𝒌) based on 𝒇(𝒌)… Feedback 𝒇(𝒌) Score 𝒄(𝒌) Reasoning 𝒛(𝟎) Answer 𝒚(𝟎) Query 𝒙: Given 𝑥 + 𝑦 = 13 and 𝑥𝑦 = 24, find the distance from the point (𝑥, 𝑦) to the origin. Socratic Verification Self-Refine: ① → 𝑲 ×② SSR-Lin: ① → 𝑲 × (④⑤⑥) SSR-Ada: ① → 𝑲 × (②④⑤⑥) SSR-Plan: ①③ → 𝑲 × (②④⑤⑥) Figure 2: Overview of Socratic Self-Refine (SSR). Block ①: Chain-of-Thought (CoT) reasoning, serves as the starting point for the iterative refinement methods; Block ②: Simple Self-Refine, generates feedback and then refines the original response based on the feedback; Block ③: Plan refinement, summarizes the high-level plan of a reasoning trace, and refines the plan and the trace if necessary; Block ④-⑥: Three building blocks of our SSR, includes Socratic decomposition, Socratic verification, and Socratic refinement. SSR-Lin: Linear SSR, faithfully applies three blocks (④-⑥) for K iterations; SSR-Ada: Adaptive SSR, only carries out Socratic blocks (④-⑥) when the normal Self- Refine cannot identify any mistakes (c = cmax); SSR-Plan: Adaptive SSR with Plan Refinement, adds an additional plan refinement round (③) before the full iterative refinement algorithm (④-⑥). reasoning trace z can be viewed as semantically equivalent to a sequence of question-answer pairs. Formally, given a query x, we assume that for any reasoning-answer pair (z, y), there exists a ground-truth decomposition ST ≡ (z, y) such that 1 ST = {st ≜ (qt, at)}t∈[T ], (3) where each st is a Socratic step, aT = y denotes the final answer, and the equivalence ST ≡ (z, y) implies that the oracle probability model p satisfies p(z, y | x) = p({(qt, at)}t∈[T ] | x). (4) Compared with the purely natural-language reasoning process z, the explicit sequence of Socratic steps offers clear advantages, most notably, finer-grained modeling and potential control of the reasoning process, enabling verification and intervention. This explicit modeling lies at the heart of our proposed method, Socratic Self-Refine (SSR), which we detail in Sec. 3.2. 3.2 SOCRATIC SELF-REFINE (SSR): DECOMPOSITION, VERIFICATION, AND REFINEMENT From Entangled Reasoning to Explicit Socratic Process. Under the assumption of Eqn. 4, our goal is to recover the full Socratic process ST from the natural-language reasoning trace z. Since no prior work explicitly models", + "(SSR), which we detail in Sec. 3.2. 3.2 SOCRATIC SELF-REFINE (SSR): DECOMPOSITION, VERIFICATION, AND REFINEMENT From Entangled Reasoning to Explicit Socratic Process. Under the assumption of Eqn. 4, our goal is to recover the full Socratic process ST from the natural-language reasoning trace z. Since no prior work explicitly models this process, and the oracle posterior p(ST | x, y, z) is unavailable, we adopt a zero-shot prompting approach with LLMs to decompose z into the Socratic process ST : ST ∼ πθ(· | x, y, z, xdec) ≈ p(· | x, y, z), (5) where xdec denotes a decomposition query that prompts the LLM to extract a sequence of sub- questions and their corresponding sub-answers. Leveraging prior work on LLM-based summarization and information extraction (Van Veen et al., 2024), this decomposition can be performed reliably with relatively little overhead. 1Note that (i) the ground-truth decomposition may not be unique. E.g., {st}T t=1 and {st}T t=2 are both valid decompositions, with the latter representing a coarser process; and (ii) the true structure of the decomposition can be non-linear (Teng et al., 2025), though it can be mapped to a linear form in CoT reasoning. 4 SSR: Socratic Self-Refine for LLM Reasoning LLM Self-Verification on Socratic Steps. We now leverage the reformulation of the original reasoning trace z into the Socratic process ST to enable LLM self-verification. The joint probability distribution of ST can be factorized into a product of conditional probabilities: πθ(ST | x) = πθ({(qt, at)}t∈[T ] | x) = �T t=1 πθ(qt | {si}i