diff --git a/.gitignore b/.gitignore index a7df437..509187e 100644 --- a/.gitignore +++ b/.gitignore @@ -2,16 +2,12 @@ __pycache__/ *.py[codz] *$py.class -poetry.lock loss-without-lines.pdf training_history.pkl fourier_power_only.pdf notebooks/figs/ notebooks/figs_temp/ -gagf/fourier_power_only.png notebooks/saved_models/ -gagf/group_learning/wandb/* -gagf/group_learning/saved_datasets/ notebooks/checkpoint* notebooks/W-weights.pdf notebooks/predictions.pdf @@ -225,4 +221,3 @@ __marimo__/ #wandb wandb/ -gagf/group_learning/wandb diff --git a/README.md b/README.md index b66aa20..d77021c 100644 --- a/README.md +++ b/README.md @@ -1,14 +1,259 @@ -# group-agf +

Sequential Group Composition

-[![CI](https://github.com/geometric-intelligence/group-agf/actions/workflows/ci.yml/badge.svg)](https://github.com/geometric-intelligence/group-agf/actions/workflows/ci.yml) +

A Window into the Mechanics of Deep Learning

-Group Alternating Gradient Flows +

+ arXiv + CI + License: MIT +

-# Installing Dependencies +

+ Paper • + PDF • + Install • + Usage • + Citation +

-``` +

+ Giovanni Luca Marchetti* · Daniel Kunin* · Adele Myers · Francisco Acosta · Nina Miolane +

+ +--- + +> **How do neural networks trained over sequences acquire the ability to perform structured operations, such as arithmetic, geometric, and algorithmic computation?** +> +> We introduce the *sequential group composition* task: networks receive a sequence of elements from a finite group encoded in a real vector space and must predict their cumulative product. We prove that two-layer networks learn this task **one irreducible representation at a time**, in an order determined by the Fourier statistics of the encoding -- producing a characteristic *staircase* in the training loss. + +

+ Staircase learning across five finite groups +

+

+ Two-layer networks learn group composition one irreducible representation at a time. Top: power spectrum of the learned function over training. Bottom: training loss showing a characteristic staircase. Each column is a different finite group. +

+ +--- + +## Installation + +### Prerequisites + +- [Conda](https://docs.conda.io/en/latest/) (Miniconda or Anaconda) +- `gfortran` (Linux only, required by some numerical dependencies) + +### Setup + +```bash +# Linux only: install gfortran sudo apt install -y gfortran + +# Create and activate the conda environment conda env create -f conda.yaml -conda activate gagf +conda activate group-agf + +# Install all Python dependencies (pinned versions from poetry.lock) poetry install ``` + +## Usage + +### Single Run + +Train a model on a specific group: + +```bash +python src/main.py --config src/config_d3.yaml +``` + +Results (loss curves, predictions, power spectra) are saved to a timestamped directory under `runs/`. + +### Supported Groups + +The repository includes preconfigured experiments for five groups: + +| Group | Config | Order | Architecture | +|:------|:-------|:-----:|:-------------| +| Cyclic \( C_{10} \) | `src/config_c10.yaml` | 10 | QuadraticRNN | +| Product \( C_4 \times C_4 \) | `src/config_c4x4.yaml` | 16 | QuadraticRNN | +| Dihedral \( D_3 \) | `src/config_d3.yaml` | 6 | TwoLayerNet | +| Octahedral | `src/config_octahedral.yaml` | 24 | TwoLayerNet | +| Icosahedral \( A_5 \) | `src/config_a5.yaml` | 60 | TwoLayerNet | + +### Parameter Sweeps + +Run experiments across multiple configurations and random seeds: + +```bash +python src/run_sweep.py --sweep src/sweep_configs/example_sweep.yaml +``` + +Multi-GPU support: + +```bash +# Auto-detect and use all available GPUs +python src/run_sweep.py --sweep src/sweep_configs/example_sweep.yaml --gpus auto + +# Use specific GPUs +python src/run_sweep.py --sweep src/sweep_configs/example_sweep.yaml --gpus 0,1,2,3 +``` + +Sweep results are saved to `sweeps/{sweep_name}_{timestamp}/` with per-seed results and aggregated summaries. + +## Configuration + +Key parameters in the YAML config files: + +| Parameter | Options | Description | +|:----------|:--------|:------------| +| `data.group_name` | `cn`, `cnxcn`, `dihedral`, `octahedral`, `A5` | Group to learn | +| `data.k` | integer | Number of elements to compose | +| `data.template_type` | `mnist`, `fourier`, `gaussian`, `onehot`, `custom_fourier` | Template generation method | +| `model.model_type` | `QuadraticRNN`, `SequentialMLP`, `TwoLayerNet` | Architecture | +| `model.hidden_dim` | integer | Hidden layer size | +| `model.init_scale` | float | Weight initialization scale | +| `training.optimizer` | `auto`, `adam`, `per_neuron`, `hybrid` | Optimizer (`auto` recommended) | +| `training.learning_rate` | float | Base learning rate | +| `training.mode` | `online`, `offline` | Training mode | +| `training.epochs` | integer | Number of epochs (offline mode) | + +
+Example config -- D3 with custom Fourier template + +```yaml +data: + group_name: dihedral + group_n: 3 + k: 2 + template_type: custom_fourier + powers: [0.0, 30.0, 3000.0] + +model: + model_type: TwoLayerNet + hidden_dim: 180 + init_scale: 0.001 + +training: + optimizer: per_neuron + learning_rate: 0.01 + mode: offline + epochs: 2000 +``` + +
+ +## Repository Structure + +``` +group-agf/ +├── src/ # Source code +│ ├── main.py # Training entry point (CLI) +│ ├── model.py # TwoLayerNet, QuadraticRNN, SequentialMLP +│ ├── optimizer.py # PerNeuronScaledSGD, HybridRNNOptimizer +│ ├── dataset.py # Dataset generation and loading +│ ├── template.py # Template construction functions +│ ├── fourier.py # Group Fourier transforms +│ ├── power.py # Power spectrum computation +│ ├── viz.py # Plotting and visualization +│ ├── train.py # Training loops (offline and online) +│ ├── run_sweep.py # Parameter sweep runner +│ └── config_*.yaml # Group-specific configurations +├── test/ # Unit and integration tests +├── notebooks/ # Jupyter notebooks for exploration +├── pyproject.toml # Project metadata and dependencies +├── poetry.lock # Pinned dependency versions +└── conda.yaml # Conda environment specification +``` + +
+Module details + +### `model.py` -- Neural Network Architectures + +| Model | Description | Input | +|:------|:------------|:------| +| **TwoLayerNet** | Two-layer feedforward network with configurable nonlinearity (square, relu, tanh, gelu) | Flattened binary pair `(N, 2 * group_size)` | +| **QuadraticRNN** | Recurrent network: `h_t = (W_mix h_{t-1} + W_drive x_t)^2` | Sequence `(N, k, p)` | +| **SequentialMLP** | Feedforward MLP with k-th power activation, permutation-invariant for commutative groups | Sequence `(N, k, p)` | + +### `optimizer.py` -- Custom Optimizers + +| Optimizer | Description | Recommended for | +|:----------|:------------|:----------------| +| **PerNeuronScaledSGD** | SGD with per-neuron learning rate scaling exploiting model homogeneity | SequentialMLP, TwoLayerNet | +| **HybridRNNOptimizer** | Scaled SGD for MLP weights + Adam for recurrent weights | QuadraticRNN | +| Adam (PyTorch built-in) | Standard Adam | QuadraticRNN | + +### `dataset.py` -- Data Generation + +- **Online datasets**: `OnlineModularAdditionDataset1D`, `OnlineModularAdditionDataset2D` -- generate samples on-the-fly (GPU-accelerated) +- **Offline builders**: `build_modular_addition_sequence_dataset_1d`, `_2d`, `_D3`, `_generic` +- **Group datasets**: `cn_dataset`, `cnxcn_dataset`, `group_dataset` -- full group multiplication tables for TwoLayerNet + +### `template.py` -- Template Construction + +- **Group templates**: `one_hot`, `fixed_cn`, `fixed_cnxcn`, `fixed_group` +- **1D synthetic**: `fourier_1d`, `gaussian_1d`, `onehot_1d` +- **2D synthetic**: `gaussian_mixture_2d`, `unique_freqs_2d`, `fixed_2d`, `hexagon_tie_2d`, `ring_isotropic_2d`, `gaussian_2d` +- **MNIST-based**: `mnist`, `mnist_1d`, `mnist_2d` + +### `fourier.py` -- Group Fourier Transforms + +- `group_fourier(group, template)` -- Fourier coefficients via irreducible representations +- `group_fourier_inverse(group, fourier_coefs)` -- reconstruct template from Fourier coefficients + +### `power.py` -- Power Spectrum Analysis + +- `GroupPower` -- power spectrum of a template over any `escnn` group +- `CyclicPower` -- specialized for cyclic groups via FFT +- `model_power_over_time` -- track how the model's learned power spectrum evolves during training +- `theoretical_loss_levels_1d`, `_2d` -- predict staircase loss plateaus from template power + +### `viz.py` -- Visualization + +Plotting functions for training analysis: `plot_train_loss_with_theory`, `plot_predictions_1d`, `plot_predictions_2d`, `plot_predictions_group`, `plot_power_1d`, `plot_power_group`, `plot_wmix_structure`, `plot_irreps`, and more. + +### `train.py` -- Training Loops + +- `train(model, loader, criterion, optimizer, ...)` -- epoch-based offline training +- `train_online(model, loader, criterion, optimizer, ...)` -- step-based online training + +
+ +## Testing + +```bash +# Unit tests +pytest test/ --ignore=test/test_notebooks.py -v + +# Integration tests (fast mode) +MAIN_TEST_MODE=1 pytest test/test_main.py -v +``` + +## Development + +```bash +# Install pre-commit hooks +pre-commit install + +# Run linting +ruff check . +ruff format --check . +``` + +## Citation + +If you find this work useful, please cite: + +```bibtex +@article{marchetti2026sequential, + title = {Sequential Group Composition: A Window into the Mechanics of Deep Learning}, + author = {Marchetti, Giovanni Luca and Kunin, Daniel and Myers, Adele and Acosta, Francisco and Miolane, Nina}, + journal = {arXiv preprint arXiv:2602.03655}, + year = {2026} +} +``` + +## License + +This project is licensed under the MIT License. See [LICENSE](LICENSE) for details. diff --git a/assets/binary_composition.png b/assets/binary_composition.png new file mode 100644 index 0000000..188144f Binary files /dev/null and b/assets/binary_composition.png differ diff --git a/assets/overview.png b/assets/overview.png new file mode 100644 index 0000000..ff03b8c Binary files /dev/null and b/assets/overview.png differ diff --git a/conda.yaml b/conda.yaml index 917147a..8b945c5 100644 --- a/conda.yaml +++ b/conda.yaml @@ -1,4 +1,4 @@ -name: gagf +name: group-agf channels: - conda-forge - defaults diff --git a/notebooks/2D.ipynb b/notebooks/2D.ipynb index b8bd4b0..eac8f90 100644 --- a/notebooks/2D.ipynb +++ b/notebooks/2D.ipynb @@ -1679,7 +1679,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf-PDhBFja6-py3.12", + "display_name": "group-agf", "language": "python", "name": "python3" }, diff --git a/notebooks/C_n.ipynb b/notebooks/C_n.ipynb index 716eff7..82a1833 100644 --- a/notebooks/C_n.ipynb +++ b/notebooks/C_n.ipynb @@ -782,7 +782,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf", + "display_name": "group-agf", "language": "python", "name": "python3" }, diff --git a/notebooks/dihedral.ipynb b/notebooks/dihedral.ipynb index f6a7bca..a7bb7ca 100644 --- a/notebooks/dihedral.ipynb +++ b/notebooks/dihedral.ipynb @@ -1042,7 +1042,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf", + "display_name": "group-agf", "language": "python", "name": "python3" }, diff --git a/notebooks/paper_figures.ipynb b/notebooks/paper_figures.ipynb index e168bb7..696c450 100644 --- a/notebooks/paper_figures.ipynb +++ b/notebooks/paper_figures.ipynb @@ -61,8 +61,6 @@ "from matplotlib.ticker import FormatStrFormatter\n", "from matplotlib.ticker import FuncFormatter\n", "from matplotlib.ticker import MaxNLocator\n", - "import setcwd\n", - "setcwd.main()\n", "\n", "import importlib\n", "import pickle\n", @@ -248,7 +246,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf", + "display_name": "group-agf", "language": "python", "name": "python3" }, @@ -267,4 +265,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/notebooks/rnn_gagf.ipynb b/notebooks/rnn_gagf.ipynb index 45bf545..fb9f402 100644 --- a/notebooks/rnn_gagf.ipynb +++ b/notebooks/rnn_gagf.ipynb @@ -2090,7 +2090,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf-PDhBFja6-py3.12", + "display_name": "group-agf", "language": "python", "name": "python3" }, diff --git a/notebooks/seq_mlp.ipynb b/notebooks/seq_mlp.ipynb index 9030713..5dd9168 100644 --- a/notebooks/seq_mlp.ipynb +++ b/notebooks/seq_mlp.ipynb @@ -2049,7 +2049,7 @@ ], "metadata": { "kernelspec": { - "display_name": "gagf-PDhBFja6-py3.12", + "display_name": "group-agf", "language": "python", "name": "python3" }, diff --git a/notebooks/seq_mlp_group_size.ipynb b/notebooks/seq_mlp_group_size.ipynb index c3ea0cf..a30e7ec 100644 --- a/notebooks/seq_mlp_group_size.ipynb +++ b/notebooks/seq_mlp_group_size.ipynb @@ 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+1,5 @@ [tool.poetry] -name = "gagf" +name = "group-agf" version = "0.1.0" description = "Learning" authors = ["John Smith "] diff --git a/setcwd.py b/setcwd.py deleted file mode 100644 index 4ed8a84..0000000 --- a/setcwd.py +++ /dev/null @@ -1,41 +0,0 @@ -"""Script that sets up the file directory tree before running a notebook. - -It uses root of github directory to make sure everyone's code runs from -the same directory, called current working directory cwd. - -It adds the repo root to sys.path so imports work correctly. - -Usage: - -import setcwd -setcwd.main() - -""" - -import os -import subprocess -import sys -import warnings - - -def main(): - """Set up the file paths and directory tree.""" - warnings.filterwarnings("ignore") - - gitroot_path = subprocess.check_output( - ["git", "rev-parse", "--show-toplevel"], universal_newlines=True - ).strip() - - os.chdir(gitroot_path) - print("Working directory: ", os.getcwd()) - - if gitroot_path not in sys.path: - sys.path.insert(0, gitroot_path) - print("Directory added to path: ", gitroot_path) - - -def get_root_dir(): - """Return the root directory of the git repository.""" - return subprocess.check_output( - ["git", "rev-parse", "--show-toplevel"], universal_newlines=True - ).strip() diff --git a/src/README.md b/src/README.md deleted file mode 100644 index b2d11b4..0000000 --- a/src/README.md +++ /dev/null @@ -1,184 +0,0 @@ -# Group AGF in RNNs - -## Models - -This codebase supports two model architectures: - -### QuadraticRNN -A recurrent neural network that processes sequences sequentially using recurrence: -- Uses temporal ordering of inputs -- Architecture: `h_t = (W_mix h_{t-1} + W_drive x_t)^2` (or multiplicative variant) - -### SequentialMLP -A feedforward MLP that processes k inputs by concatenation: -- No temporal ordering (permutation-invariant for commutative groups) -- Architecture: `y = (concat(x_1, ..., x_k) @ W_in)^k @ W_out` -- Uses k-th power activation function (k=2 → quadratic, k=3 → cubic, etc.) - -## Optimizers - -The codebase supports three optimizer types: - -### Adam (`'adam'`) -Standard Adam optimizer. Works with all models. -- Recommended for QuadraticRNN -- Learning rate: typically 1e-3 to 1e-4 - -### Per-Neuron Scaled SGD (`'per_neuron'`) -SGD with per-neuron learning rate scaling that exploits model homogeneity. -- **Recommended for SequentialMLP** -- Auto-infers degree of homogeneity from model (equals k+1 for SequentialMLP, where k is sequence length) -- Learning rate: typically 1.0 for SequentialMLP -- Exploits the property: scaling all parameters of neuron i by α scales output by α^degree - -### Hybrid (`'hybrid'`) -Combines per-neuron scaled SGD (for W_in, W_drive, W_out) with Adam (for W_mix). -- **Only for QuadraticRNN** -- Best for exploiting both MLP-like and recurrent structure - -### Auto Selection (`'auto'`) -Automatically selects the recommended optimizer: -- SequentialMLP → `'per_neuron'` -- QuadraticRNN → `'adam'` - -## Training - -### Single Run - -To train a model on modular addition tasks: -- **1D**: $(C_p)^k$ - Cyclic group of order $p$ -- **2D**: $(C_{p1} \times C_{p2})^k$ - Product of two cyclic groups -- **Dihedral D3**: $D_3$ - Dihedral group of order 3 - -**Steps:** - -1. Edit `gagf/rnns/config.yaml` to specify your experiment. - - **Key configuration parameters:** - - | Parameter | Options | Description | - |-----------|---------|-------------| - | `data.dimension` | `1` or `2` | Use 1D cyclic group or 2D product group | - | `data.p` | integer | Cyclic group dimension (1D only) | - | `data.p1`, `data.p2` | integers | Product group dimensions (2D only) | - | `data.k` | integer | Sequence length | - | `data.template_type` | `'mnist'`, `'fourier'`, `'gaussian'` | How to generate template | - | `model.model_type` | `'QuadraticRNN'`, `'SequentialMLP'` | Architecture choice | - | `model.transform_type` | `'quadratic'`, `'multiplicative'` | Transform (QuadraticRNN only) | - | `model.hidden_dim` | integer | Hidden layer size | - | `training.optimizer` | `'auto'`, `'adam'`, `'per_neuron'`, `'hybrid'` | Optimizer (auto recommended) | - | `training.learning_rate` | float | Base learning rate | - - **Example configurations:** - - ```yaml - # 1D task with QuadraticRNN - data: - dimension: 1 - p: 100 - k: 3 - template_type: 'fourier' - model: - model_type: 'QuadraticRNN' - hidden_dim: 200 - ``` - - ```yaml - # 2D task with SequentialMLP - data: - dimension: 2 - p1: 10 - p2: 10 - k: 3 - template_type: 'mnist' - model: - model_type: 'SequentialMLP' - hidden_dim: 600 # SequentialMLP typically needs more capacity - ``` - -2. Run the training script from the root directory: - -```bash -python gagf/rnns/main.py --config gagf/rnns/config.yaml -``` - -This will train the model and save results to the `runs/` directory. - -### Parameter Sweeps - -To run parameter sweeps with multiple configurations and seeds: - -1. Create or modify a sweep configuration file in `gagf/rnns/sweeps/`. The sweep config should specify: - - `base_config`: Path to the base configuration file - - `n_seeds`: Number of random seeds per experiment - - `experiments`: List of experiments with parameter overrides - -Example sweep config (`gagf/rnns/sweeps/example_sweep.yaml`): -```yaml -base_config: "gagf/rnns/config.yaml" -n_seeds: 3 - -experiments: - - name: "hidden_dim_32" - overrides: - model: - hidden_dim: 32 - - - name: "hidden_dim_64" - overrides: - model: - hidden_dim: 64 -``` - -2. Run the sweep from the root directory: - -```bash -python gagf/rnns/run_sweep.py --sweep gagf/rnns/sweeps/example_sweep.yaml -``` - -This will: -- Run each experiment configuration (potentially with multiple seeds) -- Save results to `sweeps/{sweep_name}_{timestamp}/` -- Generate summary statistics across seeds -- Create experiment and sweep-level summary files - -**Multi-GPU Usage:** - -The sweep runner supports automatic parallel execution across multiple GPUs: - -```bash -# Use all available GPUs automatically (recommended) -python gagf/rnns/run_sweep.py --sweep gagf/rnns/sweeps/example_sweep.yaml --gpus auto - -# Use specific GPUs (e.g., GPUs 0-7) -python gagf/rnns/run_sweep.py --sweep gagf/rnns/sweeps/example_sweep.yaml --gpus 0,1,2,3,4,5,6,7 - -# Use a single GPU (backward compatible) -python gagf/rnns/run_sweep.py --sweep gagf/rnns/sweeps/example_sweep.yaml --gpu 0 -``` - -When multiple GPUs are specified, experiments and seeds are automatically distributed across GPUs using round-robin assignment, allowing parallel execution of multiple training runs simultaneously. This significantly speeds up parameter sweeps. - -**Note:** The `--gpus` flag takes precedence over `--gpu`. If neither is specified, the code will auto-detect and use all available GPUs if multiple GPUs are present, otherwise it falls back to the device setting in the config file. - -### Sweep Results Structure - -``` -sweeps/ -└── example_sweep_20231112_143022/ - ├── sweep_metadata.yaml # Overall sweep information - ├── sweep_summary.yaml # Aggregated results - ├── configs/ # Saved configs for each experiment - ├── hidden_dim_32/ - │ ├── experiment_summary.yaml - │ ├── seed_0/ # Results for seed 0 - │ ├── seed_1/ # Results for seed 1 - │ └── seed_2/ # Results for seed 2 - └── hidden_dim_64/ - ├── experiment_summary.yaml - ├── seed_0/ - ├── seed_1/ - └── seed_2/ -``` - -See `gagf/rnns/sweeps/` for more example sweep configurations. diff --git a/src/sweep_configs/example_sweep.yaml b/src/sweep_configs/example_sweep.yaml index ad0ebfb..674a43e 100644 --- a/src/sweep_configs/example_sweep.yaml +++ b/src/sweep_configs/example_sweep.yaml @@ -2,7 +2,7 @@ # This demonstrates how to sweep over different hyperparameters # Base configuration to inherit from -base_config: "gagf/rnns/config.yaml" +base_config: "src/config.yaml" # Number of seeds per configuration (for uncertainty quantification) n_seeds: 1 diff --git a/src/sweep_configs/learning_rate_sweep.yaml b/src/sweep_configs/learning_rate_sweep.yaml index b71e8ef..b8f95a4 100644 --- a/src/sweep_configs/learning_rate_sweep.yaml +++ b/src/sweep_configs/learning_rate_sweep.yaml @@ -1,7 +1,7 @@ # Learning rate sweep configuration # Compares different learning rates and optimizers -base_config: "gagf/rnns/config.yaml" +base_config: "src/config.yaml" n_seeds: 5 experiments: diff --git a/src/sweep_configs/model_size_sweep.yaml b/src/sweep_configs/model_size_sweep.yaml index 6129788..8241122 100644 --- a/src/sweep_configs/model_size_sweep.yaml +++ b/src/sweep_configs/model_size_sweep.yaml @@ -1,7 +1,7 @@ # Model architecture and data complexity sweep # Explores different hidden dimensions, sequence lengths, and grid sizes -base_config: "gagf/rnns/config.yaml" +base_config: "src/config.yaml" n_seeds: 3 experiments: diff --git a/src/sweep_configs/onehot_scaling_sweep.yaml b/src/sweep_configs/onehot_scaling_sweep.yaml index 70b8891..4e2170f 100644 --- a/src/sweep_configs/onehot_scaling_sweep.yaml +++ b/src/sweep_configs/onehot_scaling_sweep.yaml @@ -2,7 +2,7 @@ # Explores different group sizes (p), hidden dimensions, and sequence lengths # Total: 20 × 20 × 3 = 1200 experiments -base_config: "gagf/rnns/config.yaml" +base_config: "src/config.yaml" n_seeds: 1 # Fixed parameters applied to all experiments diff --git a/sweeps b/sweeps deleted file mode 120000 index 9972dec..0000000 --- a/sweeps +++ /dev/null @@ -1 +0,0 @@ -/data/facosta/sweeps \ No newline at end of file