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TL;DR

Indexing

Searching

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Indexing is understanding

What does it mean by understanding? Usually, it is use as the opposite of just memorizing. When you memorize something, you just remember it. But when you understand something, there are a few more magic happening:

You know which part of the knowledge is relevant to the context.

This is quite difficult because the context usually doesn't match the knowledge exactly. For example, if the doctor says: "don't drink any water". You may think that you can drink juice, but you can't drink juice either. You can't drink anything.

You know how different parts of the knowledge are related.

This is even more difficult. The reason is two-fold:

Ancient approaches

The most important example of the use of indexing is search engine. Search engines collect the keywords in the documents and index them. When you search for a keyword, the search engine will return the documents that contain the keyword. This is the most basic form of indexing.

Search engines provide an efficient way to find a webpage with some keywords. However, you cannot imagine you discover the gravity by searching "apple" in Google. This is because the search engine doesn't understand the relation between the keywords. It only knows that the keywords appear in the same document. This approach is already very powerful, but we obviously want more.

A way to analyze the relation and the context of the keywords is to use a knowledge graph. A knowledge graph is a graph that contains the objects and the relations between them. For example, juice and water can be two nodes linked by an edge has ingrediant. In this way, it might help understanding whether you can drink juice when the doctor says "don't drink any water".

However, obviously, none of these ancient approaches has a chance to draw a relation between celestial bodies and gravity. Ever after decades of development, they still struggle with understanding everything that is a little bit abstract. Certainly we need something new.

In the large language model (LLM) era

I will not introduce the history of the reason why LLMs work. But I believe every one of you who are reading this article must have some feeling that LLM can understand abstract mathematical concepts. If you ask ChatGPT:

When I dress myself, I can put on my shirt and then my pants. 
+I can also put on my pants and then my shirt. It won't make a difference.
+
+What mathematical concept is this?
+

ChatGPT will recognize that the order of the two actions doesn't matter, so it is related to commutativity. The answer won't change a lot if you modify the situation as long as it represents the concept of commutativity. It's quite hard to imagine how a search engine or a knowledge graph can do this. The word "commutativity" doesn't even appear in the question.

However, this good performance of LLM is at a cost. The most important limitation is that LLM the size of its input is limited, and it is completely not at the same scale as the knowledge graph and traditional search engines. You have to decide what is the most important context that the LLM have to know before you ask the question. This, again, requires some understanding of the knowledge. LLM helps you the best when you already have some understanding of the knowledge.

Embedding-based indexing

Good news is that LLM not only helps us by directly giving the answer. It also helps us index existing knowledge. Notice that LLM are built with deep learning technology, in which neural networks are used to process the knowledge. In the intermediate layers of the neural network, the knowledge is represented as vectors called embeddings.

These embeddings carry all the information about the input and have already been processed by the neural network for abstract understanding. Therefore, if two inputs to the LLM have similar embeddings, they are likely to be related, even in an abstract way. This is the key idea of embedding-based indexing.

Giving a few pieces of knowledge, we can use LLM to generate their embeddings as their index. Whenever a context is given, we generate the embedding of the context and find the similar embeddings in the knowledge base. This will have the model to gain essential knowledge before answering a question. Importantly, this embedding similarity-based indexing is totally scalable, meaning that you have the chance to index the knowledge of astronomy and gravity together!

Wrap up

Though there might be still a lot of steps before we let the model rediscover gravity, we have already seen the potential of LLM in indexing. Importantly, we find a good roadmap to solve the two problems we put in the beginning. For the first, by embedding similarity, we have the tool for finding the relevant knowledge to the context and retrieve them. "Don't drink water" will have a high similarity with "don't drink juice". For the second, with the abstract understanding ability of LLM, we can extract relation of two pieces of knowledge. It can discover that "don't drink water" actually means "don't drink any liquid".

With embedding-based search in hand, it seems what left for us to build is simply improve its performance. However, you will find it as a surprisingly tricky task which involves much philosophical effort. Let's discuss it in another article.

Related works

History of retrieval: https://dl.acm.org/doi/pdf/10.1145/3486250

LlamaIndex: https://www.llamaindex.ai/

ACL 2023 Tutorial on Retrieval-based Language Models: https://acl2023-retrieval-lm.github.io/

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Tree indexing

Tree might be the most common traditional indexing that are adopted by human-being before the advent of computers. People have practiced organizing books in nested section for thousands of year.　It has two advantages:

This is the most obvious reason and this is why we call it indexing. However, there are more subtle reasons:

These reasons are important when the reader is not familiar with the knowledge. It makes it possible to understand the knowledge better without reading the whole book. It works by the following mechanism:

What does it mean to LLM?

The reason why we underscore the importance of tree indexing is obviously not because we want to make a better book. Our question is whether LLM can benefit from tree indexing. The answer is obviously yes. The reason is from the following points:

Further, if we make the LLM into an agent who can actively travel on the book and add new content to the book.

What is the difference between tree indexing for human and for LLM?

Usually, in human made books, the tree structure is quite coarse. One of the reasons might be this: explicit fine-grained tree structure is hard to make and read. Though human writers might make a lot of list and aside to make the tree structure actually more fine-grained, it is laborious to give a name to every small section. The human readers are also not willing to read a book with too many small sections.

However, the situation does not hold for LLM. This is because

Wrap up

With the discussion above, we know that

As we discussed in the first article, indexing is closed related to understanding. Surely, we can see that tree indexing can help organizing and retrieve knowledge. However, could it really help LLM to understand abstract things like science?

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Method of Loci

Method of Loci, also known as memory palace, is a method to memorize things by associating them with a place. It is a very old method and has been used for thousands of years. It is also a very effective method.

When you try to memorize a list of things, you can just imagine a place you are familiar with and put the things in the place. When you want to recall the things, you can just imagine the place and the things will come to your mind.

Why is the method good?

Why this method is efficient? Here is the claim:

Method of Loci is efficient because it creates a graph of knowledge with each node has only limited number of edges. That is, it is a sparse graph.

Here, in the graph of knowledge, the nodes are the context (situation) and the edges leads to the memory or another situation. The whole point of method of loci is to turn a list of things, which is densely indexed, into a sparsely connected structure.

Why sparse graph is good?

Here is the claim:

Sparse graph performs better because it fits in context window of human brain better.

Thinking with a sparse graph limits the number of things you need to think about at one time. In this meantime, because the knowledge are still interconnected, you can still think about the whole knowledge.

What does it mean to LLM?

',12),l={href:"https://arxiv.org/abs/2307.03172",target:"_blank",rel:"noopener noreferrer"},u=e("p",null,"Maybe it can be improved in the future, but I strongly don't believe that will happen very fast. We can use the sparsity of the graph to decrease the number of things LLM needs to think about at one time and enhance the performance.",-1),p=e("h2",{id:"how-about-evonote",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#how-about-evonote","aria-hidden":"true"},"#"),t(" How about EvoNote?")],-1),m=e("p",null,"EvoNote uses the tree structure to index the knowledge. It has a natural advantage to make the connection at each node (note) sparse. Compared to the approaches that use a flat list (e.g., chunks) or a dense graph (e.g., knowledge graph) to index the knowledge, it is more efficient.",-1),f=e("h2",{id:"how-about-docinpy",tabindex:"-1"},[e("a",{class:"header-anchor",href:"#how-about-docinpy","aria-hidden":"true"},"#"),t(" How about DocInPy")],-1),g=e("p",null,"DocInPy provides a way to add sections to your Python codes to separate the functions and classes for arranging them into a tree structure. It makes it possible to make the tree sparse.",-1),b=e("p",null,"There are a lot of Python projects put a tons of functions in one file. This have put a barrier for both human and LLM to understand the code for a long time. DocInPy can help to solve this problem.",-1);function y(w,_){const o=n("ExternalLinkIcon");return s(),i("div",null,[c,e("p",null,[t("LLM also has a limited number of token in the context window. Current technology still struggles to make the context window large. When it seems to be large, the performance is usually not good. (See "),e("a",l,[t("Lost in the Middle: How Language Models Use Long Contexts"),h(o)]),t(")")]),u,p,m,f,g,b])}const x=a(d,[["render",y],["__file","2.1 Method of Loci and sparsity.html.vue"]]);export{x as default}; diff --git a/assets/2.1 Method of Loci and sparsity.html-5b3177ed.js b/assets/2.1 Method of Loci and sparsity.html-5b3177ed.js new file mode 100644 index 0000000..2c1c293 --- /dev/null +++ b/assets/2.1 Method of Loci and sparsity.html-5b3177ed.js @@ -0,0 +1 @@ +const o=JSON.parse('{"key":"v-5ebcc181","path":"/writings/2.1%20Method%20of%20Loci%20and%20sparsity.html","title":"Method of Loci","lang":"en-US","frontmatter":{},"headers":[{"level":2,"title":"Why is the method good?","slug":"why-is-the-method-good","link":"#why-is-the-method-good","children":[]},{"level":2,"title":"Why sparse graph is good?","slug":"why-sparse-graph-is-good","link":"#why-sparse-graph-is-good","children":[]},{"level":2,"title":"What does it mean to LLM?","slug":"what-does-it-mean-to-llm","link":"#what-does-it-mean-to-llm","children":[]},{"level":2,"title":"How about EvoNote?","slug":"how-about-evonote","link":"#how-about-evonote","children":[]},{"level":2,"title":"How about DocInPy","slug":"how-about-docinpy","link":"#how-about-docinpy","children":[]}],"git":{"updatedTime":1696805165000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":2}]},"filePathRelative":"writings/2.1 Method of Loci and sparsity.md"}');export{o as data}; diff --git a/assets/3. Copernicus and indexing.html-8dd5fa84.js b/assets/3. Copernicus and indexing.html-8dd5fa84.js new file mode 100644 index 0000000..b6b2411 --- /dev/null +++ b/assets/3. Copernicus and indexing.html-8dd5fa84.js @@ -0,0 +1 @@ +import{_ as e,o as t,c as n,b as a}from"./app-28def544.js";const i={},o=a('

What are different understandings?

In the previous article, we found that indexing is deeply related to understanding. However, can we somehow give a definition of understanding? We mentioned in the first article that memorization is different from understanding. So the explicit knowledge must not be the understanding and understanding must be something other than the knowledge itself. Naturally, because the "other" thing must be related to the stand-alone knowledge, we can call it the implicit context of the knowledge. With this definition, I claim that

To understand a thing, you must know that implicit context of it.

and consequently,

The way to understand a thing, is the way to assign the implicit context to it.

Let's illustrate this with a few examples.

Modern educated human think they understand earthquake and treat it as a result of the movement of tectonic plates. They think they understand because they can fit the phenomenon of earthquake into his existing knowledge of geology and use it as a context.

Ancient Japanese people think they understand earthquake and treat it as a result of the movement of a giant catfish supporting the Japanese islands. They think they understand because they can fit the phenomenon of earthquake into his existing knowledge of mythology and use it as a context.

In this example, we show that different people have different understanding of the same thing. They assign different implicit context to one thing and both strongly believes so.

Here, I want to emphasize that, we do not care about which context they assign is correct or not. We only care about the fact that they assign different context. Importantly, the context they assign might be both correct, but the context they assign is different.

A person who believes geocentric model thinks he understands the movement planets because they can perfectly fit into his existing knowledge of astronomy and use it as a context, though in the context planets move in a very complicated way.

A person who believes heliocentric model thinks he understands the movement planets because they can perfectly fit into his existing knowledge of astronomy and use it as a context. The context is different from the previous one and the planets move in a very simple way.

Tree indexing as an understanding

As we introduced in the previous article, tree indexing can help assign a context to the knowledge. With a tree indexing, we can find existing knowledge that is similar to the incoming ones. With the help of the paths of the existing knowledge, a new path, namely a new context, can be created. This is the way tree indexing helps LLM to understand the knowledge. Specifically, the understanding can be carried out in the following way

Step 1. Search similar knowledge in the knowledge base.

Step 2. Gather the paths of the similar knowledge.

Step 3. Synthesize new paths for the incoming knowledge.

Step 4. Use the new paths as the context of the incoming knowledge for rephrasing them.

Step 5. Put the rephrased knowledge into the knowledge base.

Tree transformation as a transformation of understanding

The generation of implicit context in tree indexing relies on the logic of paths. Therefore, we can say the logic of path generation can be used to characterize understandings. People can change the path logic to achieve a new understanding. For example: TODO.

Understanding inside LLM

LLM can understand sentences. Where is the implicit context? My interpretation is that the layers of the LLM is responsible for adding these implicit contexts, including the grammar, meaning of tokens and world knowledge. After being processed by layers, the hidden state, which is the embedding of the sentence, contains the implicit context. Therefore, we can say that even the simplest embedding based search provides a way to understand the knowledge, even when no tree structure is involved.

Related works

A Contextual Approach to Scientific Understanding: https://link.springer.com/article/10.1007/s11229-005-5000-4

',21),s=[o];function r(h,d){return t(),n("div",null,s)}const l=e(i,[["render",r],["__file","3. Copernicus and indexing.html.vue"]]);export{l as default}; diff --git a/assets/3. Copernicus and indexing.html-a31b919b.js b/assets/3. Copernicus and indexing.html-a31b919b.js new file mode 100644 index 0000000..e301655 --- /dev/null +++ b/assets/3. Copernicus and indexing.html-a31b919b.js @@ -0,0 +1 @@ +const n=JSON.parse('{"key":"v-416a7838","path":"/writings/3.%20Copernicus%20and%20indexing.html","title":"What are different understandings?","lang":"en-US","frontmatter":{},"headers":[{"level":2,"title":"Tree indexing as an understanding","slug":"tree-indexing-as-an-understanding","link":"#tree-indexing-as-an-understanding","children":[]},{"level":2,"title":"Tree transformation as a transformation of understanding","slug":"tree-transformation-as-a-transformation-of-understanding","link":"#tree-transformation-as-a-transformation-of-understanding","children":[]},{"level":2,"title":"Understanding inside LLM","slug":"understanding-inside-llm","link":"#understanding-inside-llm","children":[]}],"git":{"updatedTime":1696131659000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":1}]},"filePathRelative":"writings/3. Copernicus and indexing.md"}');export{n as data}; diff --git a/assets/4. Continuous and discrete knowledge.html-6e3c1c16.js b/assets/4. Continuous and discrete knowledge.html-6e3c1c16.js new file mode 100644 index 0000000..d030839 --- /dev/null +++ b/assets/4. Continuous and discrete knowledge.html-6e3c1c16.js @@ -0,0 +1 @@ +const e=JSON.parse('{"key":"v-43d2144f","path":"/writings/4.%20Continuous%20and%20discrete%20knowledge.html","title":"Continuous and discrete knowledge","lang":"en-US","frontmatter":{},"headers":[{"level":2,"title":"Discrete knowledge","slug":"discrete-knowledge","link":"#discrete-knowledge","children":[{"level":3,"title":"What is discrete knowledge?","slug":"what-is-discrete-knowledge","link":"#what-is-discrete-knowledge","children":[]},{"level":3,"title":"What is the property of discrete knowledge?","slug":"what-is-the-property-of-discrete-knowledge","link":"#what-is-the-property-of-discrete-knowledge","children":[]}]},{"level":2,"title":"Continuous knowledge","slug":"continuous-knowledge","link":"#continuous-knowledge","children":[{"level":3,"title":"What is continuous knowledge?","slug":"what-is-continuous-knowledge","link":"#what-is-continuous-knowledge","children":[]},{"level":3,"title":"How to tell whether the knowledge is continuous?","slug":"how-to-tell-whether-the-knowledge-is-continuous","link":"#how-to-tell-whether-the-knowledge-is-continuous","children":[]},{"level":3,"title":"What is the property of continuous knowledge?","slug":"what-is-the-property-of-continuous-knowledge","link":"#what-is-the-property-of-continuous-knowledge","children":[]}]},{"level":2,"title":"How all this related to EvoNote?","slug":"how-all-this-related-to-evonote","link":"#how-all-this-related-to-evonote","children":[]}],"git":{"updatedTime":1696465299000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":2}]},"filePathRelative":"writings/4. Continuous and discrete knowledge.md"}');export{e as data}; diff --git a/assets/4. Continuous and discrete knowledge.html-b3874fd9.js b/assets/4. Continuous and discrete knowledge.html-b3874fd9.js new file mode 100644 index 0000000..e18599c --- /dev/null +++ b/assets/4. Continuous and discrete knowledge.html-b3874fd9.js @@ -0,0 +1 @@ +import{_ as e,o as t,c as o,b as n}from"./app-28def544.js";const a={},i=n('

Continuous and discrete knowledge

Surely, there are many criteria to classify knowledge. The important thing is how much insight we can get from the classification. In this article, I will introduce how to use the idea of continuous and discrete to classify knowledge.

Discrete knowledge

What is discrete knowledge?

Discrete knowledge is the ones whose state is defined in a discrete space. Variation on it cannot be infinitesimal.

For example, a coin has two states: head and tail. The state of a coin is discrete knowledge.

More importantly, logic deductions are operating discrete knowledge. All the system with a flavour of logic and have a clear border of what is true and what is wrong, e.g., knowledge graph and symbolic deductions, are mainly operating discrete knowledge.

What is the property of discrete knowledge?

Discrete knowledge is clear and easy to operate with computers. They can ensure 100% correctness given correct assumptions. For fields that have a concrete assumption, e.g., mathematics, discrete knowledge and its deduction will suffice.

However, not all fields have concrete assumptions. In the long debate of rationalism and empiricism, people found that it is absolutely not easy to find reliable and non-trivial assumption to reason from (See Kant and Hume).

Continuous knowledge

What is continuous knowledge?

Continuous knowledge is the ones whose state is defined in a continuous space. It allows an infinitesimal variation.

For example, the probability that a coin will be head is continuous knowledge. The probability is a real number between 0 and 1.

More importantly, neural networks hold continuous knowledge. The state of a neural network is defined by the weights of the connections between neurons. The weights are real numbers, which is a continuous space.

How to tell whether the knowledge is continuous?

It might be tricky to check whether a piece of knowledge is continuous or not. The key is to imagine whether the knowledge can have a very small variation and still remain mostly true. For example, when you try to recall a voice of someone, you can never ensure that your memory today is the same as your memory yesterday. It also works for smell, visual or kinetic memory.

Most importantly, though also containing discrete knowledge like grammar, a large part of our knowledge about language is also continuous. For example, your feeling about a certain word is continuous. The most obvious example is brands. You must have a certain feeling about Coca-cola, Pepsi, Tesla and BMW; and they don't have a clear border of correctness, nor you can check your feeling is stable.

What is the property of continuous knowledge?

The representation power of continuous knowledge is much stronger than discrete knowledge. It is very hard to imagine how to represent the feeling of ski or recalling a picture with a discrete format.

Continuous knowledge is more natural for human to process. Most of the physics theory also assume that the space is continuous or its discreteness is negligible for human. The power of continuous knowledge can also be proved by the success of neural network. There was a shift of the paradigm of artificial intelligence in the 1990s from discrete to continuous and then follows the triumph of neural networks in nearly all the field.

However, the intrinsic drawbacks of continuous knowledge are still there. Even in 2023, we still cannot handle math, logic and coding satisfactorily with neural networks. This is surely because of the discrete nature of these tasks. How to bridge continuous knowledge with discrete knowledge will be the main challenge of building AI.

EvoNote is trying to add more discrete structure to the continuous knowledge.

Here, we first claim that the knowledge need to be interpreted by large language models are continuous. Though they might look like discrete because they are symbols, but they are meaningless symbols without an interpreter.

Admittedly, you can parse a sentence into a syntax tree. But syntax tree can never represent the accurate meaning. For example, I can set a question: "If apple means eat in the next sentence. 'Mike apple an apple.' What did Mike intake?" This question is easy for human to answer but will break any natural language parser.

The way we want to do this, is to use the tree structure to organize the natural languages in a macro scale (Recall the section: Tree indexing). This can assign the continuous knowledge a discrete structure (tree), which we believe can help building a continuous-discrete hybrid knowledge to help making AI capable at discrete tasks.

',27),s=[i];function r(l,h){return t(),o("div",null,s)}const c=e(a,[["render",r],["__file","4. Continuous and discrete knowledge.html.vue"]]);export{c as default}; diff --git a/assets/4.1 Interface of continuous and discrete.html-29c66cb7.js b/assets/4.1 Interface of continuous and discrete.html-29c66cb7.js new file mode 100644 index 0000000..235d488 --- /dev/null +++ b/assets/4.1 Interface of continuous and discrete.html-29c66cb7.js @@ -0,0 +1 @@ +import{_ as e,o as a,c as t,b as o}from"./app-28def544.js";const n={},r=o('

Interface of continuous and discrete

Topology

Topology is an example where continuous entities can be unambiguously represented by discrete entities.

Condense matter physics loves topology very much. Part of the reason is the topological properties of condensed matter system nearly the only way to describe them in a discrete way.

Natural language classifier

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Comment on previous philosophical works

My comments are mainly made on the following paper:

What is Understanding? An Overview of Recent Debates in Epistemology and Philosophy of Science: https://philpapers.org/rec/BAUWIU

A decisive question

My decisive question to philosophers: Is Pavlov's dog and Russell's chicken understand bell and the coming of the farmer?

My answer: yes! They understand to the extend that they can draw and context. We should not require the context to be always true. Even human believe mythology.

My observation: Most of the philosophers do not agree with me according to the reference.

Chapter-wise comments

4.1 Understanding and the facts

My comment: factivity, to any extend, is not related to understanding. Understanding can easily be totally wrong. Mythology is a good example.

4.2.2. Grasping

My comment: It seems like the philosophers care about knowing the causality and thinks this might be a standard of understanding. In my view, causality is just a piece of knowledge. People usually forming an implicit context with it does not make it a necessary piece of understanding.

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diff --git a/assets/back-to-top-8efcbe56.svg b/assets/back-to-top-8efcbe56.svg new file mode 100644 index 0000000..8323678 --- /dev/null +++ b/assets/back-to-top-8efcbe56.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/assets/evonote-8fd48474.svg b/assets/evonote-8fd48474.svg new file mode 100644 index 0000000..4765e6f --- /dev/null +++ b/assets/evonote-8fd48474.svg @@ -0,0 +1,19 @@ + + + + + background + + + + + + + Layer 1 + + + + + voNote + + \ No newline at end of file diff --git a/assets/index.html-2bf63421.js b/assets/index.html-2bf63421.js new file mode 100644 index 0000000..1099ecb --- /dev/null +++ b/assets/index.html-2bf63421.js @@ -0,0 +1 @@ +const t=JSON.parse('{"key":"v-aa34d5c2","path":"/writings/","title":"Writings","lang":"en-US","frontmatter":{},"headers":[],"git":{"updatedTime":1696801705000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":1}]},"filePathRelative":"writings/index.md"}');export{t as data}; diff --git a/assets/index.html-628c8f88.js b/assets/index.html-628c8f88.js new file mode 100644 index 0000000..a2d5e52 --- /dev/null +++ b/assets/index.html-628c8f88.js @@ -0,0 +1 @@ +const e=JSON.parse('{"key":"v-8daa1a0e","path":"/","title":"","lang":"en-US","frontmatter":{},"headers":[],"git":{"updatedTime":1696801705000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":3}]},"filePathRelative":"index.md"}');export{e as data}; diff --git a/assets/index.html-730bf6ac.js b/assets/index.html-730bf6ac.js new file mode 100644 index 0000000..eed859a --- /dev/null +++ b/assets/index.html-730bf6ac.js @@ -0,0 +1 @@ +const e=JSON.parse('{"key":"v-f7496066","path":"/development/","title":"Class","lang":"en-US","frontmatter":{},"headers":[{"level":2,"title":"Knowledge storage","slug":"knowledge-storage","link":"#knowledge-storage","children":[]},{"level":2,"title":"Indexing","slug":"indexing","link":"#indexing","children":[]},{"level":2,"title":"Cache","slug":"cache","link":"#cache","children":[]},{"level":2,"title":"Debug","slug":"debug","link":"#debug","children":[]}],"git":{"updatedTime":1696823015000,"contributors":[{"name":"Zijian Zhang","email":"doomspec@outlook.com","commits":2}]},"filePathRelative":"development/index.md"}');export{e as data}; diff --git a/assets/index.html-c55a1727.js b/assets/index.html-c55a1727.js new file mode 100644 index 0000000..1f162a2 --- /dev/null +++ b/assets/index.html-c55a1727.js @@ -0,0 +1,4 @@ +import{_ as e,o as a,c as n,b as o}from"./app-28def544.js";const t={},c=o(`

Class

Knowledge storage

Note: The node of knowledge. It only contains the knowledge itself.

Tree: The collection of the references to Note objects. It contains the relationship among knowledge. It includes parents, children and path in the tree structure. It also contains the indexings of the notes.

Indexing

Indexing: The class for storing the data of one indexing. It can return related notes when provided with queries. It must be interpreted by the Indexer class.

Indexer: The factory of Indexing objects. Indexers are stateless and their state are stored in the Indexing object. A Indexer should never be instantiated and all its methods should be static.

Cache

CacheManager: The class for managing the cache of expensive tasks.

cache_manager: The instance of CacheManager for the whole program. You should import it whenever you want to read and write the caches.

cache_manager.read_cache(self, input: any, type: str) -> Cache: input should be a hashable. Cache storage and retrieval is realized by matching both input and type. See https://github.com/EvoEvolver/EvoNote/blob/main/evonote/search/fine_searcher.py for an example of usage.

When you want to discard a certain type of cache. You can use with cache_manager.refresh_cache(cache_type: str): to wrap the code that generates the cache. This will disable the cache of the type cache_type.

Debug

In the debug file, many useful function for revealing the intermediate results are provided. You can use them to debug the program. For example:

from evonote.debug import display_chats
+with display_chats():
+    some_code()
+

All the calling of chat completion will be displayed.

See https://github.com/EvoEvolver/EvoNote/blob/main/playground/debug.py for examples of usage.

Important functionalities

search: The folder includes the codes for searching in the knowledge base.

builder: The folder includes the codes for building the knowledge base.

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Class

Knowledge storage

Note: The node of knowledge. It only contains the knowledge itself.

Tree: The collection of the references to Note objects. It contains the relationship among knowledge. It includes parents, children and path in the tree structure. It also contains the indexings of the notes.

Indexing

Indexing: The class for storing the data of one indexing. It can return related notes when provided with queries. It must be interpreted by the Indexer class.

Indexer: The factory of Indexing objects. Indexers are stateless and their state are stored in the Indexing object. A Indexer should never be instantiated and all its methods should be static.

Cache

CacheManager: The class for managing the cache of expensive tasks.

cache_manager: The instance of CacheManager for the whole program. You should import it whenever you want to read and write the caches.

cache_manager.read_cache(self, input: any, type: str) -> Cache: input should be a hashable. Cache storage and retrieval is realized by matching both input and type. See https://github.com/EvoEvolver/EvoNote/blob/main/evonote/search/fine_searcher.py for an example of usage.

When you want to discard a certain type of cache. You can use with cache_manager.refresh_cache(cache_type: str): to wrap the code that generates the cache. This will disable the cache of the type cache_type.

Debug

In the debug file, many useful function for revealing the intermediate results are provided. You can use them to debug the program. For example:

from evonote.debug import display_chats
+with display_chats():
+    some_code()
+

All the calling of chat completion will be displayed.

See https://github.com/EvoEvolver/EvoNote/blob/main/playground/debug.py for examples of usage.

Important functionalities

search: The folder includes the codes for searching in the knowledge base.

builder: The folder includes the codes for building the knowledge base.

Last Updated:
Contributors: Zijian Zhang
+ + + diff --git a/html/project_tree.html b/html/project_tree.html new file mode 100644 index 0000000..1e3177c --- /dev/null +++ b/html/project_tree.html @@ -0,0 +1,43 @@ + + + + + + + + +
+ \ No newline at end of file diff --git a/image/favicon.ico b/image/favicon.ico new file mode 100644 index 0000000..9ceb642 Binary files /dev/null and b/image/favicon.ico differ diff --git a/index.html b/index.html new file mode 100644 index 0000000..3f31a82 --- /dev/null +++ b/index.html @@ -0,0 +1,33 @@ + + + + + + + + + + + + + + + + + diff --git a/writings/0. TL_DR.html b/writings/0. TL_DR.html new file mode 100644 index 0000000..2fa3b13 --- /dev/null +++ b/writings/0. TL_DR.html @@ -0,0 +1,33 @@ + + + + + + + + + TL;DR + + + + +

TL;DR

  • Indexing and understanding have many similarities. They both require adding context to the objective.
  • Therefore, we want to implement better understand by AI with super-fine indexing with a rich structure which allows the AI find the context easily and precisely.
  • Our plan is from two sides. One for the structure of the knowledge (indexing), one for the retrieval of the knowledge (searching).

Indexing

  • We want to use the tree structure to index the knowledge, because the path from the root to the interested node forms a natural context.
  • We want to use LLM (or agent) to generate characterizing strings as the vector indexing of the knowledge, instead of using their embedding directly.
  • We want to construct multiple trees in difference levels, with each level corresponding to a different level of abstraction.

Searching

  • We want to use the tree structure to search the knowledge. An agent travelling on the tree will be developed.
  • We want to use LLM (or agent) to generate characterizing strings for the queries, instead of using their embedding directly.
  • We want to use multiple levels of trees to search the knowledge. The agent should go from the most abstract level to the most concrete level.
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+ + + diff --git a/writings/1. Indexing is non-trivial.html b/writings/1. Indexing is non-trivial.html new file mode 100644 index 0000000..bb1eac5 --- /dev/null +++ b/writings/1. Indexing is non-trivial.html @@ -0,0 +1,37 @@ + + + + + + + + + Indexing is understanding + + + + +

Indexing is understanding

What does it mean by understanding? Usually, it is use as the opposite of just memorizing. When you memorize something, you just remember it. But when you understand something, there are a few more magic happening:

You know which part of the knowledge is relevant to the context.

This is quite difficult because the context usually doesn't match the knowledge exactly. For example, if the doctor says: "don't drink any water". You may think that you can drink juice, but you can't drink juice either. You can't drink anything.

You know how different parts of the knowledge are related.

This is even more difficult. The reason is two-fold:

  • Nearly every knowledge can be related in some way. For example, PNAS sounds like peanuts. Gravity and computer are related to apple by Newton and Turing. All these relations are true, but they are merely dry humor and not useful.
  • Important relations are usually not obvious. For example, the observation of the movement of celestial bodies proves the existence of gravity. But no one notices this relation until Newton.

Ancient approaches

The most important example of the use of indexing is search engine. Search engines collect the keywords in the documents and index them. When you search for a keyword, the search engine will return the documents that contain the keyword. This is the most basic form of indexing.

Search engines provide an efficient way to find a webpage with some keywords. However, you cannot imagine you discover the gravity by searching "apple" in Google. This is because the search engine doesn't understand the relation between the keywords. It only knows that the keywords appear in the same document. This approach is already very powerful, but we obviously want more.

A way to analyze the relation and the context of the keywords is to use a knowledge graph. A knowledge graph is a graph that contains the objects and the relations between them. For example, juice and water can be two nodes linked by an edge has ingrediant. In this way, it might help understanding whether you can drink juice when the doctor says "don't drink any water".

However, obviously, none of these ancient approaches has a chance to draw a relation between celestial bodies and gravity. Ever after decades of development, they still struggle with understanding everything that is a little bit abstract. Certainly we need something new.

In the large language model (LLM) era

I will not introduce the history of the reason why LLMs work. But I believe every one of you who are reading this article must have some feeling that LLM can understand abstract mathematical concepts. If you ask ChatGPT:

When I dress myself, I can put on my shirt and then my pants. 
+I can also put on my pants and then my shirt. It won't make a difference.
+
+What mathematical concept is this?
+

ChatGPT will recognize that the order of the two actions doesn't matter, so it is related to commutativity. The answer won't change a lot if you modify the situation as long as it represents the concept of commutativity. It's quite hard to imagine how a search engine or a knowledge graph can do this. The word "commutativity" doesn't even appear in the question.

However, this good performance of LLM is at a cost. The most important limitation is that LLM the size of its input is limited, and it is completely not at the same scale as the knowledge graph and traditional search engines. You have to decide what is the most important context that the LLM have to know before you ask the question. This, again, requires some understanding of the knowledge. LLM helps you the best when you already have some understanding of the knowledge.

Embedding-based indexing

Good news is that LLM not only helps us by directly giving the answer. It also helps us index existing knowledge. Notice that LLM are built with deep learning technology, in which neural networks are used to process the knowledge. In the intermediate layers of the neural network, the knowledge is represented as vectors called embeddings.

These embeddings carry all the information about the input and have already been processed by the neural network for abstract understanding. Therefore, if two inputs to the LLM have similar embeddings, they are likely to be related, even in an abstract way. This is the key idea of embedding-based indexing.

Giving a few pieces of knowledge, we can use LLM to generate their embeddings as their index. Whenever a context is given, we generate the embedding of the context and find the similar embeddings in the knowledge base. This will have the model to gain essential knowledge before answering a question. Importantly, this embedding similarity-based indexing is totally scalable, meaning that you have the chance to index the knowledge of astronomy and gravity together!

Wrap up

Though there might be still a lot of steps before we let the model rediscover gravity, we have already seen the potential of LLM in indexing. Importantly, we find a good roadmap to solve the two problems we put in the beginning. For the first, by embedding similarity, we have the tool for finding the relevant knowledge to the context and retrieve them. "Don't drink water" will have a high similarity with "don't drink juice". For the second, with the abstract understanding ability of LLM, we can extract relation of two pieces of knowledge. It can discover that "don't drink water" actually means "don't drink any liquid".

With embedding-based search in hand, it seems what left for us to build is simply improve its performance. However, you will find it as a surprisingly tricky task which involves much philosophical effort. Let's discuss it in another article.

Related works

History of retrieval: https://dl.acm.org/doi/pdf/10.1145/3486250

LlamaIndex: https://www.llamaindex.ai/

ACL 2023 Tutorial on Retrieval-based Language Models: https://acl2023-retrieval-lm.github.io/

Last Updated:
Contributors: Zijian Zhang
+ + + diff --git a/writings/2. Tree indexing.html b/writings/2. Tree indexing.html new file mode 100644 index 0000000..0ede1ae --- /dev/null +++ b/writings/2. Tree indexing.html @@ -0,0 +1,33 @@ + + + + + + + + + Tree indexing + + + + +

Tree indexing

Tree might be the most common traditional indexing that are adopted by human-being before the advent of computers. People have practiced organizing books in nested section for thousands of year.　It has two advantages:

  • Tree structure help the reader locate the knowledge, when the reader has already understood parts of the knowledge.
  • Tree structure help the readers to understand the relation between different knowledge. Similar knowledge are usually put in the same section or subsection.

This is the most obvious reason and this is why we call it indexing. However, there are more subtle reasons:

  • Tree structure help the readers to understand the context of the knowledge.

These reasons are important when the reader is not familiar with the knowledge. It makes it possible to understand the knowledge better without reading the whole book. It works by the following mechanism:

  • The path from the root section to the current section forms a natural context for the knowledge.
  • The readers can choose which section to move to if they find the current section is too trivial, too difficult or too irrelevant to what they want. The tree structure offers a natural path to move.

What does it mean to LLM?

The reason why we underscore the importance of tree indexing is obviously not because we want to make a better book. Our question is whether LLM can benefit from tree indexing. The answer is obviously yes. The reason is from the following points:

  • We only want LLM to read a book when it does not understand it well. Therefore, it is more similar to the case when the reader is not familiar with the knowledge. This means they need more hint of the context. The path can be a good hint.
  • When we want carry out embedding search on the knowledge, it is always more reasonable to include the context. The path can be a good context to make the embedding better.

Further, if we make the LLM into an agent who can actively travel on the book and add new content to the book.

  • The tree structure helps the agent explore related knowledge along the tree and filter out the useful ones. This improves the search result especially when the query is abstract and implicitly related to the knowledge.
  • The existing tree structure offers a good reference to create new ones to keep the book organized and easy to read even when the book is very large.

What is the difference between tree indexing for human and for LLM?

Usually, in human made books, the tree structure is quite coarse. One of the reasons might be this: explicit fine-grained tree structure is hard to make and read. Though human writers might make a lot of list and aside to make the tree structure actually more fine-grained, it is laborious to give a name to every small section. The human readers are also not willing to read a book with too many small sections.

However, the situation does not hold for LLM. This is because

  • The cost of LLM to write or read is much lower than human. It is not a problem to write a lot of small sections or read them.
  • Because LLM does not come with a long-term memory system, it is more important to make the context explicit. The books for human does not assume the readers read each section directly. They can use their long-term memory to make the context. However, LLM does not have such ability.

Wrap up

With the discussion above, we know that

  • Tree indexing is a time-tested way to organize knowledge.
  • Tree indexing is important for LLM to understand the knowledge better.
  • Tree indexing for LLM can be more fine-grained than that for human.

As we discussed in the first article, indexing is closed related to understanding. Surely, we can see that tree indexing can help organizing and retrieve knowledge. However, could it really help LLM to understand abstract things like science?

Last Updated:
Contributors: Zijian Zhang
+ + + diff --git a/writings/2.1 Method of Loci and sparsity.html b/writings/2.1 Method of Loci and sparsity.html new file mode 100644 index 0000000..daad225 --- /dev/null +++ b/writings/2.1 Method of Loci and sparsity.html @@ -0,0 +1,33 @@ + + + + + + + + + Method of Loci + + + + +

Method of Loci

Method of Loci, also known as memory palace, is a method to memorize things by associating them with a place. It is a very old method and has been used for thousands of years. It is also a very effective method.

When you try to memorize a list of things, you can just imagine a place you are familiar with and put the things in the place. When you want to recall the things, you can just imagine the place and the things will come to your mind.

Why is the method good?

Why this method is efficient? Here is the claim:

Method of Loci is efficient because it creates a graph of knowledge with each node has only limited number of edges. That is, it is a sparse graph.

Here, in the graph of knowledge, the nodes are the context (situation) and the edges leads to the memory or another situation. The whole point of method of loci is to turn a list of things, which is densely indexed, into a sparsely connected structure.

Why sparse graph is good?

Here is the claim:

Sparse graph performs better because it fits in context window of human brain better.

Thinking with a sparse graph limits the number of things you need to think about at one time. In this meantime, because the knowledge are still interconnected, you can still think about the whole knowledge.

What does it mean to LLM?

LLM also has a limited number of token in the context window. Current technology still struggles to make the context window large. When it seems to be large, the performance is usually not good. (See Lost in the Middle: How Language Models Use Long Contextsopen in new window)

Maybe it can be improved in the future, but I strongly don't believe that will happen very fast. We can use the sparsity of the graph to decrease the number of things LLM needs to think about at one time and enhance the performance.

How about EvoNote?

EvoNote uses the tree structure to index the knowledge. It has a natural advantage to make the connection at each node (note) sparse. Compared to the approaches that use a flat list (e.g., chunks) or a dense graph (e.g., knowledge graph) to index the knowledge, it is more efficient.

How about DocInPy

DocInPy provides a way to add sections to your Python codes to separate the functions and classes for arranging them into a tree structure. It makes it possible to make the tree sparse.

There are a lot of Python projects put a tons of functions in one file. This have put a barrier for both human and LLM to understand the code for a long time. DocInPy can help to solve this problem.

Last Updated:
Contributors: Zijian Zhang
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What are different understandings?

In the previous article, we found that indexing is deeply related to understanding. However, can we somehow give a definition of understanding? We mentioned in the first article that memorization is different from understanding. So the explicit knowledge must not be the understanding and understanding must be something other than the knowledge itself. Naturally, because the "other" thing must be related to the stand-alone knowledge, we can call it the implicit context of the knowledge. With this definition, I claim that

To understand a thing, you must know that implicit context of it.

and consequently,

The way to understand a thing, is the way to assign the implicit context to it.

Let's illustrate this with a few examples.

Modern educated human think they understand earthquake and treat it as a result of the movement of tectonic plates. They think they understand because they can fit the phenomenon of earthquake into his existing knowledge of geology and use it as a context.

Ancient Japanese people think they understand earthquake and treat it as a result of the movement of a giant catfish supporting the Japanese islands. They think they understand because they can fit the phenomenon of earthquake into his existing knowledge of mythology and use it as a context.

In this example, we show that different people have different understanding of the same thing. They assign different implicit context to one thing and both strongly believes so.

Here, I want to emphasize that, we do not care about which context they assign is correct or not. We only care about the fact that they assign different context. Importantly, the context they assign might be both correct, but the context they assign is different.

A person who believes geocentric model thinks he understands the movement planets because they can perfectly fit into his existing knowledge of astronomy and use it as a context, though in the context planets move in a very complicated way.

A person who believes heliocentric model thinks he understands the movement planets because they can perfectly fit into his existing knowledge of astronomy and use it as a context. The context is different from the previous one and the planets move in a very simple way.

Tree indexing as an understanding

As we introduced in the previous article, tree indexing can help assign a context to the knowledge. With a tree indexing, we can find existing knowledge that is similar to the incoming ones. With the help of the paths of the existing knowledge, a new path, namely a new context, can be created. This is the way tree indexing helps LLM to understand the knowledge. Specifically, the understanding can be carried out in the following way

Step 1. Search similar knowledge in the knowledge base.

Step 2. Gather the paths of the similar knowledge.

Step 3. Synthesize new paths for the incoming knowledge.

Step 4. Use the new paths as the context of the incoming knowledge for rephrasing them.

Step 5. Put the rephrased knowledge into the knowledge base.

Tree transformation as a transformation of understanding

The generation of implicit context in tree indexing relies on the logic of paths. Therefore, we can say the logic of path generation can be used to characterize understandings. People can change the path logic to achieve a new understanding. For example: TODO.

Understanding inside LLM

LLM can understand sentences. Where is the implicit context? My interpretation is that the layers of the LLM is responsible for adding these implicit contexts, including the grammar, meaning of tokens and world knowledge. After being processed by layers, the hidden state, which is the embedding of the sentence, contains the implicit context. Therefore, we can say that even the simplest embedding based search provides a way to understand the knowledge, even when no tree structure is involved.

Related works

A Contextual Approach to Scientific Understanding: https://link.springer.com/article/10.1007/s11229-005-5000-4

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Continuous and discrete knowledge

Surely, there are many criteria to classify knowledge. The important thing is how much insight we can get from the classification. In this article, I will introduce how to use the idea of continuous and discrete to classify knowledge.

Discrete knowledge

What is discrete knowledge?

Discrete knowledge is the ones whose state is defined in a discrete space. Variation on it cannot be infinitesimal.

For example, a coin has two states: head and tail. The state of a coin is discrete knowledge.

More importantly, logic deductions are operating discrete knowledge. All the system with a flavour of logic and have a clear border of what is true and what is wrong, e.g., knowledge graph and symbolic deductions, are mainly operating discrete knowledge.

What is the property of discrete knowledge?

Discrete knowledge is clear and easy to operate with computers. They can ensure 100% correctness given correct assumptions. For fields that have a concrete assumption, e.g., mathematics, discrete knowledge and its deduction will suffice.

However, not all fields have concrete assumptions. In the long debate of rationalism and empiricism, people found that it is absolutely not easy to find reliable and non-trivial assumption to reason from (See Kant and Hume).

Continuous knowledge

What is continuous knowledge?

Continuous knowledge is the ones whose state is defined in a continuous space. It allows an infinitesimal variation.

For example, the probability that a coin will be head is continuous knowledge. The probability is a real number between 0 and 1.

More importantly, neural networks hold continuous knowledge. The state of a neural network is defined by the weights of the connections between neurons. The weights are real numbers, which is a continuous space.

How to tell whether the knowledge is continuous?

It might be tricky to check whether a piece of knowledge is continuous or not. The key is to imagine whether the knowledge can have a very small variation and still remain mostly true. For example, when you try to recall a voice of someone, you can never ensure that your memory today is the same as your memory yesterday. It also works for smell, visual or kinetic memory.

Most importantly, though also containing discrete knowledge like grammar, a large part of our knowledge about language is also continuous. For example, your feeling about a certain word is continuous. The most obvious example is brands. You must have a certain feeling about Coca-cola, Pepsi, Tesla and BMW; and they don't have a clear border of correctness, nor you can check your feeling is stable.

What is the property of continuous knowledge?

The representation power of continuous knowledge is much stronger than discrete knowledge. It is very hard to imagine how to represent the feeling of ski or recalling a picture with a discrete format.

Continuous knowledge is more natural for human to process. Most of the physics theory also assume that the space is continuous or its discreteness is negligible for human. The power of continuous knowledge can also be proved by the success of neural network. There was a shift of the paradigm of artificial intelligence in the 1990s from discrete to continuous and then follows the triumph of neural networks in nearly all the field.

However, the intrinsic drawbacks of continuous knowledge are still there. Even in 2023, we still cannot handle math, logic and coding satisfactorily with neural networks. This is surely because of the discrete nature of these tasks. How to bridge continuous knowledge with discrete knowledge will be the main challenge of building AI.

EvoNote is trying to add more discrete structure to the continuous knowledge.

Here, we first claim that the knowledge need to be interpreted by large language models are continuous. Though they might look like discrete because they are symbols, but they are meaningless symbols without an interpreter.

Admittedly, you can parse a sentence into a syntax tree. But syntax tree can never represent the accurate meaning. For example, I can set a question: "If apple means eat in the next sentence. 'Mike apple an apple.' What did Mike intake?" This question is easy for human to answer but will break any natural language parser.

The way we want to do this, is to use the tree structure to organize the natural languages in a macro scale (Recall the section: Tree indexing). This can assign the continuous knowledge a discrete structure (tree), which we believe can help building a continuous-discrete hybrid knowledge to help making AI capable at discrete tasks.

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Interface of continuous and discrete

Topology

Topology is an example where continuous entities can be unambiguously represented by discrete entities.

Condense matter physics loves topology very much. Part of the reason is the topological properties of condensed matter system nearly the only way to describe them in a discrete way.

Natural language classifier

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Tyranny of science

See Nietzsche and Foucault.

Scientific discourse

Science is meant to be accurate, whose cost is ignore the rich context that real-life situation might have. By making science the absolute premium way to think, it put a coercive discretizer to human world, which leads to a deviation from the fact and many tragedies.

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Comment on previous philosophical works

My comments are mainly made on the following paper:

What is Understanding? An Overview of Recent Debates in Epistemology and Philosophy of Science: https://philpapers.org/rec/BAUWIU

A decisive question

My decisive question to philosophers: Is Pavlov's dog and Russell's chicken understand bell and the coming of the farmer?

My answer: yes! They understand to the extend that they can draw and context. We should not require the context to be always true. Even human believe mythology.

My observation: Most of the philosophers do not agree with me according to the reference.

Chapter-wise comments

4.1 Understanding and the facts

My comment: factivity, to any extend, is not related to understanding. Understanding can easily be totally wrong. Mythology is a good example.

4.2.2. Grasping

My comment: It seems like the philosophers care about knowing the causality and thinks this might be a standard of understanding. In my view, causality is just a piece of knowledge. People usually forming an implicit context with it does not make it a necessary piece of understanding.

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