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The boundary of neural network trainability is fractal

arxiv.org

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Re: The boundary of neural network trainability is fractal

#61

Post by ks1723 »

bosco_mcnasty wrote: post #60
catlifeonmars wrote: post #55

Earlier quoted context omitted.

I saw this, but am still not clear on what the axes represent. I assume two hyperparameters, or possibly two orthogonal principal components. I guess my point is it’s not clear how/which parameters are mapped onto the image.

your point is valid but the paper explains it clearly and obviously. they are NOT dimensionally reduced hyperparameters, no. The hyperparameters are learning rates, that's it. X axis, learning rate for input (1 hidden layer). Y axis, learning rate for output layer. So what this is saying, for certain ill-chosen learning weights, model convergence is for lack of a better word, chaotic and unstable.

Just to add to this, only the two learning rates are changed, everything else including initialization and data is fixed. From the paper:

Training consists of 500 (sometimes 1000) iterations of full batch steepest gradient descent. Training is performed for a 2d grid of η0 and η1 hyperparameter values, with all other hyperparameters held fixed (including network initialization and training data).

Re: The boundary of neural network trainability is fractal

#62

Post by drdeca »

thomastjeffery wrote: post #56
pmayrgundter wrote: post #29

One of Wofram's comments is that there appears to be much more internal structure in language semantics that we had expected, contra-Chomsky. We also know the brain, cortex esp, is highly recurrent, so it should be primed for creating fractals and chaotic mixing. So maybe the hidden structure is the set of neural hyperparams needed to put a given cluster of neurons into fractal/chaotic oscillations like this. Seems p…

An LLM does not model language . The name is misleading, and should be changed to Large Text Model. Text is infinitely complex. Written text is only somewhat less so. The text people choose to write is full of complex entropy. The language patterns we use to read text, on the other hand, are much more simple. The most complicated part is ambiguity, and we don't resolve that with language. Instead, we resolve ambiguit…

> Text is infinitely complex.

No, it isn’t.

> An LLM does not model language. The name is misleading, and should be changed to Large Text Model.

What, because it isn’t processing speech?

Presumably you are aware of models that model recordings of speech, and therefore this isn’t what you mean.

In that case, it seems to me like you are probably jerrymandering some concepts?

Re: The boundary of neural network trainability is fractal

#63

Post by drdeca »

thomastjeffery wrote: post #58
dr_kiszonka wrote: post #57

Earlier quoted context omitted.

I wonder if we use LLM because LTM (and LSTM) was taken.

I doubt it. The entire purpose of an LLM is to make a model that does language (or at least something close enough). It's an easy mistake to name something what you hope it will do instead of what it literally is. Unfortunately, that distinction becomes important later. It's a similar problem with "AI". Artificial Intelligence does not exist, yet we put that name on all kinds of things. This causes real problems, too…

Intelligence does not imply sapience, or person-like-ness.

Re: The boundary of neural network trainability is fractal

#64

Post by thomastjeffery »

drdeca wrote: post #62
thomastjeffery wrote: post #56

Earlier quoted context omitted.

An LLM does not model language . The name is misleading, and should be changed to Large Text Model. Text is infinitely complex. Written text is only somewhat less so. The text people choose to write is full of complex entropy. The language patterns we use to read text, on the other hand, are much more simple. The most complicated part is ambiguity, and we don't resolve that with language. Instead, we resolve ambiguit…

> Text is infinitely complex. No, it isn’t. > An LLM does not model language. The name is misleading, and should be changed to Large Text Model. What, because it isn’t processing speech? Presumably you are aware of models that model recordings of speech, and therefore this isn’t what you mean. In that case, it seems to me like you are probably jerrymandering some concepts?

The set of all possible written text is infinitely complex. That's not what is being modeled, though: LLMs model text that was written intentionally by humans. That's less complicated, but it's not simple enough for language rules to completely define it. Natural language is "context-sensitive", so the meaning of a written language statement is dependent on more than the language itself. That's why we can't just parse natural language like we can programming languages.

An LLM is a model of written text. It doesn't know anything about language rules. In fact, it doesn't follow any rules whatsoever. It only follows the model, which tells you what text is most likely to come next.

Re: The boundary of neural network trainability is fractal

#65

Post by thomastjeffery »

drdeca wrote: post #63
thomastjeffery wrote: post #58

Earlier quoted context omitted.

I doubt it. The entire purpose of an LLM is to make a model that does language (or at least something close enough). It's an easy mistake to name something what you hope it will do instead of what it literally is. Unfortunately, that distinction becomes important later. It's a similar problem with "AI". Artificial Intelligence does not exist, yet we put that name on all kinds of things. This causes real problems, too…

Intelligence does not imply sapience, or person-like-ness.

It doesn't need to to be a problem.

An LLM is a model, not an actor. As soon as we call it "AI", that distinction gets muddled, and the whole narrative follows.

Re: The boundary of neural network trainability is fractal

#66

Post by catlifeonmars »

pmayrgundter wrote: post #46
catlifeonmars wrote: post #39

Earlier quoted context omitted.

Two quibbles: (1) neural nets don’t necessarily operate on language, (2) they only loosely model biological neurons in that they operate in discrete space. All that is to say that any similarities are purely incidental without accounting for these two facts.

1) agreed. it's exciting seeing the same basic architecture broadly applied 2) not sure what you mean by "operate in discrete space" I'd emphasize the potential similarity to biological recurrence. Deep ANNs don't need to have this explicitly (tho e.g. LSTM has explicit recurrence), but it is known that recurrent NNs can be emulated by unrolling, in a process similar to function currying. In this mode, a learned netw…

I didn’t phrase (2) particularly well. I meant that digital neural networks typically use floating point numbers, which can represent only discrete values. Do aliasing effects show up in the behavior of these networks that wouldn’t apply for continuously variable systems, or perhaps more appropriate for biological NNs, temporal coding via spike trains?

Re: The boundary of neural network trainability is fractal

#67

Post by drdeca »

thomastjeffery wrote: post #64
drdeca wrote: post #62

Earlier quoted context omitted.

> Text is infinitely complex. No, it isn’t. > An LLM does not model language. The name is misleading, and should be changed to Large Text Model. What, because it isn’t processing speech? Presumably you are aware of models that model recordings of speech, and therefore this isn’t what you mean. In that case, it seems to me like you are probably jerrymandering some concepts?

The set of all possible written text is infinitely complex. That's not what is being modeled, though: LLMs model text that was written intentionally by humans. That's less complicated, but it's not simple enough for language rules to completely define it. Natural language is "context-sensitive", so the meaning of a written language statement is dependent on more than the language itself. That's why we can't just pars…

The set of all strings over an alphabet is infinite in cardinality. I don’t think I would say that it is infinitely complex. I don’t know how you are defining complexity, but the shortest program that recognizes the language “all strings (over this alphabet)” is pretty short.

A program that has a good rate at distinguishing whether a string is human written, would be substantially longer than one that recognizes the language of all strings over a particular alphabet.

If you want to generate strings instead of recognizing them, a program that enumerates all possible strings over a given alphabet, can also be pretty short.

Not sure what you mean by complexity.

I don’t know what you mean by “it doesn’t follow any rules at all”.

Re: The boundary of neural network trainability is fractal

#68

Post by sigmoid10 »

nyrikki wrote: post #31
sigmoid10 wrote: post #14

Earlier quoted context omitted.

Fractals are not caused by randomness. Fractals arise from scale invariance and self similarity, which in turn can come from non linear systems and iterative processes. It is very easy to generate fractals in practice and even the most vanilla neural networks trivially fulfill the requirements (at least when you look at training output). In that sense it would be weird not to find fractal structures when you look har…

Not exactly, Newton's fractal, which is topological, specifically the wada property, is a boundary condition. It relates to fractal (non-integer) dimensions, which was first described by Mandelbrot in a paper about self similarity. Here is a paper that covers some of that. https://www.minvydasragulskis.com/sites/default/files/public... In Newton's fractal, no matter how small a circle you can draw, your circle will e…

Chaos is just another possible consequence of non linear systems. And newtons's fractal is also generated by just another iterative process. That doesn't mean the origin is necessarily random.

Re: The boundary of neural network trainability is fractal

#69

Post by thomastjeffery »

drdeca wrote: post #67
thomastjeffery wrote: post #64

Earlier quoted context omitted.

The set of all possible written text is infinitely complex. That's not what is being modeled, though: LLMs model text that was written intentionally by humans. That's less complicated, but it's not simple enough for language rules to completely define it. Natural language is "context-sensitive", so the meaning of a written language statement is dependent on more than the language itself. That's why we can't just pars…

The set of all strings over an alphabet is infinite in cardinality. I don’t think I would say that it is infinitely complex. I don’t know how you are defining complexity, but the shortest program that recognizes the language “all strings (over this alphabet)” is pretty short. A program that has a good rate at distinguishing whether a string is human written, would be substantially longer than one that recognizes the…

When you write a parser, you build it out of language (syntax) rules. The parser uses those rules to translate text into an abstract syntax tree. This approach is explicit: syntax is known ahead of time, and any correctly written text can be correctly parsed.

When you train an LLM, you don't write any language rules. Instead, you provide examples of written text. This approach is implicit: syntax is not known ahead of time. The core feature is that there is no distinction between what is correct and what is not correct. The LLM is liberated from the syntax rules of language. The benefit is that it can work with ambiguity. The limitation is that it can't decide what interpretation of that ambiguity is correct. It can only guess what interpretation is most likely, based on the text it was trained on.

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