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Alice's adventures in a differentiable wonderland

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Re: Alice's adventures in a differentiable wonderland

#61

Post by xanderlewis »

kadushka wrote: post #59
captainclam wrote: post #12

Earlier quoted context omitted.

Ugh, exactly, it's so cool. I've been a deep learning practitioner for ~3 years now, and I feel like this notion has really been impressed upon me only recently. I've spent an awful lot of mental energy trying to conceive of how these things work, when really it comes down to "does increasing this parameter improve the performance on this task? Yes? Move the dial up a bit. No? Down a bit..." x 1e9. And the cool part…

it comes down to "does increasing this parameter improve the performance on this task? Yes? Move the dial up a bit. No? Down a bit..." x 1e9 This is not how gradient based NN optimization works. What you described is called "random weight perturbation", a variant of evolutionary algorithms. It does not scale to networks larger than a few thousand parameters for obvious reasons. NNs are optimized by directly computing…

I don’t think the author literally meant tweaking the parameters and seeing what happens; it’s probably an analogy meant to give a sense of how the gradient indicates what direction and to what degree the parameters should be tweaked. Basically, substitute ‘the gradient is positive’ for ‘increasing this parameter decreases performance’ and vice versa and it becomes correct.

Re: Alice's adventures in a differentiable wonderland

#62

Post by xanderlewis »

naasking wrote: post #60
xanderlewis wrote: post #57

Earlier quoted context omitted.

My point is that you seem to think neurons in the sense of artificial neural networks and neurons in the human brain are equivalent because: (1) Neural networks are Turing complete, and hence can do anything brains can. [debatable anyway; We don’t know this to be the case since brains might be doing more than computation. Ask a philosopher or a cognitive scientist. Or Roger Penrose.] (2) Neural networks were very loo…

The brain certainly could be doing super-Turing computation, but that would overturn quite a bit of physics seeing as how not even quantum computers are more powerful than Turing machines (they're just faster on some problems). Extraordinary claims and all that. As for equivalency, that depends on how that's defined. Real neurons would not feature any more computational power than Turing machines or artificial neural…

The original comment you were in defence of was suggesting that artificial neurons were somehow very close to biological ones, since supposedly that’s where their inspiration came from.

If you’re interested in pure computational ‘power’, then if the brain is nothing more than a Turing machine (which, as you agree, it might not be), fine. You can call them ‘equivalent’. It’s just not very meaningful.

What’s interesting about neural nets has nothing to do with what they can compute; indeed they can compute anything any other Turing machine can, and nothing more. What’s interesting is how they do it, since they can ‘learn’ and hence allow us to produce solutions to hard problems without any explicit programming or traditional analysis of the problem.

> that would overturn quite a bit of physics

Our physics is currently woefully incomplete, so… yes. That would be welcome.

Re: Alice's adventures in a differentiable wonderland

#63

Post by p1esk »

xanderlewis wrote: post #61
kadushka wrote: post #59

Earlier quoted context omitted.

it comes down to "does increasing this parameter improve the performance on this task? Yes? Move the dial up a bit. No? Down a bit..." x 1e9 This is not how gradient based NN optimization works. What you described is called "random weight perturbation", a variant of evolutionary algorithms. It does not scale to networks larger than a few thousand parameters for obvious reasons. NNs are optimized by directly computing…

I don’t think the author literally meant tweaking the parameters and seeing what happens; it’s probably an analogy meant to give a sense of how the gradient indicates what direction and to what degree the parameters should be tweaked. Basically, substitute ‘the gradient is positive’ for ‘increasing this parameter decreases performance’ and vice versa and it becomes correct.

That substitution is the main difference between SGD and RWP.

It’s like describing bubble sort when you meant to describe quick sort. Would not fly on an ML 101 exam, or in an ML job interview.

Re: Alice's adventures in a differentiable wonderland

#64

Post by naasking »

andoando wrote: post #58
naasking wrote: post #44

Earlier quoted context omitted.

> the biological version of a neuron (i.e. a neuron) is much more complicated than the neural network version This is a difference of degree not of kind, because neural networks are Turning complete. Whatever additional complexity the neuron has can itself be modelled as a neural network. Edit: meaning, that if the greater complexity of a biological neuron is relevant to its information processing component, then tha…

And assembly is also turing complete, so if two models being both Turing completeness means they are equivalent, there would be no need for coding neural networks at all. Would you consider LLMs a different kind of computation than writing assembly code? Perhaps fundamentally they are not, but its also true that just writing more and more random assembly code isn't going to lead to an LLM.

LLMs aren't randomly generated though, they are shaped by training data. This means there would, in principle, be a comparable way to synthesize an equivalent assembly program from that same training data.

The difference here is that it's just more obvious how to do this in one case than the other.

My point was only that 1) neural networks are sufficient, even if real neurons have additional complexity, and 2) whatever that additional complexity, artificial neural networks can learn to reproduce it.

Re: Alice's adventures in a differentiable wonderland

#65

Post by newrotik »

xanderlewis wrote: post #25
jxy wrote: post #23

Earlier quoted context omitted.

> > Stripped of anything else, neural networks are compositions of differentiable primitives > I’m a sucker for statements like this. It almost feels philosophical, and makes the whole subject so much more comprehensible in only a single sentence. And I hate inaccurate statements like this. It pretends to be rigorous mathematical, but really just propagates erroneous information, and makes the whole article so much m…

It’s not ‘inaccurate’. The mark of true mastery is an ability to make terse statements that convey a huge amount without involving excessive formality or discussion of by-the-by technical details. If ever you’ve spoken to world-renowned experts in pure mathematics or other highly technical and pendantic fields, you’ll find they’ll say all sorts of ‘inaccurate’ things in conversation (or even in written documents). It…

Lack of differentiability is actually a very important feature of the underlying optimization problem.

You might think that it doesn't matter because ReLU is, e.g., non-differentiable "only at one point".

Gradient based methods (what you find in pytorch) generally rely on the idea that gradients should taper to 0 in the proximity of a local optimum. This is not the case for non-differentiable functions, and in fact gradients can be made to be arbitrarily large even very close to the optimum.

As you may imagine, it is not hard to construct examples where simple gradient methods that do not properly take these facts into account fail to converge. These examples are not exotic.

Re: Alice's adventures in a differentiable wonderland

#66

Post by andoando »

xanderlewis wrote: post #56
andoando wrote: post #54

Earlier quoted context omitted.

So when I think of functions in lambda calculus, I think of the I,S,K functions which when composed can produce functions like "copy", "add", "remove", "if", etc which then can do different computations like "copy every other symbol if the symbol is true", "multiply 5 times then add 2". Since lambda calculus is complete, any computation/program can be composed. When I think of functions in a traditional mathematical…

I think you’re actually massively overthinking it. The state of a neural network is described entirely by its parameters, which usually consist of a long array (well, a matrix, or a tensor, or whatever…) of floating point numbers. What is being optimised when a network is trained is these parameters and nothing else. When you evaluate a neural network on some input (often called performing ‘inference’), that is when…

I appreciate your responses, sorry I hope I don't seem like Im arguing for the sake of arguing.

>Essentially what the parameters represent is how likely each neuron is to be activated (have a high value) if others in the previous layer are. So you can think of the parameters as encoding strengths of connections between each pair of neurons in consecutive layers. Thinking about ‘what path to take through the neural layers’ is way too sophisticated — it’s not doing anything like that.

Im a little confused. The discussion thus far about how neural networks are essentially just compositions of functions, but you are now saying that the function is static, and only the parameters change.

But that aside, if these parameters change which neurons are activated, and this activation affects which neurons are activated in the next layer, are these parameters effectively not changing the path taken through the layers?

>Sure, if you incorporate that extra state as one of your inputs, it might be, but that’s a different function.

So say we have this program " let c = 2; function 3sum (a,b) { return a+b + c; } let d = 3sum(3,4)"

I believe you are saying, if we had constructed this instead as

"function(a,b,c) { return a+b+c } let d = 3sum(3,4,2) "

then, this is a different function.

Certainly, these are different in a sense, but at a fundamental level, when you compile this all down and run it, there is an equivalency in the transformation that is happening. That is, the two functions equivalently take some input state A (composed of a,b,c) and return the same output state B, while applying the same intermediary steps (add a to b, add c to result of (add to b)). Really, in the first case where c is defined outside the scope of the function block, the interpreter is effectively producing the function 3sum(x,y,c) as it has to at some point, one way or another, inject c into a+b+c.

Similarly, I am won't argue that the current, formal definitions of functions in mathematics are exactly that of functions as they're generally defined in programming.

Rather, what I saying is that there is an equivalent way to think and study functions that equally apply to both fields. That is, a function is simply a transformation from A to B, where A and B can be anything, whether that is bits, numbers, or any other construction in any system. The only primitive distinction to make here is whether A and B are the same thing or different.

Re: Alice's adventures in a differentiable wonderland

#67

Post by andoando »

naasking wrote: post #64
andoando wrote: post #58

Earlier quoted context omitted.

And assembly is also turing complete, so if two models being both Turing completeness means they are equivalent, there would be no need for coding neural networks at all. Would you consider LLMs a different kind of computation than writing assembly code? Perhaps fundamentally they are not, but its also true that just writing more and more random assembly code isn't going to lead to an LLM.

LLMs aren't randomly generated though, they are shaped by training data. This means there would, in principle, be a comparable way to synthesize an equivalent assembly program from that same training data. The difference here is that it's just more obvious how to do this in one case than the other. My point was only that 1) neural networks are sufficient, even if real neurons have additional complexity, and 2) whatev…

I understand that, what I am saying though is the fact that they can doesn't mean that they will by simply scaling their number. It still entirely depends on how they are trained/arranged, meaning it may take a completely different way of composing/glueing neurons together to stimulate any additional complexity. Its like saying a nand gate is turing complete, I put 1000000000 of them in a series, but its not doing anything, what gives, do I need to add a billion more?

Just as a modeling and running a single neuron takes x amount of transistors configured in a very specific way for example, it may take y amount of neurons arranged in some very specific, unknown to model something that has extra properties.

And its not clear either whether neurons are fundamentally the correct approach to reach this higher level construction than some other kind of node.

Re: Alice's adventures in a differentiable wonderland

#68

Post by xanderlewis »

p1esk wrote: post #63
xanderlewis wrote: post #61

Earlier quoted context omitted.

I don’t think the author literally meant tweaking the parameters and seeing what happens; it’s probably an analogy meant to give a sense of how the gradient indicates what direction and to what degree the parameters should be tweaked. Basically, substitute ‘the gradient is positive’ for ‘increasing this parameter decreases performance’ and vice versa and it becomes correct.

That substitution is the main difference between SGD and RWP. It’s like describing bubble sort when you meant to describe quick sort. Would not fly on an ML 101 exam, or in an ML job interview.

It’s not like that at all. You couldn’t accidentally sound like you’re describing quick sort when describing bubble sort, or vice versa. I can’t think of any substitution of a few words that would do that.

The meaning of the gradient is perfectly adequately described by the author. They weren’t describing an algorithm for computing it.

Re: Alice's adventures in a differentiable wonderland

#69

Post by captainclam »

kadushka wrote: post #59
captainclam wrote: post #12

Earlier quoted context omitted.

Ugh, exactly, it's so cool. I've been a deep learning practitioner for ~3 years now, and I feel like this notion has really been impressed upon me only recently. I've spent an awful lot of mental energy trying to conceive of how these things work, when really it comes down to "does increasing this parameter improve the performance on this task? Yes? Move the dial up a bit. No? Down a bit..." x 1e9. And the cool part…

it comes down to "does increasing this parameter improve the performance on this task? Yes? Move the dial up a bit. No? Down a bit..." x 1e9 This is not how gradient based NN optimization works. What you described is called "random weight perturbation", a variant of evolutionary algorithms. It does not scale to networks larger than a few thousand parameters for obvious reasons. NNs are optimized by directly computing…

I guess you could say I don't know RWP from Adam! :D

My og comment wasn't to accurately explain gradient optimization, I was just expressing a sentiment not especially aimed at experts and not especially requiring details.

Though I'm afraid I subjected you to the same "cringe" I experience when I read pop sci/tech articles describe deep learning optimization as "the algorithm" being "rewarded" or "punished," haha.

Re: Alice's adventures in a differentiable wonderland

#70

Post by gessha »

whimsicalism wrote: post #34
gessha wrote: post #33

Earlier quoted context omitted.

Complexity also comes from the number of papers that work out how different elements of network work and how to intuitively change them. Why do we use conv operators, why do we use attention operators, when do we use one over the other? What augmentations do you use, how big of a dataset do you need, how do you collect the dataset, etc etc etc

idk, just using attention and massive web crawls gets you pretty far. a lot of the rest is more product-style decisions about what personality you want your LM to take. I fundamentally don't think this technology is that complex.

No? In his recent tutorial, Karpathy showed just how much complexity there is in the tokenizer.

This technology has been years in the making with many small advances pushing the performance ever so slightly. There’s been theoretical and engineering advances that contributed to where we are today. And we need many more to get the technology to an actually usable level instead of the current word spaghetti that we get.

Also, the post is generally about neural networks and not just LMs.

When making design decisions about an ML system you shouldn’t just choose the attention hammer and hammer away. There’s a lot of design constraints you need to consider which is why I made the original reply.

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