How do neural networks learn?

https://phys.org/news/2024-03-neural-networks-mathematical-formula-relevant.html

by wglb • 2 years ago

214 129 2 years ago

malux85• 2 years ago

Does anyone else find reading sites like this on mobile unbearable? The number and size of ads is crazy, in terms of pixel space I think there’s more ads than content

zipping1549• 2 years ago

uBO + Firefox reader mode man.. I just don't read whatever they show me if I don't have adblock handy

SCUSKU• 2 years ago

TIL about Firefox reader mode! Thank you! Option + Command + R on MacOS, will commit that to memory and use that from now on!

xcv123• 2 years ago

https://brave.com

No ads

bongodongobob• 2 years ago

I block that at the DNS level via pihole. Nothing on my network sees that stuff.

spurgu• 2 years ago

Sucks when you leave your comfy dungeon. Hence I use NextDNS to achieve the same thing, anywhere.

tomduncalf• 2 years ago

Firefox Focus seems to block them all, I just use that as a content blocker in Safari and am rarely bothered by ads.

I really am not opposed to sites using ads to monetise and resisted ad blocking for many years, but advertisers took it way too far with both the number and intrusiveness of ads so I ended up relenting and installing an ad blocker.

salesynerd• 2 years ago

Blokada works great for me.

UberFly• 2 years ago

Best not to use the default browser on any device.

jamboca• 2 years ago

The article is not so specific on how the research actually works. Then, "We hope this will help democratize AI," but the linked paper is behind a paywall.

Curious to see how they would go about explaining how a network selects its important features

psyklic• 2 years ago

Arxiv (2023 paper w/ similar title&authors): https://arxiv.org/abs/2212.13881

Summary by co-author (of the above): https://twitter.com/dbeagleholeCS/status/1627819164906975232

zwaps2• 2 years ago

Before I read this, is this yet another paper where physicists believe that modern NN are trained by gradient descent and consist of only linear FNN (or another simplification) and can therefore be explained by <insert random grad level physics method here>? Because we already had hundreds of those.

Or is this more substantial?

pcw7321• 2 years ago

It's yet another.. just more adds..

3abiton• 2 years ago

Why is spinning a physics lens to NN a bad thing?

toxik• 2 years ago

It isn't, but the kinds of paper referred to make so many assumptions that the conclusions lack external validity for actual deep learning. In other words, they typically don't actually say anything about state-of-the-art deep networks.

gammalost• 2 years ago

What do you mean with "modern NN" that differ from the basic FNN?

How do you train a modern NN if not through backpropagation?

zwaps2• 2 years ago

Fnn are easy for sequential data because there is no relationship between the elements. Hence, these NN are a frequent target of simplified analyses. However, they also never led to exciting models which we now call AI.

Instead, real models are an eclectic mix of attention or other sequential mixers, gates, ffn, norms and positional tomfoolery.

In other words, everything that makes AI models great is what these analyses usually skip. Of course, while wildly claiming generalized insights about how AI really works.

There’s a dozen papers like that every few months.

g4zj• 2 years ago

believe that modern NN are trained by gradient descent

Are they not?

Genuine question. I'm very new to machine learning and neural networks.

phkahler• 2 years ago

> > believe that modern NN are trained by gradient descent
> Are they not?

While technically true, that answer offers almost zero insight into how they work. Maybe another way to say it is that during inference there is no gradient descent happening - the network is already trained. Ignoring that gradient descent might be an overgeneralization of the training process, it tells you nothing about how ChatGPT plays chess or carries a conversation.

Telling someone what methodology was used to create a thing says nothing about how it works. Just like saying our own brain is "a product of evolution" doesn't tell how it works. Nor does "you are a product of your own life experience" put psychologists out of business. "It's just gradient descent" is a great way to trivialize something that nobody really seems to understand yet.

tech_ken6• 2 years ago

There proposal is actually that gradient descent is a bad representation of the NN learning behavior, and that instead this NFM tracks the “learning” behavior of the model better than simply its loss function over training.

Xcelerate• 2 years ago

What would be the requirements in order for most researchers to agree that a “conclusive” answer has been established to the question “How do neural networks work?”

I ask not because this paper isn’t insightful research, but rather because if you search Google Scholar or arXiv for papers purporting to describe how neural networks “actually work”, you get thousands upon thousands of results all claiming to answer the question, and yet you never really come away with the sense that the question has truly been resolved in a satisfactory way (see also: the measurement problem).

I’ve noticed that each paper uses a totally different approach to addressing the matter that just happens to correspond to the researchers’ existing line of work (It’s topology! No, group theory has the answer! Actually, it’s compressed sensing... computational complexity theory... rebranded old-school quantum chemistry techniques... and so on.)

I suppose my question is more about human psychology than neural networks, since neural networks seem to be working just fine regardless of how well we understand them. But I think it could be useful to organize a multi-disciplinary conference where some open questions regarding machine learning are drafted (similar to Hilbert’s problems), that upon their successful resolution would mean neural networks are no longer widely considered “black boxes”.

sabas123• 2 years ago

What do you mean when you say "how they work"?

A technique that is applied to widely different fields obviously yield a large set of interpretations each with the lense of their own field. But that doesn't invalidate any of those interpretations no?

smokel3• 2 years ago

The problem lies in our understanding of the concept "understanding". It is still pretty unclear at a fundamental level what it means to understand, learn, or conceptualize things.

This quickly leads to thought about consciousness and other metaphysical issues that have not been resolved, and probably never will be.

logicchains2• 2 years ago

It was resolved just over 100 years ago by Wittgenstein. Either you fully define "understanding", in which case you've answered your question, or you don't clearly define it, it in which case you can't have a meaningful discussion about it because you don't even have an agreement on exactly what the word means.

jprete3• 2 years ago

This is a non sequitur. We know what understanding means well enough for basically any technological object other than neural nets.

QuadmasterXLII• 2 years ago

If a paper provided general tools that let me sit down with pen and paper and derive that SWIGLU is better than RELU, and batch normalization trains 6 pi /root 5 times faster than no normalization, etc, and I could get the derivation right before running the experiment, then I wpuld believe that I understood how neural networks train

SiempreViernes3• 2 years ago

Pretty much this, so long as you can't make any prediction ahead of time of the approximate performance of a architecture on a dataset one shouldn't claim they have a good understanding of how a network "learns".

chermi• 2 years ago

This doesn't make sense as a requirement - you make no mention of the data. "How it works" will always depend, in part, on the data, you can't fully separate the algorithm from the data if you want to answer questions about why learning works the way it does. IMO.

paulblazek• 2 years ago

A conclusive answer to how neural networks work should be both descriptive and prescriptive. It should not only tell you how they work but give you new insights into how to train them or how to fix their errors.

For example, does your theory tell you how to initialize weights? How the weights in the NN were derived from specific training samples? If you removed a certain subset of training samples, how would the weights change? If the model makes a mistake, which neurons/layers are responsible? Which weights would have to change, and what training data would need to be added/removed to have the model learn better weights?

If you can't answer these sorts of questions, you can't really say you know how they work. Kind of like steam engines before Carnot, or Koch's principles in microbiology, a theory is often only as good as it can be operationalized.

uoaei3• 2 years ago

There are reasonable attempts at answering those questions. We're not lost in the woods, we have a lot of precedent in research that has brought us closer to understanding these things.

janalsncm• 2 years ago

Perhaps part of the description of the problem should also be that we understand descriptions of how neural networks work but there are a lot of things about training them that we don’t understand. And by “understanding” I mean we often don’t have a better way of training things than trial and error. Prescriptive definitions. Maybe it works, maybe it doesn’t, maybe it’s suboptimal (it almost certainly is). And a lot of these things are data-dependent.

HarHarVeryFunny9• 2 years ago

It seems they are trying to answer "WHAT do NN's learn?", and "How do NN's WORK?", as much as their title question of "How do NN's learn?".

Here's an excerpt from the article:

"The researchers found that a formula used in statistical analysis provides a streamlined mathematical description of how neural networks, such as GPT-2, a precursor to ChatGPT, learn relevant patterns in data, known as features. This formula also explains how neural networks use these relevant patterns to make predictions."

The trite answer to "HOW do NN's learn?" is obviously gradient descent - error minimization, with the features being learnt being those that best support error minimization by the higher layers, effectively learning some basis set of features that can be composed into more complex higher level patterns.

The more interesting question perhaps is WHAT (not HOW) do NN's learn, and there doesn't seem to be any single answer to that - it depends on the network architecture. What a CNN learns is not the same as what an LLM such GPT-2 (which they claim to address) learns.

What an LLM learns is tied to the question of how does a trained LLM actually work, and this is very much a research question - the field of mechanistic interpretability (induction head circuits, and so forth). I guess you could combine this with the question of HOW does an LLM learn if you are looking for a higher level transformer-specific answer, and not just the generic error minimization answer: how does a transformer learn those circuits?

Other types of NN may be better understood, but anyone claiming to fully know how an LLM works is deluding themselves. Companies like Anthropic don't themselves fully know, and in fact have mechanistic interpretability as a potential roadblock to further scaling since they have committed to scaling safely, and want to understand the inner workings of the model in order both to control it and provide guarantees that a larger model has not learnt to do anything dangerous.

tarsinge• 2 years ago

In short we do know how NNs learn and work, but not what NNs learn. The corollary being we don't understand where do the emergent properties come from?

hnuser123456• 2 years ago

It's curve fitting at its core. It just so happens that when you fit a function with enough parameters, you can start using much more abstract and higher-level methods to more quickly describe other outcomes and applications of this curve fitting. Really simple algebra just with a lot of variables. It's not a black box at all and it's disingenuous when people call it that. It outputs what it does because it's multiplying A and B and adding C to the input you gave it.

jprete3• 2 years ago

That's not a useful description, it's the equivalent of explaining the entire software stack as a pile of logic gates.

ogogmad2• 2 years ago

This is a misunderstanding. You're right that you can always find some weights that approximate any reasonable (that is, continuous) mathematical function. The problem is, you have to find those weights in a small amount of computation time, and you need to estimate them from only finitely many samples. In general, ***no neural network architecture can solve this problem efficiently in every single case***. See "No Free Lunch theorem". The fact that current architectures work well in practice, despite the NFL theorem - for seemingly difficult problems - is surprising, and demands an explanation.

Appendix: By "current architecture", I mean Transformers plus Stochastic Gradient Descent.

wrsh07• 2 years ago

I think there's also an element of moving goalposts. Maybe we understand certain structures of a fully connected nn, but then we need to understand what's happening within a transformer.

They're going to continue to get more complex, and so we will always have more to understand.

I think what you're hoping for is some theory that once discovered will apply to all future NN architectures (and very likely help us find the "best" ones). Do you think that exists?

jprete3• 2 years ago

We don't understand how GenAI systems work, so we can't analytically predict their behavior; I think they're artifacts of synthetic biology, or chaos theory, not engineering or computer science. Giving GenAI goals and the ability to act outside of a sandbox is roughly parallel to releasing a colony of foreign predators in Australia, or creating an artificial pathogen that is so foreign the immune system doesn't have the tools to fight it.

That's why I consider understanding the internals of GenAI systems to be very important, independent of human psychology.

uoaei3• 2 years ago

AI is not and really never has been computer science -- if you trust the pedigree of statistical learning as the appropriate one for modern AI, computers don't enter the picture til you want to approximate a solution numerically to an otherwise well-posed analytical question.

mytailorisrich• 2 years ago

We know how neural networks work.

What's tricky is to understand the model a particular network has come up with during training so indeed how they "learn".

garyiskidding• 2 years ago

The 2013 Zeiler and Fergus paper also explains this based on activations during training of the network resulting in feature detection across layers.

Paper : https://arxiv.org/pdf/1311.2901.pdf

richrichie• 2 years ago

It is funny how they left out the first author of the paper :) Way too complicated name!

FrustratedMonky2• 2 years ago

From article

"But these networks remain a black box whose inner workings engineers and scientists struggle to understand."

"We are trying to understand neural networks from first principles,""

There is a large contingent of CS people in HN that think that since we built AI, and can examine the code, the models, the weights, that this means we understand it.

Hope this article helps explain the problem.

biophysboy• 2 years ago

Here’s a question I’ve been asking myself with the latest ML advancements: what is the difference between understanding and pretending to understand really, really well?

est• 2 years ago

my 2 cents:

understanding is getting know what it is.

understanding really well is getting know what it isn't.

A "stochastic parrot" can emulate a topic really well, until you push the limits and it fails at corner cases. If a model "understand really well" then it knows exactly where the boundaries are.

Solvency• 2 years ago

I don't understand.

s_dev3• 2 years ago

what is the difference between understanding and pretending to understand really, really well?

Predicting the outcome of an experiment. A person/thing who understands something, can predict outcomes to a degree. A person pretending to understand cannot predict with any degree of reliability.

jdthedisciple• 2 years ago

I don't think that is correct.

LLMs are literally predicting the outcome of an experiment really well constantly, yet they are best described as pretending to understand really, really well ...

willmadden• 2 years ago

Pretending to understand a subject is part of the process of learning a subject.

andoando2• 2 years ago

Not strictly speaking of ML, but you can pretend to understand by having a giant map of questions to answers, but unable to infer an answer to a new question.

jejeyyy77• 2 years ago

wth is pretending to understand?

tech_ken6• 2 years ago

High rate of success generalizing learnings to inputs which are well outside the training space.

mikewarot3• 2 years ago

Restating that: How can we train a Mapper AI instead of a Packer AI?

Once you've trained the model, it only has it's context window to work with for long term memory. Adding a memory prosthesis in the manner of MemGPT is likely to result in a superhuman level Packer.

It's the deep drive for consistency in a knowledge base that mappers possess that would result in the most powerful AGI.

canjobear• 2 years ago

Does it explain double descent?

bilsbie• 2 years ago

Am I wrong or is this a breakthrough?

cfgauss27189• 2 years ago

By minimizing a loss functional with respect to a bunch of numbers that amount to entries in matrices (or tensors, whatever) using an approximate hill climbing approach. I’m not sure what insights there are to be gained here, it doesn’t seem more exotic or interesting to me then asking “how does the pseudo inverse of A ‘learn’ to approximate the formula Ax=b?”. Maybe this seems reductive, but once you nail down what the loss functional is (often MSE loss for regression or diffusion models, cross entropy for classification, and many others) and perhaps the particulars of the model architecture (feed-forward vs recurrent, fully connected bits vs convolutions, encoder/decoders) then it’s unclear to me what is left for us to discover about how “learning” works beyond understanding old fundamental algorithms like Newton-Krylov for minimizing nonlinear functions (which subsumes basically all deep learning and goes well beyond). My gut tells me that the curious among you should spend more time learning about fundamentals of optimization than puzzling over some special (and probably non-existent) alchemy inherent in deep networks.

johndhi• 2 years ago

I don't understand many of most of these words (highest I got was college calculus) but this sounds interesting to me.

jpeterson• 2 years ago

It's all really just basic calculus, with a couple nifty tricks layered on top:

1) Create a bunch of variables and initialize them to random values. We're going to add and multiply these variables. The specific way that they're added and multiplied doesn't matter so much, though it turns out in practice that certain "architectures" of addition and multiplication patterns are better than others. But the key point is that it's just addition and multiplication.

2) Take some input, or a bunch of numbers that convey properties of some object, say a house (think square feet, number of bedrooms, number of bathrooms, etc) and add/multiply them into the set of variables we created in step 1. Once we plug and chug through all the additions and multiplications, we get a number. This is the output. At first this number will be random, because we initialized all our variables to random numbers. Measure how far the output is from the expected value corresponding to the given inputs (say, purchase price of the house). This is the error or "loss". In the case of purchase price, we can just subtract the predicted price from the expected price (and then square it, to make the calculus easier).

3) Now, since all we're doing is adding and multiplying, it's very straight-forward to set up a calculus problem that minimizes the error of the output with respect to our variables. The number of multiplication/addition steps doesn't even matter, since we have the chain rule. It turns out this is very powerful: it gives us a procedure to minimize the error of our system of variables (i.e. model), by iteratively "nudging" the variables according to how they affect the "error" of the output. The iterative nudging is what we call "learning". At the end of the procedure, rather than producing random outputs, the model will produce predictions of house prices that correlate with the distribution input square footage, bedrooms, bathrooms, etc. we saw in the training set.

In a sense, ML and AI are really just the next logical step of calculus once we have big data and computational capacity.

HarHarVeryFunny9• 2 years ago

Calculus is all you need! Neural nets are trained to minimize their errors (what they actually output vs what we want them to output). When we build a neural net we know the function corresponding to the output error, so training them (finding the minimum of the error function) is done just by following the gradient (derivative) of the error function.

HarHarVeryFunny9• 2 years ago

Sure, but their title seems poorly chosen and doesn't match what they are claiming in the article itself, which includes understanding how GPT-2 makes it's predictions.

How does GPT-2 learn, for example, that copying a word from way back in the context helps it to minimize the prediction error? How does it even manage to copy a word from the context to the output? We know that it is minimizing prediction errors, and learned to do so via gradient descent, but HOW is it doing it? (we've discovered a few answers, but it's still a research area)

cfgauss27189• 2 years ago

I haven’t read the manuscript yet, and am not sure that I will. However I don’t agree with the question. Gradient descent, the properties of the loss function are the “how”. It seems like you want to know how some properties of the data are manifested in the network itself during/after training (what these properties are doesn’t seem to be something that people know they are looking for). Maybe that’s what the authors are interested in as well. If I could bet money in Vegas on the answer to that question, my bet would be in most cases that structures we may probe in the network and see in them correlations to aspects of the problem or task that we (as humans) can recognize, well very likely this will boil down to approximations of fundamental and eminently useful quantities like, say, approximate singular value decompositions of regions in the data manifold, or approximate eigenfunctions etc. I could see how these kind of empirical investigations are interesting, but what would their impact be? Another guess, that these investigations may lead to insights that help engineers design better architectures or incrementally improve training methods. But I think that’s about it - this type of research strikes me as engineering and application.

HPsquared• 2 years ago

LLMs really get those mirror neurons firing and people tend to anthropomorphize them a bit too much.

cfgauss27189• 2 years ago

Indeed, hopefully they can be diverted from interest in LLMs towards actual science, like the neuroscience which revealed the existence of said mirror neurons.

andoando2• 2 years ago

Im with you. My only understanding of ML is a class in 2016 where we implemented basic ML algos and not neutral nets, gpts or whatever but I always assumed its no radically different.

Take a bunch of features or make up a billion features, find a function to that best predicts the greatest number of outputs correctly. Any "emergent" behavior I imagine is just a result of finding new features or sets of features.

cfgauss27189• 2 years ago

I agree with your interpretation. There is something there to be learned for sure, but I’m doubtful whatever that thing is will be a breakthrough in machine learning or optimization, nor that it will come by applying the tools of analysis. The idea of “emergence” is interesting although vague and bordering on unscientific. Maybe complexity theory, graph theory, and information theory might provide some insights. But in the end, I would guess those insights impact will be limited to tricks that can be used to engineer marginally better architectures or marginally faster training methods.

amelius• 2 years ago

You are missing one important point.

Your network can learn some dataset very well. However, that doesn't say anything about how well it generalizes, and thus how useful your network is.

cfgauss27189• 2 years ago

Your point is a salient one. It would be useful if we could provide guarantees/bounds on generalization, or representation power, or understand how brittle a model is to shifts in the data distributions. Are these questions of the kind that are answered in part by the authors? I haven’t read the manuscript, but the title doesn’t indicate this is the aim of the research, but it indicates an eye to something much broader and vague (“learning”).

6gvONxR4sf7o• 2 years ago

it doesn’t seem more exotic or interesting to me then asking “how does the pseudo inverse of A ‘learn’ to approximate the formula Ax=b?

Asking things like properties of the pseudoinverse against a dataset on some distribution (or even properties of simple regression) is interesting and useful. If we could understand neural networks as well as we understand linear regression, it would be a massive breakthrough, not a boring "it's just minimizing a loss function" statement.

Hell even if you just ask about minimizing things, you get a whole theory of M estimators [0]. This kind of dismissive comment doesn't add anything.

[0] https://en.wikipedia.org/wiki/M-estimator

cfgauss27189• 2 years ago

You raise a fair point, I do think that it’s important to understand how the properties of the data manifest in the least-squares solution to Ax=b. Without that, the only insights we have are from analysis, while we would be remiss to overlook the more fundamental theory, which is linear algebra. However, my suspicion is that the answer to these same questions but applied to nonlinear function approximators is probably not much different from the insights we have already gained in more basic systems. However, the overly broad title of the manuscript doesn’t seem to point toward those kinds of questions (specifically, things like “how do properties of the data manifold manifest in the weight tensors”) and I’m not sure that one should equate those things to “learning”.

xanderlewis2• 2 years ago

By minimizing a loss functional with respect to a bunch of numbers that amount to entries in matrices (or tensors, whatever) using an approximate hill climbing approach.

Are the rules of chess all there is to it? Is there really no more to be said?

calf• 2 years ago

Well, if neural nets are nothing more than their optimization problem then why isn't there a mathematical proof of this already?

And why isn't that reductionism? We don't say human learning is merely the product of millions of years of random evolution, and leave it at that. So if we take a position on reductionist account of learning, then how do we prove it or disprove it?

Are there arguments that don't rest on our gut feelings? Otherwise this is just different experts factions arguing that "neural nets are/aren't superautocomplete / stochastic parrots" but with more technobabble.

IanCal• 2 years ago

This is overly reductive. Understanding what they're doing at a higher level is useful. If you knew enough about neuron activations and how they change with stimulus that wouldn't be enough for a human to develop a syllabus for teaching maths even if they "understand how people learn".

What you describe also doesn't answer the question of how to structure and train a model, which surely is quite important. How do the choices impact real world problems?

cs7022• 2 years ago

Interesting: Given an input x to a layer f(x)=Wσ(x), where σ is an activation function and W is a weight matrix, the authors define the layer's "neural feature matrix" (NFM) as WᵀW, and show that throughout training, it remains proportional to the average outer product of the layer's gradients, i.e., WᵀW ∝ mean(∇f(x)∇f(x)ᵀ), with the mean computed over all samples in the training data. The authors posit that layers learn to up-weight features strongly related to model output via the NFM.

The authors do interesting things with the NFM, including explaining why pruning should even be possible and why we see grokking during learning. They also train a kernel machine iteratively, at each step alternating between (1) fitting the model's kernel matrix to the data and (2) computing the average gradient outer product of the model and replacing the kernel matrix with it. The motivation is to induce the kernel machine to "learn to identify features." The approach seems to work well. The authors' kernel machine outperforms all previous approaches on a common tabular data benchmark.

cfgauss27189• 2 years ago

This NFM is a curious quantity . It has the flavor of a metric on the space of inputs to that layer. However, the fact that W’W remains proportional to DfDf’ seems to be an obvious consequence of the very form of f… since Df is itself Ds’WW’Ds, then this should be expected under some assumptions (perhaps mild) on the statistics of Ds, no?

cs7022• 2 years ago

Yes, that sounds right, but it doesn't make the work less worthwhile or less interesting.

The authors do interesting things with the NFM, including explaining why pruning should even be possible and why we see grokking during learning. They also train a kernel machine iteratively, at each step alternating between (1) fitting the model's kernel matrix to the data and (2) computing the average gradient outer product of the model and replacing the kernel matrix with it. The motivation is to induce the kernel machine to "learn to identify features." The approach seems to work well, outperforming all previous approaches on tabular data.

PS. I've updated my comment to add these additional points.

tech_ken6• 2 years ago

It has more than just the flavor of a metric, it’s exactly a metric because any “square” matrix (M’M) is positive definite (since x’M’Mx=y’y=<y,y>, where y=Mx). It could be interpreted as a metric which only cares about distances along dimensions that the NN cares about.

I agree that the proportionality seems a little obvious, I think what’s most interesting is what they do with the quantity, but I’m surprised no one else has tried this.

swalsh• 2 years ago

I've been trying to figure out how LLMs learn logic/reasoning. It's just not intuitive to me how that works.

mikewarot3• 2 years ago

It's the same way we do it, form a number of possible variants and use the ones that work best.

They have the advantage of millions or even billions of times more compute to throw at the learning process. Something that might be a one in a million insight happens consistently at that scale.

tech_ken6• 2 years ago

Full pub is up on arXiv here: https://arxiv.org/pdf/2212.13881.pdf

My 2c: The phys.org summary isn't great. The authors are focused on a much narrower topic than simply "how NNs learn", they're trying to characterize the mechanism by which deep NNs develop 'features'. They identify a quantity which is definable for each layer of the NN (outer product of the input weight matrix), and posit that this quantity is proportional to the average derivative of the layer with respect to its inputs, where the average is taken over all training data. They (claim to, I haven't evaluated) prove this formally for the case of deep FNNs trained on gradient descent. They argue that, by treating this quantity as a measure of 'feature importance', it can be used to explain certain behaviors of NNs that are otherwise difficult to understand. Specifically they address:

* Simple and spurious features (they argue that their proposal can identify when this has occurred)

* "Lottery ticket" NNs (they argue that their proposal can help explain why pruning the connections of a fully connected NN improves its performance)

* Grokking (they argue that their proposal can help explain why NNs can exhibit sudden performance improvements, even after training performance is 100%)

Finally they propose a heuristic ML algorithm which updates their proposal directly during training, rather than the underlying weights, and shows that this achieves superior performance to some existing alternatives.

Overall I would say that they have defined a nice tool for measuring NN feature importance, in terms of features that the NN itself is defining (not in terms of the original space). I can definitely see why this has a lot of value, and I'm especially intrigued by their comparisons of the NFM to testing performance in their 'grokking' case study.

With that said, I'm not really active in the NN space, so it seems a little surprising that their result is really that novel. The quantity they define (outer product of the weight matrix) seems fairly intuitive as a way to rank the importance of inputs at any given layer of the NN, so I'm wondering if truly nobody else has ever done this before? Possibly the novelty is in their derivation of the proportionality, or in the analysis of this quantity over training iterations. I'd guess that their model proposal is totally new, and I'm curious to try it out on some test cases, it seems promising for cases where light-weight models are required. It also seems interesting to point out how both training performance AND the development of feature importance both jointly influence testing accuracy, but again I'm surprised that this is really novel. I also have to wonder how this extends to more complicated architectures with, eg. recursive elements; it's not discussed anywhere, but seems like it would be an important extension of this framework given where genAI is currently at (although first draft was pub'd in '22 so it's possible that this just wasn't as pressing when it was being written).

mikewarot3• 2 years ago

Learning how deep networks learn features isn't obvious, and teasing out the details is valuable research.

Superhuman levels of feature recognition are at play during the training of LLMs, and those insights are compiled into the resulting weights in ways we have little visibility into.

How do neural networks learn?

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