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There Will Be a Scientific Theory of Deep Learning

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Re: There Will Be a Scientific Theory of Deep Learning

#91

Post by 18al »

hodgehog11 wrote: post #45
Animats wrote: post #42

This is encouraging. The title is a bit much. "Potential points of attack for understanding what deep learning is really doing" would be more accurate but less attention-grabbing. It might lead to understanding how to measure when a deep learning system is making stuff up or hallucinating. That would have a huge payoff. Until we get that, deep learning systems are limited to tasks where the consequences of outputting…

> measure when a deep learning system is making stuff up or hallucinating That's a great problem to solve! (Maybe biased, because this is my primary research direction). One popular approach is OOD detection, but this always seemed ill-posed to me. My colleagues and I have been approaching this from a more fundamental direction using measures of model misspecification, but this is admittedly niche because it is very…

Could you elaborate on what you mean by OOD detection seeming ill-posed?

Re: There Will Be a Scientific Theory of Deep Learning

#92

Post by leoc »

anvuong wrote: post #80
hodgehog11 wrote: post #72

Earlier quoted context omitted.

It wouldn't work if your landscape has more local minima than atoms in the known universe (which it does) and only some of them are good. Neural networks can easily fail, but there's a lot of things one can do to help ensure it works.

A funny thing is, in very high-dimensional space, like millions and billions of parameters, the chance that you'd get stuck in a local minima is extremely small. Think about it like this, to be stuck in a local minima in 2D, you only need 2 gradient components to be zero, in higher dimension, you'd need every single one of them, millions up millions of them, to be all zero. You'd only need 1 single gradient component…

(‘Minimum’ is the singular of ‘minima’.)

Re: There Will Be a Scientific Theory of Deep Learning

#93

Post by hodgehog11 »

anvuong wrote: post #80
hodgehog11 wrote: post #72

Earlier quoted context omitted.

It wouldn't work if your landscape has more local minima than atoms in the known universe (which it does) and only some of them are good. Neural networks can easily fail, but there's a lot of things one can do to help ensure it works.

A funny thing is, in very high-dimensional space, like millions and billions of parameters, the chance that you'd get stuck in a local minima is extremely small. Think about it like this, to be stuck in a local minima in 2D, you only need 2 gradient components to be zero, in higher dimension, you'd need every single one of them, millions up millions of them, to be all zero. You'd only need 1 single gradient component…

You are essentially correct, which is why stochastic gradient optimizers induce a low-sharpness bias. However, there is an awful lot more that complicates things. There are plenty of wide minima that it can get stuck in far away from where people typically initialise, so the initialisation scheme proves extremely important (but is mostly done for you).

Perhaps more important, just because it is easy to escape any local minimum does not mean that there is necessarily a trend towards a really good optimum, as it can just bounce between a bunch of really bad ones for a long time. This actually happens almost all the time if you try to design your entire architecture from scratch, e.g. highly connected networks. People who are new to the field sometimes don't seem to understand why SGD doesn't just always fix everything; this is why. You need very strong inductive biases in your architecture design to ensure that the loss (which is data-dependent so you cannot ascertain this property a priori) exhibits a global bowl-like shape (we often call this a 'funnel') to provide a general trajectory for the optimizer toward good solutions. Sometimes this only works for some optimizers and not others.

This is why architecture design is something of an art form, and explaining "why neural networks work so well" is a complex question involving a ton of parts, all of which contribute in meaningful ways. There are often plenty of counterexamples to any simpler explanation.

Re: There Will Be a Scientific Theory of Deep Learning

#95

Post by seanhunter »

mystraline wrote: post #43
pash wrote: post #14

Earlier quoted context omitted.

The inflection point was 2012, when AlexNet [0], a deep convolutional neural net, achieved a step-change improvement in the ImageNet classification competition. After seeing AlexNet’s results, all of the major ML imaging labs switched to deep CNNs, and other approaches almost completely disappeared from SOTA imaging competitions. Over the next few years, deep neural networks took over in other ML domains as well. The…

Ive yet to see a model that trains AND applies the trained data real-time. Thats basically every living being, from bacteria to plants to mammals. Even PID loops have a training phase separate from recitation phase.

That’s not a meaningful technical obstacle. If you wanted to, you could just take the output of the model and use it at each iteration of the training phase to perform (badly) whatever task the model is intended to do.

The reason noone does this is you don’t have to and you’ll get much better results if you first fully train and then apply the best model you have to whatever problem. Biological systems don’t have that luxury.

Re: There Will Be a Scientific Theory of Deep Learning

#96

Post by ngruhn »

NooneAtAll3 wrote: post #85
jmalicki wrote: post #66

Earlier quoted context omitted.

The properties that the uniform approximation theorem proves are not unique to neural networks. Any models using an infinite dimensional Hilbert space, such as SVMs with RBF or polynomial kernels, Gaussian process regression, gradient boosted decision trees, etc. have the same property (though proven via a different theorem of course). So the universal approximation theorem tells us nothing about why should expect ne…

Universal approximation is like saying that a problem is computable sure, that gives some relief - but it says nothing in practice unlike f.e. which side of P/NP divide the problem is on

> unlike f.e. which side of P/NP divide the problem is on

Actually the P/NP divide is a similar case in my opinion. In practice a quadratic algorithm is sometimes unacceptably slow and an NP problem can be virtually solved. E.g. SAT problems are routinely solved at scale.

Re: There Will Be a Scientific Theory of Deep Learning

#97

Post by hodgehog11 »

skydhash wrote: post #68
hodgehog11 wrote: post #65

Earlier quoted context omitted.

No it isn't, and it's frustrating when the "common wisdom" tries to boil it down to this. If this was true, then the models with "infinitely many" parameters would be amazing. What about just training a gigantic two-layer network? There is a huge amount of work trying to engineer training procedures that work well. The actual reason is due to complex biases that arise from the interaction of network architectures and…

> The actual reason is due to complex biases that arise from the interaction of network architectures and the optimizers and persist in the regime where data scales proportionally to model size. The multiscale nature of the data induces neural scaling laws that enable better performance than any other class of models can hope to achieve. That’s a lot of words to say that, if you encode a class of things as numbers, t…

No, it is relatively few words to quickly touch on several different concepts that go well beyond basic approximation theory.

I can construct a Gaussian process model (essentially fancy linear regression) that will fit _all_ of my medical image data _exactly_, but it will perform like absolute rubbish for determining tumor presence compared to if I trained a convolutional neural network on the same data and problem _and_ perfectly fit the data.

I could even train a fully connected network on the same data and problem, get any degree of fit you like, and it would still be rubbish.

Re: There Will Be a Scientific Theory of Deep Learning

#98

Post by hodgehog11 »

niksmather wrote: post #84
hodgehog11 wrote: post #39

As someone who works in the area, this provides a decent summary of the most popular research items. The most useful and impressive part is the set of open problems at the end, which just about covers all of the main research directions in the field. The skepticism I'm seeing in the comments really highlights how little of this work is trickling down to the public, which is very sad to see. While it can offer few mat…

Do neural networks work better than other models? They can definitely model a wider class of problems than traditional ML models (images being the canonical example). However, I thought where a like for like comparison was possible they tend to worse than gradient boosting.

Gradient boosting handles tabular data better than neural networks, often because the structure is simpler, and it becomes more of an issue to deal with the noise. You can do like-to-like comparisons between them for unstructured data like images, audio, video, text, and a well-designed NN will mop the floor with gradient boosting. This is because to handle that sort of data, you need to encode some form of bias around expected convolutional patterns in the data, or you won't get anywhere. Both CNNs and transformers do this.

Re: There Will Be a Scientific Theory of Deep Learning

#99

Post by r0ze-at-hn »

hodgehog11 wrote: post #39

As someone who works in the area, this provides a decent summary of the most popular research items. The most useful and impressive part is the set of open problems at the end, which just about covers all of the main research directions in the field. The skepticism I'm seeing in the comments really highlights how little of this work is trickling down to the public, which is very sad to see. While it can offer few mat…

We’re in a strange era where the Information-Theoretic foundations of deep learning are solidifying. The 'Why' is largely solved: it’s the efficient minimization of irreversible information loss relative to the noise floor. There is so much waste scaling models bigger and bigger when the math points to how to do it much more efficiently. One can take a great 70B model and have it run in only ~16GB with no loss in capability and the ability to keep training, but the last few years funding only went for "bigger".

As you noted, the industry has moved the goalposts to Agency and Long-horizon Persistence. The transition from building 'calculators that predict' to 'systems that endure' is a non-equilibrium thermodynamics problem. There is math/formulas and basic laws at play here that apply to AI just as much as it applies to other systems. Ironically it is the same math. The same thing that results in a signal persisting in a model will result in agents persisting.

This is my specific niche. I study how things persist. It’s honestly a bit painful watching the AI field struggle to re-learn first principles that other disciplines have already learned. I have a doc I use to help teach folks how the math works and how to apply it to their domain and it is fun giving it folks who then stop guessing and know exactly how to improve the persistence of what they are working on. Like the idea of "How many hours we can have a model work" is so cute compared to the right questions.

Re: There Will Be a Scientific Theory of Deep Learning

#100

Post by geokon »

mathisfun123 wrote: post #59
hodgehog11 wrote: post #39

As someone who works in the area, this provides a decent summary of the most popular research items. The most useful and impressive part is the set of open problems at the end, which just about covers all of the main research directions in the field. The skepticism I'm seeing in the comments really highlights how little of this work is trickling down to the public, which is very sad to see. While it can offer few mat…

> why do neural networks work better than other models The only people for whom this is an open question are the academics - everyone else understands it's entirely because of the bagillions of parameters.

normally more parameters leads to overfitting (like fitting a polynomial to points), but neural nets are for some reason not as susceptible to that and can scale well with more parameters.

Thats been my understanding of the crux of mystery.

Would love to be corrected by someone more knowledgable though

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