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Why deep learning works even though it shouldn’t

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Re: Why deep learning works even though it shouldn’t

#131
post #79

Earlier quoted context omitted.

Personally I've wanted a 1-page IEEE publication for a while that accepts smaller contributions, where people can share these kinds of insights. Just a "we tried this, this is what happened" or "we were not able to repeat this" or "we found this interesting, but we need more data". You could argue it's kind of like a long abstract, but a long abstract really indicates you intend to probe it further, but in actual fac…

I'm not sure that would be a net benefit over research blogs or something like a technical report directly published by a lab/working group to be quite honest. In a few domains I've recently looked at these notes to the editor / commentary sections seem to only be pseudo-reviewed and I'd say the likelihood of an IEEE rubberstamped one pager on perpetual motion would be non-zero.

> I'm not sure that would be a net benefit over research

> blogs or something like a technical report directly

> published by a lab/working group to be quite honest.

I think this is kind of the problem, half of this stuff sits on a webpage somewhere completely unread and not really reference-able.

> I'd say the likelihood of an IEEE rubberstamped one pager

> on perpetual motion would be non-zero.

I would hope that each single page would be reviewed with the same integrity as a six pager. Of course, it's not impossible crap leaks through to any conference/journal.

Re: Why deep learning works even though it shouldn’t

#132

But it doesn't. Researchers have been saying for several years now that computer vision is more accurate than human vision, and face recognition was one of the first problems "solved." And yet when the pandemic hit, Apple had to scramble to adjust its unlock mechanism in iOS 13.5 because Face ID cannot recognize people wearing masks [1]. Humans have no trouble identifying people wearing masks. We are now almost a yea…

Intuitively, it seems like voice signatures, body language (like walking habits), and height/weight would play a larger role in helping humans identify a masked person than exposed facial features. Because the network behind Apple's facial recognition software cannot have access to this kind of data (well, maybe voice, but that doesn't seem secure), I'm not sure this is a fair comparison. Would love to be refuted, ho…

I don't know that I'm looking to refute you per se but...

A better example than face masks maybe is the recent controversy over Twitter's AI and Obama images (https://www.theverge.com/2020/9/20/21447998/twitter-photo-pr...).

A lot was made of racial issues, which is fine, but the broader issue is why subtle changes in photos, like cropping, should confuse things so completely.

The target piece (the focus of this HN thread) sums itself up this way:

"There’s a good set of params somewhere nearby. When we start walking to it, we can’t ever get stuck along the way, because there are no local optima. Once we’ve stumbled upon a good set of parameters, we’ll know it and we can just stop."

I think there's some useful insights there, but this is in many ways the definition of local optima. What I might argue is that because there's so many locations in high-dimensional space that will satisfy some classification goal, it's "easy" to find one that works with regard to some population that defines the model development space (training + test). However, that model development space/population is itself implicitly defined by a certain set of constraints -- it's a subpopulation of some broader population. What you want to generalize to to define overfitting is broader. You can still not overfit to your model development space, but be overfitting with regard to some broader set of possible inputs.

Whether or not the constraints of the model development population/space are important and reasonable considerations -- e.g., in your argument, not having access to things like body language etc -- is maybe a little variable. In some cases the implicit defining characteristics of the model development population are meaningful, but in other cases they're hidden.

In Twitter's case, you end up finding out later that there's weird things that probably defined the space of their images that they didn't intend. It's only in the adversarial case that you learn about this.

In classical statistics, you talk about generalization and overfitting, but there's an implicit population you're sampling from that defines both of those things. That is, you have a training/fitting/initial sample, and you ask yourself how well your model would perform on a test/validation sample. But implicit in that is some assumption about what it means to be a random sample from the same population.

I think lots of times with DL, the cross-validation/test sample is also implicitly defined as coming from some population. But the population isn't some model, it's some source. Some image dataset, something like that. There will be things about that source that are "of interest", but other things that are idiosyncratic about it, and unrepresentative of the "real" population of interest. In this way, I'm not sure that held-out samples from some source are really the right way to think of generalization and overfitting -- I think the adversarial setting is the generalization setting.

https://www.sciencemag.org/news/2020/05/eye-catching-advance...

Along the way from the classical to the DL regime I think there have been some overlooked issues about what it means to generalize, what you're really sampling from, and what your "population" actually is. It parallels tensions about theory versus experimentation because having a population in the classical case that you're sampling from requires a certain data-generating theory, which is often lacking in DL. The closest thing in the classical regime to DL generalization theory is maybe a sort of ultra-high-dimensional bootstrapping with random effects: showing that your bootstrap samples are close to your observed sample isn't the same thing as showing they're close to the population, or to other samples drawn from that population, especially in the presence of random effects.

Re: Why deep learning works even though it shouldn’t

#133

But it doesn't. Researchers have been saying for several years now that computer vision is more accurate than human vision, and face recognition was one of the first problems "solved." And yet when the pandemic hit, Apple had to scramble to adjust its unlock mechanism in iOS 13.5 because Face ID cannot recognize people wearing masks [1]. Humans have no trouble identifying people wearing masks. We are now almost a yea…

Intuitively, it seems like voice signatures, body language (like walking habits), and height/weight would play a larger role in helping humans identify a masked person than exposed facial features. Because the network behind Apple's facial recognition software cannot have access to this kind of data (well, maybe voice, but that doesn't seem secure), I'm not sure this is a fair comparison. Would love to be refuted, ho…

Even when just going by face/head, my personal anecdotal data runs counter to what GP wrote.

I've been growing my hair since shortly before the pandemic hit (from a few mm buzzcut which I had for years previously), and combining that with a mask, I'm apparently unrecognizable. I've run into people in the street that would recognize me in a heartbeat otherwise, but with the additional change of hair, people only recognize me when I pull my mask down. So humans aren't that amazing at recognition either.

Re: Why deep learning works even though it shouldn’t

#134
post #79

Earlier quoted context omitted.

It seems toxic to me that there's no accepted public venue for that stuff, though. The fact that people are too afraid to relay certain useful information until they're tipsy; the emphasis on "doing impression management". Maybe it should remain separate from the rigorous stuff, but where's the "Op-Ed section" of academic publishing?

Personally I've wanted a 1-page IEEE publication for a while that accepts smaller contributions, where people can share these kinds of insights. Just a "we tried this, this is what happened" or "we were not able to repeat this" or "we found this interesting, but we need more data". You could argue it's kind of like a long abstract, but a long abstract really indicates you intend to probe it further, but in actual fac…

When I worked in crypto 20 years ago there was a journal like this which took papers that were only a few paragraphs long for quick results. I think it was called Electronics Letters.

Re: Why deep learning works even though it shouldn’t

#135

Setting aside the primary subject, this is an excellent observation: > What I find however is that there are a base of unspoken intuitions that underlie expert understanding of a field, that are never directly stated in the literature, because they can’t be easily proved with the rigor that the literature demands. And as a result, the insights exist only in conversation and subtext, which make them inaccessible to th…

This is NOT TRUE that it's NOT SHARED, especially in learning. Just browse quora on any deep learning realted fields, it's a bunch of guys shareing their (more or less relevant and exact) hunch. Also most ML vulgarisation articles focus on that too.

Not sure it's true for the other fields tho.

Re: Why deep learning works even though it shouldn’t

#136
post #100

There is another reason why training deep neural networks is not as difficult as it sounds: the landscape of the loss function seems to be made of broad "U"-shaped valleys that gently descend towards a small loss region. At initialization, the network is likely close to such valley, and once it gets there the rest of training is just a leisurely stroll. Formally, people have studied the spectrum of the Hessian and fo…

If anything for large models I thought the idea is everything is a saddle point. Your link looks at a relatively small dense network.

As dimensionality increases the likelihood of a local minima decreases because there is almost always a dimension where the curvature is in the other direction.

Re: Why deep learning works even though it shouldn’t

#137

Earlier quoted context omitted.

No, it's not constrained at all. In fact, even single hidden layer networks with nearly arbitrary activation functions are universal approximators (Hornik et al. 1989). Polynomials are also universal approximators (Weierstrass).

I'm not trying to say that neural networks are inherently constrained. I'm saying that, in typical usage, they tend to be used a certain way that I believe introduces some useful constraints. You can use a single hidden layer and an arbitrary activation functions, but, in practice, it's a heck of a lot more common to use multiple hidden layers and tanh. It's worth noting that neural networks didn't take off with Horn…

This kind of stuff is called inductive bias and is a sexy topic nowadays.

Re: Why deep learning works even though it shouldn’t

#138

Earlier quoted context omitted.

> but I don't get the "no minimal at all" argument. That's just wrong, no need to think about it. Only unbounded loss functions don't have minima, but using such a loss function would not make sense.

This isn't true. A loss function that asymptotes can also have no minima, which commonly used loss functions do.

Doesn't the fact the network is discrete (floats have a maximum precision) mean this isn't actually the case? There's a finite number of states the net can be in, and one (or more) is best.

Re: Why deep learning works even though it shouldn’t

#139

Earlier quoted context omitted.

That's true. I left out saying that deeper networks represent a wider variety of functions more easily, because that seems generally intuitive to everyone. But the arguments about how easy it is to optimize them should apply equally well to wide and shallow networks as to very deep ones.

Thanks for the response. Hmm, it's still pretty mysterious to me. Why should a deep network with the same number of parameters as a wide network represent a wider variety of functions? In some sense they represent the "same" number of functions, in the sense that the manifold of functions given by two network architectures with the same number of parameters have have the same dimension, even if one is wide while the…

I think a deeper network has less degrees of freedom in which to move, or rather, in which to move usefully, because parameters are more interdependent. That means in order to generate a useful function, it has to learn more abstract features than a shallow and wide network. This is because any adjustment to irrelevant features that are unique to a small number of examples has a larger negative impact on the rest of the data than it would in a shallower net (except in the latter layers). Over time, abstract changes are stochastically rewarded and specific changes are penalised, at least for the earlier layers, and the latter layers then have to work with this more abstract information so they simply can't overfit that much.

Would be interested in OP's take on this though.

Re: Why deep learning works even though it shouldn’t

#140

But it doesn't. Researchers have been saying for several years now that computer vision is more accurate than human vision, and face recognition was one of the first problems "solved." And yet when the pandemic hit, Apple had to scramble to adjust its unlock mechanism in iOS 13.5 because Face ID cannot recognize people wearing masks [1]. Humans have no trouble identifying people wearing masks. We are now almost a yea…

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