I disagree re: the 1000s of titans thing. Google, Baidu, etc are building large GPU clusters and have basically shown "similar resources = similar results", but everyone else is mostly using single machine--maybe multi-GPU--and doing fine. A single Titan X is a BEAST for deep learning--nobody is using 1000s and you only need 1 for great results on most datasets I've seen.
On the subject of Schmidhuber, I saw him speak once and he spent half the talk explaining how he invented everything he's talking about (EVERYTHING!) and the other half talking about how no one gives him credit. I'm half joking, but I think there's more to his story. Or it's a miscarriage of justice.
ReLUs fit combinations of piece-wise linear functions. Whereas sigmoids are more nonlinear and can be harder to optimize. They were originally continuous approximations of binary threshold functions.
All these things can approximate each other. Neurons can approximate the max function, and ReLUs can approximate sigmoids. So there really isn't much to fret over.
It's like asking for a theory of which programming language is better. In practice they will have different advantages in different domains, but they are all Turing complete.
There's nothing wrong with just ignoring programming-language theory and just deciding on one, seat of the pants style. But this is because programming as it exists now is a static "art form" with only marginal progress expected.
However, assuming deep learning currently works unexplainably well and one aims to scientifically explain that good working, one would want an explanation which guides one's approach to extending the process.
I've done a bit of applied math, where knowing which kind of function to pull out of one's toolbox for which situation was the really-smart-people's purview, a fairly well guarded folk-knowledge, actually. I'm used to the "little bit of this, little bit of that" kind of explanation for which functions to use when and why. If one weighs them long enough, I assume one can intuitively figure out what to do.
But if we're aiming to advance fundamentally beyond the state-of-the-art, we would aim to quantify these advantages and disadvantages, to automate one more layer. So here we really should know and have a "real" theory here.
From Geoff Hinton's AMA on Reddit: The pooling operation used in convolutional neural networks is a big mistake and the fact that it works so well is a disaster.
The basic effect of this is to decrease the resolution, so it's more tractable to operate on. Without pooling you are stuck with a huge resolution at each layer.
Is that not essentially the process of evolution through natural selection? One giant optimisation problem?
For example: you don't need to show a baby a 1000 photos of mugs before it can tell what's a mug and what isn't. Just show it 1 example of a mug a couple of times, and from then on it's able to identify mugs and mug-like objects pretty reliably.
I beg to differ. Newborn babies can hardly do anything. Their brains are undergoing "parallel training and tuning" 24/7 starting even before they are born. Babies train themselves on thousands of hours of visual stimuli to gain the 3D object recognition capabilities to reliably identify objects such as mugs.
I don't think your examples are good though, Max polling reduces noise. RuLU learn faster than Sigmoid or tanh.
That's not theory, that's just observation of the results. Why should we expect it to work that way?
Well that's what makes it research then. It's a new field, and obviously there needs to be more science and creative thinking involved into drawing theories about deep learning. The field seems already pretty hard for beginners, so of course there will be less scientists involved into making theories.
I'm no biologist, but I don't think our brains are going around trying to do a grid search for the best hyperparameters. Most DL results today are the result of throwing 1000s of Titans on the problem and then sitting back for a week for the beast to cough up a solution.
Tangential nitpick: one (very minor) nit I have with Prof LeCun's presentations is that I don't see him give more credit to Hinton and Schmidhuber. Hinton is mentioned a couple of times (3), but Schmidhuber is totally ignored; for example, when he mentions LSTM, it's cited as [Hochreiter 1997], even though it was a join publication with Schmidhuber. It should be cited as [Hochreiter et 1997], as he does in the very next line.