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DeepMath Conference 2020 – Conference on the Mathematical Theory of DNN's
- a-nikolaev 6y ago"Deep" is such a good prefix for all sorts of Deep Learning, Deep Math, Deep Thinking, Deep Engineering etc. Wonder if the networks were originally called Thick neural networks, would the ML/AI revolution as we know it still happened?
- WanderPanda 6y agoIf thick neural networks would indeed exist they would probably be a special case of something Schmidhuber invented 30 years ago.
- webmaven 6y ago> If thick neural networks would indeed exist they would probably be a special case of something Schmidhuber invented 30 years ago. Heh. A burn both pointed and subtle. A+.
- subtypefiddler 6y agoWhilst I agree with the general sentiment, in this particular instance it has to do with the depth of network that could be trained efficiently thanks to hardware advances. LeNet was 7 layers deep, Dan's 9, VGG's 13, GoogleNet's 22, etc. There is theory w.r.t to thick networks as well (e.g the link to Gaussian processes require infinite width). Deep makes sense here.
- The_rationalist 6y agoWell except that most neural network are not deep, they have a very low number of layers but each layer can be tremendously wide. This should have been called wide learning. But we could imagine some learning algorithm that exploit more depth than wideness. A more correct naming would take into account both dimensions: depth and wideness. Note that this is hortogonal to sparsedness vs density
- subtypefiddler 6y agoIt's also important to note that they work despite being wide, you can see that with the efficiency of pruning, and ideas such as the lottery ticket hypothesis that state that "successful" sub-networks within the wide network account for most of the performance. In the theory literature, if you have a K-deep network, K=1 is the shallow case, K>1 is deep. Agreed naming could be better, but it's not like "deep work" or "deep thoughts" as the parent was stating.
- sdenton4 6y agoI dunno, in the resnet age, many and perhaps most networks are 20+ layers. I feel like the shallowest networks I see these days are RNNs being used for fast on device ML, which trends not to be terribly wide due to the same hardware constraints.
- canjobear 6y agoAround the time the phrase "deep learning" came into vogue, the advances were indeed in training deeper networks, not wider. Later on it turned out that shallow wide networks are sufficient for many problems. (Also, it turned out the pre-training tricks that people came up with for training deep networks weren't really necessary either.)
- laleopue 6y agoThe adjective "deep" came from deep belief networks, which are a variation on restricted boltzmann machines. RBNs have one visible and one hidden layers, DNBs have more hidden layers - hence "deep". So it's not exactly based on a distinction between "deep" and "shallow" models.
- antognini 6y agoThe depth seems to matter more than the width, at least as long as the layers are sufficiently wide. In fact, in the limit that the layer becomes infinitely wide, you just end up with a Gaussian process. In practice a width of ~100--1000 is sufficient to get behavior that is pretty close to a Gaussian process, so in general doubling the width of a layer doesn't gain you all that much compared to using those parameters for an extra layer. The real representational power seems to come from increasing depth.
- thecleaner 6y ago> ....Thick neural networks, would the ML/AI revolution as we know it still happened? Cancel culture will ensure that the conference doesnt happen in the name of fat shaming.
- cool_dude85 6y agoFinger on the pulse, my man - people HATE being called thick these days.
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- naringas 6y agoit's the the new e-
- TrackerFF 6y agoOf all the nouns available (deep, dense, thick, big, condensed, etc.), "deep" is def. the on that brings most hype - makes it sound very advanced, and more marketable. Deep Learning with Big Data That stuff sells itself.
- AnHonestComment 6y agoBruh, it’s all about “multi-mode learning with hyper-scale data”, you’re like five years late. The lingo treadmill is brutal.
- aborsy 6y agoAs soon as I saw the word Deep I stopped continuing. Nnets have always been multi layer since they were invented. That’s the whole idea of progressive feature extraction, and the analogy with biological brain. Theoreticians referred to them properly as nnets or multilayer nnets. Later experimentalists simulated them, thanks to the availability of the computing resources, and experimentally verified that a multi layer nnet can be more efficient than a single layer one. They added superficial terms “deep” and “AI,” “singularity,” etc., which the media and tech industry amplified for obvious reasons.
- notsuoh 6y agoForgive me, but that seems like an excessively pedantic outright dismissal of what I am seeing to be the presentation of interesting results in the field. Whatever you want to call it—deep learning, multilayer nnets, whatever—it’s the same thing and results are exciting. Also, I believe that there is a difference between deep learning and multilayer nnets (though I can't quite articulate it), but throwing in things like “singularity” is a bit much as it’s not really related at all to the math results being presented.
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- Der_Einzige 6y agoWhile in practice this is true, a lot of work is being done to try to figure out how to make shallow neural networks train as fast as deep ones. We know by the UAT that in principle a shallow network with similar paramaters counts to a deep one should be capable of learning the same decision boundary... https://en.m.wikipedia.org/wiki/Universal_approximation_theorem https://en.m.wikipedia.org/wiki/Universal_approximation_theo...
- aborsy 6y agoIt depends on the function that you are trying to approximate. I can give you a function that a shallow nnet would approximate better and functions that deep nets approximate exponentially better even with one more layer (in terms of number of neurons n). In the limit n->\infty, both reach arbitrary small errors (obviously often with different number of parameters).
- cosmic_ape 6y agoThis is like a workshop at a usual conference, no proceedings, right?
- la_fayette 6y agoIs there any good reason why a fully-connected network needs more than one hidden layer? Theoretically, any non-linear function could be mapped into a fqn with only one hidden layer. Does deep has anything to do with fqns or only with cnns?
- fantod 6y agoIIRC the number of hidden units required scales exponentially in the desired approximation error.
- bobbylarrybobby 6y agoIf you have only a single layer, aren’t you limiting the functions you can approximate to linear combinations of your activation function on the inputs? With deep networks you can take functions of linear combinations of functions of linear combinations of...
- webmaven 6y ago> Is there any good reason why a fully-connected network needs more than one hidden layer? A sufficiently (infinitely?) wide shallow fcnn can work in theory, but is basically impossible to train[0]. It might be feasible to transform or 'compile' a trained deep network into a shallow & wide one, but I'm not sure there would be any benefits, absent sufficiently wide parallel hardware[1] [0] Then again, deep networks were impossible to train for quite a while too, due to the exploding gradient problem. [1] Although, the Cerebras Wafer-Scale chip does exist. Hmm.