They have a patent on it but did open sourced the code. They claim it's up to 24x faster than standard. But that is only true for an extreme use case, its only 2x faster on average.
It breaks even at 5x5 or so and gets dramatically better shortly thereafter. However, most of the convolutional nets in use rely on 3x3 convolutions because I guess reasons:
http://arxiv.org/pdf/1409.1556.pdf (all 3x3)
http://www.cs.unc.edu/~wliu/papers/GoogLeNet.pdf (3x3 and 5x5)
There's probably a new Imagenet winner in this somewhere IMO...
For example, the usual way to have a DNN learn rotation/scaling/translation is to do data augmentation and simply learn with all the data rotated/translated/shifted.
But there must be a way to have these input space symmetries reflect somehow in the structure of the network?
I tried googling this a bit but wasn't really successful - does anyone know whether this has been done?
Rotation-invariance is probably not really a thing you want. The visual world is not, in fact, rotation-invariant, and the "up" direction on Earth-bound, naturally-occurring images has different statistics than the "down" direction, and you'd like to exploit these. Animal visual systems are not rotation-invariant either; an entertainingly powerful demo of this is "the Thatcher Effect" (https://en.wikipedia.org/wiki/Thatcher_effect).
Reflection across a vertical axis, on the other hand, often is exploitable, at least in image recognition contexts (as opposed to, say, handwriting recognition). If you look at the features image recognition convnets are learning they are often symmetric around some axis or other, or sometimes come in "pairs" of left-hand/right-hand twins. As far as I know nobody has tried to exploit this architecturally in any way other than just data augmentation, but it's a big world out there and people have been trying this stuff for a long time.
I know that some translation invariance comes from e.g. the usual conv+maxpool layer structure, but there must still be several representations existing in the first hidden layer of the network stack, for the different translation shifts?
Especially rotation looks like something that should produce a lot of symmetry and shared parameters, but it also looks difficult enough for me that I rather would like to know about someone with mad math/group theory(?) skills who looked at that.
But thank you for the detailed reply anyways!
There have been papers about scale/rotation invariant convnets (again at the structure level) and also Networks that learn invariances without encoding them into the structure.
The former I am very interested in! Do you have any links?
My gut feeling is that the first convolutional layer's kernels, for example, would probably have a 'some are orthogonal' constraint due to this symmetry.