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ref: -2020 tags: Principe modular deep learning kernel trick MNIST CIFAR date: 10-06-2021 16:54 gmt revision:2 [1] [0] [head]

Modularizing Deep Learning via Pairwise Learning With Kernels

  • Shiyu Duan, Shujian Yu, Jose Principe
  • The central idea here is to re-interpret deep networks, not with the nonlinearity as the output of a layer, but rather as the input of the layer, with the regression (weights) being performed on this nonlinear projection.
  • In this sense, each re-defined layer is implementing the 'kernel trick': tasks (like classification) which are difficult in linear spaces, become easier when projected into some sort of kernel space.
    • The kernel allows pairwise comparisons of datapoints. EG. a radial basis kernel measures the radial / gaussian distance between data points. A SVM is a kernel machine in this sense.
      • As a natural extension (one that the authors have considered) is to take non-pointwise or non-one-to-one kernel functions -- those that e.g. multiply multiple layer outputs. This is of course part of standard kernel machines.
  • Because you are comparing projected datapoints, it's natural to take contrastive loss on each layer to tune the weights to maximize the distance / discrimination between different classes.
    • Hence this is semi-supervised contrastive classification, something that is quite popular these days.
    • The last layer is of tuned with cross-entropy labels, but only a few are required since the data is well distributed already.
  • Demonstrated on small-ish datasets, concordant with their computational resources ...

I think in general this is an important result, even if its not wholly unique / somewhat anticipated (it's a year old at the time of writing). Modular training of neural networks is great for efficiency, parallelization, and biological implementations! Transport of weights between layers is hence non-essential.

Classes still are, but I wonder if temporal continuity can solve some of these problems?

(There is plenty of other effort in this area -- see also {1544})

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ref: -2019 tags: Arild Nokland local error signals backprop neural networks mnist cifar VGG date: 02-15-2019 03:15 gmt revision:6 [5] [4] [3] [2] [1] [0] [head]

Training neural networks with local error signals

  • Arild Nokland and Lars H Eidnes
  • Idea is to use one+ supplementary neural networks to measure within-batch matching loss between transformed hidden-layer output and one-hot label data to produce layer-local learning signals (gradients) for improving local representation.
  • Hence, no backprop. Error signals are all local, and inter-layer dependencies are not explicitly accounted for (! I think).
  • L simL_{sim} : given a mini-batch of hidden layer activations H=(h 1,...,h n)H = (h_1, ..., h_n) and a one-hot encoded label matrix Y=(y 1,...,y nY = (y_1, ..., y_n ,
    • L sim=||S(NeuralNet(H))S(Y)|| F 2 L_{sim} = || S(NeuralNet(H)) - S(Y)||^2_F (don't know what F is..)
    • NeuralNet()NeuralNet() is a convolutional neural net (trained how?) 3*3, stride 1, reduces output to 2.
    • S()S() is the cosine similarity matrix, or correlation matrix, of a mini-batch.
  • L pred=CrossEntropy(Y,W TH)L_{pred} = CrossEntropy(Y, W^T H) where W is a weight matrix, dim hidden_size * n_classes.
    • Cross-entropy is H(Y,W TH)=Σ i,jY i,jlog((W TH) i,j)+(1Y i,j)log(1(W TH) i,j) H(Y, W^T H) = \Sigma_{i,j} Y_{i,j} log((W^T H)_{i,j}) + (1-Y_{i,j}) log(1-(W^T H)_{i,j})
  • Sim-bio loss: replace NeuralNet()NeuralNet() with average-pooling and standard-deviation op. Plus one-hot target is replaced with a random transformation of the same target vector.
  • Overall loss 99% L simL_sim , 1% L predL_pred
    • Despite the unequal weighting, both seem to improve test prediction on all examples.
  • VGG like network, with dropout and cutout (blacking out square regions of input space), batch size 128.
  • Tested on all the relevant datasets: MNIST, Fashion-MNIST, Kuzushiji-MNIST, CIFAR-10, CIFAR-100, STL-10, SVHN.
  • Pretty decent review of similarity matching measures at the beginning of the paper; not extensive but puts everything in context.
    • See for example non-negative matrix factorization using Hebbian and anti-Hebbian learning in and Chklovskii 2014.
  • Emphasis put on biologically realistic learning, including the use of feedback alignment {1423}
    • Yet: this was entirely supervised learning, as the labels were propagated back to each layer.
    • More likely that biology is setup to maximize available labels (not a new concept).

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ref: -0 tags: feedback alignment Arild Nokland MNIST CIFAR date: 02-14-2019 02:15 gmt revision:0 [head]

Direct Feedback alignment provides learning in deep neural nets

  • from {1423}
  • Feedback alignment is able to provide zero training error even in convolutional networks and very deep networks, completely without error back-propagation.
  • Biologically plausible: error signal is entirely local, no symmetric or reciprocal weights required.
    • Still, it requires supervision.
  • Almost as good as backprop!
  • Clearly written, easy to follow math.
    • Though the proof that feedback-alignment direction is within 90 deg of backprop is a bit impenetrable, needs some reorganization or additional exposition / annotation.
  • 3x400 tanh network tested on MNIST; performs similarly to backprop, if faster.
  • Also able to train very deep networks, on MNIST - CIFAR-10, CIFAR-100, 100 layers (which actually hurts this task).