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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).