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So when looking at Radial Basis Function Neural Networks, I've noticed that people only ever recommend the usage of 1 hidden layer, whereas with multilayer perceptron neural networks more layers is considered better.

Given that RBF networks can be trained with version of back propagation is there any reasons why deeper RBF networks wouldn't work, or that an RBF layer couldn't be used as the penultimate or first layer in a deep MLP network? (I was thinking the penultimate layer so it could essentially be trained on the features learned by the previous MLP layers)

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  • $\begingroup$ I'm not a NN expert, but my impression is that with standard feed-forward NN's, multiple hidden layers don't typically add much. $\endgroup$ – gung - Reinstate Monica May 10 '15 at 22:02
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    $\begingroup$ That was in the earlier days of NN research, however now more layers is typically the recipe for greater performance (deep learning). I think the current favourite approach is a smart initialisation, as many layers as possible, regularisation via dropout and softmax instead of sigmoidal activations to avoid saturation. (But I may be wrong on the techniques). I think some people also use iterative deepening to get better results. Also, Google got state of the art on imageNet in 2014 with a 100 layer network. $\endgroup$ – user1646196 May 11 '15 at 10:37
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The fundamental problem is that RBFs are a) too nonlinear, b) do not do dimension reduction.

because of a) RBFs were always trained by k-means rather than gradient descent.

I would claim that the main success in Deep NNs is conv nets, where one of the key parts is dimension reduction: although working with say 128x128x3=50,000 inputs, each neuron has a restricted receptive field, and there are much fewer neurons in each layer.In a given layer in an MLP- each neuron represents a feature/dimension) so you are constantly reducing dimensionality (in going from layer to layer).

Although one could make the RBF covariance matrix adaptive and so do dimension reduction, this makes it even harder to train.

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  • $\begingroup$ I recently read a paper that proposed a back-propagation algorithm for training RBF networks. Given this could their be a benefit in having an RBF as the final layer in a deep network? I suppose in this form the rest of the deep network would essentially be detecting features that the RBF can classify $\endgroup$ – user1646196 May 12 '15 at 19:35
  • $\begingroup$ maybe you should link to the paper and then people can give more informed answers. I don't see any benefit...given that the RBF is too non linear (and eg sigmoids have been replaced by relu because they were too non linear- vanishing gradient...). What people do is train with conv net with standard mlp on top, then throw away mlp and use svm $\endgroup$ – seanv507 May 13 '15 at 7:26
  • $\begingroup$ The paper is "Training RBF networks with selective backpropagation" not sure if you can read it here or if there's a paywall sciencedirect.com/science/article/pii/S0925231203005411 . I wasn't aware sigmoids had been replaced by relu because of non-linearity, but given that I can see how increased non-linearity would be shied away from. I'll mark the answer as accepted :) $\endgroup$ – user1646196 May 13 '15 at 8:42

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