A single hidden layered NN but the weight matrix is a diagonal matrix (with a bias) -- how to design that?

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Shashi Kant
Shashi Kant 2020-4-30
评论： Shashi Kant 2020-5-29
I am wondering if I can create a single hidden layered NN but the weight matrix is a diagonal matrix (with a bias). How to design that?
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Background
Let's say that a single layered hidden model (with m neurons) is given as
, where
  • is input vector,
  • is a first weight matrix connecting input with the hidden layer with m nodes,
  • is a bias
  • is an activation function which operates component wise, say $\tanh$
  • is second weight matrix connecting the hidden layer with the output,
  • is a bias, and
  • is an output vector.
My model wants the weight matrices and as only diagonal matrices. How to do that?

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采纳的回答

Srivardhan Gadila
Refer to Weight and Bias Values, Input Weights, Layer Weights & net.layerWeights{i,j}.learn.
You can access the layer weights as follows:
net.LW{i,j}
You can set any values to the above weights and set the net.layerWeights{i,j}.learn to 0 so that the weights won't be altered during the training & adaption. In this case setting a specific weight for a connection is not possible since the property net.layerWeights{i,j}.learn is defined for the entire connections between layers i and j.
net.layerWeights{i,j}.learn = 0
net.LW{i,j} = ones(size(net.LW{i,j})) % any weights of size(net.LW{i,j})
If your network architecture is defined and trained already:
Then you can set weight of a connection between nodes k & l of layers i & j as follows:
net.LW{i,j}(k,l) = 1
and then use the network.
The above things can be done to Input wieghts too.
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Srivardhan Gadila
Srivardhan Gadila 2020-5-29
编辑：Srivardhan Gadila 2020-5-29
@Shashi Kant, as per my knowledge on shallow neural networks:
  1. I listed the possible things you can do w.r.t the weights of layers of shallow nerual networks in the Answer.
  2. The property net.layerWeights{i,j}.learn is defined for the entire connections between layers i and j hence you cannot set the diagonal weights to learn only & non-diagonal weights to not learn.
  3. You can instead define custom Deep Learning layer to achieve your functionality. Refer to Define Custom Deep Learning Layers & Define Custom Deep Learning Layer with Learnable Parameters
Shashi Kant
Shashi Kant 2020-5-29
@Srivardhan Gadila Thank you for your suggestion. I will look into that. I am not very familar with the deep learning toolbox. But I will dig into it.

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