gradient descent for custom function

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L 2024-4-24

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https://ww2.mathworks.cn/matlabcentral/answers/2110961-gradient-descent-for-custom-function

编辑： Torsten 2024-4-24

I have four equations:

1) e = m - y

2) y = W_3 * h

3) h = z + W_2 * z + f

4) f = W_1 * x

I want to update W_1, W_2 and W_3 in order to minimize a cost function J = (e^T e ) by using gradient descent.

x is an input, y is the output and m is the desired value for each sample in the dataset

I would like to do W_1 = W_1 - eta* grad(J)_w_1

W_2 = W_2 - eta* grad(J)_w_2

W_3 = W_3 - eta* grad(J)_w_3

Going through documentation I found out that you can train standard neural networks. But notice that I have some custom functions, so I guess it would be more of an optimization built in function to use.

Any ideas?

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Matt J 2024-4-24

x is an input, y is the output and m is the desired value for each sample in the dataset

It looks like z is also an input. It is not given by any other equations.

L 2024-4-24

Yes, z is another input.

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回答（2 个）

Matt J 2024-4-24

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编辑：Matt J 2024-4-24

so I guess it would be more of an optimization built in function to use.

No, not necessarily. Your equations can be implemented with fullyConnectedLayers and additionLayers.

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Matt J 2024-4-24

You would create a dlnetwork and then use trainnet.

L 2024-4-24

编辑：L 2024-4-24

dlnet.mlx

Thanks @Matt J. I found the documentation hard to follow. I tried using the DL tool box, but I was only able to generate the topology. What should I do next ? how to train it on the x, z inputs? For each x,z input, I have a desired output m. For all matrices I don't wish to learn a bias term, so, in the tool box I set learnratebias =0

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