feat: implement backward computation for more operators #921
Conversation
We use the following formulas to compute the gradients: Let g be `tensor->grad`, let x be `src0`, and let y be `tensor`. For tanh, `g * (1 - tanh^2(x)) = g * (1 - y^2) = g - gy^2`. For sigmoid, `g * (sigmoid(x) * (1 - sigmoid(x))) = g * (y * (1 - y)) = gy - gy^2`.
This comes with a breaking change: `ggml_clamp` is no longer an in-place
operation. If you still want/need that behavior, use `ggml_clamp_inplace`.
I hope no one depended on that.
Also introduces `GGML_OP_CLAMP_BACK`, whose implementations for other
backends will be added in a subsequent commit.
The definition of `clamp_back` is as follows:
{ 0 if x < min
d/dx(clamp(x, min, max)) = { 1 if min <= x <= max
{ 0 if x > max
Slice the gradient using a view operation, reshape, and then add to the inputs' gradients.
Introduces `GGML_UNARY_OP_ELU_BACK`, defined as the following:
ELU'(x) = { e^x if x <= 0
{ x if x > 0
d/dx(LeakyRELU(x, negative_slope)) = { 1 if x > 0
{ negative_slope if x <= 0
The equivalent formula `negative_slope * step(-x) + step(x)` is used
for backward computation.
…GELU_BACK` Introduces corresponding `*_BACK` operators for both. Backend-specific accelerated implementations forthcoming.
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I'm currently working on adding training support for the MNIST example in #908 . I have a working backward pass for |
d/dx(ELU(x)) is 1 if x >= 0, not x
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It might be better to wait for @JohannesGaessler to merge #908 and then continue this PR? |
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That's probably best, considering the changes needed for the tests. |
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I extended the code in |
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Perfect. I plan to finish this PR this weekend. |
This PR will add backward computations for most operators once completed.
Leaving
pad,im2col, andnormfor a future PR now.Currently unsure if I should fuse the multiply + gradient computation for
gelu_back/gelu_quick_backlike withsilu_back.