9 ms·
In the nnpack implementation, the same exponential (i.e. expf) is computed twice for each element, which is a waste of time. A faster implementation should save
by acmj 10y ago
In the nnpack implementation, the same exponential (i.e. expf) is computed twice for each element, which is a waste of time. A faster implementation should save each expf result to output[sample][channel] first, compute the sum and then rescale output[sample][channel] by the sum.
- Marat_Dukhan 10y agoIf you have an efficient vectorized implementation of expf (NNPACK does), softmax is a memory/cache bandwidth-bound kernel, and storing data is less efficient than recomputing.
- acmj 10y agoWhere is this vectorized expf implemented? I am only seeing softmax is calling the standard expf. Let's suppose expf from libm is vectorized. Is there any benchmark showing nnpack's implementation is really faster? I doubt, actually. Exp is quite expensive even if vectorized.
- Marat_Dukhan 10y agoThis is the reference implementation of softmax, i.e. implementation used as a reference in unit tests. It is designed to be simple, readable, and correct, which is why I linked it here. Optimized implementation is in assembly (PeachPy). See https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64-fma/exp.py https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64... for the vectorized expf
- Marat_Dukhan 10y agoOops, here is the actually used vectorized expf (similar to the one I linked, but with optional unrolling): https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64-fma/vecmath/exp.py https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64...
- acmj 10y agoThanks for the pointer. The full softmax implementation is here [1]. I have not read the code, but I can trust the developer to have a very fast implementation. Nonetheless, I don't think the reference implementation in your original link is optimal. Exp is expensive and should not be called twice (EDIT: unless you can show a benchmark to prove me wrong). [1]: https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64-fma/softmax.py https://github.com/Maratyszcza/NNPACK/blob/master/src/x86_64...
- barrkel 10y agoFWIW, you're replying to the developer of the file you linked to.
- acmj 10y agoI later realized he is the developer, but this does not change this discussion. Here is a micro benchmark, computing softmax 1 million times over a random vector of size 1000. On an old Linux server, calling the libm expf once takes 11.76 CPU seconds; calling it twice takes 25.15s. The implementation for calling expf once: void softmax1(int n, const float *x, float *y) { int i; float s, max = -FLT_MAX; for (i = 0; i < n; ++i) max = max > x[i]? max : x[i]; for (i = 0, s = 0.0f; i < n; ++i) s += (y[i] = expf(x[i] - max)); for (i = 0, s = 1.0f / s; i < n; ++i) y[i] *= s; } This micro benchmark proves my point: using expf from libm, the reference implementation in nnpack is suboptimal. It is possible that a vectorized expf may change the fact, but the developer needs to prove it with numbers.
- deleted 10y ago[deleted]