(from https://github.com/Maratyszcza/NNPACK) is also a pretty reasonable AVX2 GEMM implementation written in a Python assembler, it's a bit easier to follow than the OpenBLAS kernels and has very reasonable performance vs OpenBLAS/MKL.

I second the guidance to just use a BLAS library. I'd guess you'd see a 2-10x speedup at least. It looks like you're only implementing a classical MLP library (which is fine for learning, but not the best choice for something like this, integrating VW into Redis would be a much better choice IMO).