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I think one particularly interesting result is that superior algorithms for numerical linear algebra exist at all and can be found by artificial intelligence.
by constantcrying 1y ago
I think one particularly interesting result is that superior algorithms for numerical linear algebra exist at all and can be found by artificial intelligence.
XX^T is the matrix of all piecewise dot products of vectors in X and as others have pointed out there are legitimate applications. Another one being e.g. transforming an undetermined linear system into a least squares problem.
- FabHK 1y agoThe solution to the least squares problem Ax ≈ b is given by x = (A'A)^-1 A'b, but modern solvers never form the matrix product A'A explicitly. Even for the SVD it isn't formed.
- jerf 1y agoGoogle put something out like this recently too. The original is https://deepmind.google/discover/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/ https://deepmind.google/discover/blog/alphaevolve-a-gemini-p..., but it's sort of buried in there. Here's the YouTube video that introduced it to me, forwarded to the spot where the host talks about the improved 4x4 matrix multiplication algorithm: https://www.youtube.com/watch?v=sGCmu7YKgPA&t=396s https://www.youtube.com/watch?v=sGCmu7YKgPA&t=396s It's only a slight tweak, but it's a slight tweak to something pretty highly studied and still impressive.