From the paper, "Notably, for multiplying two 4 × 4 matrices, applying the algorithm of Strassen recursively results in an algorithm with 49 multiplications, which works over any field...AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications." If you do naive matrix multiplication, you get a sense that you're doing similar work multiple times, but i…
By googling "4x4 matrices multiplication 48" I ended up on this discussion on math.stackexchange https://math.stackexchange.com/questions/578342/number-of-el... , where in 2019 someone stated "It is possible to multiply two 4×4 matrix A,B with only 48 multiplications.", with a link to a PhD thesis. This might mean that the result was already known (I still have to check the outline of the algorithm).
Re: AlphaEvolve: A Gemini-powered coding agent for designing advanced algorithms
#291So, did LLM (namely Gemini-Flash) helepd with the combinatorial optimization process? I'm sure not all of their discoveries (one on kissing numbers, etc.) have previous solutions in some other form, but yeah these findings looks more like very large combinatorial optimization tasks.