Neural Weight Norm = Kolmogorov Complexity

ArXi:2605.10878v1 Announce Type: new Why does weight decay work? We prove that, in any fixed-precision regime, the smallest weight norm of a looped neural network outputting a binary string equals the Kolmogoro complexity of that string, up to a logarithmic factor. This implies that weight decay induces a prior matching Solomonoff's universal prior, the optimal prior over computable functions, up to a polynomial factor.