Circuit priors in NN-bayes: more results

We're posting lots of papers written with GPT-6 Astra on generalization properties of bayesian neural net learning. [1] The following picture emerges: For various reasonable priors on MLP weights, [2] the induced prior on functions is a circuit prior: for fixed depth, the ordering of functions by negative log prior is roughly their ordering by minimal circuit width. From a quantitative version of this statement, one gets the following sample complexity bound: if the function mjx-math { display: ...