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 functi