“Circuit priors in NN-bayes: more results” by Kaarel, Dmitry Vaintrob

LessWrong (30+ Karma) · Oct 21, 2026 · 2m

We're posting lots of papers written with GPT-6 Astra on generalization properties of bayesian neural net learning. The following picture emerges:

For various reasonable priors on MLP weights, 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 is implemented by a circuit of width , then conditioning on train data points is sufficient to get test accuracy.

These results…