Width-Robust Learnability in Mean-Field Bayesian Neural Networks
Infinite-width limits are a standard way to reason about neural networks, but it is not automatic that the limiting learner has the same complexity-theoretic inductive bias as large finite networks. We study this question for Bayesian neural networks at the mean-field, or critical feature-learning, scaling. The central quantity is the \emph{reduced entropy} \[ s_\infty(y,\varepsilon)=\limsup_N -\frac{1}{N}\log π_N^0(L\le \varepsilon), \] the intensive prior cost of representing a target function $y$ to population mean-squared error $\varepsilon$. Our main result is a width-robust learnability theorem. At fixed depth, a family of Boolean-cube targets is learnable from polynomially many sam...
| Authors | Dmitry Vaintrob, Kaarel Hänni |
|---|---|
| Primary category | stat.ML |
| Published | 7 July 2026 |
| Last updated at source | 7 July 2026 |
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