arXiv:2607.05735v1 Announce Type: cross Abstract: 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} \[ s_\infty(y,\varepsilon)=\limsup_N -\frac{1}{N}\log \pi_N^0(L\le \varepsilon), \] the intensive prior cost of representing a target function $y$ to population mean-squared error $\varepsil
This paper represents continued academic inquiry into the theoretical underpinnings of neural networks, coinciding with sustained interest in making AI trustworthy and predictable.
Understanding the learnability and inductive biases of large neural networks is crucial for their reliable development and deployment, especially as they become more ubiquitous.
This research contributes to a deeper theoretical understanding of how infinite-width limits relate to finite, practical neural networks, potentially informing future architectural designs.
- · AI researchers
- · ML academia
- · AI developers
- · Overly simplistic AI models
The immediate effect is a refinement of theoretical models for Bayesian neural networks.
This could lead to more robust and theoretically grounded designs for large-scale AI models.
Improved theoretical understanding may eventually contribute to more predictable and safer AI systems.
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Read at arXiv cs.LG