Dimension-Free PAC-Bayes Generalization for Deep Neural Networks via Dirichlet Processes
Classical PAC-Bayesian generalization theory places prior distributions over Euclidean parameter space $Θ\subseteq \mathbb{R}^D$, causing relative entropy to scale with network dimension $D$. For modern overparameterized neural networks where $D \gg n$, this parameter-counting dependency yields vacuous generalization bounds ($> 1{,}000\%$). In this work, we resolve this barrier by shifting prior specification from internal parameters to the non-parametric space of data distributions $\mathcal{M}_1(\mathcal{Z})$ via a \textbf{Dirichlet Process (DP)}, $\mathcal{DP}(α, F_0)$, inducing parameter distributions through push-forward measures under the learning algorithm. By the Data Processing I...
| Authors | Sumit Vashishtha |
|---|---|
| Primary category | stat.ML |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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