Bayesian neural network (BNN) posteriors are often considered impractical for inference, as symmetries fragment them, non-identifiabilities inflate dimensionality, and weight-space priors are seen as meaningless. In this work, we study how overparametrization and priors together reshape BNN posteriors and derive implications allowing us to better understand their interplay. We show that redundancy introduces three key phenomena that fundamentally reshape the posterior geometry: balancedness, weight reallocation on equal-probability manifolds, and prior conformity. We validate our findings through extensive experiments with posterior sampling budgets that far exceed those of earlier works, and demonstrate how overparametrization induces structured, prior-aligned weight posterior distributions.

翻译：贝叶斯神经网络（BNN）后验通常被认为不适用于推理，因为对称性使其碎片化，不可辨识性导致维度膨胀，且权重空间先验被视为无意义。在本工作中，我们研究了过度参数化与先验如何共同重塑BNN后验，并推导出启示以更好地理解它们的相互作用。我们证明冗余引入了三种关键现象，从根本上重塑了后验几何：平衡性、等概率流形上的权重再分配以及先验一致性。我们通过远超早期工作的后验采样预算进行大量实验来验证发现，并展示了过度参数化如何诱导出结构化、与先验对齐的权重后验分布。