An Infinite-Feature Extension for Bayesian ReLU Nets That Fixes Their Asymptotic Overconfidence
This addresses uncertainty calibration issues in Bayesian deep learning, offering a practical fix for overconfidence in ReLU networks, though it is incremental as it builds on existing theoretical insights.
The paper tackles the problem of asymptotic overconfidence in Bayesian ReLU neural networks far from training data by extending them with infinite ReLU features via a Gaussian process, resulting in a model that becomes maximally uncertain away from data while maintaining predictive power near data, with application to pre-trained networks at low cost.
A Bayesian treatment can mitigate overconfidence in ReLU nets around the training data. But far away from them, ReLU Bayesian neural networks (BNNs) can still underestimate uncertainty and thus be asymptotically overconfident. This issue arises since the output variance of a BNN with finitely many features is quadratic in the distance from the data region. Meanwhile, Bayesian linear models with ReLU features converge, in the infinite-width limit, to a particular Gaussian process (GP) with a variance that grows cubically so that no asymptotic overconfidence can occur. While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs. We extend finite ReLU BNNs with infinite ReLU features via the GP and show that the resulting model is asymptotically maximally uncertain far away from the data while the BNNs' predictive power is unaffected near the data. Although the resulting model approximates a full GP posterior, thanks to its structure, it can be applied \emph{post-hoc} to any pre-trained ReLU BNN at a low cost.