# Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations Source: [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations]() Collection index: [llms.txt]() Data updated: 2025-10-25T23:55:05.513Z Authors: Winnie Xu, Ricky T.Q. Chen, Xuechen Li, David Duvenaud Published: 2021-02-12T14:48:58.000Z ## Abstract We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive comparison against discrete-depth alternatives, while inheriting the memory-efficient training and tunable precision of Neural ODEs. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR-10 (Accuracy, AUC, NLL)](): Image Classification; CIFAR-10; Accuracy: 87.56. - [Image Classification on MNIST (Accuracy, AUC, NLL)](): Image Classification; MNIST; Accuracy: 98.9. ## Original sources and implementation [Original paper]() [PDF]()