The paper introduces a new algorithm called *Bayes by Backprop* for learning probability distributions over the weights of neural networks. This algorithm regularizes the weights by minimizing a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. The authors demonstrate that this principled regularization yields comparable performance to dropout on MNIST classification tasks. They also show how the learned uncertainty in the weights can be used to improve generalization in non-linear regression problems and to drive the exploration-exploitation trade-off in reinforcement learning. The method is based on variational Bayesian inference and uses an efficient, backpropagation-compatible algorithm to learn a distribution over the weights. The paper includes empirical results on classification, regression, and contextual bandit problems, showing that Bayes by Backprop can achieve good performance and improve upon standard methods in various domains.The paper introduces a new algorithm called *Bayes by Backprop* for learning probability distributions over the weights of neural networks. This algorithm regularizes the weights by minimizing a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. The authors demonstrate that this principled regularization yields comparable performance to dropout on MNIST classification tasks. They also show how the learned uncertainty in the weights can be used to improve generalization in non-linear regression problems and to drive the exploration-exploitation trade-off in reinforcement learning. The method is based on variational Bayesian inference and uses an efficient, backpropagation-compatible algorithm to learn a distribution over the weights. The paper includes empirical results on classification, regression, and contextual bandit problems, showing that Bayes by Backprop can achieve good performance and improve upon standard methods in various domains.