Comparing the inductive biases of simple neural networks and Bayesian models

Understanding the relationship between connectionist and probabilistic models is important for evaluating the compatibility of these approaches. We use mathematical analyses and computer simulations to show that a linear neural network can approximate the generalization performance of a probabilistic model of property induction, and that training this network by gradient descent with early stopping results in similar performance to Bayesian inference with a particular prior. However, this prior differs from distributions defined using discrete structure, suggesting that neural networks have inductive biases that can be differentiated from probabilistic models with structured representations.