The Inevitability of Probability: Probabilistic Inference in Generic Neural Networks Trained with Non-Probabilistic Feedback
A. Emin Orhan, Wei Ji Ma · arXiv (Cornell University) · 2016
Humans and other animals have been shown to perform near-optimal probabilistic inference in a wide range of psychophysical tasks. On the face of it, this is surprising because optimal probabilistic inference in each case is associated with highly non-trivial behavioral strategies. Yet, typically subjects receive little to no feedback during most of these tasks and the received feedback is not explicitly probabilistic in nature. How can subjects learn such non-trivial behavioral strategies from scarce non-probabilistic feedback? We show that generic feed-forward and recurrent neural networks trained with a relatively small number of non-probabilistic examples using simple error-based learning rules can perform near-optimal probabilistic inference in standard psychophysical tasks. The hidden layers of the trained networks develop a novel sparsity-based probabilistic population code. In all tasks, performance asymptotes at very small network sizes, usually on the order of tens of hidden units, due to the low computational complexity of the typical psychophysical tasks. For the same reason, the trained networks also display remarkable generalization to stimulus conditions not seen during training. We further show that in a probabilistic binary categorization task involving arbitrary categories where both human and monkey subjects have been shown to perform probabilistic inference, a monkey subject's performance (but not human subjects' performance) is consistent with an error-based learning rule. Our results suggest that near-optimal probabilistic inference in standard psychophysical tasks emerges naturally and robustly in generic neural networks trained with error-based learning rules, even when neither the training objective nor the training examples are explicitly probabilistic, and that these types of networks can be used as simple plausible neural models of probabilistic inference.