# Efficient Probabilistic Inference in Generic Neural Networks Trained with Non-Probabilistic Feedback

arXiv: https://arxiv.org/abs/1601.03060 · HTML: https://mlsanity.com/paper/1601.03060/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)
- [How does the brain compute with probabilities?](https://mlsanity.com/paper/2409.02709/) (2024)

## Abstract (arXiv)

Animals perform near-optimal probabilistic inference in a wide range of psychophysical tasks. Probabilistic inference requires trial-to-trial representation of the uncertainties associated with task variables and subsequent use of this representation. Previous work has implemented such computations using neural networks with hand-crafted and task-dependent operations. We show that generic neural networks trained with a simple error-based learning rule perform near-optimal probabilistic inference in nine common psychophysical tasks. In a probabilistic categorization task, error-based learning in a generic network simultaneously explains a monkey's learning curve and the evolution of qualitative aspects of its choice behavior. In all tasks, the number of neurons required for a given level of performance grows sub-linearly with the input population size, a substantial improvement on previous implementations of probabilistic inference. The trained networks develop a novel sparsity-based probabilistic population code. Our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error-based learning rules.