# From statistical inference to a differential learning rule for stochastic neural networks

arXiv: https://arxiv.org/abs/1805.10714 · HTML: https://mlsanity.com/paper/1805.10714/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2018.

## Built on by (most cited first, 1 of 1)

- [Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplings](https://mlsanity.com/paper/2507.05147/) (2025)

## Abstract (arXiv)

Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity rule that relies only on delayed activity correlations, and that shows a number of remarkable features. Our "delayed-correlations matching" (DCM) rule satisfies some basic requirements for biological feasibility: finite and noisy afferent signals, Dale's principle and asymmetry of synaptic connections, locality of the weight update computations. Nevertheless, the DCM rule is capable of storing a large, extensive number of patterns as attractors in a stochastic recurrent neural network, under general scenarios without requiring any modification: it can deal with correlated patterns, a broad range of architectures (with or without hidden neuronal states), one-shot learning with the palimpsest property, all the while avoiding the proliferation of spurious attractors. When hidden units are present, our learning rule can be employed to construct Boltzmann machine-like generative models, exploiting the addition of hidden neurons in feature extraction and classification tasks.