# Spatiotemporal Local Propagation

## TL;DR

This paper introduces SpatioTemporal Local Propagation (STLP), a biologically plausible neural computation scheme based on variational principles, which operates locally in space and time without requiring backpropagation.

## Contribution

It presents a novel variational framework for neural networks that achieves spatial and temporal locality, addressing biological plausibility issues of traditional backpropagation methods.

## Key findings

- STLP does not require backpropagation of errors.
- The scheme is local in both space and time.
- It surpasses BPTT and RTRL in biological plausibility.

## Abstract

This paper proposes an in-depth re-thinking of neural computation that parallels apparently unrelated laws of physics, that are formulated in the variational framework of the least action principle. The theory holds for neural networks that are also based on any digraph, and the resulting computational scheme exhibits the intriguing property of being truly biologically plausible. The scheme, which is referred to as SpatioTemporal Local Propagation (STLP), is local in both space and time. Space locality comes from the expression of the network connections by an appropriate Lagrangian term, so as the corresponding computational scheme does not need the backpropagation (BP) of the error, while temporal locality is the outcome of the variational formulation of the problem. Overall, in addition to conquering the often invoked biological plausibility missed by BP, the locality in both space and time that arises from the proposed theory can neither be exhibited by Backpropagation Through Time (BPTT) nor by Real-Time Recurrent Learning (RTRL).