# Nature-Inspired Local Propagation

arXiv: https://arxiv.org/abs/2402.05959 · HTML: https://mlsanity.com/paper/2402.05959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Predictive Coding Approximates Backprop along Arbitrary Computation Graphs](https://mlsanity.com/paper/2006.04182/) (2020)
- [Biologically Motivated Algorithms for Propagating Local Target Representations](https://mlsanity.com/paper/1805.11703/) (2018)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [A Unified Framework of Online Learning Algorithms for Training Recurrent Neural Networks](https://mlsanity.com/paper/1907.02649/) (2019)
- [The Predictive Forward-Forward Algorithm](https://mlsanity.com/paper/2301.01452/) (2023)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Online learning of long-range dependencies](https://mlsanity.com/paper/2305.15947/) (2023)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [Exploring the Promise and Limits of Real-Time Recurrent Learning](https://mlsanity.com/paper/2305.19044/) (2023)
- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)
- [A Gradient Estimator for Time-Varying Electrical Networks with Non-Linear Dissipation](https://mlsanity.com/paper/2103.05636/) (2021)
- [Cognitive Action Laws: The Case of Visual Features](https://mlsanity.com/paper/1808.09162/) (2018)
- [Learning Visual Features Under Motion Invariance](https://mlsanity.com/paper/1909.00350/) (2019)

## Abstract (arXiv)

The spectacular results achieved in machine learning, including the recent advances in generative AI, rely on large data collections. On the opposite, intelligent processes in nature arises without the need for such collections, but simply by online processing of the environmental information. In particular, natural learning processes rely on mechanisms where data representation and learning are intertwined in such a way to respect spatiotemporal locality. This paper shows that such a feature arises from a pre-algorithmic view of learning that is inspired by related studies in Theoretical Physics. We show that the algorithmic interpretation of the derived "laws of learning", which takes the structure of Hamiltonian equations, reduces to Backpropagation when the speed of propagation goes to infinity. This opens the doors to machine learning studies based on full on-line information processing that are based the replacement of Backpropagation with the proposed spatiotemporal local algorithm.