# Emergent learning in physical systems as feedback-based aging in a glassy landscape

arXiv: https://arxiv.org/abs/2309.04382 · HTML: https://mlsanity.com/paper/2309.04382/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 6 of 6)

- [A jamming transition from under- to over-parametrization affects loss landscape and generalization](https://mlsanity.com/paper/1810.09665/) (2018)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Comparing Dynamics: Deep Neural Networks versus Glassy Systems](https://mlsanity.com/paper/1803.06969/) (2018)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [Learning by non-interfering feedback chemical signaling in physical networks](https://mlsanity.com/paper/2203.12098/) (2022)
- [Frequency propagation: Multi-mechanism learning in nonlinear physical networks](https://mlsanity.com/paper/2208.08862/) (2022)

## Abstract (arXiv)

By training linear physical networks to learn linear transformations, we discern how their physical properties evolve due to weight update rules. Our findings highlight a striking similarity between the learning behaviors of such networks and the processes of aging and memory formation in disordered and glassy systems. We show that the learning dynamics resembles an aging process, where the system relaxes in response to repeated application of the feedback boundary forces in presence of an input force, thus encoding a memory of the input-output relationship. With this relaxation comes an increase in the correlation length, which is indicated by the two-point correlation function for the components of the network. We also observe that the square root of the mean-squared error as a function of epoch takes on a non-exponential form, which is a typical feature of glassy systems. This physical interpretation suggests that by encoding more detailed information into input and feedback boundary forces, the process of emergent learning can be rather ubiquitous and, thus, serve as a very early physical mechanism, from an evolutionary standpoint, for learning in biological systems.