# Harnessing intuitive local evolution rules for physical learning

arXiv: https://arxiv.org/abs/2507.19561 · HTML: https://mlsanity.com/paper/2507.19561/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Estimating the Carbon Footprint of BLOOM, a 176B Parameter Language Model](https://mlsanity.com/paper/2211.02001/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [Gpt-4: A Review on Advancements and Opportunities in Natural Language Processing](https://mlsanity.com/paper/2305.03195/) (2023)
- [Learning by non-interfering feedback chemical signaling in physical networks](https://mlsanity.com/paper/2203.12098/) (2022)
- [One-step regression and classification with crosspoint resistive memory arrays](https://mlsanity.com/paper/2005.01988/) (2020)

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

- [Reciprocity Separates Gradient Flow from Rotation in Conservative Physical Learning](https://mlsanity.com/paper/2608.30778/) (2026)

## Abstract (arXiv)

Machine Learning, however popular and accessible, is computationally intensive and highly power-consuming, prompting interest in alternative physical implementations of learning tasks. We introduce a training scheme for physical systems that minimize power dissipation in which only boundary parameters (i.e. inputs and outputs) are externally controlled. Using this scheme, these Boundary-Enabled Adaptive State Tuning Systems (BEASTS) learn by exploiting local physical rules. Our scheme, BEASTAL (BEAST-Adaline), is the closest analog of the Adaline algorithm for such systems. We demonstrate this autonomous learning in silico for regression and classification tasks. Our approach advances previous physical learning schemes by using intuitive, local evolution rules without requiring large-scale memory or complex internal architectures. BEASTAL can perform any linear task, achieving best performance when the local evolution rule is non-linear.