# Agnostic Physics-Driven Deep Learning

arXiv: https://arxiv.org/abs/2205.15021 · HTML: https://mlsanity.com/paper/2205.15021/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 14 of 14)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [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)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementations](https://mlsanity.com/paper/2010.07859/) (2020)
- [Equilibrium Propagation with Continual Weight Updates](https://mlsanity.com/paper/2005.04168/) (2020)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [A contrastive rule for meta-learning](https://mlsanity.com/paper/2104.01677/) (2021)
- [Learning by non-interfering feedback chemical signaling in physical networks](https://mlsanity.com/paper/2203.12098/) (2022)
- [Towards deep learning with spiking neurons in energy based models with contrastive Hebbian plasticity](https://mlsanity.com/paper/1612.03214/) (2016)
- [Mitigating Asymmetric Nonlinear Weight Update Effects in Hardware Neural Network based on Analog Resistive Synapse](https://mlsanity.com/paper/1712.05895/) (2017)

## Built on by (most cited first, 15 of 15)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Energy-based learning algorithms for analog computing: a comparative study](https://mlsanity.com/paper/2312.15103/) (2023)
- [Frequency propagation: Multi-mechanism learning in nonlinear physical networks](https://mlsanity.com/paper/2208.08862/) (2022)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems](https://mlsanity.com/paper/2406.00879/) (2024)
- [Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity](https://mlsanity.com/paper/2406.06482/) (2024)
- [Learning long range dependencies through time reversal symmetry breaking](https://mlsanity.com/paper/2506.05259/) (2025)
- [Towards the Training of Deeper Predictive Coding Neural Networks](https://mlsanity.com/paper/2506.23800/) (2025)
- [A Fast Algorithm to Simulate Nonlinear Resistive Networks](https://mlsanity.com/paper/2402.11674/) (2024)
- [Towards training digitally-tied analog blocks via hybrid gradient computation](https://mlsanity.com/paper/2409.03306/) (2024)
- [Equilibrium Propagation for Non-Conservative Systems](https://mlsanity.com/paper/2602.03670/) (2026)
- [Training a Predictive Coding Network on ImageNet using Equilibrium Propagation](https://mlsanity.com/paper/2606.03584/) (2026)
- [Energy-Efficient Supervised Learning with a Binary Stochastic Forward-Forward Algorithm](https://mlsanity.com/paper/2507.06461/) (2025)
- [Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines](https://mlsanity.com/paper/2606.13454/) (2026)
- [Unifying Physical Backpropagation](https://mlsanity.com/paper/2608.11585/) (2026)

## Abstract (arXiv)

This work establishes that a physical system can perform statistical learning without gradient computations, via an Agnostic Equilibrium Propagation (Aeqprop) procedure that combines energy minimization, homeostatic control, and nudging towards the correct response. In Aeqprop, the specifics of the system do not have to be known: the procedure is based only on external manipulations, and produces a stochastic gradient descent without explicit gradient computations. Thanks to nudging, the system performs a true, order-one gradient step for each training sample, in contrast with order-zero methods like reinforcement or evolutionary strategies, which rely on trial and error. This procedure considerably widens the range of potential hardware for statistical learning to any system with enough controllable parameters, even if the details of the system are poorly known. Aeqprop also establishes that in natural (bio)physical systems, genuine gradient-based statistical learning may result from generic, relatively simple mechanisms, without backpropagation and its requirement for analytic knowledge of partial derivatives.