mlsanityData to 14 Oct 2026

Near-Equilibrium Propagation training in nonlinear wave systems

arXiv 2510.16084 ↗First posted 17 Oct 2025cs.LG cond-mat.quant-gas math-phcited by 3

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Abstract (arXiv)

Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong potential for in-situ training. We extend EP learning to both discrete and continuous complex-valued wave systems. In contrast to previous EP implementations, our scheme is valid in the weakly dissipative regime, and readily applicable to a wide range of physical settings, even without well defined nodes, where trainable inter-node connections can be replaced by trainable local potential. We test the method in driven-dissipative exciton-polariton condensates governed by generalized Gross-Pitaevskii dynamics. Numerical studies on standard benchmarks, including a simple logical task and handwritten-digit recognition, demonstrate stable convergence, establishing a practical route to in-situ learning in physical systems in which system control is restricted to local parameters.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 18 of its 36 references that are in the map. First posted on arXiv 17 Oct 2025.

Builds on

18 of 36 references.

References · 18

  1. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 259
  2. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 128
  3. 2020Photonics for artificial intelligence and neuromorphic computingcited by 112
  4. 2020Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Biascited by 64
  5. 2024Training of Physical Neural Networkscited by 49
  6. 2022Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networkscited by 44
  7. 2019Wave Physics as an Analog Recurrent Neural Networkcited by 43
  8. 2023Backpropagation-free Training of Deep Physical Neural Networkscited by 42
  9. 2023The physics of optical computingcited by 33
  10. 2017Equivalence of Equilibrium Propagation and Recurrent Backpropagationcited by 32
  11. 2020EqSpike: Spike-driven Equilibrium Propagation for Neuromorphic Implementationscited by 31
  12. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
6 more
  1. 2023Machine Learning Without a Processor: Emergent Learning in a Nonlinear Electronic Metamaterialcited by 20
  2. 2024Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagationcited by 16
  3. 2024Equilibrium Propagation: the Quantum and the Thermal Casescited by 10
  4. 2024Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systemscited by 10
  5. 2024Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocitycited by 9
  6. 2025Equilibrium Propagation for Learning in Lagrangian Dynamical Systemscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Equilibrium Propagation for Non-Conservative Systemscited by 3
  2. 2026Training a Predictive Coding Network on ImageNet using Equilibrium Propagationcited by 3
  3. 2026Unifying Physical Backpropagationcited by 0