# Heterogeneous Time Constants Improve Stability in Equilibrium Propagation

arXiv: https://arxiv.org/abs/2603.03402 · HTML: https://mlsanity.com/paper/2603.03402/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [Equivalence of Equilibrium Propagation and Recurrent Backpropagation](https://mlsanity.com/paper/1711.08416/) (2017)
- [Toward Lifelong Learning in Equilibrium Propagation: Sleep-like and Awake Rehearsal for Enhanced Stability](https://mlsanity.com/paper/2508.14081/) (2025)
- [Biologically-inspired neuronal adaptation improves learning in neural networks](https://mlsanity.com/paper/2204.14008/) (2022)

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

- [Dendritic Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2605.08135/) (2026)

## Abstract (arXiv)

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation for training neural networks. However, existing EP models use a uniform scalar time step dt, which corresponds biologically to a membrane time constant that is heterogeneous across neurons. Here, we introduce heterogeneous time steps (HTS) for EP by assigning neuron-specific time constants drawn from biologically motivated distributions. We show that HTS improves training stability while maintaining competitive task performance. These results suggest that incorporating heterogeneous temporal dynamics enhances both the biological realism and robustness of equilibrium propagation.