StochEP: Stochastic Equilibrium Propagation for Spiking Convergent Recurrent Neural Networks

2025-11-14

AI Summary

Existing equilibrium propagation (EP) methods for spiking neural networks (SNNs) rely predominantly on deterministic neurons, limiting their ability to capture the intrinsic discontinuity of spiking dynamics and hindering scalability to complex visual tasks. This work proposes Stochastic EP—a novel framework that introduces stochasticity into EP to faithfully model spike generation. We integrate probabilistic spiking neurons with a convergent recurrent architecture, enabling scalable deep convolutional spiking recurrent networks. Theoretically, we prove that Stochastic EP converges to deterministic EP in the mean-field limit, thus preserving both biological plausibility and optimization stability. Experiments demonstrate that our method achieves performance comparable to backpropagation-through-time (BPTT)-trained SNNs and EP-trained artificial neural networks (ANNs) on visual benchmarks, while retaining fully local synaptic updates. This establishes a new paradigm for online learning on neuromorphic hardware.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Spiking Neural Networks (SNNs) promise energy-efficient, sparse, biologically inspired computation. Training them with Backpropagation Through Time (BPTT) and surrogate gradients achieves strong performance but remains biologically implausible. Equilibrium Propagation (EP) provides a more local and biologically grounded alternative. However, existing EP frameworks, primarily based on deterministic neurons, either require complex mechanisms to handle discontinuities in spiking dynamics or fail to scale beyond simple visual tasks. Inspired by the stochastic nature of biological spiking mechanism and recent hardware trends, we propose a stochastic EP framework that integrates probabilistic spiking neurons into the EP paradigm. This formulation smoothens the optimization landscape, stabilizes training, and enables scalable learning in deep convolutional spiking convergent recurrent neural networks (CRNNs). We provide theoretical guarantees showing that the proposed stochastic EP dynamics approximate deterministic EP under mean-field theory, thereby inheriting its underlying theoretical guarantees. The proposed framework narrows the gap to both BPTT-trained SNNs and EP-trained non-spiking CRNNs in vision benchmarks while preserving locality, highlighting stochastic EP as a promising direction for neuromorphic and on-chip learning.

Problem

• Develops stochastic Equilibrium Propagation for spiking neural networks
• Addresses biological plausibility and scalability limitations in existing methods
• Enables energy-efficient neuromorphic learning with theoretical guarantees

Innovation

• Stochastic EP integrates probabilistic spiking neurons
• Framework smoothens optimization landscape and stabilizes training
• Enables scalable learning in deep convolutional spiking CRNNs