Spike-timing-dependent Hebbian learning as noisy gradient descent

2025-05-15

AI Summary

Spike-timing-dependent plasticity (STDP) lacks a rigorous optimization-theoretic interpretation. Method: We formulate a stochastic differential equation model of STDP and analyze it through the lens of optimization theory and neural dynamics, establishing its equivalence to noisy gradient descent and mirror descent on the probability simplex. Contribution/Results: We provide the first rigorous proof that STDP asymptotically identifies the presynaptic neuron with maximal activation, and uncover its intrinsic natural loss function structure. This work delivers the first stochastic optimization interpretation of Hebbian learning grounded explicitly in precise spike timing, thereby establishing a theoretical bridge between neuroscience and stochastic optimization. It significantly advances the understanding of convergence properties and functional significance of biologically inspired learning mechanisms.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

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

Hebbian learning is a key principle underlying learning in biological neural networks. It postulates that synaptic changes occur locally, depending on the activities of pre- and postsynaptic neurons. While Hebbian learning based on neuronal firing rates is well explored, much less is known about learning rules that account for precise spike-timing. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a natural loss function on the probability simplex. This connection allows us to prove that the learning rule eventually identifies the presynaptic neuron with the highest activity. We also discover an intrinsic connection to noisy mirror descent.

Problem

• Explores Hebbian learning with precise spike-timing dependence
• Relates spike-timing plasticity to noisy gradient descent
• Proves rule identifies highest-activity presynaptic neuron

Innovation

• Hebbian learning based on spike-timing
• Noisy gradient descent optimization method
• Connection to noisy mirror descent