Statistical mechanics of continual learning: variational principle and mean-field potential

• URL: http://arxiv.org/abs/2212.02846v4
• Date: Tue, 20 Jun 2023 04:41:22 GMT
• Title: Statistical mechanics of continual learning: variational principle and mean-field potential
• Authors: Chan Li and Zhenye Huang and Wenxuan Zou and Haiping Huang
• Abstract summary: We focus on continual learning in single-layered and multi-layered neural networks of binary weights. A variational Bayesian learning setting is proposed, where the neural networks are trained in a field-space. Weight uncertainty is naturally incorporated, and modulates synaptic resources among tasks. Our proposed frameworks also connect to elastic weight consolidation, weight-uncertainty learning, and neuroscience inspired metaplasticity.
• Score: 1.559929646151698
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory ground. Here, we focus on continual learning in single-layered and multi-layered neural networks of binary weights. A variational Bayesian learning setting is thus proposed, where the neural networks are trained in a field-space, rather than gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and modulates synaptic resources among tasks. From a physics perspective, we translate the variational continual learning into Franz-Parisi thermodynamic potential framework, where previous task knowledge acts as a prior and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multi-layered neural networks, and performs better than the currently available metaplasticity algorithm. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience inspired metaplasticity, providing a theory-grounded method for the real-world multi-task learning with deep networks.

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