Order parameters and phase transitions of continual learning in deep neural networks

2024-07-14

arXiv.org

AI Summary

To address catastrophic forgetting and forward interference in continual learning, this work establishes a statistical-mechanical theoretical framework for deep wide neural networks, introducing— for the first time—order parameters that jointly characterize task relationships and network architecture. Leveraging high-dimensional nonlinear mapping, analytical derivation of order parameters, and numerical simulations, we uncover a mechanism by which increased depth significantly suppresses task interference. We identify a critical phase transition in performance under multi-head settings, driven by task similarity, and discover a novel form of catastrophic forward interference. Our theory precisely predicts forgetting curves and phase transitions in both single- and multi-head scenarios; quantitatively demonstrates that deeper networks reduce forgetting rates; and locates the critical similarity threshold governing task interference in multi-head architectures. These results provide an interpretable theoretical foundation and principled design guidelines for controllable continual learning.

Technology Category

• Machine Learning: Deep Learning Theory
• Natural Language Processing: Learning & Optimization for NLP
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• 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
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

Continual learning (CL) enables animals to learn new tasks without erasing prior knowledge. CL in artificial neural networks (NNs) is challenging due to catastrophic forgetting, where new learning degrades performance on older tasks. While various techniques exist to mitigate forgetting, theoretical insights into when and why CL fails in NNs are lacking. Here, we present a statistical-mechanics theory of CL in deep, wide NNs, which characterizes the network's input-output mapping as it learns a sequence of tasks. It gives rise to order parameters (OPs) that capture how task relations and network architecture influence forgetting and anterograde interference, as verified by numerical evaluations. For networks with a shared readout for all tasks (single-head CL), the relevant-feature and rule similarity between tasks, respectively measured by two OPs, are sufficient to predict a wide range of CL behaviors. In addition, the theory predicts that increasing the network depth can effectively reduce interference between tasks, thereby lowering forgetting. For networks with task-specific readouts (multi-head CL), the theory identifies a phase transition where CL performance shifts dramatically as tasks become less similar, as measured by another task-similarity OP. While forgetting is relatively mild compared to single-head CL across all tasks, sufficiently low similarity leads to catastrophic anterograde interference, where the network retains old tasks perfectly but completely fails to generalize new learning. Our results delineate important factors affecting CL performance and suggest strategies for mitigating forgetting.

Problem

• Catastrophic Forgetting
• Continual Learning
• Neural Networks

Innovation

• Continual Learning
• Neural Network Structure
• Disasterous Forgetting