A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix
arXiv:2010.04003
Abstract
Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets.
arXiv commentAccepted to AISTATS 2021. Keywords: continual learning, catastrophic forgetting, NTK regime, orthgonal gradient descent
References in corpus (14)
- Neural Tangent Kernel: Convergence and Generalization in Neural Networks
- Continual Learning Through Synaptic Intelligence
- An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks
- Efficient Lifelong Learning with A-GEM
- On Exact Computation with an Infinitely Wide Neural Net
- Gradient Descent Provably Optimizes Over-parameterized Neural Networks
- Towards Robust Evaluations of Continual Learning
- Understanding the Role of Training Regimes in Continual Learning
- Angles between subspaces and their tangents
- Continual Deep Learning by Functional Regularisation of Memorable Past
- Toward Understanding Catastrophic Forgetting in Continual Learning
- Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics
- Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent
- Artificial Neural Variability for Deep Learning: On Overfitting, Noise Memorization, and Catastrophic Forgetting