Timezone: »
The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may "forget" how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called "Ideal Continual Learner" (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify "how rehearsal affects generalization". Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.
Author Information
Liangzu Peng (University of Pennsylvania)
Paris Giampouras (Mathematical Institute for Data Science, Johns Hopkins University)
Rene Vidal (University of Pennsylvania)
More from the Same Authors
-
2023 Workshop: HiLD: High-dimensional Learning Dynamics Workshop »
Courtney Paquette · Zhenyu Liao · Mihai Nica · Elliot Paquette · Andrew Saxe · Rene Vidal -
2023 Poster: On the Convergence of Gradient Flow on Multi-layer Linear Models »
Hancheng Min · Rene Vidal · Enrique Mallada -
2023 Poster: Learning Globally Smooth Functions on Manifolds »
Juan Cervino · Luiz Chamon · Benjamin Haeffele · Rene Vidal · Alejandro Ribeiro -
2022 Poster: Understanding Doubly Stochastic Clustering »
Tianjiao Ding · Derek Lim · Rene Vidal · Benjamin Haeffele -
2022 Spotlight: Understanding Doubly Stochastic Clustering »
Tianjiao Ding · Derek Lim · Rene Vidal · Benjamin Haeffele -
2022 Poster: Reverse Engineering $\ell_p$ attacks: A block-sparse optimization approach with recovery guarantees »
Darshan Thaker · Paris Giampouras · Rene Vidal -
2022 Spotlight: Reverse Engineering $\ell_p$ attacks: A block-sparse optimization approach with recovery guarantees »
Darshan Thaker · Paris Giampouras · Rene Vidal -
2021 Poster: Dual Principal Component Pursuit for Robust Subspace Learning: Theory and Algorithms for a Holistic Approach »
Tianyu Ding · Zhihui Zhu · Rene Vidal · Daniel Robinson -
2021 Spotlight: Dual Principal Component Pursuit for Robust Subspace Learning: Theory and Algorithms for a Holistic Approach »
Tianyu Ding · Zhihui Zhu · Rene Vidal · Daniel Robinson -
2021 Poster: Understanding the Dynamics of Gradient Flow in Overparameterized Linear models »
Salma Tarmoun · Guilherme Franca · Benjamin Haeffele · Rene Vidal -
2021 Poster: On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks »
Hancheng Min · Salma Tarmoun · Rene Vidal · Enrique Mallada -
2021 Spotlight: On the Explicit Role of Initialization on the Convergence and Implicit Bias of Overparametrized Linear Networks »
Hancheng Min · Salma Tarmoun · Rene Vidal · Enrique Mallada -
2021 Spotlight: Understanding the Dynamics of Gradient Flow in Overparameterized Linear models »
Salma Tarmoun · Guilherme Franca · Benjamin Haeffele · Rene Vidal -
2021 Poster: A Nullspace Property for Subspace-Preserving Recovery »
Mustafa D Kaba · Chong You · Daniel Robinson · Enrique Mallada · Rene Vidal -
2021 Spotlight: A Nullspace Property for Subspace-Preserving Recovery »
Mustafa D Kaba · Chong You · Daniel Robinson · Enrique Mallada · Rene Vidal -
2019 Poster: Noisy Dual Principal Component Pursuit »
Tianyu Ding · Zhihui Zhu · Tianjiao Ding · Yunchen Yang · Daniel Robinson · Manolis Tsakiris · Rene Vidal -
2019 Oral: Noisy Dual Principal Component Pursuit »
Tianyu Ding · Zhihui Zhu · Tianjiao Ding · Yunchen Yang · Daniel Robinson · Manolis Tsakiris · Rene Vidal