A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix

Thang Doan, Mehdi Abbana Bennani, Bogdan Mazoure, Guillaume Rabusseau, Pierre Alquier
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1072-1080, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-doan21a, title = { A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix }, author = {Doan, Thang and Abbana Bennani, Mehdi and Mazoure, Bogdan and Rabusseau, Guillaume and Alquier, Pierre}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1072--1080}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/doan21a/doan21a.pdf}, url = {https://proceedings.mlr.press/v130/doan21a.html}, 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. } }
Endnote
%0 Conference Paper %T A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix %A Thang Doan %A Mehdi Abbana Bennani %A Bogdan Mazoure %A Guillaume Rabusseau %A Pierre Alquier %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-doan21a %I PMLR %P 1072--1080 %U https://proceedings.mlr.press/v130/doan21a.html %V 130 %X 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.
APA
Doan, T., Abbana Bennani, M., Mazoure, B., Rabusseau, G. & Alquier, P.. (2021). A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1072-1080 Available from https://proceedings.mlr.press/v130/doan21a.html.

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