The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913207380082688 |
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| author | Goldfarb, Daniel Evron, Itay Weinberger, Nir Soudry, Daniel Hand, Paul |
| author_facet | Goldfarb, Daniel Evron, Itay Weinberger, Nir Soudry, Daniel Hand, Paul |
| contents | In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12617 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model Goldfarb, Daniel Evron, Itay Weinberger, Nir Soudry, Daniel Hand, Paul Machine Learning In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks. |
| title | The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2401.12617 |