Sketchy Moment Matching: Toward Fast and Provable Data Selection for Finetuning
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910817988902912 |
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| author | Dong, Yijun Phan, Hoang Pan, Xiang Lei, Qi |
| author_facet | Dong, Yijun Phan, Hoang Pan, Xiang Lei, Qi |
| contents | We revisit data selection in a modern context of finetuning from a fundamental perspective. Extending the classical wisdom of variance minimization in low dimensions to high-dimensional finetuning, our generalization analysis unveils the importance of additionally reducing bias induced by low-rank approximation. Inspired by the variance-bias tradeoff in high dimensions from the theory, we introduce Sketchy Moment Matching (SkMM), a scalable data selection scheme with two stages. (i) First, the bias is controlled using gradient sketching that explores the finetuning parameter space for an informative low-dimensional subspace $\mathcal{S}$; (ii) then the variance is reduced over $\mathcal{S}$ via moment matching between the original and selected datasets. Theoretically, we show that gradient sketching is fast and provably accurate: selecting $n$ samples by reducing variance over $\mathcal{S}$ preserves the fast-rate generalization $O(\dim(\mathcal{S})/n)$, independent of the parameter dimension. Empirically, we concretize the variance-bias balance via synthetic experiments and demonstrate the effectiveness of SkMM for finetuning in real vision tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sketchy Moment Matching: Toward Fast and Provable Data Selection for Finetuning Dong, Yijun Phan, Hoang Pan, Xiang Lei, Qi Machine Learning Numerical Analysis We revisit data selection in a modern context of finetuning from a fundamental perspective. Extending the classical wisdom of variance minimization in low dimensions to high-dimensional finetuning, our generalization analysis unveils the importance of additionally reducing bias induced by low-rank approximation. Inspired by the variance-bias tradeoff in high dimensions from the theory, we introduce Sketchy Moment Matching (SkMM), a scalable data selection scheme with two stages. (i) First, the bias is controlled using gradient sketching that explores the finetuning parameter space for an informative low-dimensional subspace $\mathcal{S}$; (ii) then the variance is reduced over $\mathcal{S}$ via moment matching between the original and selected datasets. Theoretically, we show that gradient sketching is fast and provably accurate: selecting $n$ samples by reducing variance over $\mathcal{S}$ preserves the fast-rate generalization $O(\dim(\mathcal{S})/n)$, independent of the parameter dimension. Empirically, we concretize the variance-bias balance via synthetic experiments and demonstrate the effectiveness of SkMM for finetuning in real vision tasks. |
| title | Sketchy Moment Matching: Toward Fast and Provable Data Selection for Finetuning |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2407.06120 |