Towards Generalization beyond Pointwise Learning: A Unified Information-theoretic Perspective

Yuxin Dong, Tieliang Gong, Hong Chen, Zhongjiang He, Mengxiang Li, Shuangyong Song, Chen Li
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:11311-11345, 2024.

Abstract

The recent surge in contrastive learning has intensified the interest in understanding the generalization of non-pointwise learning paradigms. While information-theoretic analysis achieves remarkable success in characterizing the generalization behavior of learning algorithms, its applicability is largely confined to pointwise learning, with extensions to the simplest pairwise settings remaining unexplored due to the challenges of non-i.i.d losses and dimensionality explosion. In this paper, we develop the first series of information-theoretic bounds extending beyond pointwise scenarios, encompassing pointwise, pairwise, triplet, quadruplet, and higher-order scenarios, all within a unified framework. Specifically, our hypothesis-based bounds elucidate the generalization behavior of iterative and noisy learning algorithms via gradient covariance analysis, and our prediction-based bounds accurately estimate the generalization gap with computationally tractable low-dimensional information metrics. Comprehensive numerical studies then demonstrate the effectiveness of our bounds in capturing the generalization dynamics across diverse learning scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-dong24a, title = {Towards Generalization beyond Pointwise Learning: A Unified Information-theoretic Perspective}, author = {Dong, Yuxin and Gong, Tieliang and Chen, Hong and He, Zhongjiang and Li, Mengxiang and Song, Shuangyong and Li, Chen}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {11311--11345}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/dong24a/dong24a.pdf}, url = {https://proceedings.mlr.press/v235/dong24a.html}, abstract = {The recent surge in contrastive learning has intensified the interest in understanding the generalization of non-pointwise learning paradigms. While information-theoretic analysis achieves remarkable success in characterizing the generalization behavior of learning algorithms, its applicability is largely confined to pointwise learning, with extensions to the simplest pairwise settings remaining unexplored due to the challenges of non-i.i.d losses and dimensionality explosion. In this paper, we develop the first series of information-theoretic bounds extending beyond pointwise scenarios, encompassing pointwise, pairwise, triplet, quadruplet, and higher-order scenarios, all within a unified framework. Specifically, our hypothesis-based bounds elucidate the generalization behavior of iterative and noisy learning algorithms via gradient covariance analysis, and our prediction-based bounds accurately estimate the generalization gap with computationally tractable low-dimensional information metrics. Comprehensive numerical studies then demonstrate the effectiveness of our bounds in capturing the generalization dynamics across diverse learning scenarios.} }
Endnote
%0 Conference Paper %T Towards Generalization beyond Pointwise Learning: A Unified Information-theoretic Perspective %A Yuxin Dong %A Tieliang Gong %A Hong Chen %A Zhongjiang He %A Mengxiang Li %A Shuangyong Song %A Chen Li %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-dong24a %I PMLR %P 11311--11345 %U https://proceedings.mlr.press/v235/dong24a.html %V 235 %X The recent surge in contrastive learning has intensified the interest in understanding the generalization of non-pointwise learning paradigms. While information-theoretic analysis achieves remarkable success in characterizing the generalization behavior of learning algorithms, its applicability is largely confined to pointwise learning, with extensions to the simplest pairwise settings remaining unexplored due to the challenges of non-i.i.d losses and dimensionality explosion. In this paper, we develop the first series of information-theoretic bounds extending beyond pointwise scenarios, encompassing pointwise, pairwise, triplet, quadruplet, and higher-order scenarios, all within a unified framework. Specifically, our hypothesis-based bounds elucidate the generalization behavior of iterative and noisy learning algorithms via gradient covariance analysis, and our prediction-based bounds accurately estimate the generalization gap with computationally tractable low-dimensional information metrics. Comprehensive numerical studies then demonstrate the effectiveness of our bounds in capturing the generalization dynamics across diverse learning scenarios.
APA
Dong, Y., Gong, T., Chen, H., He, Z., Li, M., Song, S. & Li, C.. (2024). Towards Generalization beyond Pointwise Learning: A Unified Information-theoretic Perspective. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:11311-11345 Available from https://proceedings.mlr.press/v235/dong24a.html.

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