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Oral
Generalization on the Unseen, Logic Reasoning and Degree Curriculum
Emmanuel Abbe · Samy Bengio · Aryo Lotfi · Kevin Rizk

Tue Jul 25 09:50 PM -- 09:58 PM (PDT) @ Meeting Room 316 A-C
in Oral A3 ML Theory »

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky min-degree solutions. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

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Author Information

Emmanuel Abbe
Samy Bengio (Apple MLR)
Aryo Lotfi (EPFL)
Kevin Rizk (EPFL - EPF Lausanne)

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