Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context

Xiang Cheng; Yuxin Chen; Suvrit Sra

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arXiv · 2312.06528

Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context

Xiang Cheng·Yuxin Chen·Suvrit Sra

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Abstract

Many neural network architectures are known to be Turing Complete, and can thus, in principle implement arbitrary algorithms. However, Transformers are unique in that they can implement gradient-based learning algorithms under simple parameter configurations. This paper provides theoretical and empirical evidence that (non-linear) Transformers naturally learn to implement gradient descent in function space, which in turn enable them to learn non-linear functions in context. Our results apply to a broad class of combinations of non-linear architectures and non-linear in-context learning tasks. Additionally, we show that the optimal choice of non-linear activation depends in a natural way on the class of functions that need to be learned.

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Xiang Cheng, Yuxin Chen, Suvrit Sra. 2023-12-11. Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context. https://arxiv.org/abs/2312.06528

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