What Algorithms can Transformers Learn? A Study in Length Generalization
AuthorsHattie Zhou, Omid Saremi, Etai Littwin, Arwen Bradley, Noam Razin, Josh Susskind, Samy Bengio, Preetum Nakkiran
This paper was accepted at the MATH workshop at NeurIPS 2023.
Large language models exhibit surprising emergent generalization properties, yet also struggle with simple reasoning tasks such as arithmetic and parity. This raises the question of if and when Transformer models can learn the true algorithm for solving a task. We study the scope of Transformers' abilities in the specific setting of length generalization on algorithmic tasks. Here, we propose a unifying framework to understand when and how Transformers can exhibit strong length generalization on a given task. Specifically, we leverage RASP (Weiss et al., 2021)—a programming language designed for the computational model of a Transformer—and introduce the RASP-Generalization Conjecture: Transformers tend to length generalize on a task if the task can be solved by a short RASP program which works for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks. Moreover, we leverage our insights to drastically improve generalization performance on traditionally hard tasks (such as parity and addition). On the theoretical side, we give a simple example where the "min-degree-interpolator" model of learning from Abbe et al. (2023) does not correctly predict Transformers' out-of-distribution behavior, but our conjecture does. Overall, our work provides a novel perspective on the mechanisms of compositional generalization and the algorithmic capabilities of Transformers.
Motivated by the effective implementation of transformer architectures in natural language processing, machine learning researchers introduced the concept of a vision transformer (ViT) in 2021. This innovative approach serves as an alternative to convolutional neural networks (CNNs) for computer vision applications, as detailed in the paper, An Image Is Worth 16x16 Words: Transformers for Image Recognition at Scale.