Predicting Transformer Ability to Handle Longer Sequences

Summary & Methodology Analysis

The paper addresses the challenge of transformer length generalization, which is the ability of a transformer (a deep learning model that uses self-attention mechanisms to process sequence data) to handle inputs longer than those encountered during training. The researchers establish a complete characterization of regular languages in the C-RASP class by extending classical decomposition theory from finite semigroups to the infinite additive group on the integers. This provides a theoretical framework for understanding the specific linguistic structures that permit generalization in these models.

To apply this theory, the authors derived a polynomial-time decision algorithm. This algorithm determines whether a regular language falls within C-RASP, providing a way to assess the generalization potential of a task before deployment. The method was validated using GPT-2, a widely used transformer model. Experimental results across a suite of 125 regular languages demonstrate that membership in C-RASP is an accurate predictor of whether a transformer will successfully generalize to longer sequence lengths.

Despite the efficacy of this classification, the research notes a significant limitation in the diagnostic criteria. A simpler profinite equation criterion exists but is not sufficient on its own to determine membership in C-RASP. Consequently, the full algebraic decomposition approach remains necessary for accurate prediction. The paper does not specify the computational overhead of the algorithm or potential impacts on model throughput beyond noting its polynomial-time complexity.