From Interpolation to Extrapolation: Complete Length Generalization for Arithmetic Transformers

Since its introduction, the transformer model has demonstrated outstanding performance across various tasks. However, there are still unresolved issues regarding length generalization, particularly in algorithmic tasks. In this paper, we investigate the inherent capabilities of transformer models in learning arithmetic algorithms, such as addition and multiplication. Through experiments and attention analysis, we identify a number of crucial factors for achieving optimal length generalization. We show that transformer models are able to generalize to long lengths with the help of targeted attention biasing. We then introduce Attention Bias Calibration (ABC), a calibration stage that enables the model to automatically learn the proper attention biases, which we link to mechanisms in relative position encoding. We demonstrate that using ABC, the transformer model can achieve unprecedented perfect length generalization on certain arithmetic tasks.