Capability and Interpretability of Transformers on Multi-task Recurrence

Transformers are widely used in various language tasks, with limited understanding of their internal mechanisms. Motivated by the recurrent structure of many linguistic rules, we study the capability and interpretability of Transformers through a controlled family of linear recurrence tasks over finite cyclic groups. These tasks range from executing a single fixed rule to identifying a latent rule from context and switching between explicitly specified rules, with and without input masking. Through extensive experiments across different configurations, we find that switching specified rules is simpler than identifying latent rules for Transformers in general. We also identify how several key factors affect the generalization capability of Transformers, including the depth, width, and the algebraic structure of the linear recurrence. Curriculum training is extremely useful when the number of rules is large. With standard tools in mechanistic interpretability like linear probing and input patching, our study reveals how Transformers represent, identify, and execute multiple rules.