Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence

Ilker Isik, Ramazan Gokberk Cinbis, Ebru Aydin Gol

Abstract: We propose a novel approach for learning interchangeable tokens in language models to obtain an extendable vocabulary that can generalize to new tokens. Our method addresses alpha-equivalence, the principle that renaming bound variables preserves semantics. This property arises in many formal languages such as temporal logics, where all proposition symbols represent the same concept but remain distinct. To handle such tokens, we develop a dual-part embedding approach. The first part is shared across all interchangeable tokens, enforcing that they represent the same core concept. The second part is randomly generated for each token, enabling distinguishability. As a baseline, we consider a simpler approach that uses alpha-renaming for data augmentation. We also present alpha-covariance, a metric for measuring robustness against alpha-conversions. When evaluated in a Transformer encoder-decoder model for solving linear temporal logic formulae and copying with extendable vocabulary, our method demonstrates promising generalization capabilities as well as a favorable inductive bias for alpha-equivalence.