Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence

• URL: http://arxiv.org/abs/2410.17161v3
• Date: Wed, 18 Jun 2025 14:42:07 GMT
• Title: Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence
• Authors: İlker Işık, Ramazan Gokberk Cinbis, Ebru Aydin Gol,
• Abstract summary: Language models lack the notion of interchangeable tokens.<n>We formalize this machine learning problem and introduce alpha-covariance.<n>Our findings establish a foundation for designing language models that can learn interchangeable token representations.
• Score: 6.991281327290525
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Language models lack the notion of interchangeable tokens: symbols that are semantically equivalent yet distinct, such as bound variables in formal logic. This limitation prevents generalization to larger vocabularies and hinders the model's ability to recognize alpha-equivalence, where renaming bound variables preserves meaning. We formalize this machine learning problem and introduce alpha-covariance, a metric for evaluating robustness to such transformations. To tackle this task, we propose a dual-part token embedding strategy: a shared component ensures semantic consistency, while a randomized component maintains token distinguishability. Compared to a baseline that relies on alpha-renaming for data augmentation, our approach demonstrates improved generalization to unseen tokens in linear temporal logic solving, propositional logic assignment prediction, and copying with an extendable vocabulary, while introducing a favorable inductive bias for alpha-equivalence. Our findings establish a foundation for designing language models that can learn interchangeable token representations, a crucial step toward more flexible and systematic reasoning in formal domains. Our code and project page are available at https://necrashter.github.io/interchangeable-token-embeddings

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