Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence

İlker Işık, Ramazan Gokberk Cinbis, Ebru Aydin Gol
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:26523-26541, 2025.

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

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-isik25a, title = {Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence}, author = {I\c{s}{\i}k, \.{I}lker and Cinbis, Ramazan Gokberk and Gol, Ebru Aydin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {26523--26541}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/isik25a/isik25a.pdf}, url = {https://proceedings.mlr.press/v267/isik25a.html}, 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} }
Endnote
%0 Conference Paper %T Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence %A İlker Işık %A Ramazan Gokberk Cinbis %A Ebru Aydin Gol %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-isik25a %I PMLR %P 26523--26541 %U https://proceedings.mlr.press/v267/isik25a.html %V 267 %X 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
APA
Işık, İ., Cinbis, R.G. & Gol, E.A.. (2025). Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:26523-26541 Available from https://proceedings.mlr.press/v267/isik25a.html.

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