@inproceedings{baeumel-etal-2025-modular,
    title = "Modular Arithmetic: Language Models Solve Math Digit by Digit",
    author = "Baeumel, Tanja  and
      Gurgurov, Daniil  and
      Al Ghussin, Yusser  and
      Genabith, Josef Van  and
      Ostermann, Simon",
    editor = "Inui, Kentaro  and
      Sakti, Sakriani  and
      Wang, Haofen  and
      Wong, Derek F.  and
      Bhattacharyya, Pushpak  and
      Banerjee, Biplab  and
      Ekbal, Asif  and
      Chakraborty, Tanmoy  and
      Singh, Dhirendra Pratap",
    booktitle = "Proceedings of the 14th International Joint Conference on Natural Language Processing and the 4th Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics",
    month = dec,
    year = "2025",
    address = "Mumbai, India",
    publisher = "The Asian Federation of Natural Language Processing and The Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-ijcnlp-aacl/2025.findings-ijcnlp.86/",
    pages = "1380--1409",
    ISBN = "979-8-89176-303-6",
    abstract = "While recent work has begun to uncover the internal strategies that Large Language Models (LLMs) employ for simple arithmetic tasks, a unified understanding of their underlying mechanisms is still lacking. We extend recent findings showing that LLMs represent numbers in a digit-wise manner and present evidence for the existence of digit-position-specific circuits that LLMs use to perform simple arithmetic tasks, i.e. modular subgroups of MLP neurons that operate independently on different digit positions (units, tens, hundreds). Notably, such circuits exist independently of model size and of tokenization strategy, i.e. both for models that encode longer numbers digit-by-digit and as one token.Using Feature Importance and Causal Interventions, we identify and validate the digit-position-specific circuits, revealing a compositional and interpretable structure underlying the solving of arithmetic problems in LLMs. Our interventions selectively alter the model{'}s prediction at targeted digit positions, demonstrating the causal role of digit-position circuits in solving arithmetic tasks."
}