@inproceedings{pan-woodard-2026-geolan,
    title = "{G}eo{LAN}: Geometric Learning of Latent Explanatory Directions in Large Language Models",
    author = "Pan, Tianyu  and
      Woodard, Damon L.",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.271/",
    pages = "5493--5521",
    ISBN = "979-8-89176-395-1",
    abstract = "Large language models (LLMs) demonstrate strong performance, but they often lack transparency. We introduce GeoLAN, a training framework that treats token representations as geometric trajectories and applies stickiness conditions inspired by recent developments related to the Kakeya Conjecture. We have developed two differentiable regularizers, Katz-Tao Convex Wolff (KT-CW) and Katz-Tao Attention (KT-Attn), that promote isotropy and encourage diverse attention. Our experiments with Gemma-3 (1B, 4B, 12B) and Llama-3-8B show that GeoLAN frequently maintains task accuracy while improving geometric metrics and reducing certain fairness biases. These benefits are most significant in mid-sized models. Our findings reveal scale-dependent trade-offs between geometric precision and performance, suggesting that geometry-aware training is a promising approach to enhance mechanistic interpretability."
}