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    <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.</abstract>
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%0 Conference Proceedings
%T GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models
%A Pan, Tianyu
%A Woodard, Damon L.
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F pan-woodard-2026-geolan
%X 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.
%U https://aclanthology.org/2026.findings-acl.271/
%P 5493-5521

Markdown (Informal)

[GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models](https://aclanthology.org/2026.findings-acl.271/) (Pan & Woodard, Findings 2026)

• GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models (Pan & Woodard, Findings 2026)

ACL

• Tianyu Pan and Damon L. Woodard. 2026. GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models. In Findings of the Association for Computational Linguistics: ACL 2026, pages 5493–5521, San Diego, California, United States. Association for Computational Linguistics.