# GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models

arXiv: https://arxiv.org/abs/2603.19460 · HTML: https://mlsanity.com/paper/2603.19460/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Post-hoc Interpretability for Neural NLP: A Survey](https://mlsanity.com/paper/2108.04840/) (2021)
- [Towards Faithful Model Explanation in NLP: A Survey](https://mlsanity.com/paper/2209.11326/) (2022)
- [IsoScore: Measuring the Uniformity of Embedding Space Utilization](https://mlsanity.com/paper/2108.07344/) (2021)
- [The Hidden Dimensions of LLM Alignment: A Multi-Dimensional Analysis of Orthogonal Safety Directions](https://mlsanity.com/paper/2502.09674/) (2025)
- [Tracing the Representation Geometry of Language Models from Pretraining to Post-training](https://mlsanity.com/paper/2509.23024/) (2025)
- [The Rogue Scalpel: Activation Steering Compromises LLM Safety](https://mlsanity.com/paper/2509.22067/) (2025)
- [From superposition to sparse codes: interpretable representations in neural networks](https://mlsanity.com/paper/2503.01824/) (2025)
- [Unboxing the Black Box: Mechanistic Interpretability for Algorithmic Understanding of Neural Networks](https://mlsanity.com/paper/2511.19265/) (2025)
- [Combatting Dimensional Collapse in LLM Pre-Training Data via Diversified File Selection](https://mlsanity.com/paper/2504.20644/) (2025)
- [Mechanistic Interpretability of Code Correctness in LLMs via Sparse Autoencoders](https://mlsanity.com/paper/2510.02917/) (2025)

## Abstract (arXiv)

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.