GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models
arXiv:2603.19460v1 Announce Type: new 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.
arXiv:2603.19460v1 Announce Type: new 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.
Executive Summary
The article 'GeoLAN: Geometric Learning of Latent Explanatory Directions in Large Language Models' presents a novel training framework for Large Language Models (LLMs) that incorporates geometric concepts to enhance transparency and fairness. The proposed framework, GeoLAN, treats token representations as geometric trajectories and applies stickiness conditions inspired by the Kakeya Conjecture. Two differentiable regularizers, KT-CW and KT-Attn, are introduced to promote isotropy and encourage diverse attention. The authors conduct experiments with Gemma-3 and Llama-3-8B models, observing improved geometric metrics and reduced fairness biases without compromising task accuracy. The findings suggest scale-dependent trade-offs between geometric precision and performance, highlighting the potential of geometry-aware training to improve mechanistic interpretability.
Key Points
- ▸ GeoLAN introduces a novel training framework for LLMs that combines geometric concepts with stickiness conditions to enhance transparency and fairness.
- ▸ The framework uses two differentiable regularizers, KT-CW and KT-Attn, to promote isotropy and encourage diverse attention.
- ▸ Experiments with Gemma-3 and Llama-3-8B models demonstrate improved geometric metrics and reduced fairness biases without compromising task accuracy.
Merits
Strength in promoting fairness
GeoLAN demonstrates the ability to reduce fairness biases in LLMs, which is a significant step towards achieving more equitable AI systems.
Potential for improved interpretability
The geometry-aware training approach in GeoLAN has the potential to enhance mechanistic interpretability of LLMs, making them more transparent and explainable.
Demerits
Limited scalability
The authors note that the benefits of GeoLAN are most significant in mid-sized models, suggesting that the framework may not be as effective for larger models.
Need for further evaluation
While the authors present promising results, further evaluation and testing are necessary to fully understand the strengths and limitations of GeoLAN.
Expert Commentary
The article presents a novel and intriguing approach to training LLMs, one that combines geometric concepts with stickiness conditions to promote transparency and fairness. While the results are promising, further evaluation and testing are necessary to fully understand the strengths and limitations of GeoLAN. The framework's potential to improve mechanistic interpretability and reduce fairness biases makes it a significant contribution to the field of AI. However, the limited scalability and need for further evaluation are notable limitations that must be addressed. Overall, GeoLAN is a promising direction for future research in AI, and its implications for policy-making and practical applications are significant.
Recommendations
- ✓ Future researchers should focus on scaling up GeoLAN to larger models and evaluating its performance in more diverse tasks and datasets.
- ✓ Developers and practitioners should consider integrating GeoLAN into their existing LLM training pipelines to take advantage of its potential benefits.
Sources
Original: arXiv - cs.LG
