ENIGMA: The Geometry of Reasoning and Alignment in Large-Language Models
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915556583538688 |
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| author | Seneque, Gareth Ho, Lap-Hang Saeedi, Nafise Erfanian Molendijk, Jeffrey Kuperman, Ariel Elson, Tim |
| author_facet | Seneque, Gareth Ho, Lap-Hang Saeedi, Nafise Erfanian Molendijk, Jeffrey Kuperman, Ariel Elson, Tim |
| contents | We present Entropic Mutual-Information Geometry Large-Language Model Alignment (ENIGMA), a novel approach to Large-Language Model (LLM) training that jointly improves reasoning, alignment and robustness by treating an organisation's policies/principles as directions to move on a model's information manifold. Our single-loop trainer combines Group-Relative Policy Optimisation (GRPO), an on-policy, critic-free RL method with Chain-of-Thought (CoT)-format only rewards; a Self-Supervised Alignment with Mutual Information (SAMI)-style symmetric InfoNCE auxiliary; and an entropic Sinkhorn optimal-transport regulariser on hidden-state distributions to bound geometry drift. We also introduce infoNCE metrics that specialise to a standard MI lower bound under matched negatives to measure how strongly a model's CoT encodes these policies. These metrics include a Sufficiency Index (SI) that enables the selection and creation of principles that maximise downstream performance prior to training. In our experiments using small (1B) LLMs, high-SI principles predict steadier training dynamics and improved benchmark performance over GRPO ablations. Our information-geometry analysis of trained models validates desirable structural change in the manifold. These results support our hypothesis that reasoning, alignment, and robustness are projections of a single information-geometric objective, and that models trained using ENIGMA demonstrate principled reasoning without the use of a reward model, offering a path to trusted capability |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ENIGMA: The Geometry of Reasoning and Alignment in Large-Language Models Seneque, Gareth Ho, Lap-Hang Saeedi, Nafise Erfanian Molendijk, Jeffrey Kuperman, Ariel Elson, Tim Machine Learning Artificial Intelligence Computation and Language 68T50 I.2.7 We present Entropic Mutual-Information Geometry Large-Language Model Alignment (ENIGMA), a novel approach to Large-Language Model (LLM) training that jointly improves reasoning, alignment and robustness by treating an organisation's policies/principles as directions to move on a model's information manifold. Our single-loop trainer combines Group-Relative Policy Optimisation (GRPO), an on-policy, critic-free RL method with Chain-of-Thought (CoT)-format only rewards; a Self-Supervised Alignment with Mutual Information (SAMI)-style symmetric InfoNCE auxiliary; and an entropic Sinkhorn optimal-transport regulariser on hidden-state distributions to bound geometry drift. We also introduce infoNCE metrics that specialise to a standard MI lower bound under matched negatives to measure how strongly a model's CoT encodes these policies. These metrics include a Sufficiency Index (SI) that enables the selection and creation of principles that maximise downstream performance prior to training. In our experiments using small (1B) LLMs, high-SI principles predict steadier training dynamics and improved benchmark performance over GRPO ablations. Our information-geometry analysis of trained models validates desirable structural change in the manifold. These results support our hypothesis that reasoning, alignment, and robustness are projections of a single information-geometric objective, and that models trained using ENIGMA demonstrate principled reasoning without the use of a reward model, offering a path to trusted capability |
| title | ENIGMA: The Geometry of Reasoning and Alignment in Large-Language Models |
| topic | Machine Learning Artificial Intelligence Computation and Language 68T50 I.2.7 |
| url | https://arxiv.org/abs/2510.11278 |