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Life sciences · Preprint
arXiv · September 10, 2026
Raises a question worth testing. It does not answer one.
This preprint proposes that large language model behaviours share a common Fisher-Rao geometric structure across architectures, and that this geometry can predict and control model outputs through local interventions. The work is theoretical and exploratory, mapping internal model geometry without peer review, and remains unvalidated in external application.
Mechanistic study with controlled experiments across multiple model architectures. Large language models spanning transformer, state-space, and recurrent architectures; human word choices used as reference for output agreement. Intervention: Geometric control via minimum-disturbance local interventions and model-only calibration; randomised experiments varying evidence depth; controlled language assignments. Compared with: Euclidean control; human word choices as reference for output alignment.
Output geometries agree more strongly than activation geometries across transformer, state-space and recurrent models Shared geometry supports semantic-category transfer between models Agreement with human word choices increases with predictive accuracy, scale and training, and improves further after model-only calibration
Generalisability to real-world model deployment and safety constraints not addressed
The source did not state who this applies to in practice.
This is a mechanistic and theoretical study of large language model geometry using mathematical frameworks; it presents exploratory analyses and controlled experiments on model internals without clinical outcomes, hard endpoints, or peer review.
As stated by the source record.
Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.
What is missing. This record has no reported figures. That is a gap in the analysis, not a judgement about the study.
Large language models learn similar behaviours, yet it remains unclear what structure they share or how to change one behaviour without disturbing others. The Fisher-Rao geometry of next-token probabilities connects these questions: behaviour determines this geometry up to output-preserving symmetries, whereas activation geometry depends on coordinates. Across transformer, state-space and recurrent models, output geometries agree more strongly than activation geometries, and shared geometry supports semantic-category transfer. Agreement with human word choices increases with predictive accuracy, scale and training, and improves further after model-only calibration. Token probabilities and read-out geometry jointly predict the spectrum and its effective dimension. Controlled language assignments show that geometry follows the language law across architectures. Pretraining corpus statistics predict held-out fact acquisition without recalibration, while randomised experiments show that deeper evidence substantially delays acquisition across every tested architecture and evidence construction. Finally, the geometry prescribes minimum-disturbance local interventions, predicts their relative cost, and supports reusable control: updates learned on donor prompts transfer to unseen prompts while better preserving behaviour on reference prompts than Euclidean control. The same geometric correction improves steering, editing, attribution, dictionary learning and fine-tuning.
Taken from the source record, never inferred. Follow any of these and new work involving them reaches your briefing.