The information geometry of large language models is shared, learned, and controllable
Fisher-Rao output geometry is shared across LLM architectures and enables minimum-disturbance interventions that transfer across prompts for steering and editing.
The paper shows the Fisher-Rao geometry of next-token probabilities, unlike activation geometry, is consistent across transformer, state-space, and recurrent models and supports semantic-category transfer. Agreement with human word choices rises with accuracy, scale, and training, and corpus statistics predict held-out fact acquisition. The geometry prescribes minimum-disturbance local interventions whose updates transfer from donor prompts to unseen prompts, improving steering, editing, attribution, dictionary learning, and fine-tuning versus Euclidean control.
- Output geometry (Fisher-Rao) is shared across transformer, SSM, and RNN architectures
- Geometry prescribes minimum-disturbance behavioral interventions with predictable cost
- Interventions learned on donor prompts transfer to unseen prompts
- Single geometric correction improves steering, editing, attribution, and fine-tuning
Full article181 words · extracted from huggingface.co · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2609.11063