Rewriting or Reweighting? A Geometric Account in Language Models

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.

Large language models are increasingly used as computational tools for modeling human-like behavior. We introduce a behavioral induction framework that modifies model policies through fine-tuning on structured decision-making tasks: using synthetic datasets inspired by maladaptive behavioral patterns, including depression and paranoia, we train transformer-based language models to consistently select specific classes of actions across diverse contexts. We then test whether this behavioral optimization produces systematic changes in generative distributions. Across two architectures, fine-tuned models show stable, context-general shifts in next-token probability distributions, including increased probability assigned to negative and threat-related interpretations in open-ended language tasks. These effects generalize beyond training contexts and are detectable in qualitative completions, psychometric-style evaluations, and quantitative distributional metrics such as Jensen-Shannon divergence. Induced behavioral profiles also show partial specificity. Models optimized for different behavioral patterns exhibit dissociable response tendencies across evaluation probes, suggesting that structured behavioral training produces differentiated policy-level biases rather than generic distributional skew. We interpret these findings as evidence that consistent behavioral optimization in LLMs can generate stable behavioral and distributional patterns consistent with altered latent priors, linking action selection and language generation. More broadly, the results support a view of LLMs as policy-based systems in which behavioral constraints shape emergent representational structure, highlighting their potential as controlled testbeds for studying the relationship between behavior, interpretation, and generative language in computational models of cognition.

Language-model post-training is the main stage at which model behavior is shaped, yet it still largely involves optimization of scalar rewards that summarize diverse desiderata. This abstraction gives practitioners little visibility into what their data actually teaches models, allowing spurious correlations to be learned by a model and inducing undesirable behaviors such as over-stylization and sycophancy. To address this problem, we ask: can we inspect a preference dataset before optimization and decide, at the level of concepts, which behaviors a model should be allowed to learn? Motivated by this, we introduce a data-centric post-training pipeline that uses interpretability protocols to develop statistical hypotheses for the latent concepts separating preferred from dispreferred generations, making them explicit for fine-grained user feedback. Building on this view, we unify several interpretability-based training protocols as ways of shaping rewards via feature or data interventions. Empirically, we show that our pipeline diagnoses undesirable signals in existing preference data, mitigates off-target learning, and can also help amplify or shape desired properties such as safeguards and model personality. More broadly, our results suggest that interpretability can turn post-training from optimizing opaque proxy rewards into a process of auditing and sculpting the learning signal itself.