Curved Inference: A Guide to Geometric Interpretability

Abstract

This paper introduces a unified framework for analyzing the internal geometry of inference in transformer-based language models. Building on a series of prior studies, we present a consolidated introduction to “Curved Inference”: a methodology that measures how token representations evolve in the residual stream as geometric trajectories. Using metrics such as curvature, salience, and semantic surface area, we show that residual trajectories reflect meaningful semantic structure, and are empirically associated with emotional and moral concern, covert intent in sleeper agents, and computational self-modeling dynamics. We consolidate these findings into a reproducible, falsifiable pipeline, supported by formal mathematical definitions and open-source tools. This geometric approach shifts the focus of interpretability from static attribution to dynamic, modelnative inference analysis. The results provide evidence that residual stream geometry is not only measurable, but also structurally related to complex behaviors in the models we study. We invite researchers to replicate, extend, or falsify these claims and test the boundaries of curved inference as a new paradigm for model understanding.

Received: 6 August 2025 | Revised: 12 January 2026 | Accepted: 21 January 2026

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

The data that support the findings of this study are openly available in GitHub at  https://github.com/robman/FRESH-model/tree/main/ benchmarks/curved-inference.

Author Contribution Statement

Rob Manson: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.