Representation trajectory geometry distinguishes deceptive from sincere alignment without creating adversarial attack surfaces because geometric patterns across reasoning steps are substantially harder to surgically remove than atomic features

The method characterizes alignment-relevant properties as geometric patterns in activation space — the curvature, divergence rate, and trajectory shape of internal representations across reasoning steps — rather than identifying specific neurons or SAE features. Empirical findings show that deceptive alignment produces measurably distinct trajectory geometries from sincere alignment: the geometry of how a model reasons to an answer differs from the geometry of how it constructs a superficially similar answer through deception. Critically, trajectory geometry is substantially harder to target for adversarial removal than feature geometry because there is no clean atomic feature to suppress; the entire trajectory must be reshaped. This creates an asymmetry: defenders can detect geometric signatures of misalignment without creating a targeting map for adversaries. This is the operationalization of Direction B from the SAE dual-use branching point — read-only interpretability that provides alignment signals without enabling surgical feature removal. The limitation is that geometric probing cannot identify which specific behaviors are deceptive, only that 'this trajectory looks like deception.'

Challenging Evidence

Source: Theseus synthetic analysis (2026-04-22)

Trajectory geometry monitoring does create adversarial attack surfaces through multi-layer SCAV generalization. The claim that geometric approaches avoid attack surface creation is incorrect for white-box adversaries with access to model weights. May need qualification to 'black-box adversaries only, contingent on rotation pattern specificity.'

Challenging Evidence

Source: Theseus synthetic analysis of SCAV generalization to multi-layer ensembles

Multi-layer ensemble analysis shows trajectory geometry monitoring DOES create attack surfaces in white-box settings. While multi-layer ensembles are harder to exploit than single-layer probes, white-box multi-layer SCAV is structurally feasible through simultaneous suppression of concept directions at all monitored layers. The claim that trajectory geometry avoids attack surfaces may need qualification to 'reduces attack surface in black-box settings if rotation patterns are model-specific.'