Truth as a Trajectory: What Internal Representations Reveal About Large Language Model Reasoning

TL;DR

This paper introduces Truth as a Trajectory (TaT), a novel method analyzing layer-wise geometric displacement in transformer models to better understand and distinguish valid reasoning from spurious behavior in large language models.

Contribution

TaT shifts the focus from static activations to dynamic layer-wise trajectories, revealing geometric invariants that improve explainability of LLM reasoning processes.

Findings

TaT outperforms traditional probing methods in identifying valid reasoning.

Trajectory analysis reduces reliance on surface-level lexical cues.

Effective across various architectures and benchmarks.

Abstract

Existing explainability methods for Large Language Models (LLMs) typically treat hidden states as static points in activation space, assuming that correct and incorrect inferences can be separated using representations from an individual layer. However, these activations are saturated with polysemantic features, leading to linear probes learning surface-level lexical patterns rather than underlying reasoning structures. We introduce Truth as a Trajectory (TaT), which models the transformer inference as an unfolded trajectory of iterative refinements, shifting analysis from static activations to layer-wise geometric displacement. By analyzing displacement of representations across layers, TaT uncovers geometric invariants that distinguish valid reasoning from spurious behavior. We evaluate TaT across dense and Mixture-of-Experts (MoE) architectures on benchmarks spanning commonsense reasoning, question answering, and toxicity detection. Without access to the activations themselves and using only changes in activations across layers, we show that TaT effectively mitigates reliance on static lexical confounds, outperforming conventional probing, and establishes trajectory analysis as a complementary perspective on LLM explainability.