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

2026-03-01

AI Summary

This work addresses the limitations of existing interpretability methods for large language models, which rely on static activations and are often confounded by superficial lexical features, thereby failing to uncover genuine reasoning mechanisms. The authors propose modeling the reasoning process as a trajectory of iterative layer-wise optimization, analyzing geometric displacements across layers rather than static snapshots to identify geometric invariants underlying reasoning. This approach introduces a trajectory-based perspective that replaces conventional probing techniques, enabling activation-free interpretability analysis in both dense and mixture-of-experts (MoE) architectures. Evaluated on tasks including commonsense reasoning, question answering, and toxicity detection, the method significantly outperforms current approaches and effectively mitigates lexical confounding, demonstrating the efficacy of trajectory modeling in revealing the true structural dynamics of model reasoning.

Technology Category

• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Machine Learning: Mixture of Experts (MoE)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Large Language Models
• explainability
• hidden states
• reasoning
• polysemantic features

Innovation

• trajectory analysis
• geometric displacement
• layer-wise dynamics
• LLM interpretability
• reasoning invariants