From Outcome to Representation: Tracing Reasoning Mechanisms through Integrated Policy Gradient

Large Language Models (LLMs) demonstrate remarkable reasoning capabilities, yet the internal mechanisms driving these multi-step processes remain opaque. Existing mechanistic interpretability approaches often rely on superficial text-pattern co-occurrences or capture only short-term effects, struggling to trace the long-horizon, outcome-driven influence of internal components such as neurons or sparse features in multi-step reasoning. In this paper, we introduce Integrated Policy Gradient (IPG), a novel, training-free framework that brings policy-based attribution into mechanistic interpretability for LLM reasoning. Grounded in *outcome-oriented* and *sequential-influence-aware* principles, it backpropagates outcome-level, non-differentiable behavioral signals (e.g., reasoning outcome correctness) through entire inference trajectories, utilizing path integration to isolate outcome-relevant mediators at component level for reliable attribution. This provides a linear approximation of Causal Mediation Analysis (CMA) in reasoning. Empirical evaluations demonstrate that IPG achieves precise localization and reveals mechanistic insights by identifying sparse, concentrated subsets of internal components associated with specific reasoning behaviors. Our method also enables modulation of reasoning capabilities, offering a powerful and reliable framework for understanding LLM reasoning.