# Directional Reasoning Trajectory Change (DRTC): Identifying Critical Trace Segments in Reasoning Models

arXiv: https://arxiv.org/abs/2602.15332 · HTML: https://mlsanity.com/paper/2602.15332/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 31 of its 33 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 31)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [Dissecting Recall of Factual Associations in Auto-Regressive Language Models](https://mlsanity.com/paper/2304.14767/) (2023)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Understanding Neural Networks through Representation Erasure](https://mlsanity.com/paper/1612.08220/) (2016)
- [Pay Less Attention with Lightweight and Dynamic Convolutions](https://mlsanity.com/paper/1901.10430/) (2019)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [Deductive Verification of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2306.03872/) (2023)
- [Ministral 3](https://mlsanity.com/paper/2601.08584/) (2026)
- [When Chain of Thought is Necessary, Language Models Struggle to Evade Monitors](https://mlsanity.com/paper/2507.05246/) (2025)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [Phi-4-Mini-Reasoning: Exploring the Limits of Small Reasoning Language Models in Math](https://mlsanity.com/paper/2504.21233/) (2025)
- [LFM2 Technical Report](https://mlsanity.com/paper/2511.23404/) (2025)
- [Efficient Reasoning for Large Reasoning Language Models via Certainty-Guided Reflection Suppression](https://mlsanity.com/paper/2508.05337/) (2025)
- [Entropy-Gated Branching for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2503.21961/) (2025)
- [The Geometry of Reasoning: Flowing Logics in Representation Space](https://mlsanity.com/paper/2510.09782/) (2025)
- [Thought Branches: Interpreting LLM Reasoning Requires Resampling](https://mlsanity.com/paper/2510.27484/) (2025)
- [Can Aha Moments Be Fake? Towards Quantifying Decorative and True Thinking in Chain-of-Thought](https://mlsanity.com/paper/2510.24941/) (2025)
- [Reasoning Models Generate Societies of Thought](https://mlsanity.com/paper/2601.10825/) (2026)
- [Towards Long-Horizon Interpretability: Efficient and Faithful Multi-Token Attribution for Reasoning LLMs](https://mlsanity.com/paper/2602.01914/) (2026)
- [Curved Inference: Concern-Sensitive Geometry in Large Language Model Residual Streams](https://mlsanity.com/paper/2507.21107/) (2025)
- [Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention](https://mlsanity.com/paper/2510.13940/) (2025)
- [Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs](https://mlsanity.com/paper/2506.07824/) (2025)
- [DeLTa: A Decoding Strategy based on Logit Trajectory Prediction Improves Factuality and Reasoning Ability](https://mlsanity.com/paper/2503.02343/) (2025)
- [Explaining the Reasoning of Large Language Models Using Attribution Graphs](https://mlsanity.com/paper/2512.15663/) (2025)

## Built on by (most cited first, 1 of 1)

- [PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning](https://mlsanity.com/paper/2605.23074/) (2026)

## Abstract (arXiv)

Understanding how language models carry out long-horizon reasoning remains an open challenge. Existing interpretability methods often highlight tokens correlated with an answer, but rarely reveal where consequential reasoning turns occur, which earlier context triggers them under causal intervention, or whether highlighted text actually steers the rollout. We introduce Directional Reasoning Trajectory Change (DRTC), a process-causal method that (i) detects pivot decision points via uncertainty and distribution-shift signals and (ii) applies receiver-side interventions that preserve the realized continuation without resampling while blocking information flow from selected earlier chunks only at a pivot. DRTC measures how each intervention redirects the log-probability trajectory relative to the realized rollout direction, yielding signed per-chunk attributions; we also compute logit-space curvature changes and curvature signatures as a complementary geometric diagnostic. Across four reasoning models, influence is sharply concentrated (Gini approximately 0.50-0.58, top-5% mass approximately 0.23-0.28), and learned pivots induce stronger effects than matched random spans. In a 500-problem MATH scaling study with R1-Distill-Qwen-1.5B, learned spans continue to outperform matched random spans (median Delta=0.409, 355/500 positive; p=2.3e-21), and curvature-impact co-localizes with DRTC within traces as a diagnostic. We benchmark against gradient- and perturbation-based chunk attributions and show graded outcome linkage: under embedding-interpolation edits, top-ranked DRTC chunks reduce teacher-forced gold-answer log-probability more than strict position-matched random chunks on a stability-filtered subset. Overall, DRTC provides a causally grounded view of how specific context elements steer on-policy reasoning trajectories.