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LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals

Lihao Sun, Hang Dong, Bo Qiao, Qingwei Lin, Dongmei Zhang, Saravan Rajmohan · Apr 7, 2026 · Citations: 0

Long Horizon
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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

  • This paper looks adjacent to evaluation work, but not like a strong protocol reference.
  • The available metadata is too thin to trust this as a primary source.
  • The abstract does not clearly name benchmarks or metrics.
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Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 15%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space."

Quality Controls

missing

Not reported

No explicit QC controls found.

"This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Unit of annotation: Trajectory (inferred)
  • Expertise required: Math

Evaluation Details

  • Evaluation modes:
  • Agentic eval: Long Horizon
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space.
  • We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth.
  • This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Research Summary

Contribution Summary

  • We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth.
  • Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories.

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

Related Papers

Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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