# Efficient Reasoning Exploration via State-Conditioned Latent Steering with Progress Guidance

arXiv: https://arxiv.org/abs/2609.24066 · HTML: https://mlsanity.com/paper/2609.24066/

## Key facts

- No citing papers in the map yet (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 49 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Mechanistic interpretability / [Steering and interpreting LLM reasoning](https://mlsanity.com/mechinterp/steering-and-interpreting-llm-reasoning/)

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

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [The Assistant Axis: Situating and Stabilizing the Default Persona of Language Models](https://mlsanity.com/paper/2601.10387/) (2026)
- [LLMs Encode Harmfulness and Refusal Separately](https://mlsanity.com/paper/2507.11878/) (2025)
- [AceReason-Nemotron 1.1: Advancing Math and Code Reasoning through SFT and RL Synergy](https://mlsanity.com/paper/2506.13284/) (2025)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Refusal Direction is Universal Across Safety-Aligned Languages](https://mlsanity.com/paper/2505.17306/) (2025)
- [Unlocking General Long Chain-of-Thought Reasoning Capabilities of Large Language Models via Representation Engineering](https://mlsanity.com/paper/2503.11314/) (2025)
- [TreeReview: A Dynamic Tree of Questions Framework for Deep and Efficient LLM-based Scientific Peer Review](https://mlsanity.com/paper/2506.07642/) (2025)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning](https://mlsanity.com/paper/2502.07154/) (2025)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [Improving Reasoning Performance in Large Language Models via Representation Engineering](https://mlsanity.com/paper/2504.19483/) (2025)
- [Dipper: Diversity in Prompts for Producing Large Language Model Ensembles in Reasoning tasks](https://mlsanity.com/paper/2412.15238/) (2024)
- [Semantic-Space Exploration and Exploitation in RLVR for LLM Reasoning](https://mlsanity.com/paper/2509.23808/) (2025)
- [Training Large Language Models To Reason In Parallel With Global Forking Tokens](https://mlsanity.com/paper/2510.05132/) (2025)
- [GuidedSampling: Steering LLMs Towards Diverse Candidate Solutions at Inference-Time](https://mlsanity.com/paper/2510.03777/) (2025)
- [Residual Decoding: Mitigating Hallucinations in Large Vision-Language Models via History-Aware Residual Guidance](https://mlsanity.com/paper/2602.01047/) (2026)
- [Beyond Outliers: A Data-Free Layer-wise Mixed-Precision Quantization Approach Driven by Numerical and Structural Dual-Sensitivity](https://mlsanity.com/paper/2603.17354/) (2026)
- [Restoring Exploration after Post-Training: Latent Exploration Decoding for Large Reasoning Models](https://mlsanity.com/paper/2602.01698/) (2026)
- [Training LLMs for Divide-and-Conquer Reasoning Elevates Test-Time Scalability](https://mlsanity.com/paper/2602.02477/) (2026)

## Abstract (arXiv)

Best-of-N is a widely used inference strategy for complex reasoning, whose effectiveness depends on whether sampled candidates can cover diverse and high-quality reasoning paths. However, post-trained reasoning models often suffer from exploration collapse, where independent rollouts repeatedly follow similar reasoning paths and limit the gains from increasing the rollout budget. Existing methods alleviate this issue by promoting broader exploration, but do not explicitly guide exploration toward continuations that make meaningful progress, resulting in limited exploration efficiency. To address this, we propose emphunderlineState-conditioned underlineProgress-guided underlineSteering (SPS), a training-free latent steering framework. Specifically, SPS constructs a state-conditioned Direction Bank containing multiple progress-guided steering vectors for different prefix-state regions. During online inference, SPS retrieves a suitable steering vector based on the current prefix state and applies it at high-uncertainty transitions to guide the next reasoning step toward meaningful progress. Extensive experiments across multiple model scales and benchmarks demonstrate that SPS consistently outperforms strong baselines. Further analyses validate the effectiveness of its key designs and offer valuable insights for future research. The code is available at https://github.com/rattlesnakey/SPS.