# From Candidate Tokens to Final Outcomes: Decoding Relative Long-Horizon Candidate Value from Reasoning Model Representations

arXiv: https://arxiv.org/abs/2610.15412 · HTML: https://mlsanity.com/paper/2610.15412/

## 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 28 of its 37 references that are in the map.
- First posted on arXiv 11 Oct 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, 28 of 28)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Think Only When You Need with Large Hybrid-Reasoning Models](https://mlsanity.com/paper/2505.14631/) (2025)
- [Reasoning Theater: Disentangling Model Beliefs from Chain-of-Thought](https://mlsanity.com/paper/2603.05488/) (2026)
- [Forking Paths in Neural Text Generation](https://mlsanity.com/paper/2412.07961/) (2024)
- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [Non-myopic Generation of Language Models for Reasoning and Planning](https://mlsanity.com/paper/2410.17195/) (2024)
- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Knowing Before Saying: LLM Representations Encode Information About Chain-of-Thought Success Before Completion](https://mlsanity.com/paper/2505.24362/) (2025)
- [The Hidden Space of Transformer Language Adapters](https://mlsanity.com/paper/2402.13137/) (2024)
- [LLMs Encode Their Failures: Predicting Success from Pre-Generation Activations](https://mlsanity.com/paper/2602.09924/) (2026)
- [Are language models aware of the road not taken? Token-level uncertainty and hidden state dynamics](https://mlsanity.com/paper/2511.04527/) (2025)
- [Token Hidden Reward: Steering Exploration-Exploitation in Group Relative Deep Reinforcement Learning](https://mlsanity.com/paper/2510.03669/) (2025)
- [Truth as a Trajectory: What Internal Representations Reveal About Large Language Model Reasoning](https://mlsanity.com/paper/2603.01326/) (2026)
- [Towards Long-Horizon Interpretability: Efficient and Faithful Multi-Token Attribution for Reasoning LLMs](https://mlsanity.com/paper/2602.01914/) (2026)
- [Hidden Error Awareness in Chain-of-Thought Reasoning: The Signal Is Diagnostic, Not Causal](https://mlsanity.com/paper/2605.09502/) (2026)
- [Chain-of-Thought Tokens are Computer Program Variables](https://mlsanity.com/paper/2505.04955/) (2025)
- [Your Language Model is Its Own Critic: Reinforcement Learning with Value Estimation from Actor's Internal States](https://mlsanity.com/paper/2605.07579/) (2026)
- [Sparse Reward Subsystem in Large Language Models](https://mlsanity.com/paper/2602.00986/) (2026)
- [The Cancellation Hypothesis in Critic-Free RL: From Outcome Rewards to Token Credits](https://mlsanity.com/paper/2605.08666/) (2026)
- [Beyond the Target: From Imitation to Collaboration in Speculative Decoding](https://mlsanity.com/paper/2605.24793/) (2026)
- [Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing](https://mlsanity.com/paper/2606.25354/) (2026)
- [Martingale Foresight Sampling: A Principled Approach to Inference-Time LLM Decoding](https://mlsanity.com/paper/2601.15482/) (2026)
- [Unleashing Implicit Rewards: Prefix-Value Learning for Distribution-Level Optimization](https://mlsanity.com/paper/2604.13197/) (2026)
- [FutureBridge: Token Selection Beyond Local Preference in Collaborative Decoding](https://mlsanity.com/paper/2608.06819/) (2026)

## Abstract (arXiv)

Large reasoning models generate reasoning trajectories token by token. At a given prefix, multiple next-token candidates may be plausible, yet shape subsequent reasoning and differ in their chances of leading to the correct answer. Whether these differences are reflected in internal representations remains unclear. To study this question, we define relative long-horizon candidate value to quantify within-prefix differences and construct the Reasoning Candidate-Token Value (RCTV) dataset, pairing mathematical reasoning prefixes with plausible next-token candidates and their empirical long-horizon candidate values. Using RCTV, we examine hidden states, multilayer perceptron outputs, and attention outputs at candidate positions with sparse linear probes. Experimental results provide evidence that relative long-horizon candidate value is linearly decodable from these representations at multiple layers. Candidate-value probes can also outperform probability- and embedding-based baselines. Furthermore, a controlled online intervention experiment shows that using the decoded signals to guide token selection during generation can improve the chances of eventual success. Our findings provide evidence that internal representations encode information about relative long-horizon candidate value, offering insights into how local candidate-level representations relate to long-horizon reasoning outcomes.