# R-Horizon: How Far Can Your Large Reasoning Model Really Go in Breadth and Depth?

arXiv: https://arxiv.org/abs/2510.08189 · HTML: https://mlsanity.com/paper/2510.08189/

## Key facts

- Cited by 8 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 35 of its 41 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## 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 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Training Language Models to Reason Efficiently](https://mlsanity.com/paper/2502.04463/) (2025)
- [When More is Less: Understanding Chain-of-Thought Length in LLMs](https://mlsanity.com/paper/2502.07266/) (2025)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [The Danger of Overthinking: Examining the Reasoning-Action Dilemma in Agentic Tasks](https://mlsanity.com/paper/2502.08235/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Nemotron-4 340B Technical Report](https://mlsanity.com/paper/2406.11704/) (2024)
- [WebShaper: Agentically Data Synthesizing via Information-Seeking Formalization](https://mlsanity.com/paper/2507.15061/) (2025)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)

## Built on by (most cited first, 8 of 8)

- [Mechanistic Evidence for Faithfulness Decay in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.11201/) (2026)
- [LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning](https://mlsanity.com/paper/2603.21065/) (2026)
- [Every Coin Has Two Sides: On the Dual Nature of Generalization in On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2608.16647/) (2026)
- [Beyond Accuracy: Unveiling Inefficiency Patterns in Tool-Integrated Reasoning](https://mlsanity.com/paper/2604.05404/) (2026)
- [VibeLifeBench: Can Your Life Agent Be Proactive and Persistent in a Living World?](https://mlsanity.com/paper/2608.10875/) (2026)
- [Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key](https://mlsanity.com/paper/2605.06638/) (2026)
- [Improving Generalization Robustness of Multimodal RLVR](https://mlsanity.com/paper/2608.08802/) (2026)
- [LexiHorizon: Stabilizing Reinforcement Learning for Long-Horizon Deep Search](https://mlsanity.com/paper/2610.05119/) (2026)

## Abstract (arXiv)

Recent trends in test-time scaling for reasoning models (e.g., OpenAI o1, DeepSeek-R1) have led to remarkable improvements through long Chain-of-Thought (CoT). However, existing benchmarks mainly focus on immediate, single-horizon tasks, failing to adequately evaluate models' ability to understand and respond to complex, long-horizon scenarios. To address this incomplete evaluation of Large Reasoning Models (LRMs), we propose R-HORIZON, a method designed to stimulate long-horizon reasoning behaviors in LRMs through query composition. Based on R-HORIZON, we construct a long-horizon reasoning benchmark, comprising complex multi-step reasoning tasks with interdependent problems that span long reasoning horizons. Through comprehensive evaluation of LRMs using the R-HORIZON benchmark, we find that even the most advanced LRMs suffer significant performance degradation. Our analysis reveals that LRMs exhibit limited effective reasoning length and struggle to allocate thinking budget across multiple problems appropriately. Recognizing these limitations, we use R-HORIZON to construct long-horizon reasoning data for reinforcement learning with verified rewards (RLVR). Compared to training with single-horizon data, RLVR with R-HORIZON not only substantially improves performance on the multi-horizon reasoning tasks, but also promotes accuracy on standard reasoning tasks, with an increase of 7.5 on AIME2024. These results position R-HORIZON as a scalable, controllable, and low-cost paradigm for enhancing and evaluating the long-horizon reasoning capabilities of LRMs.