# CounterRoute: Self-Routed Reasoning via Hierarchical Counterfactual Credit Assignment

arXiv: https://arxiv.org/abs/2609.29109 · HTML: https://mlsanity.com/paper/2609.29109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 25 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 21 of 21)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Self-play with Execution Feedback: Improving Instruction-following Capabilities of Large Language Models](https://mlsanity.com/paper/2406.13542/) (2024)
- [Think Only When You Need with Large Hybrid-Reasoning Models](https://mlsanity.com/paper/2505.14631/) (2025)
- [Learning When to Think: Shaping Adaptive Reasoning in R1-Style Models via Multi-Stage RL](https://mlsanity.com/paper/2505.10832/) (2025)
- [Think or Not? Selective Reasoning via Reinforcement Learning for Vision-Language Models](https://mlsanity.com/paper/2505.16854/) (2025)
- [Shop-R1: Rewarding LLMs to Simulate Human Behavior in Online Shopping via Reinforcement Learning](https://mlsanity.com/paper/2507.17842/) (2025)
- [Learning When to Think: Adaptive Reasoning for Test-Time Compute Allocation](https://mlsanity.com/paper/2608.20256/) (2026)

## Abstract (arXiv)

Reasoning-capable language models often produce long chains of thought when direct answers suffice, wasting inference compute. Dual-mode models offer both thinking and direct-answer modes, but typically leave mode selection to users. Automating this selection while improving responses under both modes is challenging because routing targets evolve with the policy, strong initial mode preferences can destabilize exploration, and sequence-level objectives entangle routing with response learning. We introduce CounterRoute, an online reinforcement-learning framework that jointly learns routing and mode-conditioned responses in one shared policy directly from a native dual-mode checkpoint, without method-specific SFT warm-up. Paired current-policy counterfactual rollouts estimate cross-mode routing credit, which is assigned only to the routing token, while within-mode GRPO trains response tokens. A paired-to-self-routed curriculum stabilizes early training with forced coverage of both modes before progressively transferring training to autonomous routing. Across nine benchmarks, CounterRoute better balances accuracy and efficiency than heuristic and learned adaptive-routing methods, improving macro-average accuracy at both Qwen3 scales while cutting mean generated tokens by 51% and 41%, respectively, versus always-thinking checkpoints. On instruction-following and commonsense benchmarks where direct answering is strong, think rates fall as low as 1% while response quality improves. Despite training only on math and synthetic instruction-following data, its routing and response quality generalize to held-out tasks in coding, science, knowledge, and commonsense.