# Understanding and Mitigating Spurious Signal Amplification in Test-Time Reinforcement Learning for Math Reasoning

arXiv: https://arxiv.org/abs/2604.21327 · HTML: https://mlsanity.com/paper/2604.21327/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [Consistent Paths Lead to Truth: Self-Rewarding Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08745/) (2025)
- [ETTRL: Balancing Exploration and Exploitation in LLM Test-Time Reinforcement Learning Via Entropy Mechanism](https://mlsanity.com/paper/2508.11356/) (2025)
- [First SFT, Second RL, Third UPT: Continual Improving Multi-Modal LLM Reasoning via Unsupervised Post-Training](https://mlsanity.com/paper/2505.22453/) (2025)
- [Large Language Models Can Self-Improve in Long-context Reasoning](https://mlsanity.com/paper/2411.08147/) (2024)
- [Benchmarking Test-Time Adaptation against Distribution Shifts in Image Classification](https://mlsanity.com/paper/2307.03133/) (2023)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)
- [SPINE: Token-Selective Test-Time Reinforcement Learning with Entropy-Band Regularization](https://mlsanity.com/paper/2511.17938/) (2025)
- [Reassessing the Role of Supervised Fine-Tuning: An Empirical Study in VLM Reasoning](https://mlsanity.com/paper/2512.12690/) (2025)
- [Test-Time Immunization: A Universal Defense Framework Against Jailbreaks for (Multimodal) Large Language Models](https://mlsanity.com/paper/2505.22271/) (2025)

## Built on by (most cited first, 3 of 3)

- [Scope3Trace: Evidence-Based Identification and Extraction of Scope 3 GHG Emissions from Sustainability Reports](https://mlsanity.com/paper/2607.17122/) (2026)
- [SelectTTRL: Representation-Guided Data Selection for Efficient Test-Time Reinforcement Learning](https://mlsanity.com/paper/2610.16104/) (2026)
- [Facts Don't Speak Louder than Words: The Behavioral Essence of Long-CoT Distillation](https://mlsanity.com/paper/2610.17607/) (2026)

## Abstract (arXiv)

Test-time reinforcement learning (TTRL) always adapts models at inference time via pseudo-labeling, leaving it vulnerable to spurious optimization signals from label noise. Through an empirical study, we observe that responses with medium consistency form an ambiguity region and constitute the primary source of reward noise. Crucially, we find that such spurious signals can be even amplified through group-relative advantage estimation. Motivated by these findings, we propose a unified framework, Debiased and Denoised test-time Reinforcement Learning (DDRL), to mitigate spurious signals. Concretely, DDRL first applies a frequency-based sampling strategy to exclude ambiguous samples while maintaining a balanced set of positive and negative examples. It then adopts a debiased advantage estimation with fixed advantages, removing the bias introduced by group-relative policy optimization. Finally, DDRL incorporates a consensus-based off-policy refinement stage, which leverages the rejection-sampled dataset to enable efficient and stable model updates. Experiments on three large language models across multiple mathematical reasoning benchmarks demonstrate that DDRL consistently outperforms existing TTRL baselines. The code will soon be released at https://github.com/yuyongcan/DDRL.