# TEMPO: Scaling Test-time Training for Large Reasoning Models

arXiv: https://arxiv.org/abs/2604.19295 · HTML: https://mlsanity.com/paper/2604.19295/

## 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 16 of its 30 references that are in the map.
- First posted on arXiv 21 Apr 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, 16 of 16)

- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [No Free Lunch: Rethinking Internal Feedback for LLM Reasoning](https://mlsanity.com/paper/2506.17219/) (2025)
- [One-shot Entropy Minimization](https://mlsanity.com/paper/2505.20282/) (2025)
- [P1: Mastering Physics Olympiads with Reinforcement Learning](https://mlsanity.com/paper/2511.13612/) (2025)
- [P1-VL: Bridging Visual Perception and Scientific Reasoning in Physics Olympiads](https://mlsanity.com/paper/2602.09443/) (2026)
- [SARL: Label-Free Reinforcement Learning by Rewarding Reasoning Topology](https://mlsanity.com/paper/2603.27977/) (2026)

## Abstract (arXiv)

Test-time training (TTT) adapts model parameters on unlabeled test instances during inference time, which continuously extends capabilities beyond the reach of offline training. Despite initial gains, existing TTT methods for LRMs plateau quickly and do not benefit from additional test-time compute. Without external calibration, the self-generated reward signal increasingly drifts as the policy model evolves, leading to both performance plateaus and diversity collapse. We propose TEMPO, a TTT framework that interleaves policy refinement on unlabeled questions with periodic critic recalibration on a labeled dataset. By formalizing this alternating procedure through the Expectation-Maximization (EM) algorithm, we reveal that prior methods can be interpreted as incomplete variants that omit the crucial recalibration step. Reintroducing this step tightens the evidence lower bound (ELBO) and enables sustained improvement. Across diverse model families (Qwen3 and OLMO3) and reasoning tasks, TEMPO improves OLMO3-7B on AIME 2024 from 33.0% to 51.1% and Qwen3-14B from 42.3% to 65.8%, while maintaining high diversity.