# Test-Time Reinforcement Learning

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arXiv Nov 8, 2026
Majority-vote test-time RL locks each question onto one answer, and a kernel probe predicts which one before training without fitted constants
Majority-vote test-time reinforcement learning makes each question lock onto one answer during training, often a wrong one on hard questions, and until now which answer that is became known only after training. The work treats this as a short race driven by sampling noise between the answers that are close at the start, and gives a closed-form probability for how the network kernel shifts the gap of the two leaders through updates of the trailing answers. In LoRA training on MMLU-Pro multiple-choice questions with three models from two families, predictions from a frozen-kernel chain computed before training forecast which answer each question locks into better than a logistic model refitted on the outcomes, using no fitted constants.
Majority-vote test-time reinforcement learning makes each question lock onto one answer during training, often a wrong one on hard questions, and until now which answer that is became known only after training. The work treats this as a short race driven by sampling noise between the answers that are close at the start, and gives a closed-form probability for how the network kernel shifts the gap of the two leaders through updates of the trailing answers. In LoRA training on MMLU-Pro multiple-choice questions with three models from two families, predictions from a frozen-kernel chain computed before training forecast which answer each question locks into better than a logistic model refitted on the outcomes, using no fitted constants.
Jaeho Hwang（First author）
Lock-In Law Test-Time Reinforcement Learning Neural Tangent Kernel LoRA MMLU-Pro
arXiv Oct 1, 2026
Freezing a 7B backbone and training only 100K bias parameters: label-free TTRL reaches 76.67% on MATH-500 and transfers to 4,500 problems unseen during optimization
The work introduces label-free bias-only test-time reinforcement learning: the pretrained backbone stays frozen while only about 100K bias parameters (down_proj.bias across 28 MLP layers) are optimized against majority-vote pseudo-label rewards, reaching 76.67% on MATH-500 with Qwen2.5-7B and 79.50% with Qwen2.5-Math-7B, improving vision-language and audio reasoning under the same procedure, and transferring frozen bias vectors to 4,500 verified-disjoint MATH problems to lift Qwen2.5-7B from 46.3% to 70.9% and Qwen2.5-Math-7B from 52.5% to 75.4%, with pseudo-label reliability and accessible gradient energy explaining why a restricted subspace still adapts.
The work introduces label-free bias-only test-time reinforcement learning: the pretrained backbone stays frozen while only about 100K bias parameters (down_proj.bias across 28 MLP layers) are optimized against majority-vote pseudo-label rewards, reaching 76.67% on MATH-500 with Qwen2.5-7B and 79.50% with Qwen2.5-Math-7B, improving vision-language and audio reasoning under the same procedure, and transferring frozen bias vectors to 4,500 verified-disjoint MATH problems to lift Qwen2.5-7B from 46.3% to 70.9% and Qwen2.5-Math-7B from 52.5% to 75.4%, with pseudo-label reliability and accessible gradient energy explaining why a restricted subspace still adapts.
University of Turku
Naveen Vakada（First author）
Bias-Only Steering Test-Time Reinforcement Learning GRPO Pseudo-labeling Mathematical Reasoning

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Majority-vote test-time RL locks each question onto one answer, and a kernel probe predicts which one before training without fitted constants

Freezing a 7B backbone and training only 100K bias parameters: label-free TTRL reaches 76.67% on MATH-500 and transfers to 4,500 problems unseen during optimization