CoT2-Meta: Budgeted Metacognitive Control for Test-Time Reasoning

Large reasoning models improve performance on challenging problems by allocating additional computation before answering, but longer reasoning does not always lead to better results and can introduce substantial redundant reasoning on simple problems. Conversely, aggressively shortening reasoning can degrade performance on difficult ones. Effective reasoning therefore requires dynamically deciding when additional computation is useful based on the reasoner's capabilities and evolving solution state. Existing approaches often rely on predefined budgets or intervention rules, retrain the target reasoner, or require additional supervision. We introduce MetaCtrl, a lightweight controller that adaptively regulates a frozen reasoner without predefined token budgets or reasoner retraining. We formulate reasoning regulation as a sequential metacognitive control problem: MetaCtrl observes the evolving reasoning trace and decides whether to continue, simplify, skip redundant steps, or conclude reasoning. It is trained directly with reinforcement learning using a reward that prioritizes correctness while favoring shorter trajectories among correct solutions, requiring neither supervised intervention trajectories nor problem-specific budgets. Across seven benchmarks spanning mathematics, science, and code, MetaCtrl consistently improves the accuracy of LRMs while reducing their reasoning length. On DeepSeek-R1-Distill-Qwen-7B, it improves average accuracy by 4.7 points while reducing generation length by 53.3%. Without further training, the same controller transfers to an unseen reasoner (e.g., Qwen3-14B), improving average accuracy by 2.9 points and reducing generation length by 50.3%. These results establish MetaCtrl as a plug-and-play controller for improving reasoning accuracy while substantially reducing inference-time generation. The code is available at https://github.com/binbin2xs/MetaCtrl.

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from how much compute to spend, to where to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes thought-level beam search. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7% absolute accuracy gain on HMMT-24 and +3.3% on AIME-25 over pruning baselines, delivers $>2\times$ higher throughput on trace completion, and reduces total token consumption by up to 68.5% relative to standard parallel sampling.

Large Reasoning Models (LRMs) improve performance by allocating additional inference-time compute to generate extended chain-of-thought reasoning. However, recent studies reveal that sequential test-time scaling often yields diminishing or even negative returns, as longer traces exhibit increased uncertainty, error compounding, and drift from the original problem. We propose ThinkRetrieve, a test-time scaling framework that augments the reasoning traces of LRMs with dynamically retrieved solved examples at each reasoning step. Given an external corpus of problems paired with step-by-step solutions, ThinkRetrieve retrieves relevant exemplars at each intermediate step and injects them directly into the thinking trace, providing the model with guidance on how to reason rather than merely what facts are relevant. Experiments across five reasoning models (1.5B--8B parameters) on GSM-8K, MATH-500, AIME 2025, and SciQ demonstrate that ThinkRetrieve consistently improves accuracy over standard test-time scaling, with relative gains of up to $60\%$ on AIME 2025.