Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning

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.

Test-time scaling improves the reasoning performance of large language models but often results in token-inefficient overthinking, where models continue reasoning beyond what is necessary for a correct answer. Existing dynamic early-exit methods typically rely on single-step confidence signals, which are often unreliable for detecting reasoning convergence in multi-step settings. To mitigate this limitation, we propose TRACE, a training-free framework for efficient test-time scaling that determines when to terminate reasoning based on temporal aggregation of multi-step evidence rather than instantaneous signals. TRACE detects reasoning convergence over time by aggregating two complementary signals across recent reasoning steps: answer consistency, capturing the persistence of predicted answers, and confidence trajectory, modeling the temporal evolution of model confidence. Benefiting from these two factors, TRACE can accurately determine whether the reasoning process has converged, thereby promptly halting inference and effectively avoiding redundant reasoning steps. Extensive experiments on multiple challenging benchmarks show that TRACE reduces reasoning token usage by 25-30% on average while maintaining accuracy within 1-2% of full-length reasoning, consistently outperforming existing dynamic reasoning methods.

Test-time scaling has become a major way to improve large language model reasoning, but its orchestration has remained designer-engineered: a fixed sample budget, a fixed refinement loop, a fixed scoring rule, or a fixed search policy decides how compute is spent, leaving the model in charge of solving but not of orchestration. We introduce ATLAS, an agentic test-time scaling framework in which an LLM orchestrator owns the control loop end-to-end. Through a single action, explore, which dispatches a fresh independent solver on the original problem, the orchestrator decides whether to gather more evidence, when to stop, and how to synthesize the final answer; the action space is extensible, with each explore call optionally specifying solver, reasoning effort, or prompting strategy. We evaluate ATLAS on four benchmarks covering scientific question answering, code generation, and multimodal reasoning under a Claude Sonnet 4.6 backbone, where it reaches 56.00% on HLE-Verified, 82.29% on LiveCodeBench, 85.75% on GPQA-Diamond, and 23.71% on BabyVision while using far fewer API calls than fixed-workflow baselines. A multi-model extension, ATLAS-MM, that exposes solver choice as an additional action dimension further improves HLE-Verified to 60.00% and LiveCodeBench to 85.63%, with consistent gains on GPQA-Diamond and BabyVision. Ablations replacing the orchestrator's direct synthesis with a separate integrator degrade or fail to improve accuracy on three of four benchmarks, consistent with the role of stateful evidence management in producing the gains.