This paper formulates test-time reasoning as a compute-allocation problem in which a system must decide whether the next unit of compute should be spent on generation, verification, or stopping, and introduces CoBa, a compute-balanced routing policy that first obtains a small set of candidates, applies cheap verification broadly, and routes uncertain or high-value candidates to stronger verification.
Abstract
Test-time scaling is often implemented by spending more compute along one axis: sampling more solutions, extending a chain of thought, or applying a stronger evaluator. Under a fixed inference budget, these choices compete. This paper formulates test-time reasoning as a compute-allocation problem in which a system must decide whether the next unit of compute should be spent on generation, verification, or stopping. We introduce CoBa, a compute-balanced routing policy that first obtains a small set of candidates, applies cheap verification broadly, and routes uncertain or high-value candidates to stronger verification. On 3,129 example-generator evaluations spanning MATH-500, AIME 2024/2025, AMC 2023, and procedural symbolic reasoning, CoBa-Routed-Strong reaches 85.13% macro accuracy, statistically matching a self-evaluation weighted-voting proxy at 85.20% while using 49.1% fewer parameter-weighted tokens. It also matches best-of-16 majority voting within 0.01 macro-accuracy points while using 58.9% fewer parameter-weighted tokens; paired tests retain a small best-of-16 edge at substantially higher cost. Paired bootstrap tests show significant gains over single-sample decoding, while the remaining gap to the pool oracle exposes headroom for sharper routing. For local reasoning systems, test-time scaling becomes a question of where the next computation is most valuable.
Fresh, objectively scored benchmark items can support auditable accuracy-cost-latency routing when features encode verifiable computational structure, and show that fresh, objectively scored benchmark items can support auditable accuracy-cost-latency routing when features encode verifiable computational structure.
Grace Xu· Journal of Science Innovatio...· 0 citations
A paired benchmark that tests whether LLM agents exhibit conscious allocation behavior under a fixed budget in two contexts: an abstract text-based formulation and a code-construction task finds that every frontier model testedacts near-optimally in the abstract framing but fails to transfer this ability to script-writing.
We provide a large-scale empirical audit of DEX routing using 2.98 million WETH-USDC swaps on Ethereum. Comparing realized routes with optimized benchmarks, we measure an average shortfall of 2.02 bps per trade or \$24 million. To attribute losses, we introduce three reproducible optimal benchmarks: a Support-Constrained Optimum (SCO) that evaluates split quality conditional on the pools actually used; a Full-Venue Optimum (FVO) that considers all available pools to quantify the value of broader pool access; and a Gas-Aware FVO (G-FVO) that augments FVO with gas costs to capture the trade-off between additional pool usage and gas expenditure. Computing these benchmarks at scale is enabled by a bisection-based algorithm for optimal routing across multiple pools for the same token pair. Two regularities emerge. First, information timeliness is crucial: moving from execution-time state to one-block lagged state optimization significantly raises mean shortfall and additional delays further degrade performance, albeit with diminishing increments; evaluated on the same stale snapshots, realized routes lie closer to optimal, indicating timing-mismatch as a key component. Second, inefficiency is heterogeneous and heavy-tailed: small trades suffer higher percentage losses, while a few extreme outliers dominate the aggregate dollar shortfalls. Finally, we demonstrate that sandwiching attacks drive a significant fraction of routing sub-optimality. Our benchmark protocol and algorithm offer a rigorous, reproducible basis for evaluating and improving information-timely, gas-aware routing.
This work introduces Risa (Routing-Informed Steering and Arbitration): within trajectories, routing encourages diverse exploration and controlled convergence during patch commitment; across separately sampled trajectories, agreement at informative patch positions selects a final candidate.
Kang Chen, Junjie Nian, Yi-Xin Cao et al.· 0 citations
Heuristic design for combinatorial optimization remains heavily reliant on expert knowledge, while existing large language model (LLM)-enhanced evolutionary methods typically evolve isolated algorithmic components, even when one determines the search state on which another operates. This paper proposes LLM-driven Heuristic Components Joint Generation (LLM-HCJG), a population-based framework that jointly generates and co-evolves interdependent heuristic components under a shared design blueprint. Applied to guided local search (GLS), LLM-HCJG couples solution initialization with penalty construction and embeds the generated pair into an enhanced online search mechanism. The resulting form is further transferred from the traveling salesman problem (TSP) to the capacitated vehicle routing problem (CVRP). Theoretical analysis establishes the non-separable state-transition effects between the two components and the advantage in generation consistency. Across synthetic instances and 41 public TSPLIB/CVRPLIB benchmarks, LLM-HCJG attains consistently low optimality gaps, including best or tied-best results on 28 of 29 TSPLIB instances and all 12 CVRPLIB instances. Ablation and structural analyses further indicate that these gains are associated with cross-component compatibility and alignment rather than isolated-component recombination. These results support effective cross-instance transfer within the evaluated routing settings under limited-sample, modest-cost training.
Junyi Wei, Yangming Zhou, Zhi-Bin Jiang et al.· 0 citations
This work introduces Test-Time Scaling via Error Localization (TTEL), an inference-time algorithm that utilizes fixed or environment feedback to perform token-level error localization and establishes strictly dominating Pareto frontiers across sequential reasoning domains.
