Can a Lightweight Multimodal Model Estimate LLM Reasoning Performance? A Study for Compute-Optimal Document Inference

Large language models (LLMs) can achieve strong reasoning performance with sufficient computation, but they do not inherently know how much computation a task requires. We study budgeted inference-time reasoning for multiple problems under a strict global token constraint and formulate it as an Ordered Stochastic Multiple-Choice Knapsack Problem (OS-MCKP). This perspective highlights a meta-cognitive requirement---anticipating problem difficulty and allocating computation strategically. We propose ROI-Reasoning, a two-stage framework that endows LLMs with intrinsic, budget-aware rationality. First, Meta-Cognitive Fine-Tuning teaches models to predict reasoning cost levels and decide whether a problem is worth attempting before generation. Next, Rationality-Aware Reinforcement Learning optimizes sequential decision making under a hard token budget, allowing models to learn long-horizon allocation strategies. Experiments across mathematical reasoning, multiple-choice question answering, and code generation show that ROI-Reasoning improves scores and generally reduces reference-order regret under tight budgets, with up to a 417% relative score improvement over the strongest same-backbone baseline in mathematics.

Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks ($p {<} 0.01$, McNemar). (iii) Oracle analysis reveals model complementarity up to $+27.8$pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain ($+1.6$ to $+5.7$pp) but are domain-specific and hurt transfer ($-1.2$pp). These results argue for budget-conditioned evaluation protocols.

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.