Lingjiao Chen
Publications
The Price Reversal Phenomenon: When Cheaper Reasoning Models End Up Costing More
Developers and consumers increasingly choose reasoning language models (RLMs) based on their listed API prices. However, how accurately do these prices reflect actual inference costs? We conduct the first systematic study of this question, evaluating 8 frontier RLMs across 9 diverse tasks covering competition math, science QA, code generation, and multi-domain reasoning. We uncover the pricing reversal phenomenon: in 21.8% of model-pair comparisons, the model with a lower listed price actually incurs a higher total cost, with reversal magnitude reaching up to 28x. For example, Gemini 3 Flash's listed price is 78% cheaper than GPT-5.2's, yet its actual cost across all tasks is 22% higher. We trace the root cause to vast heterogeneity in thinking token consumption: on the same query, one model may use 900% more thinking tokens than another. In fact, removing thinking token costs reduces ranking reversals by 70% and raises the rank correlation (Kendall's $τ$ ) between price and cost rankings from 0.563 to 0.873. We further show that per-query cost prediction is fundamentally difficult: repeated runs of the same query yield thinking token variation up to 9.7x, establishing an irreducible noise floor for any predictor. Our findings demonstrate that listed API pricing is an unreliable proxy for actual cost, calling for cost-aware model selection and transparent per-request cost monitoring.
ZEBRAARENA: A Diagnostic Simulation Environment for Studying Reasoning-Action Coupling in Tool-Augmented LLMs
Tool-augmented large language models (LLMs) must tightly couple multi-step reasoning with external actions, yet existing benchmarks often confound this interplay with complex environment dynamics, memorized knowledge or dataset contamination. In this paper, we introduce ZebraArena, a procedurally generated diagnostic environment for studying reasoning-action coupling in tool-augmented LLMs, with controllable difficulty and a knowledge-minimal design, which limits gains from memorization or dataset contamination. Each task in ZebraArena requires a set of critical information which is available only through targeted tool use, yielding an interpretable interface between external information acquisition and deductive reasoning. This design provides deterministic evaluation via unique solutions, and a theoretical optimal query count for measuring efficient tool use. We show that ZebraArena requires a combination of in-depth reasoning and accurate external tool calling, which remains a challenge as frontier reasoning models such as GPT-5 and Gemini 2.5 Pro only achieves 60% accuracy on the hard instances. We also observe a persistent gaps between theoretical optimality and practical tool usage. For example, GPT-5 uses 70-270% more tool calls than the theoretical optimum. We highlight the key findings in our evaluation, and hope ZebraArena stimulates further research on the interplay between internal reasoning and external action.