Unified Inference Framework for Single and Multi-Player Performative Prediction: Method and Asymptotic Optimality

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals

Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

Semi-structured LLM Reasoners Can Be Rigorously Audited

As Large Language Models (LLMs) become increasingly capable at reasoning, the problem of "faithfulness" persists: LLM "reasoning traces" can contain errors and omissions that are difficult to detect, and may obscure biases in model outputs. To address these limitations, we introduce Semi-Structured Reasoning Models (SSRMs), which internalize a semi-structured Chain-of-Thought (CoT) reasoning format within the model. Our SSRMs generate reasoning traces in a Pythonic syntax. While SSRM traces are not executable, they adopt a restricted, task-specific vocabulary to name distinct reasoning steps, and to mark each step's inputs and outputs. Through extensive evaluation on ten benchmarks, SSRMs demonstrate strong performance and generality: they outperform comparably sized baselines by nearly ten percentage points on in-domain tasks while remaining competitive with specialized models on out-of-domain medical benchmarks. Furthermore, we show that semi-structured reasoning is more amenable to analysis: in particular, they can be automatically audited to identify reasoning flaws. We explore both hand-crafted structured audits, which detect task-specific problematic reasoning patterns, and learned typicality audits, which apply probabilistic models over reasoning patterns, and show that both audits can be used to effectively flag probable reasoning errors.