Bridging the Know-Act Gap via Task-Level Autoregressive Reasoning

LLMs often generate seemingly valid answers to flawed or ill-posed inputs. This is not due to missing knowledge: under discriminative prompting, the same models can mostly identify such issues, yet fail to reflect this in standard generative responses. This reveals a fundamental know-act gap between discriminative recognition and generative behavior. Prior work largely characterizes this issue in narrow settings, such as math word problems or question answering, with limited focus on how to integrate these two modes. In this work, we present a comprehensive analysis using FaultyScience, a newly constructed large-scale, cross-disciplinary benchmark of faulty scientific questions. We show that the gap is pervasive and stems from token-level autoregression, which entangles task selection (validate vs. answer) with content generation, preventing discriminative knowledge from being utilized. To address this, we propose DeIllusionLLM, a task-level autoregressive framework that explicitly models this decision. Through self-distillation, the model unifies discriminative judgment and generative reasoning within a single backbone. Empirically, DeIllusionLLM substantially reduces answer-despite-error failures under natural prompting while maintaining general reasoning performance, demonstrating that self-distillation is an effective and scalable solution for bridging the discriminative-generative know-act gap

Evaluating Autoformalization Robustness via Semantically Similar Paraphrasing

Large Language Models (LLMs) have recently emerged as powerful tools for autoformalization. Despite their impressive performance, these models can still struggle to produce grounded and verifiable formalizations. Recent work in text-to-SQL, has revealed that LLMs can be sensitive to paraphrased natural language (NL) inputs, even when high degrees of semantic fidelity are preserved (Safarzadeh, Oroojlooyjadid, and Roth 2025). In this paper, we investigate this claim in the autoformalization domain. Specifically, we evaluate the robustness of LLMs generating formal proofs with semantically similar paraphrased NL statements by measuring semantic and compilation validity. Using the formal benchmarks MiniF2F (Zheng, Han, and Polu 2021) and Lean 4 version of ProofNet (Xin et al. 2024), and two modern LLMs, we generate paraphrased natural language statements and cross-evaluate these statements across both models. The results of this paper reveal performance variability across paraphrased inputs, demonstrating that minor shifts in NL statements can significantly impact model outputs.