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

Structure-Preserving Nonlinear Sufficient Dimension Reduction for Tensors

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the meaning of the tensor modes, for improved interpretation; the second is to substantially reduce the number of parameters in dimension reduction, thereby achieving model parsimony and enhancing estimation accuracy. Our two tensor dimension reduction methods echo the two commonly used tensor decomposition mechanisms: one is the Tucker decomposition, which reduces a larger tensor to a smaller one; the other is the CP-decomposition, which represents an arbitrary tensor as a sequence of rank-one tensors. We developed the Fisher consistency of our methods at the population level and established their consistency and convergence rates. Both methods are easy to implement numerically: the Tucker-form can be implemented through a sequence of least-squares steps, and the CP-form can be implemented through a sequence of singular value decompositions. We investigated the finite-sample performance of our methods and showed substantial improvement in accuracy over existing methods in simulations and two data applications.