Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale to large datasets (which are common in modern applications), since it requires the solution of a linear system whose size scales quadratically with the number of samples in the dataset. We propose an approximate, distributed, accelerated sketch-and-project algorithm ($\texttt{ADASAP}$) for solving these linear systems, which improves scalability. We use the theory of determinantal point processes to show that the posterior mean induced by sketch-and-project rapidly converges to the true posterior mean. In particular, this yields the first efficient, condition number-free algorithm for estimating the posterior mean along the top spectral basis functions, showing that our approach is principled for GP inference.

Most image fusion methods are designed for ideal scenarios and struggle to handle noise. Existing noise-aware fusion methods are supervised and heavily rely on constructed paired data, limiting performance and generalization. This paper proposes a novel unsupervised noisy visible and infrared image fusion method, comprising two key modules. First, when only noisy source images are available, a convolutional low-rank optimization module decomposes clean components based on convolutional low-rank priors, guiding subsequent optimization. The unsupervised approach eliminates data dependency and enhances generalization across various and variable noise. Second, a unified network jointly realizes denoising and fusion. It consists of both intra-modal recovery and inter-modal recovery and fusion, also with a convolutional low-rankness loss for regularization. By exploiting the commonalities of denoising and fusion, the joint framework significantly reduces network complexity while expanding functionality. Extensive experiments validate the effectiveness and generalization of the proposed method for image fusion under various and variable noise conditions.

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and test data differ, presenting additional challenges for learning. Although kernel methods have optimal statistical properties, their high computational demands in terms of time and, particularly, memory, limit their scalability to large datasets. To address this limitation, the main focus of this paper is to explore the trade-off between computational efficiency and statistical accuracy under covariate shift. We investigate the use of random projections where the hypothesis space consists of a random subspace within a given RKHS. Our results show that, even in the presence of covariate shift, significant computational savings can be achieved without compromising learning performance.

As AI becomes more closely integrated with peoples' daily activities, socially intelligent AI that can understand and interact seamlessly with humans in daily lives is increasingly important. However, current works in AI social reasoning all rely on language-only or language-dominant approaches to benchmark and training models, resulting in systems that are improving in verbal communication but struggle with nonverbal social understanding. To address this limitation, we tap into a novel data source rich in nonverbal social interactions -- mime videos. Mimes refer to the art of expression through gesture and movement without spoken words, which presents unique challenges and opportunities in interpreting nonverbal social communication. We contribute a new dataset called MimeQA, obtained by sourcing ~8 hours of videos clips from YouTube and developing a comprehensive video question-answering benchmark comprising 806 carefully annotated and verified question-answer pairs, designed to probe nonverbal social reasoning capabilities. Using MimeQA, we evaluate state-of-the-art video large language models (VideoLLMs) and find that they achieve low accuracy, generally ranging from 20-30%, while humans score 86\%. Our analysis reveals that VideoLLMs often fail to ground imagined objects and over-rely on the text prompt while ignoring subtle nonverbal interactions. We hope to inspire future work in AI models that embody true social intelligence capable of interpreting non-verbal human interactions.

Recent advances in retrieval-based in-context learning (ICL) train the retriever using a classification objective, which categorizes in-context examples (ICEs) into the most useful and the rest based on absolute scores. However, during inference, ICEs are retrieved by score ranking rather than classification -- The classification training objective deviates from this test scenario. Hence, in this paper, we propose a novel algorithm that trains a retrieval model by ranking formulation, where the preference rankings between ICEs are given by comparing the likelihood of the LLM generating the correct answer conditioned on each exemplar. By learning to rank, we motivate the retriever to automatically learn diverse rationales why specific examples are more useful for ICL decisions. This addresses the issue that classification models poorly capture broader utility. Experimental results demonstrate the top-1 performance of our proposal across 9 NLP tasks, with ablation studies and case studies further validating the effectiveness of our design.

Reasoning-focused LLMs sometimes alter their behavior when they detect that they are being evaluated--which can lead them to optimize for test-passing performance or to comply more readily with harmful prompts if real-world consequences appear absent. We present the first quantitative study of how such "test awareness" impacts model behavior, particularly its performance on safety-related tasks. We introduce a white-box probing framework that (i) linearly identifies awareness-related activations and (ii) steers models toward or away from test awareness while monitoring downstream performance. We apply our method to different state-of-the-art open-weight reasoning LLMs across both realistic and hypothetical tasks (denoting tests or simulations). Our results demonstrate that test awareness significantly impacts safety alignment (such as compliance with harmful requests and conforming to stereotypes) with effects varying in both magnitude and direction across models. By providing control over this latent effect, our work aims to provide a stress-test mechanism and increase trust in how we perform safety evaluations.

When a vision model performs image recognition, which visual attributes drive its predictions? Detecting unintended reliance on specific visual features is critical for ensuring model robustness, preventing overfitting, and avoiding spurious correlations. We introduce an automated framework for detecting such dependencies in trained vision models. At the core of our method is a self-reflective agent that systematically generates and tests hypotheses about visual attributes that a model may rely on. This process is iterative: the agent refines its hypotheses based on experimental outcomes and uses a self-evaluation protocol to assess whether its findings accurately explain model behavior. When inconsistencies arise, the agent self-reflects over its findings and triggers a new cycle of experimentation. We evaluate our approach on a novel benchmark of 130 models designed to exhibit diverse visual attribute dependencies across 18 categories. Our results show that the agent's performance consistently improves with self-reflection, with a significant performance increase over non-reflective baselines. We further demonstrate that the agent identifies real-world visual attribute dependencies in state-of-the-art models, including CLIP's vision encoder and the YOLOv8 object detector.

Pre-trained diffusion models are commonly used to generate clean data (e.g., images) from random noises, effectively forming pairs of noises and corresponding clean images. Distillation on these pre-trained models can be viewed as the process of constructing advanced trajectories within the pair to accelerate sampling. For instance, consistency model distillation develops consistent projection functions to regulate trajectories, although sampling efficiency remains a concern. Rectified flow method enforces straight trajectories to enable faster sampling, yet relies on numerical ODE solvers, which may introduce approximation errors. In this work, we bridge the gap between the consistency model and the rectified flow method by proposing a Straight-Consistent Trajectories~(SCoT) model. SCoT enjoys the benefits of both approaches for fast sampling, producing trajectories with consistent and straight properties simultaneously. These dual properties are strategically balanced by targeting two critical objectives: (1) regulating the gradient of SCoT's mapping function to a constant and (2) ensuring trajectory consistency. Extensive experimental results demonstrate the effectiveness and efficiency of SCoT.

Bayesian networks (BNs), represented by directed acyclic graphs (DAGs), provide a principled framework for modeling complex dependencies among random variables. As data dimensionality increases into the tens of thousands, fitting and marginalizing a full BN becomes computationally prohibitive--particularly when inference is only needed for a small subset of variables. Estimation-collapsibility addresses this challenge by ensuring that directly fitting a submodel, obtained by ignoring non-essential variables, still yields exact inference on target variables. However, current DAG-based criterion for checking estimation-collapsibility is computationally intensive, involving exhaustive vertex searches and iterative removals. Additionally, practical applications typically identify the underlying DAG only up to its Markov equivalence class, represented by a completed partially directed acyclic graph (CPDAG). To bridge this gap, we introduce sequential $c$-simplicial sets--a novel graphical characterization of estimation-collapsibility applicable directly to CPDAGs. We further propose DSCS, a computationally efficient algorithm for verifying estimation-collapsibility within CPDAG framework that scales effectively to high-dimensional BNs. Extensive numerical experiments demonstrate the practicality, scalability, and efficiency of our proposed approach.

Despite the growing success of transform-based tensor models such as the t-product, their underlying geometric principles remain poorly understood. Classical differential geometry, built on real-valued function spaces, is not well suited to capture the algebraic and spectral structure induced by transform-based tensor operations. In this work, we take an initial step toward a geometric framework for tensors equipped with tube-wise multiplication via orthogonal transforms. We introduce the notion of smooth t-manifolds, defined as topological spaces locally modeled on structured tensor modules over a commutative t-scalar ring. This formulation enables transform-consistent definitions of geometric objects, including metrics, gradients, Laplacians, and geodesics, thereby bridging discrete and continuous tensor settings within a unified algebraic-geometric perspective. On this basis, we develop a statistical procedure for testing whether tensor data lie near a low-dimensional t-manifold, and provide nonasymptotic guarantees for manifold fitting under noise. We further establish approximation bounds for tensor neural networks that learn smooth functions over t-manifolds, with generalization rates determined by intrinsic geometric complexity. This framework offers a theoretical foundation for geometry-aware learning in structured tensor spaces and supports the development of models that align with transform-based tensor representations.