As the length of input text increases, the key-value (KV) cache in LLMs imposes prohibitive GPU memory costs and limits long-context inference on resource constrained devices. Existing approaches, such as KV quantization and pruning, reduce memory usage but suffer from numerical precision loss or suboptimal retention of key-value pairs. In this work, Low Rank Query and Key attention (LRQK) is introduced, a two-stage framework that jointly decomposes full-precision query and key matrices into compact rank-r factors during the prefill stage, and then employs these low-dimensional projections to compute proxy attention scores in O(lr) time at each decode step. By selecting only the top-k tokens and a small fixed set of recent tokens, LRQK employs a mixed GPU-CPU cache with a hitand-miss mechanism where only missing full-precision KV pairs are transferred, thereby preserving exact attention outputs while reducing CPU-GPU data movement.

Current evaluation paradigms for large language models (LLMs) represent a critical blind spot in AI research--relying on opaque numerical metrics that conceal fundamental limitations in spatial reasoning while providing no intuitive understanding of model capabilities. This deficiency creates a dangerous disconnect between reported performance and practical abilities, particularly for applications requiring physical world understanding. We introduce LTD-Bench, a breakthrough benchmark that transforms LLM evaluation from abstract scores to directly observable visual outputs by requiring models to generate drawings through dot matrices or executable code. This approach makes spatial reasoning limitations immediately apparent even to non-experts, bridging the fundamental gap between statistical performance and intuitive assessment. LTD-Bench implements a comprehensive methodology with complementary generation tasks (testing spatial imagination) and recognition tasks (assessing spatial perception) across three progressively challenging difficulty levels, methodically evaluating both directions of the critical language-spatial mapping. Our extensive experiments with state-of-the-art models expose an alarming capability gap: even LLMs achieving impressive results on traditional benchmarks demonstrate profound deficiencies in establishing bidirectional mappings between language and spatial concepts--a fundamental limitation that undermines their potential as genuine world models. Furthermore, LTD-Bench's visual outputs enable powerful diagnostic analysis, offering a poten-

We aim to provide a unified convergence analysis for permutation-based Stochastic Gradient Descent (SGD), where data examples are permuted before each epoch. By examining the relations among permutations, we classify existing permutation-based SGD algorithms into three categories: Arbitrary Permutations, Independent Permutations (including Random Reshuffling and FlipFlop [Rajput et al., 2022]), Dependent Permutations (including GraBs [Lu et al., 2022a; Cooper et al., 2023]). Existing unified analyses failed to encompass the Dependent Permutations category due to the inter-epoch permutation dependency. In this work, we propose a generalized assumption that explicitly characterizes the dependence of permutations across epochs. Building upon this assumption, we develop a unified framework for permutation-based SGD with arbitrary permutations of examples, incorporating all the existing permutation-based SGD algorithms. Furthermore, we adapt our framework for Federated Learning (FL), developing a unified framework for regularized client participation FL with arbitrary permutations of clients.

Modeling interactive driving behaviors in complex scenarios remains a fundamental challenge for autonomous driving planning. Learning-based approaches attempt to address this challenge with advanced generative models, removing the dependency on over-engineered architectures for representation fusion. However, brute-force implementation by simply stacking transformer blocks lacks a dedicated mechanism for modeling interactive behaviors that are common in real driving scenarios. The scarcity of interactive driving data further exacerbates this problem, leaving conventional imitation learning methods ill-equipped to capture high-value interactive behaviors. We propose Flow Planner, which tackles these problems through coordinated innovations in data modeling, model architecture, and learning scheme. Specifically, we first introduce fine-grained trajectory tokenization, which decomposes the trajectory into overlapping segments to decrease the complexity of whole trajectory modeling. With a sophisticatedly designed architecture, we achieve efficient temporal and spatial fusion of planning and scene information, to better capture interactive behaviors. In addition, the framework incorporates flow matching with classifier-free guidance for multi-modal behavior generation, which dynamically reweights agent interactions during inference to maintain coherent response strategies, providing a critical boost for interactive scenario understanding. Experimental results on the large-scale nuPlan dataset and challenging interactive interPlan dataset demonstrate that Flow Planner achieves state-of-the-art performance among learning-based approaches while effectively modeling interactive behaviors in complex driving scenarios.

Medical image segmentation based on neural networks is pivotal in promoting digital health equity. The attention mechanism increasingly serves as a key component in modern neural networks, as it enables the network to focus on regions of interest, thus improving the segmentation accuracy in medical images. However, current attention mechanisms confront an accuracy-complexity trade-off paradox: accuracy gains demand higher computational costs, while reducing complexity sacrifices model accuracy. Such a contradiction inherently restricts the real-world deployment of attention mechanisms in resource-limited settings, thus exacerbating healthcare disparities. To overcome this dilemma, we propose a parameter-free Neighborhood Self-Dissimilarity Attention (NSDA), inspired by radiologists' diagnostic patterns of prioritizing regions exhibiting substantial differences during clinical image interpretation.

Large language models (LLMs) are increasingly capable of processing long inputs and locating specific information within them, as evidenced by their performance on the Needle in a Haystack (NIAH) test. However, while models excel at recalling surprising information, they still struggle to identify clearly omitted information. We introduce AbsenceBench to assesses LLMs' capacity to detect missing information across three domains: numerical sequences, poetry, and GitHub pull requests. AbsenceBenchasks models to identify which pieces of a document were deliberately removed, given access to both the original and edited contexts. Despite the apparent straightforwardness of these tasks, our experiments reveal that even state-of-the-art models like Claude-3.7-Sonnet

Data Shapley values provide a principled approach for quantifying the contribution of individual training examples to machine learning models. However, computing these values often requires computational complexity that is exponential in the data size, and this has led researchers to pursue efficient algorithms tailored to specific machine learning models. Building on the prior success of the Shapley valuation for K-nearest neighbor (KNN) models, in this paper, we introduce a localized data Shapley framework that significantly accelerates the valuation of data points.

Mean-field variational inference (VI), despite its scalability, is limited by the independence assumption, making it unsuitable for scenarios with correlated data instances. Existing structured VI methods either focus on correlations among latent dimensions which lack scalability for modeling instance-level correlations, or are restricted to simple first-order dependencies, limiting their expressiveness. In this paper, we propose High-order Tree-structured Variational Inference (HoT-VI)2, that explicitly models k-order instance-level correlations among latent variables. By expressing the global posterior through overlapping k-dimensional local marginals, our method enables efficient parameterized sampling via a sequential procedure. To ensure the validity of these marginals, we introduce a conditional correlation parameterization method that guarantees positive definiteness of their correlation matrices. We further extend our method with a tree-structured backbone to capture more flexible dependency patterns. Extensive experiments on time-series and graphstructured datasets demonstrate that modeling higher-order correlations leads to significantly improved posterior approximations and better performance across various downstream tasks.

Real-world data distributions often shift continuously across multiple latent factors such as time, geography, and socioeconomic contexts. However, existing domain generalization approaches typically treat domains as discrete or as evolving along a single axis (e.g., time). This oversimplification fails to capture the complex, multidimensional nature of real-world variation. This paper introduces the task of Continuous Domain Generalization (CDG), which aims to generalize predictive models to unseen domains defined by arbitrary combinations of continuous variations. We present a principled framework grounded in geometric and algebraic theories, showing that optimal model parameters across domains lie on a low-dimensional manifold. To model this structure, we propose a Neural Lie Transport Operator (NeuralLio), which enables structure-preserving parameter transitions by enforcing geometric continuity and algebraic consistency. To handle noisy or incomplete domain variation descriptors, we introduce a gating mechanism to suppress irrelevant dimensions and a local chart-based strategy for robust generalization. Extensive experiments on synthetic and real-world datasets, including remote sensing, scientific documents, and traffic forecasting, demonstrate that our method significantly outperforms existing baselines in both generalization accuracy and robustness.

In this paper, we consider a score-based Integer Programming (IP) approach for solving the Bayesian Network Structure Learning (BNSL) problem. State-of-theart BNSLIP formulations suffer from the exponentially large number of variables and constraints. A standard approach in IP to address such challenges is to employ row and column generation techniques, which dynamically generate rows and columns, while the complex pricing problem remains a computational bottleneck for BNSL. For the general class of ℓ0-penalized likelihood scores, we show how the pricing problem can be reformulated as a difference of submodular optimization problem, and how the Difference of Convex Algorithm (DCA) can be applied as an inexact method to efficiently solve the pricing problems. Empirically, we show that, for continuous Gaussian data, our row and column generation approach yields solutions with higher quality than state-of-the-art score-based approaches, especially when the graph density increases, and achieves comparable performance against benchmark constraint-based and hybrid approaches, even when the graph size increases.