Beyond Averaging in John Ellipsoid Approximation: High-Accuracy Algorithms in the Leverage-Score Model

The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins, Lee and Yang (COLT 2019) to its successors [WY24, CLS+25], all reaching a $(1+\varepsilon)$-approximation in $Θ(\varepsilon^{-1}\log(n/d))$ iterations. We separate this complexity into three costs the modern line conflates (certification, identification, and accuracy) and locate the historical $\varepsilon^{-1}$ in the first alone. In the equivalent D-optimal-design form $\min_{\mathbf{p}\inΔ_n}-\log\det(\sum_i p_i\mathbf{a}_i\mathbf{a}_i^\top)$, the leverage-score oracle is exactly the first-order oracle and the $(1+\varepsilon)$-John guarantee the Frank-Wolfe gap $g(\mathbf{p})\le\varepsilon d$; through this dictionary the costs come apart. The $\varepsilon^{-1}$ is a certification artifact: the uniform average of the iterates, the certificate used throughout the line, has gap exactly $Θ(1/T)$, however cheap each iteration is made. Pointed instead at the last iterate the same oracle is fast: a warm-started accelerated method reaches the guarantee in $C(\mathbf{A})+O(\sqrtκ\log(1/\varepsilon))$ queries after an $\varepsilon$-independent setup $C(\mathbf{A})$, and once the optimal face is identified the facial problem is an unconstrained self-concordant minimization whose Hessian the oracle recovers exactly, so damped Newton needs only $O(\log\log(1/\varepsilon))$ steps, for a total of $C(\mathbf{A})+O(d^2\log\log(1/\varepsilon))$ queries. The accuracy dependence is thus doubly logarithmic after an $\varepsilon$-independent, condition-dependent setup; the open problem is the remaining identification cost (a condition-free bound on reaching the optimal face) and lower bounds. Accuracy is not the obstruction.

Stateful Visual Encoders for Vision-Language Models

Vision-language models (VLMs) are increasingly used in multi-image, multi-turn agentic settings where decisions depend on visual changes. However, in existing open-weight VLMs, visual comparisons happen only inside the language model, while the visual encoder itself remains stateless: each image is encoded independently, without access to the prior visual context. As a result, small but task-critical changes may be attenuated before the language model has a chance to compare them, especially when those changes do not affect the high-level semantics of the scene. We introduce a Stateful Visual Encoder, which conditions each visual representation on prior visual features. Under supervised finetuning, VLMs equipped with stateful encoders achieve consistent improvements on controlled tasks involving cross-image spatial aggregation, multi-object visual differencing, and visual trajectory behavior cloning. These improvements are consistent across input resolutions, language model sizes, and VLM backbones. Finally, we validate our model on real-world tasks, including longitudinal radiology, fine-grained image comparison, and remote sensing, where stateful encoders consistently improve generalist VLM baselines and can match or surpass specialized models in selected domains. Project page: https://statefulvisualencoders.github.io/

Structural Feature Engineering for Generative Engine Optimization: How Content Structure Shapes Citation Behavior

The proliferation of AI-powered search engines has shifted information discovery from traditional link-based retrieval to direct answer generation with selective source citation, creating new challenges for content visibility. While existing Generative Engine Optimization (GEO) approaches focus primarily on semantic content modification, the role of structural features in influencing citation behavior remains underexplored. In this paper, we propose GEO-SFE, a systematic framework for structural feature engineering in generative engine optimization. Our approach decomposes content structure into three hierarchical levels: macro-structure (document architecture), meso-structure (information chunking), and micro-structure (visual emphasis), and models their impact on citation probability across different generative engine architectures. We develop architecture-aware optimization strategies and predictive models that preserve semantic integrity while improving structural effectiveness. Experimental evaluation across six mainstream generative engines demonstrates consistent improvements in citation rate (17.3 percent) and subjective quality (18.5 percent), validating the effectiveness and generalizability of the proposed framework. This work establishes structural optimization as a foundational component of GEO, providing a data-driven methodology for enhancing content visibility in LLM-powered information ecosystems.

UnSAMv2: Self-Supervised Learning Enables Segment Anything at Any Granularity

The Segment Anything Model (SAM) family has become a widely adopted vision foundation model, but its ability to control segmentation granularity remains limited. Users often need to refine results manually - by adding more prompts or selecting from pre-generated masks - to achieve the desired level of detail. This process can be ambiguous, as the same prompt may correspond to several plausible masks, and collecting dense annotations across all granularities is prohibitively expensive, making supervised solutions infeasible. To address this limitation, we introduce UnSAMv2, which enables segment anything at any granularity without human annotations. UnSAMv2 extends the divide-and-conquer strategy of UnSAM by discovering abundant mask-granularity pairs and introducing a novel granularity control embedding that enables precise, continuous control over segmentation scale. Remarkably, with only $6$K unlabeled images and $0.02\%$ additional parameters, UnSAMv2 substantially enhances SAM-2, achieving segment anything at any granularity across interactive, whole-image, and video segmentation tasks. Evaluated on over $11$ benchmarks, UnSAMv2 improves $\text{NoC}_{90}$ (5.69 $\rightarrow$ 4.75), 1-IoU (58.0 $\rightarrow$ 73.1), and $\text{AR}_{1000}$ (49.6 $\rightarrow$ 68.3), showing that small amounts of unlabeled data with a granularity-aware self-supervised learning method can unlock the potential of vision foundation models.

DynTaskMAS: A Dynamic Task Graph-driven Framework for Asynchronous and Parallel LLM-based Multi-Agent Systems

The emergence of Large Language Models (LLMs) in Multi-Agent Systems (MAS) has opened new possibilities for artificial intelligence, yet current implementations face significant challenges in resource management, task coordination, and system efficiency. While existing frameworks demonstrate the potential of LLM-based agents in collaborative problem-solving, they often lack sophisticated mechanisms for parallel execution and dynamic task management. This paper introduces DynTaskMAS, a novel framework that orchestrates asynchronous and parallel operations in LLM-based MAS through dynamic task graphs. The framework features four key innovations: (1) a Dynamic Task Graph Generator that intelligently decomposes complex tasks while maintaining logical dependencies, (2) an Asynchronous Parallel Execution Engine that optimizes resource utilization through efficient task scheduling, (3) a Semantic-Aware Context Management System that enables efficient information sharing among agents, and (4) an Adaptive Workflow Manager that dynamically optimizes system performance. Experimental evaluations demonstrate that DynTaskMAS achieves significant improvements over traditional approaches: a 21-33% reduction in execution time across task complexities (with higher gains for more complex tasks), a 35.4% improvement in resource utilization (from 65% to 88%), and near-linear throughput scaling up to 16 concurrent agents (3.47X improvement for 4X agents). Our framework establishes a foundation for building scalable, high-performance LLM-based multi-agent systems capable of handling complex, dynamic tasks efficiently.

Fast John Ellipsoid Computation with Differential Privacy Optimization

Determining the John ellipsoid - the largest volume ellipsoid contained within a convex polytope - is a fundamental problem with applications in machine learning, optimization, and data analytics. Recent work has developed fast algorithms for approximating the John ellipsoid using sketching and leverage score sampling techniques. However, these algorithms do not provide privacy guarantees for sensitive input data. In this paper, we present the first differentially private algorithm for fast John ellipsoid computation. Our method integrates noise perturbation with sketching and leverage score sampling to achieve both efficiency and privacy. We prove that (1) our algorithm provides $(\epsilon,\delta)$-differential privacy, and the privacy guarantee holds for neighboring datasets that are $\epsilon_0$-close, allowing flexibility in the privacy definition; (2) our algorithm still converges to a $(1+\xi)$-approximation of the optimal John ellipsoid in $O(\xi^{-2}(\log(n/\delta_0) + (L\epsilon_0)^{-2}))$ iterations where $n$ is the number of data point, $L$ is the Lipschitz constant, $\delta_0$ is the failure probability, and $\epsilon_0$ is the closeness of neighboring input datasets. Our theoretical analysis demonstrates the algorithm's convergence and privacy properties, providing a robust approach for balancing utility and privacy in John ellipsoid computation. This is the first differentially private algorithm for fast John ellipsoid computation, opening avenues for future research in privacy-preserving optimization techniques.