We study the problem of robustly estimating the edge density of Erdos Renyi random graphs $\mathbb{G}(n, d^\circ/n)$ when an adversary can arbitrarily add or remove edges incident to an $\eta$-fraction of the nodes.

Series Section Electron Microscopy (ssEM) has emerged as a pivotal technology for deciphering nanoscale biological architectures. Three-dimensional (3D) registration is a critical step in ssEM, tasked with rectifying axial misalignments and nonlinear distortions introduced during serial sectioning. The core scientific challenge lies in achieving distortion mitigation without erasing the natural morphological deformations of biological tissues, thereby enabling faithful reconstruction of 3D ultrastructural organization. In this study, we present a paradigm-shifting optimization framework that rethinks 3D registration through the lens of manifold trajectory optimization. We propose the first continuous trajectory dynamics formulation for 3D registration and introduce a novel optimization strategy. Specifically, we introduce a dual optimization objective that inherently balances global trajectory smoothness with local structural preservation, while developing a solver that combines Gauss-Seidel iteration with Neural ODEs to systematically integrate biophysical priors with data-driven deformation compensation. A key strength of our method is its fully unsupervised training, which avoids reliance on ground truth and suits ssEM scenarios where annotations are difficult to obtain. Extensive experiments on multiple datasets spanning diverse tissue types demonstrate our method's superior performance in structural restoration accuracy and cross-tissue robustness.

Contrastive learning---a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones---has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of \emph{approximate sufficient statistics}, which we extend beyond its original definition in~\cite{oko2025statistical} for contrastive language-image pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general $f$-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.

Blind-spot denoising (BSD) method is a powerful paradigm for zero-shot image denoising by training models to predict masked target pixels from their neighbors. However, they struggle with real-world noise exhibiting strong local correlations, where efforts to suppress noise correlation often weaken pixel-value dependencies, adversely affecting denoising performance. This paper presents a theoretical analysis quantifying the impact of replacing masked pixels with observations exhibiting weaker noise correlation but potentially reduced similarity, revealing a trade-off that impacts the statistical risk of the estimation. Guided by this insight, we propose a computational scheme that replaces masked pixels with distant ones of similar appearance and lower noise correlation. This strategy improves the prediction by balancing noise suppression and structural consistency. Experiments confirm the effectiveness of our method, outperforming existing zero-shot BSD methods.

Tactile perception is essential for embodied agents to understand the physical attributes of objects that cannot be determined through visual inspection alone. While existing methods have made progress in visual and language modalities for physical understanding, they fail to effectively incorporate tactile information that provides crucial haptic feedback for real-world interaction. In this paper, we present VTV-LLM, the first multi-modal large language model that enables universal Visuo-Tactile Video (VTV) understanding, bridging the gap between tactile perception and natural language. To address the challenges of cross-sensor and cross-modal integration, we contribute VTV150K, a comprehensive dataset comprising 150,000 video frames from 100 diverse objects captured across three different tactile sensors (GelSight Mini, DIGIT, and Tac3D), annotated with four fundamental tactile attributes (hardness, protrusion, elasticity, and friction). We develop a novel three-stage training paradigm that includes VTV enhancement for robust visuo-tactile representation, VTV-text alignment for cross-modal correspondence, and text prompt finetuning for natural language generation. Our framework enables sophisticated tactile reasoning capabilities including feature assessment, comparative analysis, and scenario-based decision-making. Extensive experimental evaluations demonstrate that VTV-LLM achieves superior performance in tactile reasoning tasks, establishing a foundation for more intuitive human-machine interaction in tactile domains.

The sparse additive model (SpAM) offers a trade-off between interpretability and flexibility, and hence is a powerful model for high-dimensional research. This paper focuses on the variable selection, i.e., the univariate function selection problem in SpAM. We establish the minimax separation rates from both the perspectives of sparse multiple testing (FDR + FNR control) and support recovery (wrong recovery probability control). We further study how adaptation to unknown smoothness affects the minimax separation rate, and propose an adaptive selection procedure. Finally, we discuss the difference between estimation and selection in SpAM: Procedures achieving optimal function estimation may fail to achieve optimal univariate function selection.

We contribute towards resolving the open question of how many hidden layers are required in ReLU networks for exactly representing all continuous and piecewise linear functions on $\mathbb{R}^d$. While the question has been resolved in special cases, the best known lower bound in general is still 2. We focus on neural networks that are compatible with certain polyhedral complexes, more precisely with the braid fan. For such neural networks, we prove a non-constant lower bound of $\Omega(\log\log d)$ hidden layers required to exactly represent the maximum of $d$ numbers. Additionally, we provide a combinatorial proof that neural networks satisfying this assumption require three hidden layers to compute the maximum of 5 numbers; this had only been verified with an excessive computation so far. Finally, we show that a natural generalization of the best known upper bound to maxout networks is not tight, by demonstrating that a rank-3 maxout layer followed by a rank-2 maxout layer is sufficient to represent the maximum of 7 numbers.

Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: \textit{can we identify/synthesize linear transformations from a minimal set of geometric primitives?} Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors---geometric objects encoding oriented planes---and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only $\mathcal{O}(\log^2 d)$ parameters, versus $\mathcal{O}(d^2)$ required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, our rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.

Graphical User Interface (GUI) agents have made substantial strides in understanding and executing user instructions across diverse platforms. Yet, grounding these instructions to precise interface elements remains challenging--especially in complex, high-resolution, professional environments. Traditional supervised fine-tuning (SFT) methods often require large volumes of diverse data and exhibit weak generalization. To overcome these limitations, we introduce a reinforcement learning (RL)-based framework that incorporates three core strategies: (1) seed data curation to ensure high-quality training samples, (2) a dense policy gradient that provides continuous feedback based on prediction accuracy, and (3) a self-evolutionary reinforcement finetuning mechanism that iteratively refines the model using attention maps. With only 3k training samples, our 7B-parameter model achieves state-of-the-art results among similarly sized models on three grounding benchmarks.

The tremendous potential has been demonstrated by large language models (LLMs) in intelligent decision-making problems, with unprecedented capabilities shown across diverse applications ranging from gaming AI systems to complex strategic planning frameworks. However, the StarCraft II platform, which has been widely adopted for validating decision-making algorithms in the past decade, has not yet provided substantial support for this emerging domain. To address issues that LLMs cannot interface with the hundreds of actions of the pysc2 backend and the lack of native support for multi-agent (MA) collaboration, we propose the LLM-PySC2 environment. This is the first environment that offers LLMs the complete pysc2 action space with sufficient multi-modal information and game Wiki knowledge. With an asynchronous query architecture, the environment efficiently interacts with LLMs that maintain a constant latency regardless of the scale of the agents' population. In the experiments, we evaluated LLMs' decision-making performance in both the macro-decision and micro-operation scenarios, with traditional StarCraft II Multi-Agent Challenge (SMAC) tasks and a series of new proposed. Results indicate that LLMs possess the potential to achieve victories in complex scenarios but cannot constantly generate correct decisions, especially in the recovered pysc2 action space and MA settings. Without task-relevant instructions, the pre-trained models suffer from issues such as hallucinations and inefficient collaboration. Our findings suggest that StarCraft II still challenges in the era of large models, revealing that there is a lot to do to develop an advanced LLM decision-making system, and the proposed LLM-PySC2 environment will support future development of LLM-based decision-making solutions.