Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable d-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset.

We study the problem of minimizing the sum of a smooth function and a nonsmooth convex regularizer over a compact Riemannian submanifold embedded in Euclidean space. By introducing an auxiliary splitting variable, we propose an adaptive Riemannian alternating direction method of multipliers (ARADMM), which, for the first time, achieves convergence without requiring smoothing of the nonsmooth term. Our approach involves only one Riemannian gradient evaluation and one proximal update per iteration. Through careful and adaptive coordination of the stepsizes and penalty parameters, we establish an optimal iteration complexity of order O(ϵ 3) for finding an ϵ-approximate KKT point, matching the complexity of existing smoothing technique-based Riemannian ADMM methods. Extensive numerical experiments on sparse PCA and robust subspace recovery demonstrate that our ARADMM consistently outperforms state-of-the-art Riemannian ADMM variants in convergence speed and solution quality.

The rapid development of LLMs has raised concerns about their potential misuse, leading to various watermarking schemes that typically offer high detectability. However, existing watermarking techniques often face trade-off between watermark detectability and generated text quality. In this paper, we introduce Learning to Watermark (LTW), a novel selective watermarking framework that leverages multi-objective optimization to effectively balance these competing goals. LTW features a lightweight network that adaptively decides when to apply the watermark by analyzing sentence embeddings, token entropy, and current watermarking ratio. Training of the network involves two specifically constructed loss functions that guide the model toward Pareto-optimal solutions, thereby harmonizing watermark detectability and text quality. By integrating LTW with two baseline watermarking methods, our experimental evaluations demonstrate that LTW significantly enhances text quality without compromising detectability. Our selective watermarking approach offers a new perspective for designing watermarks for LLMs and a way to preserve high text quality for watermarks.

Large Vision-Language Models (VLMs) have achieved remarkable success in understanding complex real-world scenarios and supporting data-driven decisionmaking processes. However, VLMs exhibit significant vulnerability against adversarial examples, either text or image, which can lead to various adversarial outcomes, e.g., jailbreaking, hijacking, and hallucination, etc. In this work, we empirically and theoretically demonstrate that VLMs are particularly susceptible to image-based adversarial examples, where imperceptible perturbations can precisely manipulate each output token. To this end, we propose a novel attack called Visionlanguage model Manipulation Attack (VMA), which integrates first-order and second-order momentum optimization techniques with a differentiable transformation mechanism to effectively optimize the adversarial perturbation.

In multi-objective learning (MOL), several possibly competing prediction tasks must be solved jointly by a single model. Achieving good trade-offs may require a model class G with larger capacity than what is necessary for solving the individual tasks. This, in turn, increases the statistical cost, as reflected in known MOL bounds that depend on the complexity of G. We show that this cost is unavoidable for some losses, even in an idealized semi-supervised setting, where the learner has access to the Bayes-optimal solutions for the individual tasks as well as the marginal distributions over the covariates. On the other hand, for objectives defined with Bregman losses, we prove that the complexity of G may come into play only in terms of unlabeled data. Concretely, we establish sample complexity upper bounds, showing precisely when and how unlabeled data can significantly alleviate the need for labeled data. This is achieved by a simple pseudo-labeling algorithm.

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. Extensive experiments on multiple datasets spanning diverse tissue types demonstrate our method's superior performance in structural restoration accuracy and cross-tissue robustness.

Training deep neural networks is a structured optimization problem, because the parameters are naturally represented by matrices and tensors rather than by vectors. Under this structural representation, it has been widely observed that gradients are low-rank and Hessians are approximately block diagonal. These structured properties are crucial for designing efficient optimization algorithms, but are not utilized by many current popular optimizers like Adam. In this paper, we present a novel optimization algorithm ASGO that capitalizes on these properties by employing a preconditioner that is adaptively updated using structured gradients. By a fine-grained theoretical analysis, ASGO is proven to achieve superior convergence rates compared to existing structured gradient methods. Based on this convergence theory, we further demonstrate that ASGO can benefit from low-rank gradients and block diagonal Hessians. We also discuss practical modifications of ASGO and empirically verify ASGO's effectiveness on language model tasks.

We consider the following question: given a submodular/supermodular set function f: 2V R, how should one minimize/maximize its average value f(S)/|S| over non-empty subsets S V? This problem generalizes several well-known objectives, including Densest Subgraph (DSG), Densest Supermodular Set (DSS), and Submodular Function Minimization (SFM). Motivated by recent applications [42, 34], we formalize two new broad problems: the Unrestricted Sparsest Submodular Set (USSS) and Unrestricted Densest Supermodular Set (UDSS), both of which allow negative and non-monotone functions. Using classical results, we show that DSS, SFM, USSS, UDSS, and Minimum Norm Point (MNP) are all equivalent under strongly polynomial-time reductions. This equivalence enables algorithmic cross-over: methods designed for one problem can be repurposed to solve others efficiently. In particular, we use the perspective of the minimum norm point in the base polyhedron of a sub/supermodular function, which, via Fujishige's results, yields the dense decomposition as a byproduct.

Boosting methods often achieve excellent classification accuracy, but can experience notable performance degradation in the presence of label noise. Existing robust methods for boosting provide theoretical robustness guarantees for certain types of label noise, and can exhibit only moderate performance degradation. However, previous theoretical results do not account for realistic types of noise and finite training sizes, and existing robust methods can provide unsatisfactory accuracies, even without noise. This paper presents methods for robust minimax boosting (RMBoost) that minimize worst-case error probabilities and are robust to general types of label noise. In addition, we provide finite-sample performance guarantees for RMBoost with respect to the error obtained without noise and with respect to the best possible error (Bayes risk). The experimental results corroborate that RMBoost is not only resilient to label noise but can also provide strong classification accuracy.

Designing de novo 3D molecules with desirable properties remains a fundamental challenge in drug discovery and molecular engineering. While diffusion models have demonstrated remarkable capabilities in generating high-quality 3D molecular structures, they often struggle to effectively control complex multi-objective constraints critical for real-world applications. In this study, we propose an uncertaintyaware Reinforcement Learning (RL) framework to guide the optimization of 3D molecular diffusion models toward multiple property objectives while enhancing the overall quality of the generated molecules. Our method leverages surrogate models with predictive uncertainty estimation to dynamically shape reward functions, facilitating balance across multiple optimization objectives. We comprehensively evaluate our framework across three benchmark datasets and multiple diffusion model architectures, consistently outperforming baselines for molecular quality and property optimization. Additionally, Molecular Dynamics (MD) simulations and ADMET profiling of top generated candidates indicate promising drug-like behavior and binding stability, comparable to known Epidermal Growth Factor Receptor (EGFR) inhibitors. Our results demonstrate the strong potential of RL-guided generative diffusion models for advancing automated molecular design.