As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement violation penalties into the training objective. To be effective, this approach requires careful tuning of these hyperparameters (weights), involving trial-anderror and cross-validation, which becomes ineffective even for a moderate number of requirements. These issues are exacerbated when the requirements involve parities or equalities, as is the case in fairness and boundary value problems. An alternative technique uses constrained optimization to formulate these learning problems. Yet, existing approximation and generalization guarantees do not apply to problems involving equality constraints. In this work, we derive a generalization theory for equality-constrained statistical learning problems, showing that their solutions can be approximated using samples and rich parametrizations. Using these results, we propose a practical algorithm based on solving a sequence of unconstrained, empirical learning problems. We showcase its effectiveness and the new formulations enabled by equality constraints in fair learning, interpolating classifiers, and boundary value problems.

Estimating causal effects from spatiotemporal observational data is essential in public health, environmental science, and policy evaluation, where randomized experiments are often infeasible. Existing approaches, however, either rely on strong structural assumptions or fail to handle key challenges such as interference, spatial confounding, temporal carryover, and time-varying confounding--where covariates are influenced by past treatments and, in turn, affect future ones. We introduce the GST-UNet (G-computation Spatio-Temporal UNet), a theoretically grounded neural framework that combines a U-Net-based spatiotemporal encoder with regression-based iterative G-computation to estimate location-specific potential outcomes under complex intervention sequences. GST-UNet explicitly adjusts for time-varying confounders and captures non-linear spatial and temporal dependencies, enabling valid causal inference from a single observed trajectory in data-scarce settings.

Bayesian Optimization (BO) is a powerful tool for optimizing expensive blackbox objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains challenging. In this paper, we propose MOBO-OSD, a multi-objective Bayesian Optimization algorithm designed to generate a diverse set of Pareto optimal solutions by solving multiple constrained optimization problems, referred to as MOBO-OSD subproblems, along orthogonal search directions (OSDs) defined with respect to an approximated convex hull of individual objective minima. By employing a well-distributed set of OSDs, MOBO-OSD ensures broad coverage of the objective space, enhancing both solution diversity and hypervolume performance. To further improve the density of the set of Pareto optimal candidate solutions without requiring an excessive number of subproblems, we leverage a Pareto Front Estimation technique to generate additional solutions in the neighborhood of existing solutions. Additionally, MOBO-OSD supports batch optimization, enabling parallel function evaluations to accelerate the optimization process when resources are available. Through extensive experiments and analysis on a variety of synthetic and real-world benchmark functions with two to six objectives, we demonstrate that MOBO-OSD consistently outperforms the state-of-the-art algorithms.

Self-distillation (SD), a technique where a model improves itself using its own predictions, has attracted attention as a simple yet powerful approach in machine learning. Despite its widespread use, the mechanisms underlying its effectiveness remain unclear. In this study, we investigate the efficacy of hyperparameter-tuned multi-stage SD with a linear classifier for binary classification on noisy Gaussian mixture data. For the analysis, we employ the replica method from statistical physics. Our findings reveal that the primary driver of SD's performance improvement is denoising through hard pseudo-labels, namely discrete labels generated from the model's own predictions, with the most notable gains observed in moderately sized datasets. We also identify two practical heuristics to enhance SD: early stopping that limits the number of stages, which is broadly effective, and bias parameter fixing, which helps under label imbalance. To empirically validate our theoretical findings derived from our toy model, we conduct additional experiments on CIFAR-10 classification using pretrained ResNet backbone. These results provide both theoretical and practical insights, advancing our understanding and application of SD in noisy settings.

Deep graph clustering (DGC) aims to partition graph nodes into distinct clusters in an unsupervised manner. Despite rapid advancements in this field, DGC remains inherently challenging due to the absence of ground-truth, which complicates the design of effective algorithms and impedes the establishment of standardized benchmarks. The lack of unified datasets, evaluation protocols, and metrics further exacerbates these challenges, making it difficult to systematically assess and compare DGC methods. To address these limitations, we introduce DGCBench, the first comprehensive and unified benchmark for DGC methods. It evaluates 12 state-ofthe-art DGC methods across 12 datasets from diverse domains and scales, spanning 6 critical dimensions: discriminability, effectiveness, scalability, efficiency, stability, and robustness. Additionally, we develop PyDGC, an open-source Python library that standardizes the DGC training and evaluation paradigm. Through systematic experiments, we reveal persistent limitations in existing methods, specifically regarding the homophily bottleneck, training instability, vulnerability to perturbations, efficiency plateau, scalability challenges, and poor discriminability, thereby offering actionable insights for future research. We hope that DGCBench, PyDGC, and our analyses will collectively accelerate the progress in the DGC community.

Developing large language models is expensive and involves making decisions with small experiments, typically by evaluating on large, multi-task evaluation suites. In this work, we analyze specific properties which make a benchmark more reliable for such decisions, and interventions to design higher-quality evaluation benchmarks. We introduce two key metrics that show differences in current benchmarks: signal, a benchmark's ability to separate better models from worse models, and noise, a benchmark's sensitivity to random variability between training steps. We demonstrate that benchmarks with a better signal-to-noiseratio are more reliable when making decisions at small scale, and those with less noisehave lower scaling law prediction error. These results suggest that improving signal or noise will lead to more useful benchmarks, so we introduce three interventions designed to directly affect signal or noise.

Although Multimodal Large Language Models (MLLMs) have advanced numerous fields, their training on extensive multimodal datasets introduces significant privacy concerns, prompting the necessity for effective unlearning methods. However, current multimodal unlearning approaches often directly adapt techniques from unimodal contexts, largely overlooking the critical issue of modality alignment, i.e., consistently removing knowledge across both unimodal and multimodal settings. To close this gap, we introduce UMU-Bench, a unified benchmark specifically targeting modality misalignment in multimodal unlearning. UMU-Benchconsists of a meticulously curated dataset featuring 653 individual profiles, each described with both unimodal and multimodal knowledge. Additionally, novel tasks and evaluation metrics focusing on modality alignment are introduced, facilitating a comprehensive analysis of unimodal and multimodal unlearning effectiveness. Through extensive experimentation with state-of-the-art unlearning algorithms on UMU-Bench, we demonstrate prevalent modality misalignment issues in existing methods. These findings underscore the critical need for novel multimodal unlearning approaches explicitly considering modality alignment.

Solving inverse problems--recovering signals from incomplete or noisy measurements--is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System-embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schrödinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT.

'Looked so real': How AI is being weaponised against India's Muslim women The freelance model from India-administered Kashmir was scrolling on her phone last year when a friend sent her a clip circulating on Instagram. But it was entirely fabricated. "It was proper stalking," Ayoub, 24, said. "They had followed my life from my first semester to the last at the university." The video stitched together photographs from Ayoub's time as a student at New Delhi's Jamia Millia Islamia University - images drawn from everyday moments of campus life, including group projects, farewell gatherings and selfies with classmates.