We propose Neural Hamiltonian Diffusion (NHD), a unified framework for learning stochastic Hamiltonian dynamics on differentiable manifolds. Unlike conventional Hamiltonian Neural Networks (HNNs), which assume noise-free dynamics in flat Euclidean spaces, our approach models stochastic differential equations (SDEs) on curved manifolds endowed with both a Riemannian metric and a Poisson structure. Specifically, we parameterize a neural Hamiltonian and define the dynamics via a Stratonovich SDE whose drift is the Poisson vector field lifted horizontally to the orthonormal frame bundle. This construction ensures coordinate-invariant, gaugeconsistent dynamics across (pseudo-)Riemannian manifolds, enabling physically plausible modeling in systems with geometric constraints, periodicity, or relativistic structure. We establish generalization guarantees under curvature-dependent complexity and demonstrate applications across diverse scientific domains, including toroidal molecular dynamics, quantum spin systems, and relativistic n-body problems in Schwarzschild spacetime.

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4 6%) and computation time (8 10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.

Language bias in Visual Question Answering (VQA) arises when models exploit spurious statistical correlations between question templates and answers, particularly in out-of-distribution scenarios, thereby neglecting essential visual cues and compromising genuine multimodal reasoning. Despite numerous efforts to enhance the robustness of VQA models, a principled understanding of how such bias originates and influences model behavior remains underdeveloped. In this paper, we address this gap through a comprehensive empirical and theoretical analysis, revealing that modality-specific gradient imbalances, which originate from the inherent heterogeneity of multimodal data, lead to skewed feature fusion and biased classifier weights. To alleviate these issues, we propose a novel MultiMargin Collaborative Debiasing (MMCD) framework2, which adaptively integrates frequency-aware, confidence-aware, and difficulty-aware angular margins with a dynamic, difficulty-aware contrastive learning mechanism to reshape decision boundaries under biased training conditions. Extensive experiments across multiple challenging VQA benchmarks confirm the consistent superiority of our proposed MMCD over state-of-the-art baselines in combating language bias.

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by conditioning on a hierarchy of lower-dimensional future state representations. Inspired by the stability properties of numerical implicit time-stepping methods, we developed an approach that leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements. By actively adjusting the temporal downsampling ratios, our design enables the model to capture dynamics across multiple granularities and enforce long-range temporal coherence. Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts, significantly outperforming non-hierarchical autoregressive baselines while adding minimal computational overhead. The codebase is available at this link1.

Random splitting of datasets in image segmentation often leads to unrepresentative test sets, resulting in biased evaluations and poor model generalization. While stratified sampling has proven effective for addressing label distribution imbalance in classification tasks, extending these ideas to segmentation remains challenging due to the multi-label structure and class imbalance typically present in such data. Building on existing stratification concepts, we introduce Iterative Pixel Stratification (IPS), a straightforward, label-aware sampling method tailored for segmentation tasks. Additionally, we present Wasserstein-Driven Evolutionary Stratification (WDES), a novel genetic algorithm designed to minimize the Wasserstein distance, thereby optimizing the similarity of label distributions across dataset splits. We prove that WDES is globally optimal given enough generations. Using newly proposed statistical heterogeneity metrics, we evaluate both methods against random sampling and find that WDES consistently produces more representative splits. Applying WDES across diverse segmentation tasks, including street scenes, medical imaging, and satellite imagery, leads to lower performance variance and improved model evaluation. Our results also highlight the particular value of WDES in handling small, imbalanced, and low-diversity datasets, where conventional splitting strategies are most prone to bias.

Correlated equilibria--and their generalizations known as Φ-equilibria--are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model fundamental settings in economics, and have been a cornerstone of economics research since the seminal paper of Arrow and Debreu [1954]. Recently, there has been growing interest, both in economics and in computer science, in studying correlated equilibria in generalized games. It is known that finding a social welfare maximizing correlated equilibrium in generalized games is NP-hard. However, the existence of efficient algorithms to find any equilibrium remains an important open question.

Real-world multivariate time series anomalies are rare and often unlabeled. Additionally, prevailing methods rely on increasingly complex architectures tuned to benchmarks, detecting only fragments of anomalous segments and overstating performance. In this paper, we introduce OracleAD, a simple and interpretable unsupervised framework for multivariate time series anomaly detection. OracleAD encodes each variable's past sequence into a single causal embedding to jointly predict the present time point and reconstruct the input window, effectively modeling temporal dynamics. These embeddings then undergo self-attention mechanism to project them into a shared latent space and capture spatial relationships.

We study fundamental connections between coalition formation games and clustering, illustrating the cross-disciplinary relevance of these concepts. We focus on graphical hedonic games where agents' preferences are compactly represented by a friendship graph and an enmity graph. In the context of clustering, friendship relations naturally align with data point similarities, whereas enmity corresponds to dissimilarities. We consider two stability notions based on single-agent deviations: local popularity and local stability.

Differential privacy (DP) limits the impact of individual training data samples by bounding their gradient norms through clipping. Conventional clipping operations assign unequal scaling factors to sample gradients with different norms, leading to a direction mismatch between the true batch gradient and the aggregation of the clipped gradients.

Data deviations in electronic health records (EHR) refer to discrepancies between recorded entries and a patient's actual physiological state, indicating a decline in EHR data fidelity. Such deviations can result from pre-analytical variability, documentation errors, or unvalidated data sources. Effectively detecting data deviations is clinically valuable for identifying erroneous records, excluding them from downstream clinical workflows, and informing corrective actions. Despite its importance and practical relevance, this problem remains largely underexplored in existing research. To bridge this gap, we propose a bi-level knowledge distillation approach centered on a task-agnostic formulation of EHR data fidelity as an intrinsic measure of data reliability. Our approach performs layered knowledge distillation in two levels: from a computation-intensive, task-specific data Shapley oracle to a neural oracle for individual tasks, and then to a unified EHR data fidelity predictor. This design enables the integration of task-specific insights into a holistic assessment of a patient's EHR data fidelity from a multi-task perspective. By tracking the outputs of this learned predictor, we detect potential data deviations in EHR data.