Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors for positional encoding in MPNNs and Graph Transformers. The expressive power of such Spectrally-enhanced GNNs (SGNNs) is usually evaluated via the $k$-WL graph isomorphism test hierarchy and homomorphism counting. Yet, these frameworks align poorly with the graph spectra, yielding limited insight into SGNNs' expressive power. In this paper, we leverage a well-studied paradigm of classifying graphs by their largest eigenvalue multiplicity to introduce an expressivity hierarchy for SGNNs. We then prove that many SGNNs are incomplete even on graphs with distinct eigenvalues. To mitigate this deficiency, we adapt rotation equivariant neural networks to the graph spectra setting, yielding equiEPNN, a novel SGNN that provably improves upon contemporary SGNNs' expressivity on simple spectrum graphs. We then demonstrate that equiEPNN achieves perfect eigenvector canonicalization on ZINC, and performs favorably on image classification on MNIST-Superpixel and graph property regression on ZINC, compared to leading spectral methods.

State-Space Models (SSMs) have proven to be powerful tools for online function approximation and for modeling long-range dependencies in sequential data. While recent methods such as HiPPO have demonstrated strong performance using a few polynomial bases, they remain limited by their reliance on closed-form solutions for specific, well-behaved bases.

Enabling virtual humans to dynamically and realistically respond to diverse auditory stimuli remains a key challenge in character animation, demanding the integration of perceptual modeling and motion synthesis. Despite its significance, this task remains largely unexplored. Most previous works have primarily focused on mapping modalities like speech, audio, and music to generate human motion. As of yet, these models typically overlook the impact of spatial features encoded in spatial audio signals on human motion. To bridge this gap and enable high-quality modeling of human movements in response to spatial audio, we introduce the first comprehensive Spatial Audio-Driven Human Motion (SAM) dataset, which contains diverse and high-quality spatial audio and motion data. For benchmarking, we develop a simple yet effective diffusion-based generative framework for human MOtion generation driven by SPatial Audio, termed MOSPA, which faithfully captures the relationship between body motion and spatial audio through an effective fusion mechanism. Once trained, MOSPA can generate diverse realistic human motions conditioned on varying spatial audio inputs. We perform a thorough investigation of the proposed dataset and conduct extensive experiments for benchmarking, where our method achieves state-of-the-art performance on this task.

The rapid extension of context windows in large vision-language models has given rise to long-context vision-language models (LCVLMs), which are capable of handling hundreds of images with interleaved text tokens in a single forward pass. In this work, we introduce MMLongBench, the first benchmark covering a diverse set of long-context vision-language tasks, to evaluate LCVLMs effectively and thoroughly. MMLongBench is composed of 13,331 examples spanning five different categories of downstream tasks, such as Visual RAG and Many-Shot ICL. It also provides broad coverage of image types, including various natural and synthetic images. To assess the robustness of the models to different input lengths, all examples are delivered at five standardized input lengths (8K-128K tokens) via a cross-modal tokenization scheme that combines vision patches and text tokens. Through a thorough benchmarking of 46 closed-source and open-source LCVLMs, we provide a comprehensive analysis of the current models' vision-language long-context ability. Our results show that: i) performance on a single task is a weak proxy for overall long-context capability; ii) both closed-source and open-source models face challenges in long-context vision-language tasks, indicating substantial room for future improvement; iii) models with stronger reasoning ability tend to exhibit better long-context performance. By offering wide task coverage, various image types, and rigorous length control, MMLongBench provides the missing foundation for diagnosing and advancing the next generation of LCVLMs.

Learning dynamics is essential for model-based control and Reinforcement Learning in systems operating in changing environments, such as robotics, autonomous vehicles, and power systems.

Human-generated reward signals are critical for aligning generative models with human preferences, guiding both training and inference-time evaluations. While large language models (LLMs) employed as proxy evaluators, i.e., LLM-as-a-Judge, significantly reduce the costs associated with manual annotations, they typically require extensive modality-specific training data and fail to generalize well across diverse multimodal tasks.

Compared to the single-image approach, our dual-image input imposes only a modest overhead for data collection, but at the same time provides important motion information, which is a reliable guide for predicting kinematic relationships between parts. Specifically, we propose a dual-image diffusion model that captures relationships between the image pair to generate part layouts and joint parameters.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

Understanding the dynamic physical world, characterized by its evolving 3D structure, real-world motion, and semantic content with textual descriptions, is crucial for human-agent interaction and enables embodied agents to perceive and act within real environments with human like capabilities. However, existing datasets are often derived from limited simulators or utilize traditional Structure-from-Motion for up-to-scale annotation and offer limited descriptive captioning, which restricts the capacity of foundation models to accurately interpret real-world dynamics from monocular videos, commonly sourced from the internet.

Cross-modal hashing aims to efficiently retrieve information across different modalities by mapping data into compact hash codes. However, most existing methods assume access to fully accurate supervision, which rarely holds in real-world scenarios. In fact, annotations are often redundant, i.e., each sample is associated with a set of candidate labels that includes both ground-truth labels and redundant noisy labels. Treating all annotated labels as equally valid introduces two critical issues: (1) the sparse presence of true labels within the label set is not explicitly addressed, leading to overfitting on redundant noisy annotations; (2) redundant noisy labels induce spurious similarities that distort semantic alignment across modalities and degrade the quality of the hash space. To address these challenges, we propose that effective cross-modal hashing requires explicitly identifying and leveraging the true label subset within all candidate annotations.