Related papers: Diffusion Operator Geometry of Feedforward Represe…

Representation learning on graphs that evolve has recently received significant attention due to its wide application scenarios, such as bioinformatics, knowledge graphs, and social networks. The propagation of information in graphs is…

Modern deep learning treats neural networks primarily as endpoint functions from inputs to outputs. Inspired by the shift from force to geometry in physics, we ask whether a network should instead be understood through the geometry of its…

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

By optimizing the rate-distortion-realism trade-off, generative image compression approaches produce detailed, realistic images instead of the only sharp-looking reconstructions produced by rate-distortion-optimized models. In this paper,…

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a…

Real-world data generation often involves certain geometries (e.g., graphs) that induce instance-level interdependence. This characteristic makes the generalization of learning models more difficult due to the intricate interdependent…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…

Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…

Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…

Hiding data using neural networks (i.e., neural steganography) has achieved remarkable success across both discriminative classifiers and generative adversarial networks. However, the potential of data hiding in diffusion models remains…

Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on…

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near…

The popularity of deep learning techniques renewed the interest in neural architectures able to process complex structures that can be represented using graphs, inspired by Graph Neural Networks (GNNs). We focus our attention on the…

The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…

Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models…

Conventional computer vision models rely on very deep, feedforward networks processing whole images and trained offline with extensive labeled data. In contrast, biological vision relies on comparatively shallow, recurrent networks that…

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…

Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data…