Related papers: GRIFDIR: Graph Resolution-Invariant FEM Diffusion …

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is…

Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

Diffusion models have achieved impressive performance on multi-focus image fusion (MFIF). However, a key challenge in applying diffusion models to the ill-posed MFIF problem is that defocus blur can make common symmetric geometric…

With the rapid evolution of synthetic media, Image Manipulation Localization (IML) has emerged as a critical component in multimedia forensics for ensuring the integrity of digital content. However, generalization remains a core challenge,…

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…

We present Diff3F as a simple, robust, and class-agnostic feature descriptor that can be computed for untextured input shapes (meshes or point clouds). Our method distills diffusion features from image foundational models onto input shapes.…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

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…

This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different…

As one of the most popular and sought-after generative models in the recent years, diffusion models have sparked the interests of many researchers and steadily shown excellent advantage in various generative tasks such as image synthesis,…

Diffusion models have emerged as powerful generative models for graph generation, yet their use for conditional graph generation remains a fundamental challenge. In particular, guiding diffusion models on graphs under arbitrary reward…