相关论文: Geometric Algebra Planes: Convex Implicit Neural V…

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between…

We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees…

Recent research on learnable neural representations has been widely adopted in the field of 3D scene reconstruction and neural rendering applications. However, traditional feature grid representations often suffer from substantial memory…

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…

Recently introduced implicit field representations offer an effective way of generating 3D object shapes. They leverage implicit decoder trained to take a 3D point coordinate concatenated with a shape encoding and to output a value which…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks,…

Shape reconstruction from imaging volumes is a recurring need in medical image analysis. Common workflows start with a segmentation step, followed by careful post-processing and,finally, ad hoc meshing algorithms. As this sequence can be…

In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that…

Current volumetric biomedical foundation models struggle to generalize as public 3D datasets are small and do not cover the broad diversity of medical procedures, conditions, anatomical regions, and imaging protocols. We address this by…

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this…

A neural implicit outputs a number indicating whether the given query point in space is inside, outside, or on a surface. Many prior works have focused on _latent-encoded_ neural implicits, where a latent vector encoding of a specific shape…

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as…

This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and…

We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…