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Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…

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…

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…

Large-scale dense mapping is vital in robotics, digital twins, and virtual reality. Recently, implicit neural mapping has shown remarkable reconstruction quality. However, incremental large-scale mapping with implicit neural representations…

A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…

Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the…

Current state-of-the-art deep neural networks for image classification are made up of 10 - 100 million learnable weights and are therefore inherently prone to overfitting. The complexity of the weight count can be seen as a function of the…

Compressive imaging (CI) reconstruction, such as snapshot compressive imaging (SCI) and compressive sensing magnetic resonance imaging (MRI), aims to recover high-dimensional images from low-dimensional compressed measurements. This process…

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…

The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…

The generalization ability of Convolutional neural networks (CNNs) for biometrics drops greatly due to the adverse effects of various occlusions. To this end, we propose a novel unified framework integrated the merits of both CNNs and…

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

There have been significant advancements in anomaly detection in an unsupervised manner, where only normal images are available for training. Several recent methods aim to detect anomalies based on a memory, comparing or reconstructing the…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…

As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…

We propose a multigrid extension of convolutional neural networks (CNNs). Rather than manipulating representations living on a single spatial grid, our network layers operate across scale space, on a pyramid of grids. They consume multigrid…

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been…

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear…