Related papers: Learning Algebraic Multigrid Using Graph Neural Ne…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…

Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined…

We consider learning an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR)…

There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for these approaches is Breadth-First Search (BFS). The algebraic…

Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, they are unable to capture long-range dependencies between nodes without adding…

Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear…

Strength-of-connection algorithms play a key role in algebraic multigrid (AMG). Specifically, they determine which matrix nonzeros are classified as weak and so ignored when coarsening matrix graphs and defining interpolation sparsity…

It is still a challenging task to learn a neural text generation model under the framework of generative adversarial networks (GANs) since the entire training process is not differentiable. The existing training strategies either suffer…

Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input…

Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

To enable heterogeneous computing systems with autonomous programming and optimization capabilities, we propose a unified, end-to-end, programmable graph representation learning (PGL) framework that is capable of mining the complexity of…

The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…

Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied. Selective segmentation, less studied, aims to use limited…

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…

Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…

The similarity of graph structures, such as Meaning Representations (MRs), is often assessed via structural matching algorithms, such as Smatch (Cai and Knight, 2013). However, Smatch involves a combinatorial problem that suffers from…