Related papers: Learning Fill-in Reduction Ordering via Graph Poli…
Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…
Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through…
Sparse matrix reordering can significantly reduce the fill-in during matrix factorization, thereby decreasing the computational and storage requirements in sparse matrix computations. Finding a minimal fill-in ordering is known to be an…
Efficiently solving sparse linear systems $Ax=b$, where $A$ is a large, sparse, symmetric positive semi-definite matrix, is a core challenge in scientific computing, machine learning, and optimization. A major bottleneck in Gaussian…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be…
Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…
Most methods in reinforcement learning use a Policy Gradient (PG) approach to learn a parametric stochastic policy that maps states to actions. The standard approach is to implement such a mapping via a neural network (NN) whose parameters…
Neural control of memory-constrained, agile robots requires small, yet highly performant models. We leverage graph hyper networks to learn graph hyper policies trained with off-policy reinforcement learning resulting in networks that are…
Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the…
We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented…
Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
The permutation flow shop scheduling (PFSS), aiming at finding the optimal permutation of jobs, is widely used in manufacturing systems. When solving large-scale PFSS problems, traditional optimization algorithms such as heuristics could…
Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
Estimating a policy that maps states to actions is a central problem in reinforcement learning. Traditionally, policies are inferred from the so called value functions (VFs), but exact VF computation suffers from the curse of…
Graph neural networks (GNNs) are emerging as a powerful technique for modeling graph structures. Due to the sparsity of real-world graph data, GNN performance is limited by extensive sparse matrix multiplication (SpMM) operations involved…
Off-policy policy optimization is a challenging problem in reinforcement learning (RL). The algorithms designed for this problem often suffer from high variance in their estimators, which results in poor sample efficiency, and have issues…