NeuKron：稀疏可重排矩阵和张量的常数大小有损压缩
NeuKron: Constant-Size Lossy Compression of Sparse Reorderable Matrices and Tensors
AI总结：
本文提出NeuKron，一种利用常数参数循环神经网络推广Kronecker积的方法，通过重排行列将稀疏可重排矩阵和张量压缩至常数大小，在近似误差和空间占用上显著优于现有方法且具备高度可扩展性。
摘要：
许多现实世界的数据自然地表示为稀疏可重排矩阵，其行和列可以任意排序（例如，二分图的邻接矩阵）。以传统方式存储稀疏矩阵所需的空间量与非零元素的数量呈线性关系，而稀疏矩阵的有损压缩（例如，截断SVD）通常所需的空间量与行数和列数呈线性关系。在这项工作中，我们提出了NeuKron，用于将稀疏可重排矩阵压缩到常数大小的空间中。NeuKron使用具有常数数量参数的循环神经网络来推广Kronecker积。NeuKron更新参数使得给定矩阵由该乘积近似，并重排矩阵的行和列以促进近似。更新所需的时间与输入矩阵中的非零元素数量呈线性关系，并且每个条目的近似值可以在对数时间内检索到。我们还将NeuKron扩展到压缩稀疏可重排张量（例如，多层图），这是矩阵的推广。通过在十个真实世界数据集上的实验，我们展示了NeuKron具有以下特性：紧凑，在相似的近似误差下，所需空间比其最佳竞争对手少多达五个数量级；准确，在相似大小的输出下，给出的近似误差比其最佳竞争对手小多达10倍；可扩展，成功压缩了一个具有超过2.3亿个非零元素的矩阵。
英文摘要：
Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an amount of space linear in the number of non-zeros, and lossy compression of sparse matrices (e.g., Truncated SVD) typically requires an amount of space linear in the number of rows and columns. In this work, we propose NeuKron for compressing a sparse reorderable matrix into a constant-size space. NeuKron generalizes Kronecker products using a recurrent neural network with a constant number of parameters. NeuKron updates the parameters so that a given matrix is approximated by the product and reorders the rows and columns of the matrix to facilitate the approximation. The updates take time linear in the number of non-zeros in the input matrix, and the approximation of each entry can be retrieved in logarithmic time. We also extend NeuKron to compress sparse reorderable tensors (e.g. multi-layer graphs), which generalize matrices. Through experiments on ten real-world datasets, we show that NeuKron is (a) Compact: requiring up to five orders of magnitude less space than its best competitor with similar approximation errors, (b) Accurate: giving up to 10x smaller approximation error than its best competitors with similar size outputs, and (c) Scalable: successfully compressing a matrix with over 230 million non-zero entries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
