Related papers: Approximating Tensor Network Contraction with Sket…
Mining massive spatio-temporal data can help a variety of real-world applications such as city capacity planning, event management, and social network analysis. The tensor representation can be used to capture the correlation between space…
Representation learning using network embedding has received tremendous attention due to its efficacy to solve downstream tasks. Popular embedding methods (such as deepwalk, node2vec, LINE) are based on a neural architecture, thus unable to…
CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq…
TensorSketch is an oblivious linear sketch introduced in Pagh'13 and later used in Pham, Pagh'13 in the context of SVMs for polynomial kernels. It was shown in Avron, Nguyen, Woodruff'14 that TensorSketch provides a subspace embedding, and…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…
Deep learning has made profound impacts in the domains of data mining and AI, distinguished by the groundbreaking achievements in numerous real-world applications and the innovative algorithm design philosophy. However, it suffers from the…
We develop a sketching algorithm to find the point on the convex hull of a dataset, closest to a query point outside it. Studying the convex hull of datasets can provide useful information about their geometric structure and their…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…
Approximate Nearest Neighbor (ANN) search and Approximate Kernel Density Estimation (A-KDE) are fundamental problems at the core of modern machine learning, with broad applications in data analysis, information systems, and large-scale…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…
The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational…
Many computational tasks benefit from being formulated as the composition of neural networks followed by a discrete symbolic program. The goal of neurosymbolic learning is to train the neural networks using end-to-end input-output labels of…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of TNs for functions from classical smoothness classes?'' and…
Simulating many-body quantum systems on a classical computer is difficult due to the large number of degrees of freedom, causing the computational complexity to grow exponentially with system size. Tensor Networks (TN) is a framework that…