Related papers: Tensor network complexity of multilinear maps
A transversal of a hypergraph is a set of vertices intersecting each hyperedge. We design and analyze new exponential-time algorithms to enumerate all inclusion-minimal transversals of a hypergraph. For each fixed k>2, our algorithms for…
Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…
Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing,…
$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate…
The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models.…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
Vassilevska and Williams (STOC 2009) showed how to count simple paths on $k$ vertices and matchings on $k/2$ edges in an $n$-vertex graph in time $n^{k/2+O(1)}$. In the same year, two different algorithms with the same runtime were given by…
Modeling the associations between real world entities from their multivariate cross-sectional profiles can provide cues into the concerted working of these entities as a system. Several techniques have been proposed for deciphering these…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…
We present an algorithm that takes as input an $n$-vertex planar graph $G$ and a $k$-vertex pattern graph $P$, and computes the number of (induced) copies of $P$ in $G$ in $2^{O(k/\log k)}n^{O(1)}$ time. If $P$ is a matching, independent…
Detection of overlapping communities in real-world networks is a generally challenging task. Upon recognizing that a network is in fact the union of its egonets, a novel network representation using multi-way data structures is advocated in…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Given a $k$-node pattern graph $H$ and an $n$-node host graph $G$, the subgraph counting problem asks to compute the number of copies of $H$ in $G$. In this work we address the following question: can we count the copies of $H$ faster if…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…