Related papers: Accuracy and Efficiency of Simplified Tensor Netwo…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
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…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information…
We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…
Complex networks are at the core of an intense research activity. However, in most cases, intricate and costly measurement procedures are needed to explore their structure. In some cases, these measurements rely on link queries: given two…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
This paper presents an algorithm for computing the contraction of two-dimensional tensor networks on a square lattice; and we combine it with solving congruence equations to compute the exact enumeration (including weighted enumeration) of…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…