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Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core…

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…

Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…

A fundamental process in the implementation of any numerical tensor network algorithm is that of contracting a tensor network. In this process, a network made up of multiple tensors connected by summed indices is reduced to a single tensor…

RNN-Transducers (RNN-Ts) have gained widespread acceptance as an end-to-end model for speech to text conversion because of their high accuracy and streaming capabilities. A typical RNN-T independently encodes the input audio and the text…

We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous…

Self-supervised speech representation learning (SSL) has shown to be effective in various downstream tasks, but SSL models are usually large and slow. Model compression techniques such as pruning aim to reduce the model size and computation…

Transformers have become foundational architectures for both natural language and computer vision tasks. However, the high computational cost makes it quite challenging to deploy on resource-constraint devices. This paper investigates the…

Prompting large language models has enabled significant recent progress in multi-step reasoning over text. However, when applied to text generation from semi-structured data (e.g., graphs or tables), these methods typically suffer from low…

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…

Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…

Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on…

ProSper is a python library containing probabilistic algorithms to learn dictionaries. Given a set of data points, the implemented algorithms seek to learn the elementary components that have generated the data. The library widens the scope…

Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

Following the general theoretical framework of VSA (Vector Symbolic Architecture), a cognitive model with the use of sparse binary hypervectors is proposed. In addition, learning algorithms are introduced to bootstrap the model from…

Recently, it has been shown that spiking neural networks (SNNs) can be trained efficiently, in a supervised manner, using backpropagation through time. Indeed, the most commonly used spiking neuron model, the leaky integrate-and-fire…