Related papers: SimTensor: A synthetic tensor data generator

The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…

Many problems in high-dimensional statistics appear to have a statistical-computational gap: a range of values of the signal-to-noise ratio where inference is information-theoretically possible, but (conjecturally) computationally…

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…

We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…

LLMs are vulnerable to hallucinations, and thus their outputs generally require laborious human verification for high-stakes applications. To this end, we propose symbolically grounded generation (SymGen) as a simple approach for enabling…

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…

Deep learning has enabled major advances in the fields of computer vision, natural language processing, and multimedia among many others. Developing a deep learning system is arduous and complex, as it involves constructing neural network…

Tensor accelerators now represent a growing share of compute resources in modern CPUs and GPUs. However, they are hard to program, leading developers to use vendor-provided kernel libraries that support tensor accelerators. As a result, the…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

Foundation models for time series analysis (TSA) have attracted significant attention. However, challenges such as training data scarcity and imbalance continue to hinder their development. Inspired by complex dynamic system theories, we…

Synthetic data are becoming a critical tool for building artificially intelligent systems. Simulators provide a way of generating data systematically and at scale. These data can then be used either exclusively, or in conjunction with real…

With the recent success of deep learning algorithms, many researchers have focused on generative models for human motion animation. However, the research community lacks a platform for training and benchmarking various algorithms, and the…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

This paper proposes a new method to generate synthetic data sets based on copula models. Our goal is to produce surrogate data resembling real data in terms of marginal and joint distributions. We present a complete and reliable algorithm…

Sparse tensors arise in problems in science, engineering, machine learning, and data analytics. Programs that operate on such tensors can exploit sparsity to reduce storage requirements and computational time. Developing and maintaining…

Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large…

The Simulation Environment for Atomistic and Molecular Modeling (SEAMM) is an open-source software package written in Python that provides a graphical interface for setting up, executing, and analyzing molecular and materials simulations.…

Computer-assisted surgical (CAS) systems enhance surgical execution and outcomes by providing advanced support to surgeons. These systems often rely on deep learning models trained on complex, challenging-to-annotate data. While synthetic…

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

Although many AI applications of interest require specialized multi-modal models, relevant data to train such models is inherently scarce or inaccessible. Filling these gaps with human annotators is prohibitively expensive, error-prone, and…