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Extensive efforts have been made to boost the performance in the domain of language models by introducing various attention-based transformers. However, the inclusion of linear layers with large dimensions contributes to significant…

The reasoning abilities of Large Language Models (LLMs) can be improved by structurally denoising their weights, yet existing techniques primarily focus on denoising the feed-forward network (FFN) of the transformer block, and can not…

Microstructural heterogeneity affects the macro-scale behavior of materials. Conversely, load distribution at the macro-scale changes the microstructural response. These up-scaling and down-scaling relations are often modeled using…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…

Large language models (LLMs) are increasingly used to convert natural language descriptions into mathematical optimization formulations. Current evaluations often treat formulations as a whole, relying on coarse metrics like solution…

Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs. Several studies on LLM efficiency optimization argue that it is possible to prune a significant portion…

Compressing large language models (LLMs), often consisting of billions of parameters, provides faster inference, smaller memory footprints, and enables local deployment. Two standard compression techniques are pruning and quantization, with…

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or…

This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…

Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the…

The predictions of the geometric collective model (GCM) for different sets of Hamiltonian parameter values are related by analytic scaling relations. For the quartic truncated form of the GCM -- which describes harmonic oscillator, rotor,…

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

We describe a simple and general neural network weight compression approach, in which the network parameters (weights and biases) are represented in a "latent" space, amounting to a reparameterization. This space is equipped with a learned…

Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

We propose a novel multilinear dynamical system (MLDS) in a transform domain, named $\mathcal{L}$-MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…