Related papers: Zero Sum SVD: Balancing Loss Sensitivity for Low R…

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…

This paper introduces a novel method of Progressive Low Rank Decomposition (PLRD) tailored for the compression of large language models. Our approach leverages a pre-trained model, which is then incrementally decompressed to smaller sizes…

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the…

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

The rapid growth of large language models (LLMs) presents significant deployment challenges due to their massive computational and memory demands. While model compression, such as network pruning, offers potential solutions, most existing…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…

Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…

Large Language Models' (LLMs) weight matrices can often be expressed in low-rank form with potential to relax memory and compute resource requirements. Unlike prior efforts that focus on developing novel matrix decompositions, in this work…

Contextual sparsity is one of the approaches used to reduce computational complexity in the inference process of large language models (LLMs). Existing techniques for efficient LLM inference acceleration based on contextual sparsity with…

Although large vision-language models (LVLMs) have demonstrated impressive capabilities in multi-modal understanding and reasoning, their practical applications are still limited by massive model parameters and high computational costs.…

We provide a new LLM-compression solution via SVD, unlocking new possibilities for LLM compression beyond quantization and pruning. We point out that the optimal use of SVD lies in truncating activations, rather than merely using…

We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…

Large language models (LLMs) significantly enhance the performance of various applications, but they are computationally intensive and energy-demanding. This makes it challenging to deploy them on devices with limited resources, such as…

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank…

Low Rank Decomposition (LRD) is a model compression technique applied to the weight tensors of deep learning models in order to reduce the number of trainable parameters and computational complexity. However, due to high number of new…

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for…

The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…