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Principal component analysis (PCA) has been widely used as an effective technique for feature extraction and dimension reduction. In the High Dimension Low Sample Size (HDLSS) setting, one may prefer modified principal components, with…

The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…

Increasing demand for high field magnetic resonance (MR) scanner indicates the need for high-quality MR images for accurate medical diagnosis. However, cost constraints, instead, motivate a need for algorithms to enhance images from low…

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…

In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

Large Language Models (LLMs) have grown increasingly expensive to deploy, driving the need for effective model compression techniques. While block pruning offers a straightforward approach to reducing model size, existing methods often…

Retrieval-augmented language models can better adapt to changes in world state and incorporate long-tail knowledge. However, most existing methods retrieve only short contiguous chunks from a retrieval corpus, limiting holistic…

Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced…

The components underpinning PLMs -- large weight matrices -- were shown to bear considerable redundancy. Matrix factorization, a well-established technique from matrix theory, has been utilized to reduce the number of parameters in PLM.…

Gaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…

Most existing structured pruning methods for Large Language Models (LLMs) require substantial computational and data resources for retraining to reestablish the corrupted correlations, making them prohibitively expensive. To address this,…

Low-rank adaptation (LoRA) has become a widely used paradigm for parameter-efficient fine-tuning of large language models, yet its representational capacity often lags behind full fine-tuning. Within the context of LoRA, a key open question…

It is common to reject undesired outputs of Large Language Models (LLMs); however, current methods to do so require an excessive amount of computation to re-sample after a rejection, or distort the distribution of outputs by constraining…

Recently CKY-based models show great potential in unsupervised grammar induction thanks to their human-like encoding paradigm, which runs recursively and hierarchically, but requires $O(n^3)$ time-complexity. Recursive Transformer based on…

Automorphism-ensemble decoding is applied to the Plotkin constituents of Reed-Muller codes, resulting in a new soft-decision decoding algorithm with state-of-the-art performance versus complexity trade-offs.

We study a family of subcodes of the $m$-dimensional product code $\mathscr{C}^{\otimes m}$ ('subproduct codes') that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases.…