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Memory compression is an important approach in computer architecture for decreasing memory footprint and improving system performance. In this paper, we use C/C++ to develop a current memory compression algorithm; the Global Bases Delta…
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a…
Large Language Models (LLMs) achieve strong performance across diverse tasks but face deployment challenges due to their massive size. Structured pruning offers acceleration benefits but leads to significant performance degradation. Recent…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
In programming education, it makes a difference whether you are dealing with beginners or advanced students. As our future students will become even more tech-savvy, it is necessary to assess programming skills appropriately and quickly to…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena…
Obfuscation poses a persistent challenge for software engineering tasks such as program comprehension, maintenance, testing, and vulnerability detection. While compiler optimizations and third-party code often introduce transformations that…
In this note, we test the performance of six algorithms from the family of graph-based splitting methods [SIAM J. Optim., 34 (2024), pp. 1569-1594] specialized to normal cones of linear subspaces. To do this, we first implement some…
Making large language models (LLMs) more efficient in memory, latency, and serving cost is crucial for edge deployment, interactive applications, and sustainable inference at scale. Pruning is a promising technique, but existing pruning…
Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally,…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
Long Short-Term Memory (LSTM) is one of the most widely used recurrent structures in sequence modeling. It aims to use gates to control information flow (e.g., whether to skip some information or not) in the recurrent computations, although…
A $(\phi,\epsilon)$-expander-decomposition of a graph $G$ (with $n$ vertices and $m$ edges) is a partition of $V$ into clusters $V_1,\ldots,V_k$ with conductance $\Phi(G[V_i]) \ge \phi$, such that there are at most $\epsilon m$…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…
The pseudo-inverse of a graph Laplacian matrix, denoted as $L^\dagger$, finds extensive application in various graph analysis tasks. Notable examples include the calculation of electrical closeness centrality, determination of Kemeny's…
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…