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A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem faced during this decomposition is that even though the given matrix may be…
Homomorphic Encryption (HE) is a commonly used tool for building privacy-preserving applications. However, in scenarios with many clients and high-latency networks, communication costs due to large ciphertext sizes are the bottleneck. In…
Fueled by its successful commercialization, the recommender system (RS) has gained widespread attention. However, as the training data fed into the RS models are often highly sensitive, it ultimately leads to severe privacy concerns,…
Homomorphic encryption (HE) and secret sharing (SS) enable computations on encrypted data, providing significant privacy benefits for large transformer-based models (TBM) in sensitive sectors like medicine and finance. However, private TBM…
Homomorphic encryption (HE)-based deep neural network (DNN) inference protects data and model privacy but suffers from significant computation overhead. We observe transforming the DNN weights into circulant matrices converts general…
Sparse matrix-matrix multiplication (SpGEMM) is a critical operation in numerous fields, including scientific computing, graph analytics, and deep learning. These applications exploit the sparsity of matrices to reduce storage and…
Homomorphic encryption (HE) is a privacy-preserving technique that enables computation directly on encrypted data. Despite its promise, HE has seen limited use due to performance overheads and compilation challenges. Recent work has made…
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
We propose an efficient first-order method, based on the alternating direction method of multipliers (ADMM), to solve the homogeneous self-dual embedding problem for a primal-dual pair of semidefinite programs (SDPs) with chordal sparsity.…
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
We propose Deep Hierarchical Machine (DHM), a model inspired from the divide-and-conquer strategy while emphasizing representation learning ability and flexibility. A stochastic routing framework as used by recent deep neural…
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian…
The graph embedding (GE) methods have been widely applied for dimensionality reduction of hyperspectral imagery (HSI). However, a major challenge of GE is how to choose proper neighbors for graph construction and explore the spatial…
Homomorphic encryption (HE) enables calculating on encrypted data, which makes it possible to perform privacypreserving neural network inference. One disadvantage of this technique is that it is several orders of magnitudes slower than…