Related papers: HYLU: Hybrid Parallel Sparse LU Factorization
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…
Neural networks have shown state-of-the-art performances in various classification and regression tasks. Rectified linear units (ReLU) are often used as activation functions for the hidden layers in a neural network model. In this article,…
We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincar\'e--Steklov (HPS) family of algorithms for…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
This paper presents implementation details and empirical results for a hybrid message passing and shared memory paralleliziation of the adaptive integral method (AIM). AIM is implemented on a (near) petaflop supercomputing cluster of…
We present a new variant of serial right-looking supernodal sparse Cholesky factorization (RL). Our comparison of RL with the multifrontal method confirms that RL is simpler, slightly faster, and requires slightly less storage. The key to…
Deep learning (DL) compilers rely on cost models and auto-tuning to optimize tensor programs for target hardware. However, existing approaches depend on large offline datasets, incurring high collection costs and offering suboptimal…
As an edge intelligence algorithm for multi-device collaborative training, federated learning (FL) can reduce the communication burden but increase the computing load of wireless devices. In contrast, split learning (SL) can reduce the…
The evolution of large language models (LLMs) towards applications with ultra-long contexts faces challenges posed by the high computational and memory costs of the Transformer architecture. While existing sparse and linear attention…
As the emerging field of machine learning, deep learning shows excellent ability in solving complex learning problems. However, the size of the networks becomes increasingly large scale due to the demands of the practical applications,…
Lazy search algorithms have been developed to efficiently solve planning problems in domains where the computational effort is dominated by the cost of edge evaluation. The existing algorithms operate by intelligently balancing…
Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…
Hashing has been widely used for efficient similarity search based on its query and storage efficiency. To obtain better precision, most studies focus on designing different objective functions with different constraints or penalty terms…
We investigate the energy efficiency of a library designed for parallel computations with sparse matrices. The library leverages high-performance, energy-efficient Graphics Processing Unit (GPU) accelerators to enable large-scale scientific…
Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs…
We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher…
Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific…
Quantization is critical for efficiently deploying large language models (LLMs). Yet conventional methods remain hardware-agnostic, limited to bit-width constraints, and do not account for intrinsic circuit characteristics such as the…