Related papers: Cache-oblivious Matrix Multiplication for Exact Fa…
This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication algorithms with ternary coefficients $\{-1,0,1\}$. The approach replaces expensive exact evaluation with fast heuristic…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
We show that assuming the availability of the processor with variable precision arithmetic, we can compute matrix-by-matrix multiplications in $O(N^2log_2N)$ computational complexity. We replace the standard matrix-by-matrix multiplications…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be…
Hierarchical matrices are space and time efficient representations of dense matrices that exploit the low rank structure of matrix blocks at different levels of granularity. The hierarchically low rank block partitioning produces…
In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is…
In order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. First, we prove the availability of rotary position embedding in the state space duality algorithm,…
Sparse matrix multiplication is an important component of linear algebra computations. In this paper, an architecture based on Content Addressable Memory (CAM) and Resistive Content Addressable Memory (ReCAM) is proposed for accelerating…
We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…
We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly…
Matrix multiplication is the dominant computation during Machine Learning (ML) inference. To efficiently perform such multiplication operations, Compute-in-memory (CiM) paradigms have emerged as a highly energy efficient solution. However,…
We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…
We introduce the Adaptive Massively Parallel Computation (AMPC) model, which is an extension of the Massively Parallel Computation (MPC) model. At a high level, the AMPC model strengthens the MPC model by storing all messages sent within a…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
Optical computing is emerging as a promising platform for energy-efficient, high-throughput hardware in deep learning. A key challenge lies in the realization of optical matrix-vector multiplication, which often requires $O(N^2)$ phase…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…