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Developing efficient hardware accelerators for mathematical kernels used in scientific applications and machine learning has traditionally been a labor-intensive task. These accelerators typically require low-level programming in Verilog or…
We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional param- eter…
An important linear algebra routine, GEneral Matrix Multiplication (GEMM), is a fundamental operator in deep learning. Compilers need to translate these routines into low-level code optimized for specific hardware. Compiler-level…
Complex-Valued Neural Networks (CVNNs) have significant advantages in handling tasks that involve complex numbers. However, existing CVNNs are unable to quantify predictive uncertainty. We propose, for the first time, dropout-based Bayesian…
Matrix--vector algorithms, particularly Krylov subspace methods, are widely viewed as the most effective algorithms for solving large systems of linear equations. This paper establishes lower bounds on the worst-case number of…
Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…
Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…
Numerical features of matrix multiplier hardware units in NVIDIA and AMD data centre GPUs have recently been studied. Features such as rounding, normalisation, and internal precision of the accumulators are of interest. In this paper, we…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
We propose an extremely energy-efficient mixed-signal approach for performing vector-by-matrix multiplication in a time domain. In such implementation, multi-bit values of the input and output vector elements are represented with…
Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
This paper proposes an auxiliary vector filtering (AVF) algorithm based on a constrained constant modulus (CCM) design for robust adaptive beamforming. This scheme provides an efficient way to deal with filters with a large number of…
We study the problem of computing matrix chain multiplications in a distributed computing cluster. In such systems, performance is often limited by the straggler problem, where the slowest worker dominates the overall computation latency.…
This paper presents an approximate signed multiplier architecture that incorporates a sign-focused compressor, specifically designed for edge detection applications in machine learning and signal processing. The multiplier incorporates two…
Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…