Related papers: In-memory eigenvector computation in time O(1)
Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of…
Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…
Transformers evaluated in a single, fixed-depth pass are provably limited in expressive power to the constant-depth circuit class TC0. Running a Transformer autoregressively removes that ceiling -- first in next-token prediction and, more…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform…
We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses complex moments to extract the eigencomponents of interest from a…
Computing-in-Memory (CIM) accelerators are a promising solution for accelerating Machine Learning (ML) workloads, as they perform Matrix-Vector Multiplications (MVMs) on crossbar arrays directly in memory. Although the bit widths of the…
Compute in-memory (CIM) is a promising technique that minimizes data transport, the primary performance bottleneck and energy cost of most data intensive applications. This has found wide-spread adoption in accelerating neural networks for…
We consider the problem of preprocessing an $n\times n$ matrix $\mathbf{M}$, and supporting queries that, for any vector $v$, returns the matrix-vector product $\mathbf{M} v$. This problem has been extensively studied in both theory and…
We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…
This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of…
In-memory computing hardware accelerators allow more than 10x improvements in peak efficiency and performance for matrix-vector multiplications (MVM) compared to conventional digital designs. For this, they have gained great interest for…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
What is the time complexity of matrix multiplication of sparse integer matrices with $m_{in}$ nonzeros in the input and $m_{out}$ nonzeros in the output? This paper provides improved upper bounds for this question for almost any choice of…
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and…
While time complexity and space complexity of an algorithm helps to determine its efficiency when time or space needs to be optimized respectively, they fail to determine the more efficient algorithm when time and space both need to be…
Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…