Related papers: A low memory, highly concurrent multigrid algorith…
Recently, studying fundamental graph problems in the \emph{Massively Parallel Computation (MPC) framework, inspired by the MapReduce paradigm, has gained a lot of attention. An assumption common to a vast majority of approaches is to allow…
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has…
We study the solution of symmetric positive-definite linear systems by way of families of full- and limited-memory methods. Our contributions are threefold. We first derive new relationships between the conjugate-gradient method (CG) and…
Searches for signals at low signal-to-noise ratios frequently involve the Fast Fourier Transform (FFT). For high-throughput searches, we here consider FFT on the homogeneous mesh of Processing Elements (PEs) of a wafer-scale engine (WSE).…
The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has been reported to be the most efficient algorithm for computing…
As large graph processing emerges, we observe a costly fork-processing pattern (FPP) that is common in many graph algorithms. The unique feature of the FPP is that it launches many independent queries from different source vertices on the…
The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…
Differentiable architecture search (DARTS) provided a fast solution in finding effective network architectures, but suffered from large memory and computing overheads in jointly training a super-network and searching for an optimal…
Binary Neural Networks (BNNs) have garnered significant attention due to their immense potential for deployment on edge devices. However, the non-differentiability of the quantization function poses a challenge for the optimization of BNNs,…
This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…
Multi-objective Neural Architecture Search (NAS) aims to discover novel architectures in the presence of multiple conflicting objectives. Despite recent progress, the problem of approximating the full Pareto front accurately and efficiently…
Linear recurrent neural networks enable powerful long-range sequence modeling with constant memory usage and time-per-token during inference. These architectures hold promise for streaming applications at the edge, but deployment in…
Non-volatile main memory (NVRAM) technologies provide an attractive set of features for large-scale graph analytics, including byte-addressability, low idle power, and improved memory-density. NVRAM systems today have an order of magnitude…
In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…
FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…