Related papers: On Stochastic Rounding with Few Random Bits
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
The main objective of this work is to investigate non-linear errors and pairwise summation using stochastic rounding (SR) in variance computation algorithms. We estimate the forward error of computations under SR through two methods: the…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…
Successful implementations of quantum technologies require protocols and algorithms that use as few quantum resources as possible. However, many important quantum operations, such as continuous rotation gates in quantum computing or…
Motivated by the advent of machine learning, the last few years have seen the return of hardware-supported low-precision computing. Computations with fewer digits are faster and more memory and energy efficient, but can be extremely…
Super-resolution (SR) is an ill-posed inverse problem which consists in proposing high-resolution images consistent with a given low-resolution one. While most SR algorithms are deterministic, stochastic SR deals with designing a stochastic…
This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…
Noise characterization methods such as randomized benchmarking (RB) are critical for the development of scalable quantum computers. Modern RB protocols for multiqubit systems extract physically relevant error rates by exploiting the…
Stochastic Computing (SC) is a computing paradigm that allows for the low-cost and low-power computation of various arithmetic operations using stochastic bit streams and digital logic. In contrast to conventional representation schemes…
Following previous theoretical work by Srinivasan (FOCS 2001) and the first author (STACS 2006) and a first experimental evaluation on random instances (ALENEX 2009), we investigate how the recently developed different approaches to…
Stochastic unary computing provides low-area circuits. However, the required area consuming stochastic number generators (SNGs) in these circuits can diminish their overall gain in area, particularly if several SNGs are required. We propose…
This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…
Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively…
In stochastic computing (SC), a real-valued number is represented by a stochastic bit stream, encoding its value in the probability of obtaining a one. This leads to a significantly lower hardware effort for various functions and provides a…
State-of-the-art generic low-precision training algorithms use a mix of 16-bit and 32-bit precision, creating the folklore that 16-bit hardware compute units alone are not enough to maximize model accuracy. As a result, deep learning…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
We introduce the abstract problem of rounding an unknown fractional bipartite $b$-matching $\bf{x}$ revealed online (e.g., output by an online fractional algorithm), exposed node-by-node on~one~side. The objective is to maximize the…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
Over the course of the past decade, a variety of randomized algorithms have been proposed for computing approximate least-squares (LS) solutions in large-scale settings. A longstanding practical issue is that, for any given input, the user…