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Reasoning About Floating Point in Re...

Lee, Wonyeol,

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Reasoning About Floating Point in Real-World Systems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Reasoning About Floating Point in Real-World Systems // Wonyeol Lee.
Author:	Lee, Wonyeol,
Description:	1 electronic resource (199 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
Contained By:	Dissertations Abstracts International85-06B.
Subject:	Computer science. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30726887
ISBN:	9798381020571

Reasoning About Floating Point in Real-World Systems /
Lee, Wonyeol,

Reasoning About Floating Point in Real-World Systems /Wonyeol Lee. - 1 electronic resource (199 pages)

Source: Dissertations Abstracts International, Volume: 85-06, Section: B.

Continuous computations, which involve continuous data and operations on them, are ubiquitous in diverse areas such as machine learning and scientific computing. In theoretical studies of such computations, we typically use real numbers and exact operations. In practice, however, we often substitute floating-point numbers for the reals and apply inexact floating-point operations, which presents a clear discrepancy between the theory and practice of continuous computations.In this dissertation, we aim at better understanding this discrepancy, especially for three different classes of real-world computations. First, for computations that implement math libraries using floats, we present automatic techniques to formally verify their correctness. Next, for computations that calculate derivatives of neural networks at floating-point inputs, we show theoretical results on their correctness. Lastly, for computations that train deep neural networks using floats, we present a systematic way to accelerate them using lower-precision floats.

English

ISBN: 9798381020571Subjects--Topical Terms:

523869
Computer science.

Reasoning About Floating Point in Real-World Systems /
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520 $a Continuous computations, which involve continuous data and operations on them, are ubiquitous in diverse areas such as machine learning and scientific computing. In theoretical studies of such computations, we typically use real numbers and exact operations. In practice, however, we often substitute floating-point numbers for the reals and apply inexact floating-point operations, which presents a clear discrepancy between the theory and practice of continuous computations.In this dissertation, we aim at better understanding this discrepancy, especially for three different classes of real-world computations. First, for computations that implement math libraries using floats, we present automatic techniques to formally verify their correctness. Next, for computations that calculate derivatives of neural networks at floating-point inputs, we show theoretical results on their correctness. Lastly, for computations that train deep neural networks using floats, we present a systematic way to accelerate them using lower-precision floats.
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