Reasoning about floating point in real-world systems
Abstract/Contents
- Abstract
- 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.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Lee, Wonyeol |
|---|---|
| Degree supervisor | Aiken, Alex |
| Thesis advisor | Aiken, Alex |
| Thesis advisor | Barrett, Clark |
| Thesis advisor | Kjoelstad, Fredrik |
| Degree committee member | Barrett, Clark |
| Degree committee member | Kjoelstad, Fredrik |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Computer Science Department |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Wonyeol Lee. |
|---|---|
| Note | Submitted to the Computer Science Department. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/hc148pv9288 |
Access conditions
- Copyright
- © 2023 by Wonyeol Lee
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...