<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-09-19T15:22:23Z</responseDate><request verb="GetRecord" identifier="oai:dspace.mit.edu:1721.1/100633" metadataPrefix="dim">https://dspace.mit.edu/server/oai/request</request><GetRecord><record><header><identifier>oai:dspace.mit.edu:1721.1/100633</identifier><datestamp>2026-06-06T00:48:50Z</datestamp><setSpec>com_1721.1_7582</setSpec><setSpec>com_1721.1_7581</setSpec><setSpec>col_1721.1_131023</setSpec></header><metadata><dim:dim xmlns:dim="http://www.dspace.org/xmlns/dspace/dim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.dspace.org/xmlns/dspace/dim http://www.dspace.org/schema/dim.xsd">
   <dim:field mdschema="dc" element="contributor" qualifier="advisor" lang="en_US">James R. Glass.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="author" lang="en_US">Liu, Leo, M. Eng. Massachusetts Institute of Technology</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="other" lang="en_US">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="department">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="accessioned">2016-01-04T20:00:37Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="available">2016-01-04T20:00:37Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="copyright" lang="en_US">2015</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="issued" lang="en_US">2015</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="uri">http://hdl.handle.net/1721.1/100633</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="oclc" lang="en_US">933230687</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">This electronic version was submitted by the student author.  The certified thesis is available in the Institute Archives and Special Collections.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Cataloged from student-submitted PDF version of thesis.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Includes bibliographical references (pages 81-83).</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="abstract" lang="en_US">Deep Neural Networks (DNNs) are eective models for machine learning. Unfortunately, training a DNN is extremely time-consuming, even with the aid of a graphics processing unit (GPU). DNN training is especially slow for tasks with large datasets. Existing approaches for speeding up the process involve parallelizing the Stochastic Gradient Descent (SGD) algorithm used to train DNNs. Those approaches do not guarantee the same results as normal SGD since they introduce non-trivial changes into the algorithm. A new approach for faster training that avoids signicant changes to SGD is to use low-precision hardware. The low-precision hardware is faster than a GPU, but it performs arithmetic with 1% error. In this arithmetic, 98 + 2 = 99:776 and 10 * 10 = 100:863. This thesis determines whether DNNs would still be able to produce state-of-the-art results using this low-precision arithmetic. To answer this question, we implement an approximate DNN that uses the low-precision arithmetic and evaluate it on the TIMIT phoneme recognition task and the WSJ speech recognition task. For both tasks, we nd that acoustic models based on approximate DNNs perform as well as ones based on conventional DNNs; both produce similar recognition error rates. The approximate DNN is able to match the conventional DNN only if it uses Kahan summations to preserve precision. These results show that DNNs can run on low-precision hardware without the arithmetic causing any loss in recognition ability. The low-precision hardware is therefore a suitable approach for speeding up DNN training.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="statementofresponsibility" lang="en_US">by Leo Liu.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="degree" lang="en_US">M.Eng.</dim:field>
   <dim:field mdschema="dc" element="format" qualifier="extent" lang="en_US">83 pages</dim:field>
   <dim:field mdschema="dc" element="language" qualifier="iso" lang="en_US">eng</dim:field>
   <dim:field mdschema="dc" element="publisher" lang="en_US">Massachusetts Institute of Technology</dim:field>
   <dim:field mdschema="dc" element="rights" lang="en_US">M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.</dim:field>
   <dim:field mdschema="dc" element="rights" qualifier="uri" lang="en_US">http://dspace.mit.edu/handle/1721.1/7582</dim:field>
   <dim:field mdschema="dc" element="subject" lang="en_US">Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="title" lang="en_US">Acoustic models for speech recognition using Deep Neural Networks based on approximate math</dim:field>
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   	&lt;Title>Acoustic models for speech recognition using Deep Neural Networks based on approximate math&lt;/Title>
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   	&lt;PublicationDate>2015&lt;/PublicationDate>
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        	&lt;DisplayName>Liu, Leo, M. Eng. Massachusetts Institute of Technology&lt;/DisplayName>
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    &lt;Keyword>Electrical Engineering and Computer Science.&lt;/Keyword>
   	&lt;Abstract>Deep Neural Networks (DNNs) are eective models for machine learning. Unfortunately, training a DNN is extremely time-consuming, even with the aid of a graphics processing unit (GPU). DNN training is especially slow for tasks with large datasets. Existing approaches for speeding up the process involve parallelizing the Stochastic Gradient Descent (SGD) algorithm used to train DNNs. Those approaches do not guarantee the same results as normal SGD since they introduce non-trivial changes into the algorithm. A new approach for faster training that avoids signicant changes to SGD is to use low-precision hardware. The low-precision hardware is faster than a GPU, but it performs arithmetic with 1% error. In this arithmetic, 98 + 2 = 99:776 and 10 * 10 = 100:863. This thesis determines whether DNNs would still be able to produce state-of-the-art results using this low-precision arithmetic. To answer this question, we implement an approximate DNN that uses the low-precision arithmetic and evaluate it on the TIMIT phoneme recognition task and the WSJ speech recognition task. For both tasks, we nd that acoustic models based on approximate DNNs perform as well as ones based on conventional DNNs; both produce similar recognition error rates. The approximate DNN is able to match the conventional DNN only if it uses Kahan summations to preserve precision. These results show that DNNs can run on low-precision hardware without the arithmetic causing any loss in recognition ability. The low-precision hardware is therefore a suitable approach for speeding up DNN training.&lt;/Abstract>
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