Improved generalisation bounds for deep learning through L∞ covering numbers
Using proof techniques involving L∞ covering numbers, we show generalisation error bounds for deep learning with two main improvements over the state of the art. First, our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating th...
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sg-smu-ink.sis_research-82142022-08-04T08:44:16Z Improved generalisation bounds for deep learning through L∞ covering numbers LEDENT, Antoine LEI, Yunwen KLOFT, Marius Using proof techniques involving L∞ covering numbers, we show generalisation error bounds for deep learning with two main improvements over the state of the art. First, our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the L 2 norm of the weight matrices, while previous bounds exhibit at least a square-root dependence on the number of classes in this case. Second, we adapt the Rademacher analysis of DNNs to incorporate weight sharing—a task of fundamental theoretical importance which was previously attempted only under very restrictive assumptions. In our results, each convolutional filter contributes only once to the bound, regardless of how many times it is applied. Finally we provide a few further technical improvements, including improving the width dependence from before to after pooling. We also examine our bound’s behaviour on artificial data. 2019-12-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/sis_research/7211 https://ink.library.smu.edu.sg/context/sis_research/article/8214/viewcontent/85_wrshpnew.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Computing and Information Systems eng Institutional Knowledge at Singapore Management University Deep Learning convolutions multi-class multi-label Databases and Information Systems Graphics and Human Computer Interfaces |
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Deep Learning convolutions multi-class multi-label Databases and Information Systems Graphics and Human Computer Interfaces LEDENT, Antoine LEI, Yunwen KLOFT, Marius Improved generalisation bounds for deep learning through L∞ covering numbers |
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Using proof techniques involving L∞ covering numbers, we show generalisation error bounds for deep learning with two main improvements over the state of the art. First, our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the L 2 norm of the weight matrices, while previous bounds exhibit at least a square-root dependence on the number of classes in this case. Second, we adapt the Rademacher analysis of DNNs to incorporate weight sharing—a task of fundamental theoretical importance which was previously attempted only under very restrictive assumptions. In our results, each convolutional filter contributes only once to the bound, regardless of how many times it is applied. Finally we provide a few further technical improvements, including improving the width dependence from before to after pooling. We also examine our bound’s behaviour on artificial data. |
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text |
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LEDENT, Antoine LEI, Yunwen KLOFT, Marius |
author_facet |
LEDENT, Antoine LEI, Yunwen KLOFT, Marius |
author_sort |
LEDENT, Antoine |
title |
Improved generalisation bounds for deep learning through L∞ covering numbers |
title_short |
Improved generalisation bounds for deep learning through L∞ covering numbers |
title_full |
Improved generalisation bounds for deep learning through L∞ covering numbers |
title_fullStr |
Improved generalisation bounds for deep learning through L∞ covering numbers |
title_full_unstemmed |
Improved generalisation bounds for deep learning through L∞ covering numbers |
title_sort |
improved generalisation bounds for deep learning through l∞ covering numbers |
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Institutional Knowledge at Singapore Management University |
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2019 |
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https://ink.library.smu.edu.sg/sis_research/7211 https://ink.library.smu.edu.sg/context/sis_research/article/8214/viewcontent/85_wrshpnew.pdf |
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