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	<title>Inverse Abstraction of Neural Networks Using Symbolic Interpolation - Revision history</title>
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	<updated>2026-06-04T14:28:35Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://murray.cds.caltech.edu/index.php?title=Inverse_Abstraction_of_Neural_Networks_Using_Symbolic_Interpolation&amp;diff=22414&amp;oldid=prev</id>
		<title>Murray at 05:21, 27 December 2018</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Inverse_Abstraction_of_Neural_Networks_Using_Symbolic_Interpolation&amp;diff=22414&amp;oldid=prev"/>
		<updated>2018-12-27T05:21:34Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 05:21, 27 December 2018&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l4&quot;&gt;Line 4:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 4:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Source=To appear, 2019 AAAI Conference on Artificial Intelligence&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Source=To appear, 2019 AAAI Conference on Artificial Intelligence&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Abstract=Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Abstract=Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|URL=http://www.cds.caltech.edu/~murray/preprints/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;aaaYY&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;place&lt;/del&gt;.pdf&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|URL=http://www.cds.caltech.edu/~murray/preprints/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dgm19&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;aiaa&lt;/ins&gt;.pdf&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Type=Conference paper&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|Type=Conference paper&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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		<author><name>Murray</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Inverse_Abstraction_of_Neural_Networks_Using_Symbolic_Interpolation&amp;diff=22413&amp;oldid=prev</id>
		<title>Murray: Created page with &quot;{{Paper |Title=Inverse Abstraction of Neural Networks Using Symbolic Interpolation |Authors=Sumanth Dathathri, Sicun Gao, Richard M. Murray |Source=To appear, 2019 AAAI Confer...&quot;</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Inverse_Abstraction_of_Neural_Networks_Using_Symbolic_Interpolation&amp;diff=22413&amp;oldid=prev"/>
		<updated>2018-12-27T05:21:22Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;{{Paper |Title=Inverse Abstraction of Neural Networks Using Symbolic Interpolation |Authors=Sumanth Dathathri, Sicun Gao, Richard M. Murray |Source=To appear, 2019 AAAI Confer...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Paper&lt;br /&gt;
|Title=Inverse Abstraction of Neural Networks Using Symbolic Interpolation&lt;br /&gt;
|Authors=Sumanth Dathathri, Sicun Gao, Richard M. Murray&lt;br /&gt;
|Source=To appear, 2019 AAAI Conference on Artificial Intelligence&lt;br /&gt;
|Abstract=Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties.&lt;br /&gt;
|URL=http://www.cds.caltech.edu/~murray/preprints/aaaYY-place.pdf&lt;br /&gt;
|Type=Conference paper&lt;br /&gt;
|ID=2018e&lt;br /&gt;
|Tag=dgm19-aiaa&lt;br /&gt;
|Funding=NSF VeHICaL&lt;br /&gt;
}}&lt;/div&gt;</summary>
		<author><name>Murray</name></author>
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