Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and differences between them, and their shortcomings....
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/7/310 |
| _version_ | 1798041348798939136 |
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| author | Maxinder S. Kanwal Joshua A. Grochow Nihat Ay |
| author_facet | Maxinder S. Kanwal Joshua A. Grochow Nihat Ay |
| author_sort | Maxinder S. Kanwal |
| collection | DOAJ |
| description | In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and differences between them, and their shortcomings. Specifically, using the Boltzmann machine architecture (a fully connected recurrent neural network) with uniformly distributed weights as our model of study, we numerically measure how complexity changes as a function of network dynamics and network parameters. We apply an extension of one such information-theoretic measure of complexity to understand incremental Hebbian learning in Hopfield networks, a fully recurrent architecture model of autoassociative memory. In the course of Hebbian learning, the total information flow reflects a natural upward trend in complexity as the network attempts to learn more and more patterns. |
| first_indexed | 2024-04-11T22:20:18Z |
| format | Article |
| id | doaj.art-ac3cd41ba5f040cc902a10430288a80e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:20:18Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ac3cd41ba5f040cc902a10430288a80e2022-12-22T04:00:13ZengMDPI AGEntropy1099-43002017-07-0119731010.3390/e19070310e19070310Comparing Information-Theoretic Measures of Complexity in Boltzmann MachinesMaxinder S. Kanwal0Joshua A. Grochow1Nihat Ay2Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USADepartments of Computer Science and Mathematics, University of Colorado, Boulder, CO 80309, USASanta Fe Institute, Santa Fe, NM 87501, USAIn the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative similarities and differences between them, and their shortcomings. Specifically, using the Boltzmann machine architecture (a fully connected recurrent neural network) with uniformly distributed weights as our model of study, we numerically measure how complexity changes as a function of network dynamics and network parameters. We apply an extension of one such information-theoretic measure of complexity to understand incremental Hebbian learning in Hopfield networks, a fully recurrent architecture model of autoassociative memory. In the course of Hebbian learning, the total information flow reflects a natural upward trend in complexity as the network attempts to learn more and more patterns.https://www.mdpi.com/1099-4300/19/7/310complexityinformation integrationinformation geometryBoltzmann machineHopfield networkHebbian learning |
| spellingShingle | Maxinder S. Kanwal Joshua A. Grochow Nihat Ay Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines Entropy complexity information integration information geometry Boltzmann machine Hopfield network Hebbian learning |
| title | Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines |
| title_full | Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines |
| title_fullStr | Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines |
| title_full_unstemmed | Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines |
| title_short | Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines |
| title_sort | comparing information theoretic measures of complexity in boltzmann machines |
| topic | complexity information integration information geometry Boltzmann machine Hopfield network Hebbian learning |
| url | https://www.mdpi.com/1099-4300/19/7/310 |
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