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Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines

Maxinder Kanwal, Joshua Grochow, Nihat Ay
<span title="2017-07-03">2017</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems.  ...  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  ...  Boltzmann Machine In this paper, we look at the aforementioned candidate measures in a concrete system in order to gain an intuitive sense of what is frequently discussed at a heavily theoretical and abstract  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e19070310">doi:10.3390/e19070310</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u7phdslvzbab3eb73pfbis4624">fatcat:u7phdslvzbab3eb73pfbis4624</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502011019/https://res.mdpi.com/entropy/entropy-19-00310/article_deploy/entropy-19-00310-v2.pdf?filename=&amp;attachment=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/47/b8/47b847c76a93ccb38af74be1d960d7612cb74824.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e19070310"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines

Song Cheng, Jing Chen, Lei Wang
<span title="2018-08-07">2018</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
Both information measures are much smaller compared to their theoretical upper bound and exhibit similar patterns, which imply a common inductive bias of low information complexity.  ...  Taking the Restricted Boltzmann Machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e20080583">doi:10.3390/e20080583</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/33265672">pmid:33265672</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xliahutkabeshfwonxvceyufgy">fatcat:xliahutkabeshfwonxvceyufgy</a> </span>
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Conference Report: NIST tutorial/workshop on lattice gas and Boltzmann methods - Gaithersburg, MD August 21-23, 1995

N.S. Martys
<span title="">1996</span> <i title="National Institute of Standards and Technology (NIST)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qg4tymbffzcs5fu7eils3hgpau" style="color: black;">Journal of Research of the National Institute of Standards and Technology</a> </i> &nbsp;
The complexity of such flow processes makes their theoretical and experimental study a great challenge.  ...  Results were compared with earlier studies of flow through artificial porous media, and with recent experimental measurements on the same media.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.6028/jres.101.068">doi:10.6028/jres.101.068</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/27805088">pmid:27805088</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4907616/">pmcid:PMC4907616</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vja42o2knnd7lorvg7vblhwtwe">fatcat:vja42o2knnd7lorvg7vblhwtwe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200207211430/http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC4907616&amp;blobtype=pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0a/b0/0ab0ba27d8f1ac82d8bd8b48197623b60bbcf4b9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.6028/jres.101.068"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907616" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method

Muneki Yasuda
<span title="2018-04-04">2018</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/63zsvf7vxzfznojpqgfvpyk2lu" style="color: black;">Algorithms</a> </i> &nbsp;
The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning.  ...  In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE) method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is  ...  In this paper, theoretical insights into the effectiveness of the 1-SMCI learning method as compared to that of MPLE are given from an asymptotic point of view.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/a11040042">doi:10.3390/a11040042</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qdasvcl6c5atzcjvwvisxp56ia">fatcat:qdasvcl6c5atzcjvwvisxp56ia</a> </span>
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Deep Learning For Computer Vision Tasks: A review [article]

Rajat Kumar Sinha, Ruchi Pandey, Rohan Pattnaik
<span title="2018-04-11">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
in the presence of noise.  ...  Deep learning has recently become one of the most popular sub-fields of machine learning owing to its distributed data representation with multiple levels of abstraction.  ...  Restricted Boltzmann Machines(RBMs) Minton et al. have in [11] , proposed a generative random neural network technique called the Restricted Boltzmann machine.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1804.03928v1">arXiv:1804.03928v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yu3gdatt5zetbf35eh3hqeyy6e">fatcat:yu3gdatt5zetbf35eh3hqeyy6e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200914011937/https://arxiv.org/ftp/arxiv/papers/1804/1804.03928.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fd/cf/fdcfec7fd2852a4b39b94d15f7c045fb90f1623b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1804.03928v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

On Macroscopic Complexity and Perceptual Coding [article]

John Scoville
<span title="2011-07-07">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The theoretical limits of 'lossy' data compression algorithms are considered.  ...  The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering the perception of the specified observer  ...  In such cases, the Boltzmann entropy of X/P is comparable to the difference between the macrocomplexity and K-complexity. This may be demonstrated via the universal probability measure.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.1684v12">arXiv:1005.1684v12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rcrrfv4mxrd23ltbaez42qnatm">fatcat:rcrrfv4mxrd23ltbaez42qnatm</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1005.1684/1005.1684.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7f/e9/7fe944b3be08c17c90ffc98686d079e9a22fc609.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.1684v12" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Confident Information First Principle for Parametric Reduction and Model Selection of Boltzmann Machines [article]

Xiaozhao Zhao, Yuexian Hou, Dawei Song, Wenjie Li
<span title="2015-02-05">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We then revisit Boltzmann machines (BM) from a model selection perspective and theoretically show that both the fully visible BM (VBM) and the BM with hidden units can be derived from the general binary  ...  In unsupervised situations, one of the main limitations of these methods lies in their dependency on the scale of data features.  ...  and theoretically compared to EM (Expectation and Maximization) algorithm in [28] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.01705v1">arXiv:1502.01705v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bwtny5sxwzg5lovxkftpjlgbda">fatcat:bwtny5sxwzg5lovxkftpjlgbda</a> </span>
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Anticipating Railway Operation Disruption Events Based on the Analysis of Discrete-Event Diagnostic Data

O. Fink, E. Zio, U. Weidmann
<span title="">2013</span> <i title="AIDIC Servizi S.r.l."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5re6yojrfja7da72zowrdasgca" style="color: black;">Chemical Engineering Transactions</a> </i> &nbsp;
This paper describes our research applying Echo-State Networks (ESN) in combination with Restricted Boltzmann Machines (RBM) and fuzzy logic to predict potential railway network disruptions based on discrete-event  ...  The research results demonstrate the suitability of the proposed combination of methods for use in predicting railway operation disruption events.  ...  The participation of Enrico Zio to this research is partially supported by the China NSFC under grant number 71231001.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3303/cet1333120">doi:10.3303/cet1333120</a> <a target="_blank" rel="external noopener" href="https://doaj.org/article/fd1d1af797c6494faf0f09f21e816d4b">doaj:fd1d1af797c6494faf0f09f21e816d4b</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/23nrcmml45eajaryjstz447c2q">fatcat:23nrcmml45eajaryjstz447c2q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829025849/http://www.aidic.it/cet/13/33/120.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/ce/7cceaf85f072f8078bd30437fee7e4aba45049c1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3303/cet1333120"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction [chapter]

Eray Özkural
<span title="">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also introduce many more variants of physical message complexity based on energy and action, and discuss the ramifications of our proposals.  ...  We show how to choose an objective reference machine for universal induction by defining a physical message complexity and physical message probability, and argue that this choice dissolves some well-known  ...  Minimum machine volume as a complexity measure In the present article, we support the above philosophical solution to the choice of the reference machine with basic observations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-21365-1_14">doi:10.1007/978-3-319-21365-1_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i4dnvmfkczh7bhb64rnqfxmajy">fatcat:i4dnvmfkczh7bhb64rnqfxmajy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225102847/http://pdfs.semanticscholar.org/6114/af867339b08f2fd5cc60fc303f4d2c08a1a2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/14/6114af867339b08f2fd5cc60fc303f4d2c08a1a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-21365-1_14"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Multi-thread implementations of the lattice Boltzmann method on non-uniform grids for CPUs and GPUs

M. Schönherr, K. Kucher, M. Geier, M. Stiebler, S. Freudiger, M. Krafczyk
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nkrwe4pmozafvnd72yxufztpku" style="color: black;">Computers and Mathematics with Applications</a> </i> &nbsp;
Two multi-thread based parallel implementations of the lattice Boltzmann method for nonuniform grids on different hardware platforms are compared in this paper: a multi-core CPU implementation and an implementation  ...  Since the compact interpolation technique is both simple and accurate, it produces almost no computational overhead as compared to the lattice Boltzmann method for uniform grids in terms of node updates  ...  In addition, funding by the DFG under grant GE 1990/2-1 (Konsistente Multiskalenströmungsmechanik mit der kaskadierten Lattice Boltzmann Methode) is also gratefully acknowledged.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.camwa.2011.04.012">doi:10.1016/j.camwa.2011.04.012</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bpzsgkf5ynh5zjmbklvu3jnws4">fatcat:bpzsgkf5ynh5zjmbklvu3jnws4</a> </span>
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Quantum machine learning

Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd
<span title="2017-09-13">2017</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/drfdii35rzaibj3aml5uhvr5xm" style="color: black;">Nature</a> </i> &nbsp;
The field of quantum machine learning explores how to devise and implement concrete quantum software that offers such advantages.  ...  Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data.  ...  Boltzmann machines.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/nature23474">doi:10.1038/nature23474</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/28905917">pmid:28905917</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/al636vs26zer5njr3guv24byvy">fatcat:al636vs26zer5njr3guv24byvy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721065129/http://hb.diva-portal.org/smash/get/diva2:1062324/FULLTEXT01" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/c7/cac709d4c44c729f863fb982bbe8a72e3cfdb14c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1038/nature23474"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> nature.com </button> </a>

Transductive Boltzmann Machines [article]

Mahito Sugiyama, Koji Tsuda, Hiroyuki Nakahara
<span title="2018-05-21">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
and popularly used restricted Boltzmann machines in terms of efficiency and effectiveness.  ...  We theoretically provide bias-variance decomposition of the KL divergence in TBMs to analyze its learnability, and empirically demonstrate that TBMs are superior to the fully visible Boltzmann machines  ...  Experiments In our simulations, we empirically found the effectiveness and efficiency of transductive Boltzmann machines (TBMs) compared to two representative energy-based models: fully visible Boltzmann  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.07938v1">arXiv:1805.07938v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oankwe3xyndhxkuuebxohnxawi">fatcat:oankwe3xyndhxkuuebxohnxawi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200913131404/https://arxiv.org/pdf/1805.07938v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/a8/5ba8a87b6ba630591d16f460802b14841cceba11.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.07938v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Deep Learning the Ising Model Near Criticality [article]

Alan Morningstar, Roger G. Melko
<span title="2017-08-15">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Deep Boltzmann machines, deep belief networks, and deep restricted Boltzmann networks are trained on thermal spin configurations from this system, and compared to the shallow architecture of the restricted  ...  Boltzmann machine.  ...  This research was supported by Natural Sciences and Engineering Research Council of Canada, the Canada Research Chair program, and the Perimeter Institute for Theoretical Physics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.04622v1">arXiv:1708.04622v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tuy6lt5by5b67juh42fccnjoue">fatcat:tuy6lt5by5b67juh42fccnjoue</a> </span>
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Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction [article]

Eray Özkural
<span title="2015-04-09">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also introduce many more variants of physical message complexity based on energy and action, and discuss the ramifications of our proposals.  ...  We show how to choose an objective reference machine for universal induction by defining a physical message complexity and physical message probability, and argue that this choice dissolves some well-known  ...  Minimum machine volume as a complexity measure In the present article, we support the above philosophical solution to the choice of the reference machine with basic observations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.00601v3">arXiv:1501.00601v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kioz6fbdvngazirv54ugsfyiw4">fatcat:kioz6fbdvngazirv54ugsfyiw4</a> </span>
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A Theory of Cheap Control in Embodied Systems

Guido Montúfar, Keyan Ghazi-Zahedi, Nihat Ay, Josh C. Bongard
<span title="2015-09-01">2015</span> <i title="Public Library of Science (PLoS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ch57atmlprauhhbqdf7x4ytejm" style="color: black;">PLoS Computational Biology</a> </i> &nbsp;
To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines.  ...  Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machine  ...  Acknowledgments This work has been conducted in part at the Santa Fe Institute. The authors would like to thank Chris Adami and three anonymous referees for their helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pcbi.1004427">doi:10.1371/journal.pcbi.1004427</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26325254">pmid:26325254</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4556690/">pmcid:PMC4556690</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z7q7psqau5dwrhpf6uvjv6tb2y">fatcat:z7q7psqau5dwrhpf6uvjv6tb2y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171015150423/http://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004427&amp;type=printable" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d0/af/d0af7ee2e349dc2af8420c48b97c020c2eb0117c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1371/journal.pcbi.1004427"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> plos.org </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4556690" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>
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