Morphological Intelligence: Measuring the Body’s Contribution to Intelligence

188 Pages·2019·5.017 MB·English

by  Keyan Ghazi-Zahedi

Keyan Ghazi-Zahedi
Morphological
Intelligence
Measuring the Body’s Contribution to
Intelligence
Morphological Intelligence
Keyan Ghazi-Zahedi
Morphological Intelligence
’
Measuring the Body s Contribution
to Intelligence
123
Keyan Ghazi-Zahedi
MaxPlanckInstitute for Mathematics
Leipzig, Sachsen,Germany
ISBN978-3-030-20620-8 ISBN978-3-030-20621-5 (eBook)
https://doi.org/10.1007/978-3-030-20621-5
©SpringerNatureSwitzerlandAG2019
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To Rieke, Maren, and Marion
Acknowledgements
Thisbookwouldnothavebeenpossiblewithoutthesupportofmanypeople.First
of all, I sincerely thank Nihat Ay for his support and critical remarks. This book
would not have been possible without him. I thank Martin Bogdan for his support
of my Habilitation at the University of Leipzig. I also thank the Max Planck
InstituteforMathematicsandtheSciencesforprovidingmewiththeresourcesthat
wereessentialtocompletingthisbook,aswellastheSantaFeInstituteforhosting
me during the initial phase of writing it. I want to thank my collaborators, without
whom the results presented in this work would not be possible: Guido Montúfar,
Oliver Brock, Daniel Häufle, Raphael Deimel, Syn Schmitt, and Johannes Rauh.
Last butnotleast, I want to thank Antje Vandenberg for herconstant supportover
the last years.
vii
Funding
This work was partly funded by the German Priority Program DFG-SPP 1527
“Autonomous Learning.” This publication was also made possible through the
supportofagrantfromtheJohnTempletonFoundation.Theopinionsexpressedin
this publication are those of the author(s) and do not necessarily reflect the views
of the John Templeton Foundation.
ix
Contents
1 From Morphological Computation to Morphological
Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 How Morphology Lifts the Computational Burden
for the Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Morphological Computation . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Morphological Control . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.3 Pre-processing (Sensors). . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.4 Post-processing (Actuators). . . . . . . . . . . . . . . . . . . . . . . 8
1.1.5 Brain Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.6 Behaviour-Enabling Physical Processes . . . . . . . . . . . . . . 11
1.2 What is Morphology, Computation, and Morphological
Computation?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 How Morphological Computation Has Changed
over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Definition of the Term Morphology . . . . . . . . . . . . . . . . 14
1.2.3 Definition of the Term Computation . . . . . . . . . . . . . . . . 15
1.2.4 What is Morphological Computation? . . . . . . . . . . . . . . . 17
1.3 Morphological Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 Organisation of This Book and Main Results. . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Information Theory—A Primer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Estimating Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Mutual Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Conditional Mutual Information. . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.6 Kolmogorov Complexity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
xi
xii Contents
2.7 Causality Versus Correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.8 Entropy Estimation on Continuous State Spaces. . . . . . . . . . . . . . 48
2.8.1 Mutual Information Estimation on Continuous Data. . . . . 51
2.8.2 Conditional Mutual Information Estimation
on Continuous Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.9 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 A Theory of Morphological Intelligence . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Related Work on Formalising Morphological Computation . . . . . . 58
3.1.1 Dynamical Systems Approach to Formalising
Morphological Intelligence . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Causal Model of the Sensorimotor Loop . . . . . . . . . . . . . . . . . . . 64
3.3 Concept One: Quantifying Morphological Intelligence
Based on the Effect of the Action on the World. . . . . . . . . . . . . . 68
3.3.1 MorphologicalIntelligenceasComparisonofBehaviour
and Controller Complexity (MI ) . . . . . . . . . . . . . . . . . 71
MI
3.3.2 MI : A Causal Variation of MI . . . . . . . . . . . . . . . . . . 73
CA A
3.3.3 Agent-Intrinsic Variations of MI and MI . . . . . . . . . . 76
A CA
3.4 Concept Two: Quantifying Morphological Intelligence
as the Contribution of the World to Itself. . . . . . . . . . . . . . . . . . . 80
3.4.1 Information Decomposition of MI . . . . . . . . . . . . . . . . 83
W
3.4.2 Agent-Intrinsic Variation of MI . . . . . . . . . . . . . . . . . . 87
W
3.5 Concept Three: Quantifying Morphological Intelligence
as Synergy of Body and Brain . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5.1 Maximum Entropy Estimation with the Iterative
Scaling Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.5.2 Quantifying Unique Information . . . . . . . . . . . . . . . . . . . 93
3.6 Concept Four: Quantifying Morphological Intelligence
as In-Sourceable Computation. . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.7 Concept Five: Quantifying Morphological Intelligence
as the Reduction of Computational Cost . . . . . . . . . . . . . . . . . . . 96
3.7.1 Denavit-Hartenberg Notation . . . . . . . . . . . . . . . . . . . . . 99
3.7.2 Denavit-Hartenberg for a Hexapod . . . . . . . . . . . . . . . . . 100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4 Numerical Analysis of the Morphological Intelligence
Quantifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1 Parametrised Model of the Sensorimotor Loop. . . . . . . . . . . . . . . 110
4.1.1 Parametrisation of the Input Distribution p(w) . . . . . . . . . 110
4.1.2 Parametrisation of the Sensor Map b(sjw) . . . . . . . . . . . . 111
4.1.3 Parametrisation of the Policy p(ajs). . . . . . . . . . . . . . . . . 111
4.1.4 Parametrisation of the World Dynamics Kernel
aðw0jw;aÞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Contents xiii
4.2 Numerical Results for CI(W0: W; A), UI(W0: WnA), MI , and
SY
MIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
W
0
4.3 Numerical Results for MI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A
4.4 Numerical Results for MI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
MI
4.5 Numerical Results for MI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
CA
4.6 Numerical Results for C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A
4.7 Numerical Results for MI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
W
4.8 Numerical Results for C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
W
4.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Quantifying Morphological Intelligence in Soft Manipulation . . . . 133
5.1.1 Identifying Morphological Intelligence and Stupidity . . . . 135
5.1.2 Characterising Behaviours by Their Covariance. . . . . . . . 136
5.1.3 Extracting Motions That Only Result from Body-
Environment Interactions . . . . . . . . . . . . . . . . . . . . . . . . 136
5.1.4 Avoiding Artefacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.1.5 Visualising Clusters of Grasp Behaviours . . . . . . . . . . . . 137
5.1.6 Determining Grasp Success . . . . . . . . . . . . . . . . . . . . . . 138
5.1.7 RBO Hand Grasp Simulations . . . . . . . . . . . . . . . . . . . . 138
5.1.8 Simulation Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.1.9 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.1.10 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.1.11 Covariance Coefficients Can Guide an Automatic
Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.1.12 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2 Quantifying Morphological Intelligence in Muscle Models . . . . . . 143
5.2.1 Definition of Muscle and DC-Motor Models . . . . . . . . . . 144
5.2.2 Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.2.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Appendix A: gomi.. .... .... ..... .... .... .... .... .... ..... .... 157