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Modularity and sparsity: evolution of neural net controllers in physically embodied robots

Frontiers in Robotics and AI, 3, 75, 2016


Status: Published

Citations:

Cite: [bibtex]


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Abstract: While modularity is thought to be central for the evolution of complexity and evolvability, it remains unclear how systems bootstrap themselves into modularity from random or fully integrated starting conditions. Clune et al. (2013) suggested that a positive correlation between sparsity and modularity is the prime cause of this transition. We sought to test the generality of this modularity–sparsity hypothesis by testing it for the first time in physically embodied robots. A population of 10 Tadros – autonomous, surface-swimming robots propelled by a flapping tail – was used. Individuals varied only in the structure of their neural net controller, a 2 × 6 × 2 network with recurrence in the hidden layer. Each of the 60 possible connections was coded in the genome and could achieve one of three states: −1, 0, and 1. Inputs were two light-dependent resistors and outputs were two motor control variables to the flapping tail, one for the frequency of the flapping and the other for the turning offset. Each Tadro was tested separately in a circular tank lit by a single overhead light source. Fitness was the amount of light gathered by a vertically oriented sensor that was disconnected from the controller net. Reproduction was asexual, with the top performer cloned and then all individuals entered into a roulette wheel selection process, with genomes mutated to create the offspring. The starting population of networks was randomly generated. Over 10 generations, the population’s mean fitness increased twofold. This evolution occurred in spite of an unintentional integer overflow problem in recurrent nodes in the hidden layer that caused outputs to oscillate. Our investigation of the oscillatory behavior showed that the mutual information of inputs and outputs was sufficient for the reactive behaviors observed. While we had predicted that both modularity and sparsity would follow the same trend as fitness, neither did so. Instead, selection gradients within each generation showed that selection directly targeted sparsity of the connections to the motor outputs. Modularity, while not directly targeted, was correlated with sparsity, and hence was an indirect target of selection, its evolution a “by-product” of its correlation with sparsity.



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Joshua Bongard - Department of Computer Science, Associate Professor

Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.


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    Josh Bongard, Victor Zykov, Hod Lipson. Resilient Machines Through
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    Joey Anetsberger and Josh Bongard. Robots can ground crowd-proposed symbols by forming theories of group mind. Proceedings of the Artificial Life Conference 2016. [Link to Proceedings]
  • Stacks Image 525375
    Sam Kriegman, Nick Cheney, and Josh Bongard. How morphological development can guide evolution. arXiv 2017. [arXiv]


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Chris Danforth -Department of Mathematics and Statistics, Flint Professor of Mathematical, Natural, and Technical Sciences

Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.

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    Peter Sheridan Dodds , Kameron Decker Harris, Isabel M. Kloumann, Catherine A. Bliss, Christopher M. Danforth. Temporal Patterns of Happiness and Information in a Global Social Network: Hedonometrics and Twitter. PLoS ONE 2011. [Journal Page].
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    Lewis Mitchell , Morgan R. Frank, Kameron Decker Harris, Peter Sheridan Dodds, Christopher M. Danforth. The Geography of Happiness: Connecting Twitter Sentiment and Expression, Demographics, and Objective Characteristics of Place. PLoS ONE 2013. [Journal Page].
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    Andrew G Reece and Christopher M Danforth. Instagram photos reveal predictive markers of depression. EPJ Data Science 2017. [Journal Page].


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Laurent Hébert-Dufresne - Assistant Professor, Computer Science

Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.

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    Laurent Hébert‐Dufresne Adam F. A. Pellegrini Uttam Bhat Sidney Redner Stephen W. Pacala Andrew M. Berdahl. Edge fires drive the shape and stability of tropical forests. Ecology Letters 2018. [Journal Page]
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    Samuel V. Scarpino, Antoine Allard, Laurent Hébert-Dufresne. The effect of a prudent adaptive behaviour on disease transmission. Nature Physics 2016. [Journal Page]
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    Laurent Hébert-Dufresne, Joshua A. Grochow, Antoine Allard. Multi-scale structure and topological anomaly detection via a new network statistic: The onion decomposition. Nature Scientific Reports 2016. [Journal Page]


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Paul Hines - School of Engineering, Associate Professor

Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.

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    Paul D. H. Hines, Ian Dobson, Pooya Rezaei. Cascading Power Outages Propagate Locally in an Influence Graph That is Not the Actual Grid Topology. IEEE Transactions on Power Systems ( Volume: 32, Issue: 2, March 2017 ). [Journal Page]
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    Mert Korkali, Jason G. Veneman, Brian F. Tivnan, James P. Bagrow & Paul D. H. Hines. Reducing Cascading Failure Risk by Increasing Infrastructure Network Interdependence. Scientific Reports volume 7, Article number: 44499 (2017. [Journal Page]
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    Pooya Rezaei, Paul D. H. Hines, Margaret J. Eppstein. Estimating Cascading Failure Risk With Random Chemistry. IEEE Transactions on Power Systems ( Volume: 30, Issue: 5, Sept. 2015 ). [Journal Page]


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James Bagrow - Assistant Professor, Department of Mathematics and Statistics

Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).

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    Y.-Y. Ahn, J. P. Bagrow and S. Lehmann. Link communities reveal multiscale complexity in networks. Nature, 466: 761-764 (2010). [Journal Page].
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    M. R. Frank, J. R. Williams, L. Mitchell, J. P. Bagrow, P. S. Dodds, C. M. Danforth. Constructing a taxonomy of fine-grained human movement and activity motifs through social media. In preparation. (2015). [Journal Page].
  • Stacks Image 525398
    J. P. Bagrow and L. Mitchell. The quoter model: a paradigmatic model of the social flow of written information. To appear, Chaos (2018). [Journal Page].