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      A Theory of Cheap Control in Embodied Systems

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          Abstract

          We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machine

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          Most cited references8

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          Self-organization, embodiment, and biologically inspired robotics.

          Robotics researchers increasingly agree that ideas from biology and self-organization can strongly benefit the design of autonomous robots. Biological organisms have evolved to perform and survive in a world characterized by rapid changes, high uncertainty, indefinite richness, and limited availability of information. Industrial robots, in contrast, operate in highly controlled environments with no or very little uncertainty. Although many challenges remain, concepts from biologically inspired (bio-inspired) robotics will eventually enable researchers to engineer machines for the real world that possess at least some of the desirable properties of biological organisms, such as adaptivity, robustness, versatility, and agility.
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            Representational power of restricted boltzmann machines and deep belief networks.

            Deep belief networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton, Osindero, and Teh (2006) along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a restricted Boltzmann machine (RBM), used to represent one layer of the model. Restricted Boltzmann machines are interesting because inference is easy in them and because they have been successfully used as building blocks for training deeper models. We first prove that adding hidden units yields strictly improved modeling power, while a second theorem shows that RBMs are universal approximators of discrete distributions. We then study the question of whether DBNs with more layers are strictly more powerful in terms of representational power. This suggests a new and less greedy criterion for training RBMs within DBNs.
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              Evolutionary Divergence in Brain Size between Migratory and Resident Birds

              Despite important recent progress in our understanding of brain evolution, controversy remains regarding the evolutionary forces that have driven its enormous diversification in size. Here, we report that in passerine birds, migratory species tend to have brains that are substantially smaller (relative to body size) than those of resident species, confirming and generalizing previous studies. Phylogenetic reconstructions based on Bayesian Markov chain methods suggest an evolutionary scenario in which some large brained tropical passerines that invaded more seasonal regions evolved migratory behavior and migration itself selected for smaller brain size. Selection for smaller brains in migratory birds may arise from the energetic and developmental costs associated with a highly mobile life cycle, a possibility that is supported by a path analysis. Nevertheless, an important fraction (over 68%) of the correlation between brain mass and migratory distance comes from a direct effect of migration on brain size, perhaps reflecting costs associated with cognitive functions that have become less necessary in migratory species. Overall, our results highlight the importance of retrospective analyses in identifying selective pressures that have shaped brain evolution, and indicate that when it comes to the brain, larger is not always better.
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                Author and article information

                Journal
                10.1371/journal.pcbi.1004427
                1407.6836
                4556690
                26325254
                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Performance, Systems & Control,Robotics,Probability
                Performance, Systems & Control, Robotics, Probability

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