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Evolutionary morphogenesis for multi-cellular systems

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Abstract

With a gene required for each phenotypic trait, direct genetic encodings may show poor scalability to increasing phenotype length. Developmental systems may alleviate this problem by providing more efficient indirect genotype to phenotype mappings. A novel classification of multi-cellular developmental systems in evolvable hardware is introduced. It shows a category of developmental systems that up to now has rarely been explored. We argue that this category is where most of the benefits of developmental systems lie (e.g. speed, scalability, robustness, inter-cellular and environmental interactions that allow fault-tolerance or adaptivity). This article describes a very simple genetic encoding and developmental system designed for multi-cellular circuits that belongs to this category. We refer to it as the morphogenetic system. The morphogenetic system is inspired by gene expression and cellular differentiation. It focuses on low computational requirements which allows fast execution and a compact hardware implementation. The morphogenetic system shows better scalability compared to a direct genetic encoding in the evolution of structures of differentiated cells, and its dynamics provides fault-tolerance up to high fault rates. It outperforms a direct genetic encoding when evolving spiking neural networks for pattern recognition and robot navigation. The results obtained with the morphogenetic system indicate that this “minimalist” approach to developmental systems merits further study.

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Notes

  1. The challenge of growth of complexity is usually associated with genetic representation [88], but other aspects may limit the complexity of evolved circuits. An important one is fitness evaluation, that may take a lot of time when complex behaviors are desired (e.g. when evolving a robot controller, sufficient time must be allowed for the robot to perform its task before assigning the fitness). Fostering environmental interactions or emergence are also key issues. Arguments in favor of genetic encodings that include developmental mechanisms were evidenced in the context of genetic programming [4] but are also relevant here.

  2. A multi-cellular circuit is a circuit composed of a number of interconnected cells that are the elementary functional blocks of the circuit. For example cells can implement the functionality of a logic gate, of a signal processing element, of a neuron, etc.

  3. This terminology does not indicate whether the developmental system “grows” directly the configuration string of physical hardware or of “virtual hardware” where e.g. an FPGA is configured to implement another circuit, which then undergoes development and evolution. In other words, intrinsic developmental system does not indicate whether evolution is constrained or unconstrained [80], although this may be a further distinction (e.g. intrinsic developmental system for constrained or unconstrained evolution).

  4. The choice of the Manhattan distance is motivated by its efficient translation in hardware. Alternatively one may interpret \(C_s^i\) not directly as the chemical concentration but as a non-linearily scaled measure of it.

  5. Step 4 is an optimized implementation of \(C_s^i=(\sum_{j,V_s^j=1}{(C_s^j-1)}) / (\sum_j{V_s^j})\) that does not require additions or divisions but gives the same result according to the properties of the signaling process.

  6. The evolvability of the morphogenetic system was tested with three distance operators DOp on the task described in Section 4: the Hamming distance, the absolute difference, and the square difference. Overall, performance was best when DOp was the Hamming distance, presumably because of its discontinuous nature which allows signals with very different intensities to map to identical entries in the expression table. Furthermore the Hamming distance can be implemented in hardware in a compact way which is why it was used.

  7. Evolvability is understood here as the capacity of the genetic representation and operators to produce offsprings with fitness higher than their parents [1]. See [62] for an overview on evolvability in different disciplines.

  8. With the exception of the patterns smaller than 32× 32 for which the border has a fixed width of one pixel, the Norwegian flag scales in length with the size of the pattern: the width of the border and the widths of the crosses inside the flag are proportional to the width of the pattern. The pattern width, the width of the border, the width of the outer cross (white) and the width of the inner cross (blue) are listed in this order in the following tuples: (8,1,1,1), (16,1,1,3), (32,1,2,5), (64,2,5,11), (96,3,7,15), (128,4,10,21), (256,8,20,41). The border of the CA-generated pattern is always one pixel wide. The first line of this pattern is randomly generated (each pixel takes randomly one of two colors), and the following lines are computed from the line above them using cellular automata rule 90.

  9. Since 4 bits can encode 16 values but there are only 12 cell functionalities, the cell functionalities F0 and F1 with excitatory and inhibitory characteristics are encoded twice by different binary codes.

  10. More complex neural models capable of learning can also be evolved with the morphogenetic system [69].

  11. A custom implementation of the algorithm was used which has an identical behavior regardless of the input size.

  12. Linear correlation coefficient \(r=0.976\) with standard deviation 0.003 using bootstrap method.

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Acknowledgments

This project is funded by the Future and Emerging Technologies programme (IST-FET) of the European Community, under grant IST-2000-28027 (POETIC). The information provided is the sole responsibility of the authors and does not reflect the Community's opinion. The Community is not responsible for any use that might be made of data appearing in this publication. The Swiss participants to this project are funded by the Swiss government grant 00.0529-1.

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  1. Daniel Roggen

    Present address: Wearable Computing Laboratory, ETH Zürich, Zürich, Switzerland

  2. Diego Federici

    Present address: Google’s Zürich European Engineering Centre, Zürich, Switzerland

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  1. Laboratory of Intelligent Systems, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Roggen & Dario Floreano

  2. Department of Computer and Information Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Diego Federici

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Roggen, D., Federici, D. & Floreano, D. Evolutionary morphogenesis for multi-cellular systems. Genet Program Evolvable Mach 8, 61–96 (2007). https://doi.org/10.1007/s10710-006-9019-1

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