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Yong-Yeol Ahn, Beom Jun Kim , Hawoong Jeong

Pattern Retrieval Performance and Role of Wiring Cost in the evolution of C. elegans neural network. Yong-Yeol Ahn, Beom Jun Kim , Hawoong Jeong. Caenorhabditis elegans. It’s a transparent nematode. All C. elegans have same neurons and synapses. We know all of them!.

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Yong-Yeol Ahn, Beom Jun Kim , Hawoong Jeong

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  1. Pattern Retrieval Performance and Role of Wiring Cost in the evolution of C. elegans neural network Yong-Yeol Ahn, Beom Jun Kim, Hawoong Jeong

  2. Caenorhabditis elegans • It’s a transparent nematode. • All C. elegans have same neurons and synapses. • We know all of them!

  3. Putting a “Neural Network Model” on a “Neural Network” • Let’s try Hopfield model on C. elegans neural network. (Beom Jun Kim, 2004) The ability to recognize patterns may be crucial for surviving and mating

  4. +1 -1 2 -3 +1 1 Hopfield Model Neurons can have two states. At each time step, each neuron’s state is determined by other neurons which have links to it. Ex)

  5. Beom Jun Kim 2004 The pattern retrieval performance of C. elegans • Performance m: overlap fraction between original pattern and retrieved pattern. • C. elegans shows more poor performance than BA model andWS(p=1.0) model. • Clustering coefficient determines the performance of network (under degree conserving rewiring). (clustering coefficient)

  6. What’s the problem? • If we assume that the Hopfield model is an appropriate model for measuring the neural network’s performance, • Then some other constraint limits the performance of C. elegans neural network. • Possible constraint is ‘wiring cost’. • Assume that the wiring cost of a connection between two neurons is equal to the Euclidean distance between them. • We can find a neuron’s geometric position at http://wormatlas.org .

  7. The C. elegans neural network Front view Side view (Drawn by pajek)

  8. Distribution of distance(cost) between two neurons • There exist large number of very long-range wirings (power-law like decay)

  9. Is C. elegans neural network optimized by wiring cost? • Using node replacement optimization method, we minimize C.elegans neural network’s cost. • Original C. Elegans network’s cost: 367.1 • Position optimized network’s cost: 199.7 • Is C. elegans neural network optimized by cost?  Not really!! : ( Node replacement optimization (conserving topology)

  10. Distance distribution of cost optimized network Node position optimized network Original network

  11. High performance network vs. Poor performance network • Using degree conserving rewiring, we can make highly clustered network and poorly clustered network from original C. elegans network Degree conserving rewiring (npo: node position optimized) Best performance

  12. Another candidates?  Ganglia structure (module) • Neurons aggregate and make ‘ganglia’ • Let’s assume that connection between ganglia can’t be modified and the neurons in one ganglion are optimized to show high performance, to reduce cost.

  13. In Ganglia • Neurons in a ganglia do not show the evidence of cost optimization! : (

  14. Conclusion • We constructu the C. elegans neural network with geometrical information • Cherniak’s remark which state that ganglia position are optimized for low cost isn’t true anymore in neuronal scale. • Under the C. elegans neuron position topology, the higher clustering coefficient, the smaller the cost. • But, C. elegans neural network is not optimized to have minimal cost. • C. elegans neural network is small, and specific. We show that cost, performance(Hopfield model) are not the central organizing principle of C. elegans neural network. • What is the design principle of C. elegans neural network?  Still open question.

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