Biologically Inspired Compu4ng: Neural Computa4on. Lecture 5. Patricia A. Vargas

Transcription

1 Biologically Inspired Compu4ng: Neural Computa4on Lecture 5 Patricia A. Vargas

2 Lecture 5 I. Lecture 4 Revision II. Ar4ficial Neural Networks (Part IV) I. Recurrent Ar4ficial Networks I. GasNet models II. Evolving Ar4ficial Neural Networks I. MLPs II. GasNet models F21BC2 BIC Neural Computa4on

3 Ar4ficial Neural Networks Recurrent Neural Networks The Hopfield Equations Hopfield Neural Network Training performed in one pass: where, w 1 n k k ij =! pi p j N k = 1 w ij is the weight between nodes i & j " N # N is the number of nodes in the network! si = sign $ wij s j % & j= 1 ' n is the number of patterns to be learnt p ik is the value required for the i-th node in pattern k totalmente realimentada (exceto auto-realim Pattern Completion (III) 64 pixel image of an H Same image with 10 pixels altered (I.e. approximately 16% noise added) Execution performed iteratively: " N # s = sign $! w s % Pattern Completion (IV) Food for thought - flight of fancy? Memories of a deceased dog named Tanya...

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10 Gas dispersion NOT centred on the node 10

11 Gas Concentration around emitter 11

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13 Nodes do NOT have a spatial relation? [0,1] is called the Mbias or Modulator Bias 13

14 Ar4ficial Neural Networks I. Evolving Ar4ficial Neural Networks I. MLPs I. Topology and weights II. Example: Evolving (training) MLPs to learn some func4ons <Toolbox> from Cazangi & Moioli (2005) VISION x 0 x 1 y 1 x 2 y 2 y o x m Camada de

15 Ar4ficial Neural Networks I. Evolving Ar4ficial Neural Networks I. GasNet models I. Topology + all network parameters + task dependent parameters < genotype >:: (< genes >) < gene >=< node >

16 I. Evolving GasNets models Original de variable in the phenotype space. Node variables Description [Range]DiscreteValues Gene locus Description Coordinates Node coordinates on the [0, 99] < x > < x value > Euclidean plane (100x100) [0, 99] < y > < y value > Electrical Defines the parameters of the [0, 50] <r p > < radius > connectivity two segments of circle centred <r p > on the node that will determine [0, 2π] < θ e > < angular extent > the excitatory and inhibitory < θ e > links < θ p > < orientation > < θ p > Recurrence Determines whether the node {-1,0,1} < rec > < recurrent status > status has an inhibitory, none or excitatory recurrent connection Emitting Determines the circumstances {0,1,2} <E s > < emitting status > status under which the node will emit gas {none, electrical, gas} Type of gas Determines which gas {1, 2} <G t > < gas type > the node will emit Rate of Determines the rate of gas [1, 11] < s > < build up/ build up/ build up and decay decay rate > decay Radius of Maximum radius of [10%,60%]* <G r > < gas radius > emission gas emission * of plane dimension 100x100 Transfer Used in (2) to determine the [1, 11] <K 0 > < transfer function function transfer parameter value K n i default value > parameter default value K 0 i Bias The b i term? on 1 [ 1.0, 1.0] <b> < bias value > Task Parameters which depend on? <? >? parameters the task, e.g. a robot vision sensors input area ([1])

17 I. phenotype Evolving GasNets models NSGasNet space. Node Description [Range] Gene Description variables DiscreteValues locus Recurrence Determines whether the node {-1,0,1} < rec > < recurrent status > status has an inhibitory, none or excitatory recurrent connection Emitting Determines the circumstances {0,1,2} <E s > < emitting status > status under which the node will emit gas {none, electrical, gas} Type of gas Determines which gas {1, 2} <G t > < gas type > the node will emit Rate of Determines the rate of gas [1, 11] < s > < build up/ build up/ build up and decay decay rate > decay Transfer Used in (2) to determine the [1, 11] <K 0 > < transfer function function transfer parameter value K n i default value > parameter default value K 0 i Bias The term b i on 1 [ 1.0, 1.0] <b> < bias value > Task Parameters which depend on? <? >? parameters the task, e.g. a robot vision sensors input area ([1]) Modulator Parameter which depend on [0, 1] < Mbias n > < Modulator bias Bias the number of nodes, for node n > (Mbias n ) i.e. there will be as many Mbias as the number of network nodes

18 1) Initialise population of 100 genotypes in 10x10 grid 2) Evaluate initial genotype fitnesses 3) Repeat until termination criteria met: Repeat 100 times for one generation: Select genotype at random Create mating pool of genotype plus eight nearest grid neighbours One parent P selected proportional to fitness rank in mating pool Offspring O mutated Offspring O evaluated Place O in mating pool, replacing genotype selected proportional to inverse of fitness rank in mating pool The steady-state genetic algorithm works as 18

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20 Original X NSGasNet 20

21 Evolu4on of: All nodes parameters 21

22 50 runs 200 evalua-ons per genera-on lutionary regime parameters employed on Parameter CPG task Mutation rate 8% Fitness function F itness CP G = ( C0 n0 )+( C1 n1 ) 2 Number of runs 50 Maximum number 1000 of generations Population size 100 Genotype size 42 (Original) 46 (NSGasNet) Trials 1 Number of evaluations 200 per trial 22

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27 Evolu4on of: Number of nodes All nodes parameters 27

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33 40 runs 10 trials per fitness evalua-on 33

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35 2d simulation 3d simulation 35

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37 Lecture 5 References: Husbands,P., Smith, T., Jakobi, N. and O Shea, M. (1998). Beier living through chemistry: Evolving GasNets for robot control, Connec4on Science, vol. 10(3 4), pp , Philippides, P. Husbands, T. Smith, and M. O Shea (1999) Flexible couplings: Diffusing neuromodulators and adap4ve robo4cs, Ar4ficial Life, vol. 11, pp , 2005.ciples and individual variability, Journal of Computa4onal Neuroscience, vol. 7, pp Smith, T. M. S. (2002). The Evolvability of Ar4ficial Neural Net works for Robot Control. University of Sussex, Brighton, England, UK, 2002, PhD thesis. Vargas, P.A., Di Paolo, E. A. & Husbands, P. (2007). "Preliminary Inves4ga4ons on the Evolvability of a Non spa4al GasNet Model". In Proceedings of the 9th European Conference on Ar4ficial life, ECAL'2007, Springer Verlag, Lisbon, Portugal, September 2007, pp: Vargas, P.A., Di Paolo, E. A., & Husbands, P. (2008). "A study of GasNet spa4al embedding in a delayed response task". In the Proc. of ALIFE XI'2008, England, UK, pp: Husbands, P., Philippides, A., Vargas, P. A., Buckley, C, Fine, P., Di Paolo, E. & O Shea, M. (2010). Spa4al, Temporal and Modulatory Factors affec4ng GasNet Evolvability, to appear in the Complexity Journal, Wiley Periodicals, Inc. (invited paper). F21BC2 BIC Neural Computa4on

38 Lecture 5 I. Lecture 4 Revision II. Ar4ficial Neural Networks (Part IV) I. Recurrent Neural Networks I. GasNet Models II. Evolving ANN I. MLP II. GasNet models F21BC2 BIC Neural Computa4on

39 Lecture 6 What s next? Ar4ficial Neural Networks (Part V) F21BC2 BIC Neural Computa4on

40 hip:// (please note that this link only works in Mozilla Firefox or Safari web VISION F21BC2 BIC Neural Computa4on