NEURALNETWORKSANDFUZZYSYSTEMS初次讲课，请大家批评指正！
NEURAL NETWORKS AND FUZZY SYSTEMS 初次讲课，请大家批评指正！
Chapter 2.Neural Dynamics:Activation and SignalsX2.1 Neurons as functionsNeurons behave as functionsNeurons transduce an unbounded input activationx(t) at time t into a bounded output signal S(x(t)
Chapter 2. Neural Dynamics:Activation and Signals ※2.1 Neurons as functions Neurons behave as functions. Neurons transduce an unbounded input activation x(t) at time t into a bounded output signal S(x(t))
Chapter 2.Neural Dynamics:Activation and Signalsx2.1 Neurons as functionsThe transduction description: a sigmoidal or S-shaped curvee.g.1 the logistic signal function1S(x)(1)1 +e-cxds(c > 0)ScS(1- S) > 0(2)dxThus the logistic signal function is sigmoidal and strictlyincreases for c>0
Chapter 2. Neural Dynamics:Activation and Signals ※2.1 Neurons as functions The transduction description: a sigmoidal or S-shaped curve e.g.1 the logistic signal function cx e S x − + = 1 1 ( ) (1) ' = = cS(1− S) 0 (c 0) dx dS S (2) Thus the logistic signal function is sigmoidal and strictly increases for c>0
Chapter 2.NeuralDynamics:Activationand SignalsX2.1 Neurons as functionsS(x)x++8-8Fig2.1 s(×)~xIf c→+oo, we get threshold signal function (dashline),Which ispiecewisedifferentiable
Chapter 2. Neural Dynamics:Activation and Signals ※2.1 Neurons as functions S(x) x -∞ - + +∞ Fig2.1 s(x)~x If c→+∞，we get threshold signal function (dash line), Which is piecewise differentiable
Chapter 2.NeuralDynamics:Activationand Signalsx2.2 Signal MonotonicityIn general,signal functions are monotone nondecreasingWhich means signal functions have an upper bound orsaturation valuecasel:differentiablecase2:piecewise-differentiable
Chapter 2. Neural Dynamics:Activation and Signals ※2.2 Signal Monotonicity In general,signal functions are monotone nondecreasing Which means signal functions have an upper bound or saturation value case1:differentiable case2:piecewise-differentiable