NEURALNETWORKTHEORYNEURONALDYNAMICS I:ACTIVATIONSAND SIGNALS2004.10.13
NEURAL NETWORK THEORY NEURONAL DYNAMICS Ⅰ: ACTIVATIONS AND SIGNALS 2004.10.13
ACTIVATIONSANDSIGNALSNEURONSASFUNCTIONSSIGNALMONOTONICITYBIOLOGICALACTIVATIONS AND SIGNALSNEURONFIELDSNEURONALDYNAMICALSYSTEMSCOMMONSIGNAL FUNCTIONPULSE-CODEDSIGNALFUNCTION
ACTIVATIONS AND SIGNALS ◼ NEURONS AS FUNCTIONS ◼ SIGNAL MONOTONICITY ◼ BIOLOGICAL ACTIVATIONS AND SIGNALS ◼ NEURON FIELDS ◼ NEURONAL DYNAMICAL SYSTEMS ◼ COMMON SIGNAL FUNCTION ◼ PULSE-CODED SIGNAL FUNCTION
NEURONSASFUNCTIONSNeurons behave as functions.Neurons transduce an unbounded input activation x(tat time t into a bounded output signal S(x(t))
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))
NEURONSASFUNCTIONSS(x)X++808Fig.1 s(x) is a bounded monotone-nondecreasing function of xIf c-→+oo, we get threshold signal function (dash line)Which is piecewise differentiable
NEURONS AS FUNCTIONS S(x) x -∞ - + +∞ Fig.1 s(x) is a bounded monotone-nondecreasing function of x If c→+∞，we get threshold signal function (dash line), Which is piecewise differentiable
NEURONS ASFUNCTIONSThe transduction description: a sigmoidal or S-shaped curvethe logistic signal function:1S(x)1+e-crdsS'(c> 0)=cS(1-S)> 0dxThe logistic signal function is sigmoidal and strictly increasesfor positive scaling constant c >0
NEURONS AS FUNCTIONS The transduction description: a sigmoidal or S-shaped curve the logistic signal function: cx e S x − + = 1 1 ( ) ' = = cS(1− S) 0 (c 0) dx dS S The logistic signal function is sigmoidal and strictly increases for positive scaling constant c >0