ACTIVATIONS AND SIGNALS ◆ NEURONS AS FUNCTIONS SIGNAL MONOTONICITY ■ BIOLOGICAL ACTIVATIONS AND SIGNALS NEURON FIELDS NEURONAL DYNAMICAL SYSTEMS COMMON SIGNAL FUNCTION PULSE-CODED SIGNAL FUNCTION
ACTIVATIONS AND SIGNALS ◼ NEURONS AS FUNCTIONS ◼ SIGNAL MONOTONICITY ◼ BIOLOGICAL ACTIVATIONS AND SIGNALS ◼ NEURON FIELDS ◼ NEURONAL DYNAMICAL SYSTEMS ◼ COMMON SIGNAL FUNCTION ◼ PULSE-CODED SIGNAL FUNCTION
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))
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))
NEURONS AS FUNCTIONS S(x) X -00 0 + +00 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 AS FUNCTIONS S(x) x -∞ - 0 + +∞ 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 AS FUNCTIONS The transduction description:a sigmoidal or S-shaped curve the logistic signal function: S(x)= l+e-cx S'= dS =cS(1-S)>0 (c>0) dx The logistic signal function is sigmoidal and strictly increases for 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
NEURONS AS FUNCTIONS S(x) X -00 0 + +00 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 AS FUNCTIONS S(x) x -∞ - 0 + +∞ 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