Calculating net input signal (3)

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  1. receives a vector of input signals z=(z1,z2,,zI)z=(z_{1},z_{2},…,z_{I})
    • usually real numbers, denoted by RIR^I
  2. each associated with a weight viv_{i} (wiw_{i} in diagram) (aka parameters) that determines how much importance or influence that particular signal has
  3. calculates the net input signal, which is the weighted sum of the inputs
  4. uses an activation function fANf_{AN}
    • to transform this net input into the output signal (oo)
      • transforms them into an output between [0,1][0, 1] or [1,1][-1, 1] (depending on the chosen fANf_{AN})
    • fANf_{AN} introduces nonlinearity to the model, enabling it to learn complex patterns
  5. also a threshold value/bias (θ\theta)
    • influences output signal's strength
    • If the output signal surpasses the threshold, the neuron "fires" (outputs 1), otherwise, it remains inactive (outputs 0)

Calculating net input signal (3)

Two types of ANs that compute the net input signal

  1. Summation Units (SU):

    • weighted sum of all input signals net=i=1Izivin e t=\sum_{i=1}^I z_i v_i
  2. Product Units (PU):

    • weighted product of all input signals net=i=1Izivin e t=\prod_{i=1}^I z_i^{v_i}
    • network can represent interactions involving more than two input signals. e.g. x1x2x3x_{1}⋅x_{2}⋅x_{3}​ would be a 3rd-order interaction
    • allows to model more complex relationships in the data

Activation Functions fANf_{AN} (4)

  • receives net input signal and bias
  • determines the output (or firing strength) of the neuron
  • outputs [0,1][0, 1] or [1,1][-1, 1]
    • in fancy terms: [fAN()=0f_{A N}(-\infty)=0 or fAN()=1f_{A N}(-\infty)=-1] and fAN()=1f_{A N}(\infty)=1
  • Types of activation functions

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