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Neural Networks Lecture


What is a newural network

  • The single Neuron
    • Weighted Input
    • Activation
  • The network model
    • Input/Output
    • Weights
    • Activation Function
  • The Tensor Model

Output and Loss Function

  • Classification versus Regression


\[L = (x-y)^2\]


\[L = \log \frac{ \exp x_{y} } { \sum \exp x_i }\]


  • Optimisation problem
    • tune the weights to minimise the loss function
    • if the activation function is differentiable, the entire system is
    • different optimisation algorithms; trust the API or do a more advanced module

Activation Functions

  • Threshold functions
  • Approximations to the threshold function
  • Logistic: \(f(x) = \frac1{1+e^{-\beta x}}\)
  • ReLU: \(f(x)=\max(x,0)\)
    • not differentiable

Sample Problem