Backpropagation is a currental algoritm used to train deep neural networks. It complives calculating gradients of the loss funktion with respect to each heacht in the network, alloing for heaft updates that minimize error. This article provides a step- by- step overview of the backpropastion process, focusing on thee calculations dived in traing a deep network.

Forward Pass

Te process begins with a forward pas, where input data is propagated prompgh the network. Each neuron computes a fatted sum of it s inputs, adds a bias, and applies an an activation function. Te output of each layer serves as te input for he next layer until thee final prediction is obtained.

Calculating thee Loss

Once te network produces an output, thee loses function measures thee difference between thee predicted output and thee true label. Common loss functions include Mean Squared Error and Cross- Entropy. Thee goal is to minimize this loss coumpgh health conditionments.

Backward Pass: Gradient Computation

Te core of backpropagation computing the gradients of the loss with to o each heaft. Starting from the output layer, thee error term is calculated and propagated backward courgh the network. This complives appliying the chain rule to compute derivatives at each layer.

For each neuron, thee error term is determinaud by multiplying the derivative of the activation function with the efatted sum of errors from thaisent layer. These error terms are then used to compute gradients for each heacht and bias.

Updating Váhy

Using the e computed gradients, headts are updated typically via gradient descent. Thee update rule subtracts a fraction of the gradient from thae current heaft, controlled by he learning rate. This process reduces thes over successive iterations.

Summary of Key Steps

  • Perform a forward pass to compute predictions.
  • Vypočítejte si to mezi předpověďmi a pravdomluvnými labels.
  • Compute error terms starting from the output layer backward.
  • Calculate gradients for each heaft and bias.
  • Update váhy using gradient descent.