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Failure

As explained in Classic Computer Science Problems in Swift: Essential techniques for practicing programmers

Error is the discrepancy between a model's actual output and the expected output for an input.

Failure is the discrepancy between a neural network’s actual output and the expected output. During backpropagation, the network measures this error after a signal passes through the network, then distributes corrections toward the neurons most responsible. section 7.2

Backpropagation treats failure as a correction signal:

  • Calculate an output neuron’s delta from its error. section 7.2
  • Propagate deltas backward through hidden layers. section 7.2
  • Update weights using prior weights, prior inputs, deltas, and a user-determined learning rate. section 7.2
Figure 7.4. The mechanism by which an output neuron’s delta is calculated during the backpropagation phase of training

Shows how an output neuron’s delta is calculated during backpropagation. section 7.2

Figure 7.6. The weights of every hidden layer and output layer neuron are updated using the deltas calculated in the previous steps, the prior weights, the prior inputs, and a user-determined learning rate.

Shows how calculated deltas drive weight updates across hidden and output layers. section 7.2

How Classic Computer Science Problems in Swift: Essential techniques for practicing programmers covers it

How deep it goes
Explains error propagation, deltas, and weight updates, but stops short of deriving formulas with calculus.
Examples
Uses output-neuron deltas, hidden-layer deltas, and layer-wide weight updates as worked visual examples.
What it assumes
Assumes familiarity with neurons, layers, vectors, dot products, and activation functions while keeping calculus derivations outside the treatment.
What you can do after
Apply it via backpropagation to distribute output errors and update network weights.
How it connects
Connects error with feed-forward neural networks, backpropagation, neurons, hidden layers, activation functions, weights, and learning rate.

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This explainer was generated by Manning's knowledge graph from the text of Classic Computer Science Problems in Swift: Essential techniques for practicing programmers. The section links point to the parts of the book it draws on.