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The video introduces the motivation for using conditional random fields after discussing neural networks. Neural networks can take a single input, compute hidden layers, and output pre-activation vectors. By using softmax non-linearity, a distribution over potential labels is obtained. This distribution represents the network's beliefs about assigning labels to inputs. Predictions are made based on the most likely label according to the network. When presented with new inputs, the process is repeated to compute activations and make classifications.