A weight is a numerical parameter that scales an input to a neuron. Each connection carries a weight representing that input’s importance to the next neuron. The neuron combines its weighted inputs with a bias term, then applies an activation function to produce an output. section 8.2.2 section 8.2.3
A two-input perceptron
Suppose the inputs are a and b, with weights P and Q. Its weighted sum is P × a + Q × b. In a threshold-based perceptron, the output is 1 when this sum exceeds the threshold and 0 otherwise. Changing either weight changes how strongly its input contributes to that decision. section 8.2.2
Weights also parameterize a layer’s transformation. During feed-forward propagation, inputs pass through hidden layers, where weights, biases, and activation functions shape the prediction. Training seeks weight and bias values that improve accuracy: backpropagation calculates how the loss changes with each weight, then updates weights over successive iterations to reduce that loss. section 8.2.3 section 8.3.2 section 8.4.1
Face identification
A network trained on face images and corresponding names learns attributes useful for distinguishing people. Its adjusted weights help turn a new image into a prediction, such as a probability score for a particular identity. section 8.2.1 section 8.3.2
Weight adjustment is not limited to supervised prediction. A Boltzmann learning rule adjusts weights to lower an energy function; a deep belief network can pretrain weights layer by layer without labeled data, then fine-tune the network using supervision. section 8.8.1 section 8.9.1
