To estimate class probabilities across multiple categories, a classification model requires an output for each class. Using a linear model, this is achieved by defining an affine function for each output. For $d$ input features and $q$ output categories, the unnormalized outputs (logits) $\mathbf{o}$ are computed as $\mathbf{o} = \mathbf{W}\mathbf{x} + \mathbf{b}$, where the weight matrix $\mathbf{W} \in \mathbb{R}^{q imes d}$ contains $q imes d$ scalars and the bias $\mathbf{b} \in \mathbb{R}^q$ contains $q$ scalars. Because every output depends on every input feature, this computation represents a fully connected layer in a single-layer neural network.