The number of outputs from a softmax regression network is strictly determined by the number of target categories in the classification task. Because each output corresponds to a predicted class probability, a dataset with $$C$$ classes requires an output dimension of $$C$$. For example, mapping a $$784$$-dimensional flattened input vector to $$10$$ distinct classes necessitates a $$784 	imes 10$$ weight matrix alongside a $$1 	imes 10$$ row vector for the biases.

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In simple linear architectures like softmax regression, each input instance must be represented as a fixed-length 1D vector. When dealing with spatial data such as $$28 	imes 28$$ pixel images, the 2D spatial structure is discarded and each image is flattened into a single vector of length $$784$$. This flattening step allows the data to be processed via standard matrix multiplication, although it ignores structural relationships that more advanced architectures like convolutional neural networks would otherwise exploit.

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