= Solution
Training minimizes the empirical <categorical cross-entropy loss>
$$
L(\theta)=-\frac1{10000}\sum_{i=1}^{10000}\sum_{k=1}^2y_{ik}\log\widehat p_k(x_i;\theta)
$$
by <stochastic gradient descent>. The independent validation set monitors generalization, while the small fixed number of epochs limits how long the network can fit training noise; using validation loss for <early stopping> would make this safeguard explicit. A forward pass computes all layer activations, class probabilities, and the mini-batch loss. There are $10000/2=5000$ training mini-batches per epoch and hence $5\cdot5000=25000$ training forward passes, in addition to validation evaluation after each epoch.
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