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The arithmetic is kept simple on purpose, which almost made me second-guess myself.
First, restate the layer computation as z = Wx + b (or z = xW + b depending on convention) and compute each pre-activation value carefully. Then apply the activation functions in sequence, showing intermediate results and keeping track of dimensions and numerical stability, especially for softmax.
Pro tip: Before computing, explicitly state your convention for matrix orientation (e.g., row vectors vs. column vectors) and whether the bias is added per output neuron; this prevents off-by-one errors and shows you think like a production ML engineer.
Confirm the shapes of the weight matrix, input vector, and bias, and state whether you treat inputs as row or column vectors. This ensures the matrix multiplication is set up correctly.
Perform the matrix-vector multiplication and add the bias to get the linear output z for each neuron. Show the arithmetic clearly, one neuron at a time.
Apply the specified activation (e.g., ReLU or sigmoid) element-wise to z, producing the first hidden layer output. Note any piecewise behavior (e.g., ReLU zeroing negatives).
If a second activation (e.g., softmax) is specified, apply it to the output of the first activation. For softmax, compute exponentials and normalize by their sum.
Check that the final output has the expected shape and properties (e.g., probabilities sum to 1 for softmax). Briefly interpret what the output represents in the context of the network.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.