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Backpropagation Through a Dense Layer

Mon, 21 Sep 2026 15:42:00 +0900

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Backpropagation computes, for one layer, three gradients: one for each parameter of the layer and one to hand to the layer before it. The third is what makes deep networks trainable — without it, error could not travel past the last layer. The procedure below is the backward pass of a single dense layer.

A Transformer Training Step (flowchart)

Mon, 21 Sep 2026 14:02:00 +0900

One training step is a fixed cycle: the model predicts, the predictions are scored against the targets, the error is propagated backwards, and the parameters move a little in the direction that reduces it. The diagram below shows that cycle; the repetition is the whole of training.