Backpropagation Gradient

• : The loss function (e.g., cross-entropy or mean squared error).
• : The weight matrix of the -th layer.
• : The activations from the previous layer ().
• : The error term (also called "delta") for the current layer , which reflects how much the output of that layer affects the loss.
• : The transpose of the previous layer’s activations, used to align dimensions for matrix multiplication.
• The expression represents how the loss changes with respect to the weights in a given layer—essential for updating weights during training using gradient descent.

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