In a residual network, the desired underlying mapping $f(\mathbf{x})$—the function the network ultimately aims to approximate—is not learned directly by a stack of layers. Instead, those layers are reformulated to learn only the residual mapping $g(\mathbf{x}) = f(\mathbf{x}) - \mathbf{x}$, and the target function is recovered as $f(\mathbf{x}) = g(\mathbf{x}) + \mathbf{x}$. This reformulation is motivated by the degradation problem: as plain networks grow deeper, their training accuracy can paradoxically worsen, suggesting that the added layers struggle to approximate even the identity function. By recasting the problem in terms of $g(\mathbf{x})$, the identity case $f(\mathbf{x}) = \mathbf{x}$ reduces to $g(\mathbf{x}) = 0$, which is significantly easier for a network to learn because it only requires driving the weights and biases of the constituent layers toward zero.