How do regularization techniques influence model performance when implementing identity mapping in deep models?

Identity mapping lets a deep network simply pass its input forward, so the layers mainly act as identity functions. Regularization methods such as dropout, weight decay, or batch‑norm add noise or shrink weights, which can slightly disturb that perfect passthrough but help the network avoid overfitting and keep gradients stable. Weight decay discourages large weights, keeping the identity mapping close to the true identity while still allowing small adjustments; dropout randomly zeros units, forcing the model to learn redundant paths that preserve the mapping. Batch‑norm normalizes activations, reducing internal covariate shift and allowing the identity mapping to remain smooth even as layers learn new features. For example, a 100‑layer residual block with identity shortcuts and weight‑decay‑regularized weights will still transmit the signal cleanly while the decay term keeps the shortcut weights near one, ensuring good performance.