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Norms in deep learning measure the size or magnitude of vectors and matrices, helping to quantify their properties. Common norms include the L1 norm (sum of absolute values) and the L2 norm (Euclidean distance), both used to regularize models and prevent overfitting. Norm-based regularization, like L2 regularization, adds a penalty to large weights, encouraging simpler models. They also help analyze gradients and ensure numerical stability during training.