This paper presents a margin-based generalization bound for neural networks that scales with their margin-normalized spectral complexity, defined as the product of the spectral norms of the weight matrices multiplied by a correction factor related to the margin. The bound is empirically evaluated on the AlexNet network trained with SGD on the MNIST and CIFAR10 datasets, both with original and random labels. The results show that the bound, the Lipschitz constants, and the excess risks are closely correlated, indicating that SGD selects predictors whose complexity aligns with the difficulty of the learning task and that the bound is sensitive to this complexity. The paper investigates a complexity measure for neural networks based on the Lipschitz constant, normalized by the margin of the predictor. The key contributions include a generalization bound that scales with the Lipschitz constant divided by the margin, has no dependence on combinatorial parameters, is multiclass, and measures complexity against a reference network. The bound is validated through empirical studies on standard datasets, showing that margins and their normalized versions provide insights into the difficulty of learning tasks. The analysis also demonstrates that margins alone are not sufficient, and proper normalization is necessary for meaningful comparisons. The paper further discusses the implications of the bound for neural network generalization, including the effects of regularization and the behavior of margins during training. The theoretical analysis includes a margin-based bound for multiclass prediction, covering number complexity upper bounds, and a Rademacher complexity lower bound, providing a comprehensive understanding of the generalization properties of neural networks.This paper presents a margin-based generalization bound for neural networks that scales with their margin-normalized spectral complexity, defined as the product of the spectral norms of the weight matrices multiplied by a correction factor related to the margin. The bound is empirically evaluated on the AlexNet network trained with SGD on the MNIST and CIFAR10 datasets, both with original and random labels. The results show that the bound, the Lipschitz constants, and the excess risks are closely correlated, indicating that SGD selects predictors whose complexity aligns with the difficulty of the learning task and that the bound is sensitive to this complexity. The paper investigates a complexity measure for neural networks based on the Lipschitz constant, normalized by the margin of the predictor. The key contributions include a generalization bound that scales with the Lipschitz constant divided by the margin, has no dependence on combinatorial parameters, is multiclass, and measures complexity against a reference network. The bound is validated through empirical studies on standard datasets, showing that margins and their normalized versions provide insights into the difficulty of learning tasks. The analysis also demonstrates that margins alone are not sufficient, and proper normalization is necessary for meaningful comparisons. The paper further discusses the implications of the bound for neural network generalization, including the effects of regularization and the behavior of margins during training. The theoretical analysis includes a margin-based bound for multiclass prediction, covering number complexity upper bounds, and a Rademacher complexity lower bound, providing a comprehensive understanding of the generalization properties of neural networks.