Abstract Formal verification is paramount for neural networks in safety-critical domains yet remains constrained by the trade-off between precision and scalability, especially with modern high frequency activation functions. However, the inherent NP-hardness of the problem forces a fundamental trade-off between scalability and precision in existing methods, which fail to adequately capture the high-frequency nonlinearities of modern activations. To address this, Quadratic Approximation based Verification via Fourier series and Taylor truncation (QAV-FT) is proposed as a framework unifying Fourier-enhanced quadratic approximation and Taylor remainder-aware error control. Specifically: (i) A Fourier-based quadratic abstraction is formulated for arbitrary activations, with a rigorous error bound established via Jackson’s theorem and Lebesgue constant analysis; (ii) A second-order propagation scheme utilizing Lagrange remainder theory is devised to analytically derive sound, tight bounds with reduced symbolic complexity; and (iii) These mechanisms are integrated into a scalable full-network verification algorithm. Empirical results on MNIST-FC and other benchmarks demonstrate that QAV-FT achieves an average certification accuracy of 96.8% across complex activations like Swish, GELU, and Mish, with favorable accuracy and efficiency over comparable methods on partial models.

Abstract The rapidly growing encrypted traffic hides a large number of malicious behaviours. The difficulty of collecting and labelling encrypted traffic makes the class distribution of dataset seriously imbalanced, which leads to the poor generalisation ability of the classification model. To solve this problem, a new representation learning method in encrypted traffic and its diversity enhancement model are proposed, which uses the diversity of images to represent the diversity of traffic samples. First, the encrypted traffic is transformed into Markov images. Then, a diversity maximisation Markov‐GAN based on the Simpson index is designed to generate new Markov images. Finally, the balanced Markov image set is sent to the CNN for classification. Experimental results show that the proposed method can predict the whole dataset space with only a few original samples. And the classification accuracies under different imbalance degrees are significantly improved, all of which are over 90%. The enhanced Markov image set can effectively alleviate performance generalisation deviation caused by different network depths. Even an ordinary CNN has almost the same classification effect as VGG13 and VGG16. Compared with other data enhancement methods, the Markov‐GAN only needs to balance the transform domain dataset, which is lightweight, easy to train and has stronger amplification ability.