用神经网络发现新积分特征，突破传统密码分析极限。

The study by Gohr et.al at CRYPTO 2019 and sunsequent related works have shown that neural networks can uncover previously unused features, offering novel insights into cryptanalysis. Motivated by these findings, we employ neural networks to learn features specifically related to integral properties and integrate the corresponding insights into optimized search frameworks. These findings validate the framework of using neural networks for feature exploration, providing researchers with novel insights that advance established cryptanalysis methods. Neural networks have inspired the development of more precise integral search models. By comparing the integral distinguishers obtained via neural networks with those identified by classical methods, we observe that existing automated search models often fail to find optimal distinguishers. To address this issue, we develop a meet in the middle search framework that balances model accuracy and computational efficiency. As a result, we reduce the number of active plaintext bits required for an 11 rounds integral distinguisher on SKINNY64/64, and further identify a 12 rounds key dependent integral distinguisher achieving one additional round over the previous best-known result. The integral distinguishers discovered by neural networks enable key recovery attacks on more rounds. We identify a 7 rounds key independent integral distinguisher from neural networks with even only one active plaintext cell, which is based on linear combinations of bits. This distinguisher enables a 15 rounds key recovery attack on SKINNYn/n, improving upon the previous record by one round. Additionally, we discover an 8 rounds key dependent integral distinguisher using neural network that further reduces the time complexity of key recovery attacks against SKINNY.