At CRYPTO 2019, Gohr demonstrated that neural networks can learn information related to differential distributions, which can then be used as distinguishers. Building upon this, training neural networks to capture deeper cryptanalytic features remains an intriguing direction. In this work, we focus on the potential of neural networks to detect cryptographic properties in multisets. First, we apply neural networks to differential-linear cryptanalysis under the condition of multisets. The trained neural differential-linear distinguisher demonstrates more rounds or higher accuracy compared to previous neural distinguishers with the multiset, achieving state-of-the-art results on SKINNY, PRESENT, LBlock, and RECTANGLE. Second, we present a more fine-grained method for constructing higher-order output masks that facilitates the generation of high-probability and key-independent differential-linear trails. This method is applied to develop a 12-round key-independent neural distinguisher for SKINNY-64-64, which is better than the previous 12-round weak-key distinguisher (ePrint 2025/852). Third, we propose a theoretical 15-round key-recovery attack on SKINNY-64-64, leveraging an integral distinguisher that utilizes a higher-order output mask. Finally, we propose a novel method for training a neural distinguisher that combines integral and differential-linear features, achieving higher accuracy than using either type of feature alone.