Lidar SLAM plays a significant role in mobile robot navigation and high-definition map construction. However, existing methods often face a trade-off between localization accuracy and system robustness in scenarios with a high proportion of dynamic objects, point cloud distortion, and unstructured environments. To address this issue, we propose a neural descriptors-based adaptive noise filtering strategy for SLAM, named ADA-DPM, which improves the performance of localization and mapping tasks through three key technical innovations. Firstly, to tackle dynamic object interference, we design the Dynamic Segmentation Head to predict and filter out dynamic feature points, eliminating the ego-motion interference caused by dynamic objects. Secondly, to mitigate the impact of noise and unstructured feature points, we propose the Global Importance Scoring Head that adaptively selects high-contribution feature points while suppressing the influence of noise and unstructured feature points. Moreover, we introduce the Cross-Layer Graph Convolution Module (GLI-GCN) to construct multi-scale neighborhood graphs, fusing local structural information across different scales and improving the discriminative power of overlapping features. Finally, experimental validations on multiple public datasets confirm the effectiveness of ADA-DPM.