Large language models (LLMs) demonstrate remarkable text generation and syntax parsing capabilities in high-resource languages. However, their performance notably declines in low-resource languages due to memory forgetting stemming from semantic interference across languages. To address this issue, we propose a novel deep hierarchical syntax understanding approach to improve the cross-lingual semantic memory capability of LLMs. First, we design a multi-task joint fine-tuning strategy to implicitly align linguistic knowledge between source and target languages in LLMs, which is leveraged to initially parse the target text. Second, we automatically construct the multilingual dependency label banks based on the statistical structure information from the Universal Dependencies (UD) data. Third, we obtain each label's memory strength via in-depth analysis of the initial parsing tree and its dependency label bank. Finally, memory strength is further exploited to guide LLMs to learn the linguistic commonalities from multilingual dependency label banks, thus activating the memory ability of weak labels. Experimental results on four benchmark datasets show that our method can dramatically improve the parsing accuracy of all baseline models, leading to new state-of-the-art results. Further analysis reveals that our approach can effectively enhance the weak syntactic label memory cognition of LLMs by combining the advantages of both implicit multi-task fine-tuning and explicit label bank guiding. Our code and label banks will be made publicly available.