In this paper, we propose $\textbf{Ne}$ural-$\textbf{Sy}$mbolic $\textbf{C}$ollaborative $\textbf{D}$istillation ($\textbf{NesyCD}$), a novel knowledge distillation method for learning the complex reasoning abilities of Large Language Models (LLMs, e.g., \textgreater 13B). We argue that complex reasoning tasks are difficult for Small Language Models (SLMs, e.g., $\leq$ 7B), as these tasks demand not only general cognitive abilities but also specialized knowledge, which is often sparse and difficult for these neural-based SLMs to effectively capture. Therefore, NesyCD distills the general capabilities and specialized knowledge in LLMs using different manners. On the one hand, we distill only general abilities from teacher LLMs into the student SLMs of parameterized neural networks. On the other hand, for the specialized abilities and uncommon knowledge of a complex reasoning task, we employ a symbolic knowledge distillation approach to obtain and store the specialized knowledge within a symbolic knowledge base (KB). By decoupling general and specialized capabilities, the proposed NesyCD can achieve superior performance cost-effectively, utilizing smaller models and blending parameterized neural networks with symbolic KB. Moreover, the specialized KB generalizes well and is comprehended and manipulated by humans. Our experiments show that NesyCD significantly boosts SLMs' complex reasoning performance on in-domain (BBH, GSM8K) and out-of-domain (AGIEval, ARC) datasets. Notably, our approach enabled the LLaMA3-8B and Qwen2-7B to surpass GPT-3.5-turbo in performance and come close to matching LLaMA3-70B, despite the latter having nine times more parameters. Our code will be available at https://github.com/Xnhyacinth/NesyCD.

Federated Knowledge Graph Embedding (FKGE) has recently garnered considerable interest due to its capacity to extract expressive representations from distributed knowledge graphs, while concurrently safeguarding the privacy of individual clients. Existing FKGE methods typically harness the arithmetic mean of entity embeddings from all clients as the global supplementary knowledge, and learn a replica of global consensus entities embeddings for each client. However, these methods usually neglect the inherent semantic disparities among distinct clients. This oversight not only results in the globally shared complementary knowledge being inundated with too much noise when tailored to a specific client, but also instigates a discrepancy between local and global optimization objectives. Consequently, the quality of the learned embeddings is compromised. To address this, we propose Personalized Federated knowledge graph Embedding with client-wise relation Graph (PFedEG), a novel approach that employs a client-wise relation graph to learn personalized embeddings by discerning the semantic relevance of embeddings from other clients. Specifically, PFedEG learns personalized supplementary knowledge for each client by amalgamating entity embedding from its neighboring clients based on their "affinity" on the client-wise relation graph. Each client then conducts personalized embedding learning based on its local triples and personalized supplementary knowledge. We conduct extensive experiments on four benchmark datasets to evaluate our method against state-of-the-art models and results demonstrate the superiority of our method.

Common-sense and background knowledge is required to understand natural language, but in most neural natural language understanding (NLU) systems, this knowledge must be acquired from training corpora during learning, and then it is static at test time. We introduce a new architecture for the dynamic integration of explicit background knowledge in NLU models. A general-purpose reading module reads background knowledge in the form of free-text statements (together with task-specific text inputs) and yields refined word representations to a task-specific NLU architecture that reprocesses the task inputs with these representations. Experiments on document question answering (DQA) and recognizing textual entailment (RTE) demonstrate the effectiveness and flexibility of the approach. Analysis shows that our model learns to exploit knowledge in a semantically appropriate way.