For large language models (LLMs), reasoning over graphs can help solve many problems. Prior work has tried to improve LLM graph reasoning through different training methods, but the merits of such approaches remain unclear and the limitations of each approach with respect to generalizability of reasoning are often not thoroughly explored. In this paper we systematically compare the ability of LLMs to learn fundamental graph tasks across a variety of training methods and their ability to generalize out of distribution across various dimensions. We highlight key tradeoffs between training methods, e.g., training specialized graph encoders and fusing their embeddings with LLMs consistently collapses in terms of generalizability; however, no single method shows clear superiority across all dimensions of generalizability, regardless of the size of the model.

Text-to-SQL aims to translate natural language queries into SQL statements, which is practical as it enables anyone to easily retrieve the desired information from databases. Recently, many existing approaches tackle this problem with Large Language Models (LLMs), leveraging their strong capability in understanding user queries and generating corresponding SQL code. Yet, the parametric knowledge in LLMs might be limited to covering all the diverse and domain-specific queries that require grounding in various database schemas, which makes generated SQLs less accurate oftentimes. To tackle this, we propose constructing the knowledge base for text-to-SQL, a foundational source of knowledge, from which we retrieve and generate the necessary knowledge for given queries. In particular, unlike existing approaches that either manually annotate knowledge or generate only a few pieces of knowledge for each query, our knowledge base is comprehensive, which is constructed based on a combination of all the available questions and their associated database schemas along with their relevant knowledge, and can be reused for unseen databases from different datasets and domains. We validate our approach on multiple text-to-SQL datasets, considering both the overlapping and non-overlapping database scenarios, where it outperforms relevant baselines substantially.