Biomedical knowledge graphs (KGs) offer structured medical knowledge that can ground large language model (LLM) reasoning in clinical diagnosis application, yet how KG signal should be integrated into LLMs remains an open question. We present a systematic study spanning five KG task formulations, three training paradigms, two KGs, and three base LLMs. At the task level, all paradigms improve over the non-finetuned baseline, but methods with comparable in-domain accuracy show substantially different knowledge transfer behavior. We introduce Gradient Intervention Density (GID) to measure how broadly an optimizer modifies the pretrained model. GID reveals a clear divide: KG-judgment training under KL regularization produces sparse, localized updates (a regime we term as surgical alignment), while task-specific SFT produces dense ones. A controlled ablation shows that the objective and KL contribute to sparsity independently, and the paradigms that produce sparse updates also improve reasoning quality, even when their in-domain accuracy is lower than task-specific SFT. Assessing KG-LLM integration thus requires complementing accuracy with optimization-geometry diagnostics. Our implementation can be found at https://github.com/LARK-NLP-Lab/Surgical-Alignment.

Knowledge graphs (KGs) are increasingly integrated with large language models (LLMs) to provide structured, verifiable reasoning. A core operation in this integration is multi-hop retrieval, yet existing systems struggle to balance efficiency, scalability, and interpretability. We introduce LogosKG, a novel, hardware-aligned framework that enables scalable and interpretable k-hop retrieval on large KGs by building on symbolic KG formulations and executing traversal as hardware-efficient operations over decomposed subject, object, and relation representations. To scale to billion-edge graphs, LogosKG integrates degree-aware partitioning, cross-graph routing, and on-demand caching. Experiments show substantial efficiency gains over CPU and GPU baselines without loss of retrieval fidelity. With proven performance in KG retrieval, a downstream two-round KG-LLM interaction demonstrates how LogosKG enables large-scale, evidence-grounded analysis of how KG topology, such as hop distribution and connectivity, shapes the alignment between structured biomedical knowledge and LLM diagnostic reasoning, thereby opening the door for next-generation KG-LLM integration. The source code is publicly available at https://github.com/LARK-NLP-Lab/LogosKG, and an online demo is available at https://lark-nlp-lab-logoskg.hf.space/.