Are Hypervectors Enough? Single-Call LLM Reasoning over Knowledge Graphs

Recent advances in large language models (LLMs) have enabled strong reasoning over structured and unstructured knowledge. When grounded on knowledge graphs (KGs), however, prevailing pipelines rely on neural encoders to embed and score symbolic paths, incurring heavy computation, high latency, and opaque decisions, which are limitations that hinder faithful, scalable deployment. We propose a lightweight, economical, and transparent KG reasoning framework, PathHD, that replaces neural path scoring with hyperdimensional computing (HDC). PathHD encodes relation paths into block-diagonal GHRR hypervectors, retrieves candidates via fast cosine similarity with Top-K pruning, and performs a single LLM call to produce the final answer with cited supporting paths. Technically, PathHD provides an order-aware, invertible binding operator for path composition, a calibrated similarity for robust retrieval, and a one-shot adjudication step that preserves interpretability while eliminating per-path LLM scoring. Extensive experiments on WebQSP, CWQ, and the GrailQA split show that PathHD (i) achieves comparable or better Hits@1 than strong neural baselines while using one LLM call per query, (ii) reduces end-to-end latency by 40-60% and GPU memory by 3-5 $\times$ thanks to encoder-free retrieval, and (iii) delivers faithful, path-grounded rationales that improve error diagnosis and controllability. These results demonstrate that HDC is a practical substrate for efficient KG-LLM reasoning, offering a favorable accuracy-efficiency-interpretability trade-off.