# Encoder-Free Knowledge-Graph Reasoning with LLMs via Hyperdimensional Path Retrieval

arXiv: https://arxiv.org/abs/2512.09369 · HTML: https://mlsanity.com/paper/2512.09369/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 18 of 18)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [The Web as a Knowledge-base for Answering Complex Questions](https://mlsanity.com/paper/1803.06643/) (2018)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning](https://mlsanity.com/paper/2310.01061/) (2023)
- [Demonstrate-Search-Predict: Composing retrieval and language models for knowledge-intensive NLP](https://mlsanity.com/paper/2212.14024/) (2022)
- [Think-on-Graph: Deep and Responsible Reasoning of Large Language Model on Knowledge Graph](https://mlsanity.com/paper/2307.07697/) (2023)
- [UniKGQA: Unified Retrieval and Reasoning for Solving Multi-hop Question Answering Over Knowledge Graph](https://mlsanity.com/paper/2212.00959/) (2022)
- [Subgraph Retrieval Enhanced Model for Multi-hop Knowledge Base Question Answering](https://mlsanity.com/paper/2202.13296/) (2022)
- [KG-Agent: An Efficient Autonomous Agent Framework for Complex Reasoning over Knowledge Graph](https://mlsanity.com/paper/2402.11163/) (2024)
- [TransferNet: An Effective and Transparent Framework for Multi-hop Question Answering over Relation Graph](https://mlsanity.com/paper/2104.07302/) (2021)
- [Generate-on-Graph: Treat LLM as both Agent and KG in Incomplete Knowledge Graph Question Answering](https://mlsanity.com/paper/2404.14741/) (2024)
- [FiDeLiS: Faithful Reasoning in Large Language Model for Knowledge Graph Question Answering](https://mlsanity.com/paper/2405.13873/) (2024)
- [Generalized Holographic Reduced Representations](https://mlsanity.com/paper/2405.09689/) (2024)

## Built on by (most cited first, 1 of 1)

- [STReasoner: Empowering LLMs for Spatio-Temporal Reasoning in Time Series via Spatial-Aware Reinforcement Learning](https://mlsanity.com/paper/2601.03248/) (2026)

## Abstract (arXiv)

Recent progress in large language models (LLMs) has made knowledge-grounded reasoning increasingly practical, yet KG-based QA systems often pay a steep price in efficiency and transparency. In typical pipelines, symbolic paths are scored by neural encoders or repeatedly re-ranked by multiple LLM calls, which inflates latency and GPU cost and makes the decision process hard to audit. We introduce PathHD, an encoder-free framework for knowledge-graph reasoning that couples hyperdimensional computing (HDC) with a single LLM call per query. Given a query, PathHD represents relation paths as block-diagonal GHRR hypervectors, retrieves candidate paths using a calibrated blockwise cosine similarity with Top-K pruning, and then performs a one-shot LLM adjudication that outputs the final answer together with supporting, citeable paths. The design is enabled by three technical components: (i) an order-sensitive, non-commutative binding operator for composing multi-hop paths, (ii) a robust similarity calibration that stabilizes hypervector retrieval, and (iii) an adjudication stage that preserves interpretability while avoiding per-path LLM scoring. Across WebQSP, CWQ, and GrailQA, PathHD matches or improves Hits@1 compared to strong neural baselines while using only one LLM call per query, reduces end-to-end latency by 40-60%, and lowers GPU memory by 3-5× due to encoder-free retrieval. Overall, the results suggest that carefully engineered HDC path representations can serve as an effective substrate for efficient and faithful KG-LLM reasoning, achieving a strong accuracy-efficiency-interpretability trade-off.