Large Language Models (LLMs) have achieved impressive reasoning abilities, but struggle with temporal understanding, especially when questions involve multiple entities, compound operators, and evolving event sequences. Temporal Knowledge Graphs (TKGs), which capture vast amounts of temporal facts in a structured format, offer a reliable source for temporal reasoning. However, existing TKG-based LLM reasoning methods still struggle with four major challenges: maintaining temporal faithfulness in multi-hop reasoning, achieving multi-entity temporal synchronization, adapting retrieval to diverse temporal operators, and reusing prior reasoning experience for stability and efficiency. To address these issues, we propose MemoTime, a memory-augmented temporal knowledge graph framework that enhances LLM reasoning through structured grounding, recursive reasoning, and continual experience learning. MemoTime decomposes complex temporal questions into a hierarchical Tree of Time, enabling operator-aware reasoning that enforces monotonic timestamps and co-constrains multiple entities under unified temporal bounds. A dynamic evidence retrieval layer adaptively selects operator-specific retrieval strategies, while a self-evolving experience memory stores verified reasoning traces, toolkit decisions, and sub-question embeddings for cross-type reuse. Comprehensive experiments on multiple temporal QA benchmarks show that MemoTime achieves overall state-of-the-art results, outperforming the strong baseline by up to 24.0%. Furthermore, MemoTime enables smaller models (e.g., Qwen3-4B) to achieve reasoning performance comparable to that of GPT-4-Turbo.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating external knowledge.Current hybrid RAG system retrieves evidence from both knowledge graphs (KGs) and text documents to support LLM reasoning.However, it faces challenges like handling multi-hop reasoning, multi-entity questions, multi-source verification, and effective graph utilization.To address these limitations, we present HydraRAG, a training-free framework that unifies graph topology, document semantics, and source reliability to support deep, faithful reasoning in LLMs.HydraRAG handles multi-hop and multi-entity problems through agent-driven exploration that combines structured and unstructured retrieval, increasing both diversity and precision of evidence.To tackle multisource verification, HydraRAG uses a tri-factor cross-source verification (source trustworthiness assessment, cross-source corroboration, and entity-path alignment), to balance topic relevance with cross-modal agreement.By leveraging graph structure, HydraRAG fuses heterogeneous sources, guides efficient exploration, and prunes noise early.Comprehensive experiments on seven benchmark datasets show that HydraRAG achieves overall state-of-theart results on all benchmarks with GPT-3.5, outperforming the strong hybrid baseline ToG-2 by an average of 20.3% and up to 30.1%.Furthermore, HydraRAG enables smaller models (e.g., Llama-3.1-8B) to achieve reasoning performance comparable to that of GPT-4-Turbo.The source code is available on https: //stevetantan.github.io/HydraRAG/.

Large Language Models (LLMs) have achieved impressive results in various tasks but struggle with hallucination problems and lack of relevant knowledge, especially in deep complex reasoning and knowledge-intensive tasks.Knowledge Graphs (KGs), which capture vast amounts of facts in a structured format, offer a reliable source of knowledge for reasoning.However, existing KG-based LLM reasoning methods face challenges like handling multi-hop reasoning, multi-entity questions, and effectively utilizing graph structures.To address these issues, we propose Paths-over-Graph (PoG), a novel method that enhances LLM reasoning by integrating knowledge reasoning paths from KGs, improving the interpretability and faithfulness of LLM outputs.PoG tackles multi-hop and multi-entity questions through a three-phase dynamic multi-hop path exploration, which combines the inherent knowledge of LLMs with factual knowledge from KGs.In order to improve the efficiency, PoG prunes irrelevant information from the graph exploration first and introduces efficient three-step pruning techniques that incorporate graph structures, LLM prompting, and a pre-trained language model (e.g., SBERT) to effectively narrow down the explored candidate paths.This ensures all reasoning paths contain highly relevant information captured from KGs, making the reasoning faithful and interpretable in problem-solving.PoG innovatively utilizes graph structure to prune the irrelevant noise and represents the first method to implement multi-entity deep path detection on KGs for LLM reasoning tasks.Comprehensive experiments on five benchmark KGQA datasets demonstrate PoG outperforms the stateof-the-art method ToG across GPT-3.5-Turbo and GPT-4, achieving an average accuracy improvement of 18.9%.Notably, PoG with GPT-3.5-Turbosurpasses ToG with GPT-4 by up to 23.9%.

k-peak is a well-regarded cohesive subgraph model in graph analysis. However, the k-peak model only considers the direct neighbors of a vertex, consequently limiting its capacity to uncover higher-order structural information of the graph. To address this limitation, we propose a new model in this paper, named (k,h)-peak, which incorporates higher-order (h-hops) neighborhood information of vertices. Employing the (k,h)-peak model, we explore the higher-order peak decomposition problem that calculates the vertex peakness for all conceivable k values given a particular h. To tackle this problem efficiently, we propose an advanced local computation based algorithm, which is parallelizable, and additionally, devise novel pruning strategies to mitigate unnecessary computation. Experiments as well as case studies are conducted on real-world datasets to evaluate the efficiency and effectiveness of our proposed solutions.