Relational Reasoning

Video Scene Graph Generation aims to obtain structured semantic representations of objects and their relationships in videos for high-level understanding. However, existing methods still have limitations in handling long-tail distributions. This paper proposes the Frequency-guided Relational Multi-level Reasoning (FReMuRe) model, which enhances the modeling ability of long-tail relationships from a mechanism perspective. We introduce relation-specific branches to deal gradient conflicts, yielding more balanced and tail-aware learning. And we design a frequency-aware dual-branch predicate embedding network to model high-frequency and low-frequency relationships separately and improve the recall rate of tail classes through gated fusion. Meanwhile, we propose two types of interchangeable relation classification heads: Bayesian Head for uncertainty estimation and new Gaussian Mixture Model Head to enhance intra-class diversity. Experimental results show that FReMuRe significantly improves the recall rate of long-tail relationships and overall reasoning robustness on the Action Genome dataset.

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models often focus on structured inputs such as tables, graphs, or synthetic tasks, and do not isolate the difficulty introduced by higher-arity relational binding. We study this problem through the lens of Relational Complexity (RC), which we define as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty while controlling for confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Across frontier LLMs, performance degrades consistently and monotonically as RC increases, even when the total number of entities is held fixed. This failure mode persists with increased test-time compute and in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than to insufficient inference steps or lack of exposure to examples. Our results identify a regime of higher-arity reasoning in which current models struggle, and motivate re-examining benchmarks through the lens of relational complexity.

Multi-document Multi-entity Question Answering inherently demands models to track implicit logic between multiple entities across scattered documents. However, existing Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) frameworks suffer from critical limitations: standard RAG's vector similarity-based coarse-grained retrieval often omits critical facts, graph-based RAG fails to efficiently integrate fragmented complex relationship networks, and both lack schema awareness, leading to inadequate cross-document evidence chain construction and inaccurate entity relationship deduction. To address these challenges, we propose DocSage, an end-to-end agentic framework that integrates dynamic schema discovery, structured information extraction, and schema-aware relational reasoning with error guarantees. DocSage operates through three core modules: (1) A schema discovery module dynamically infers query-specific minimal joinable schemas to capture essential entities and relationships; (2) An extraction module transforms unstructured text into semantically coherent relational tables, enhanced by error-aware correction mechanisms to reduce extraction errors; (3) A reasoning module performs multi-hop relational reasoning over structured tables, leveraging schema awareness to efficiently align cross-document entities and aggregate evidence. This agentic design offers three key advantages: precise fact localization via SQL-powered indexing, natural support for cross-document entity joins through relational tables, and mitigated LLM attention diffusion via structured representation. Evaluations on two MDMEQA benchmarks demonstrate that DocSage significantly outperforms state-of-the-art long-context LLMs and RAG systems, achieving more than 27% accuracy improvements respectively.

Graph-based retrieval-augmented generation (RAG) methods, typically built on knowledge graphs (KGs) with binary relational facts, have shown promise in multi-hop open-domain QA. However, their rigid retrieval schemes and dense similarity search often introduce irrelevant context, increase computational overhead, and limit relational expressiveness. In contrast, n-ary hypergraphs encode higher-order relational facts that capture richer inter-entity dependencies and enable shallower, more efficient reasoning paths. To address this limitation, we propose HyperRAG, a RAG framework tailored for n-ary hypergraphs with two complementary retrieval variants: (i) HyperRetriever learns structural-semantic reasoning over n-ary facts to construct query-conditioned relational chains. It enables accurate factual tracking, adaptive high-order traversal, and interpretable multi-hop reasoning under context constraints. (ii) HyperMemory leverages the LLM's parametric memory to guide beam search, dynamically scoring n-ary facts and entities for query-aware path expansion. Extensive evaluations on WikiTopics (11 closed-domain datasets) and three open-domain QA benchmarks (HotpotQA, MuSiQue, and 2WikiMultiHopQA) validate HyperRAG's effectiveness. HyperRetriever achieves the highest answer accuracy overall, with average gains of 2.95% in MRR and 1.23% in Hits@10 over the strongest baseline. Qualitative analysis further shows that HyperRetriever bridges reasoning gaps through adaptive and interpretable n-ary chain construction, benefiting both open and closed-domain QA.

Learning algorithmic computation often requires explicit relational intermediate states, yet many graph processors maintain their primary states on individual entities. We introduce \fnet and Pivotal Attention (PA), which maintain ordered pair states and update a target relation $(i,k)$ by attending over candidates formed from $(i,j)$ and $(j,k)$ for every pivot $j$. Motivated by the pair-and-pivot structure of Floyd--Warshall, PA learns relation composition and pivot weighting in parallel rather than executing its ordered min-plus recurrence. The \kfnet{k} framework extends this operation to ordered $k$-tuples, with Self-Attention and PA as its $k=1$ and $k=2$ cases at the attention-operation level. Under atomic tuple initialization and invariant readout, we show that \kfnet{k} is no more graph-discriminative than k-FWL; on BREC, each evaluated variant matches the success set of its corresponding WL reference. \fnet further achieves 96.64% mean accuracy under the reported CLRS-30 protocol and a 99.8% optimality rate with 10 samples on held-out non-metric TSP instances.