Multi-Hop Reasoning

Cyber-attacks continue to grow in scale and sophistication, yet existing network intrusion detection approaches lack the semantic depth required for path reasoning over attacker-victim interactions. We address this by first modelling network alerts as a knowledge graph, then formulating hyper-relational alert prediction as a hyper-relational knowledge graph completion (HR-KGC) problem, representing each network alert as a qualified statement (h, r, t, Q), where h and t are source and destination IPs, r denotes the attack type, and Q encodes flow-level metadata such as timestamps, ports, protocols, and attack intensity, going beyond standard KGC binary triples (h, r, t) that would discard this contextual richness. We introduce five models across three contributions: first, Hyper-relational Neural Bellman-Ford (HR-NBFNet) extends Neural Bellman-Ford Networks to the hyper-relational setting with qualifier-aware multi-hop path reasoning, while its multi-task variant MT-HR-NBFNet jointly predicts tail, relation, and qualifier-value within a single traversal pass; second, AlertStar fuses qualifier context and structural path information entirely in embedding space via cross-attention and learned path composition, and its multi-task extension MT-AlertStar eliminates the overhead of full knowledge graph propagation; third, HR-NBFNet-CQ extends qualifier-aware representations to answer complex first-order logic queries, including one-hop, two-hop chain, two-anchor intersection, and union, enabling multi-condition threat reasoning over the alert knowledge graph. Evaluated inductively on the Warden and UNSW-NB15 benchmarks across three qualifier-density regimes, AlertStar and MT-AlertStar achieve superior MR, MRR, and Hits@k, demonstrating that local qualifier fusion is both sufficient and more efficient than global path propagation for hyper-relational alert prediction.

Recent work reports strong performance from multi-agent LLM systems (MAS), but these gains are often confounded by increased test-time computation. When computation is normalized, single-agent systems (SAS) can match or outperform MAS, yet the theoretical basis and evaluation methodology behind this comparison remain unclear. We present an information-theoretic argument, grounded in the Data Processing Inequality, suggesting that under a fixed reasoning-token budget and with perfect context utilization, single-agent systems are more information-efficient. This perspective further predicts that multi-agent systems become competitive when a single agent's effective context utilization is degraded, or when more compute is expended. We test these predictions in a controlled empirical study across three model families (Qwen3, DeepSeek-R1-Distill-Llama, and Gemini 2.5), comparing SAS with multiple MAS architectures under matched budgets. We find that SAS consistently match or outperform MAS on multi-hop reasoning tasks when reasoning tokens are held constant. Beyond aggregate performance, we conduct a detailed diagnostic analysis of system behavior and evaluation methodology. We identify significant artifacts in API-based budget control (particularly in Gemini 2.5) and in standard benchmarks, both of which can inflate apparent gains from MAS. Overall, our results suggest that, for multi-hop reasoning tasks, many reported advantages of multi-agent systems are better explained by unaccounted computation and context effects rather than inherent architectural benefits, and highlight the importance of understanding and explicitly controlling the trade-offs between compute, context, and coordination in agentic systems.

The use of knowledge graphs for grounding agents in real-world Q&A applications has become increasingly common. Answering complex queries often requires multi-hop reasoning and the ability to navigate vast relational structures. Standard approaches rely on prompting techniques that steer large language models to reason over raw graph context, or retrieval-augmented generation pipelines where relevant subgraphs are injected into the context. These, however, face severe limitations with enterprise-scale KGs that cannot fit in even the largest context windows available today. We present GraphWalk, a problem-agnostic, training-free, tool-based framework that allows off-the-shelf LLMs to reason through sequential graph navigation, dramatically increasing performance across different tasks. Unlike task-specific agent frameworks that encode domain knowledge into specialized tools, GraphWalk equips the LLM with a minimal set of orthogonal graph operations sufficient to traverse any graph structure. We evaluate whether models equipped with GraphWalk can compose these operations into correct multi-step reasoning chains, where each tool call represents a verifiable step creating a transparent execution trace. We first demonstrate our approach on maze traversal, a problem non-reasoning models are completely unable to solve, then present results on graphs resembling real-world enterprise knowledge graphs. To isolate structural reasoning from world knowledge, we evaluate on entirely synthetic graphs with random, non-semantic labels. Our benchmark spans 12 query templates from basic retrieval to compound first-order logic queries. Results show that tool-based traversal yields substantial and consistent gains over in-context baselines across all model families tested, with gains becoming more pronounced as scale increases, precisely where in-context approaches fail catastrophically.

Large Language Models (LLMs) demonstrate impressive natural language capabilities but often struggle with knowledge-intensive reasoning tasks. Knowledge Base Question Answering (KBQA), which leverages structured Knowledge Graphs (KGs) exemplifies this challenge due to the need for accurate multi-hop reasoning. Existing approaches typically perform sequential reasoning steps guided by predefined pipelines, restricting flexibility and causing error cascades due to isolated reasoning at each step. To address these limitations, we propose KG-Hopper, a novel Reinforcement Learning (RL) framework that empowers compact open LLMs with the ability to perform integrated multi-hop KG reasoning within a single inference round. Rather than reasoning step-by-step, we train a Reasoning LLM that embeds the entire KG traversal and decision process into a unified ``thinking'' stage, enabling global reasoning over cross-step dependencies and dynamic path exploration with backtracking. Experimental results on eight KG reasoning benchmarks show that KG-Hopper, based on a 7B-parameter LLM, consistently outperforms larger multi-step systems (up to 70B) and achieves competitive performance with proprietary models such as GPT-3.5-Turbo and GPT-4o-mini, while remaining compact, open, and data-efficient. The code is publicly available at: https://github.com/Wangshuaiia/KG-Hopper.

Existing prompting paradigms structure LLM reasoning in limited topologies: Chain-of-Thought (CoT) produces linear traces, while Tree-of-Thought (ToT) performs branching search. Yet complex reasoning often requires merging intermediate results, revisiting hypotheses, and integrating evidence from multiple sources. We propose Network-of-Thought (NoT), a framework that models reasoning as a directed graph with typed nodes and edges, guided by a heuristic-based controller policy. Across four benchmarks (GSM8K, Game of 24, HotpotQA, ProofWriter) and three models (GPT-4o-mini, Llama-3.3-70B-Instruct, Qwen2.5-72B-Instruct), we investigate when network topology outperforms chain or tree structures, whether LLM-generated heuristics can guide graph-based reasoning search, and the computation-accuracy tradeoff across topologies, evaluating each method on accuracy, topology simplicity, and token efficiency. Our results show that CoT remains effective for sequential tasks with GPT-4o-mini (89.5% on GSM8K), while NoT surpasses ToT on multi-hop reasoning (91.0% vs.\ 88.0% on HotpotQA with LLM-as-Judge). With 72B open-source models, NoT achieves the highest accuracy on GSM8K (91.5%), and Qwen2.5-72B achieves the best multi-hop QA result overall (91.7% on HotpotQA). Self-generated controller heuristics outperform fixed and random strategies on logical reasoning, with uncertainty-only weighting achieving 57.0% on ProofWriter. We also find that evaluation methodology significantly impacts method rankings: string-match underestimates all methods on open-ended QA, with the largest gap for NoT, a pattern consistent across all three models (14--18 percentage point gap on HotpotQA).

Evaluating the reasoning abilities of large language models (LLMs) solely from final answers can obscure failures in intermediate steps, especially in multi-hop QA benchmarks without step-level annotations. To address this gap, we introduce Omanic, an open-domain 4-hop QA benchmark designed not only to measure final-answer accuracy but also to diagnose where reasoning breaks down. Omanic contains 10,296 machine-generated training examples (OmanicSynth) and 967 expert-reviewed human-annotated evaluation examples (OmanicBench), with each evaluation question decomposed into single-hop sub-questions, intermediate answers, and structured graph topologies. Experiments with proprietary and open-source LLMs show that Omanic is challenging, while step-wise analysis reveals a later-hop bottleneck, factual knowledge floor, and error propagation along reasoning chains. Fine-tuning on OmanicSynth transfers to six reasoning and mathematics benchmarks, yielding a 7.41-point average gain and validating its effectiveness as supervision for reasoning-capability transfer. We release the data at https://huggingface.co/datasets/li-lab/Omanic and the code at https://github.com/XiaojieGu/Omanic.

GraphRAG is increasingly adopted for converting unstructured corpora into graph structures to enable multi-hop reasoning. However, standard graph algorithms rely heavily on static connectivity and explicit edges, often failing in real-world scenarios where Knowledge Graphs (KGs) are noisy, sparse, or incomplete. To address this limitation, we introduce INSES (Intelligent Navigation and Similarity Enhanced Search), a dynamic framework designed to reason beyond explicit edges. INSES couples LLM-guided navigation, which prunes noise and steers exploration, with embedding-based similarity expansion to recover hidden links and bridge semantic gaps. Recognizing the computational cost of graph reasoning, we complement INSES with a lightweight router that delegates simple queries to Naïve RAG and escalates complex cases to INSES, balancing efficiency with reasoning depth. Experimental results show that INSES performs favorably compared to established RAG and GraphRAG baselines on multiple benchmarks. In particular, on the MINE benchmark, it exhibits notable robustness and adaptability across KGs constructed by varying methods. Our code and data are publicly available at https://github.com/hanggao-gh/INSES .

We present a Temporal Rule-Anchored Chain-of-Evidence (TRACE) on knowledge graphs for interpretable stock movement prediction that unifies symbolic relational priors, dynamic graph exploration, and LLM-guided decision making in a single end-to-end pipeline. The approach performs rule-guided multi-hop exploration restricted to admissible relation sequences, grounds candidate reasoning chains in contemporaneous news, and aggregates fully grounded evidence into auditable UP/DOWN verdicts with human-readable paths connecting text and structure. On an S&P~500 benchmark, the method achieves 55.1% accuracy, 55.7% precision, 71.5% recall, and 60.8% F1, surpassing strong baselines and improving recall and F1 over the best graph baseline under identical evaluation. The gains stem from (i) rule-guided exploration that focuses search on economically meaningful motifs rather than arbitrary walks, and (ii) text-grounded consolidation that selectively aggregates high-confidence, fully grounded hypotheses instead of uniformly pooling weak signals. Together, these choices yield higher sensitivity without sacrificing selectivity, delivering predictive lift with faithful, auditably interpretable explanations.

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data, often sourced from human annotations, generated from frontier LLMs, or scored by LLM-based verifiers. All three have considerable limitations: human-annotated datasets are small and expensive to curate, LLM-generated data is hallucination-prone and costly, and LLM-based verifiers are inaccurate and slow. In this work, we investigate a cheaper alternative: RL fine-tuning on rule-generated synthetic data for multi-hop reasoning tasks. We discover that LLMs fine-tuned on synthetic data perform significantly better on popular real-world question-answering benchmarks, despite the synthetic data containing only fictional knowledge. On stratifying performance by question difficulty, we find that synthetic data teaches LLMs to compose knowledge -- a fundamental and generalizable reasoning skill. Our work highlights rule-generated synthetic reasoning data as a free and scalable resource to improve LLM reasoning capabilities.

Answering complex first-order logic (FOL) queries on knowledge graphs is essential for reasoning. Symbolic methods offer interpretability but struggle with incomplete graphs, while neural approaches generalize better but lack transparency. Neural-symbolic models aim to integrate both strengths but often fail to capture the hierarchical structure of logical queries, limiting their effectiveness. We propose HYQNET, a neural-symbolic model for logic query reasoning that fully leverages hyperbolic space. HYQNET decomposes FOL queries into relation projections and logical operations over fuzzy sets, enhancing interpretability. To address missing links, it employs a hyperbolic GNN-based approach for knowledge graph completion in hyperbolic space, effectively embedding the recursive query tree while preserving structural dependencies. By utilizing hyperbolic representations, HYQNET captures the hierarchical nature of logical projection reasoning more effectively than Euclidean-based approaches. Experiments on three benchmark datasets demonstrate that HYQNET achieves strong performance, highlighting the advantages of reasoning in hyperbolic space.

Question Answering over Temporal Knowledge Graphs (TKGQA) has attracted growing interest for handling time-sensitive queries. However, existing methods still struggle with: 1) weak incorporation of temporal constraints in question representation, causing biased reasoning; 2) limited ability to perform explicit multi-hop reasoning; and 3) suboptimal fusion of language and graph representations. We propose a novel framework with temporal-aware question encoding, multi-hop graph reasoning, and multi-view heterogeneous information fusion. Specifically, our approach introduces: 1) a constraint-aware question representation that combines semantic cues from language models with temporal entity dynamics; 2) a temporal-aware graph neural network for explicit multi-hop reasoning via time-aware message passing; and 3) a multi-view attention mechanism for more effective fusion of question context and temporal graph knowledge. Experiments on multiple TKGQA benchmarks demonstrate consistent improvements over multiple baselines.

Current context augmentation methods, such as retrieval-augmented generation, play a crucial role in bridging a model's internal knowledge boundary and external evidence for multi-hop reasoning. However, they often follow a rigid policy and treat external retrieval as the default action at each step. Such brute-force context expansion incurs unnecessary computational cost and may degrade reasoning performance by saturating the context with redundant or weakly relevant evidence. In this paper, we propose cross-boundary Context Evolution (EvoCtx), a framework that models complex reasoning as an adaptive process of boundary-aware context evolution. EvoCtx dynamically decides whether the next reasoning transition should cross the current evidence boundary through retrieval or refine the reasoning state within the existing context. It estimates the semantic gap between the reasoning state and the accumulated evidence, and strategically alternates between boundary expansion and intra-boundary trajectory refinement. This eliminates redundant retrieval steps and preserves a compact, evidence-supported reasoning trajectory. Extensive experiments on challenging open-domain and multi-hop QA benchmarks demonstrate that EvoCtx significantly outperforms previous methods, offering an effective approach to complex reasoning tasks. The source code can be accessed at https://github.com/Anya-RB-Chen/EvoCtx.

Multi-hop kinship reasoning is a natural testbed for LLM compositionality, but existing benchmarks (notably CLUTRR) cover only the descriptive Eskimo system. We introduce KinshipQA, a procedurally-generated benchmark covering seven anthropologically-documented kinship systems (Eskimo, Sudanese, Hawaiian, Iroquois, Dravidian, Crow, Omaha) and up to six reasoning hops, with a tunable simulator horizon that eliminates exact-instance pretraining overlap. Evaluating six LLMs, we find a 40.9% accuracy drop when reasoning shifts from biological multi-hop to culturally-marked classification on the five non-descriptive systems. The drop holds for every non-descriptive system and is largest for the two skewing systems (Crow, Omaha), persists under chain-of-thought and few-shot prompting, and compounds with depth: at 5--6 hops cultural override falls to 10.6% while biological composition over the same chains remains at 58.6%. Under identical rule access humans reach 89.0% versus 50.7% for LLMs, so the questions are reliably solvable once the rule is supplied. Two follow-up experiments suggest distinct contributors. A fictional-rule control swapping system labels and kin terms for invented strings raises accuracy by 6.1%, implicating familiar English surface forms. An in-context-rule probe prepending the override rule helps skewing systems (+17.1%) but hurts non-skewing systems whose baseline already exceeds about 60% (-13.4%), consistent with a missing skewing prior alongside rule interference where the model already has a working approximation. Our code and data are publicly available on GitHub.

Complex query answering (CQA) goes beyond the widely studied link prediction task by addressing more sophisticated queries that require multi-hop reasoning over incomplete knowledge graphs (KGs). Research on neural and neurosymbolic CQA methods is still an emerging field. Almost all of these methods can be regarded as black-box models, which may raise concerns about user trust. Although neurosymbolic approaches like CQD are slightly more interpretable, allowing intermediate results to be tracked, the importance of different parts of the query remains unexplained. In this paper, we propose CQD-SHAP, a novel framework that computes the contribution of each query part to the ranking of a specific answer. This contribution explains the value of leveraging a neural predictor that can infer new knowledge from an incomplete KG, rather than a symbolic approach relying solely on existing facts in the KG. CQD-SHAP is formulated based on Shapley values from cooperative game theory and satisfies all fundamental Shapley axioms. Automated evaluation of these explanations in terms of necessary and sufficient explanations, and comparisons with various baselines, show the consistent effectiveness of this approach across all studied datasets and query types.

Large Language Models (LLMs) excel at multi-hop reasoning in distribution, yet fail on unseen compositions, a phenomenon known as the curse of two-hop reasoning. In this work, we argue that this phenomenon can be attributed to a missing supervision on the bridge entity. We formalize this gap by introducing identity bridge, a minimal supervision that enforces a identity mapping on bridge tokens. Under this supervision, even a one-layer transformer with uniform attention (Emb-MLP) can achieve out-of-distribution (OOD) two-hop generalization. We provide a theoretical analysis demonstrating that identity bridge induces an implicit regularization effect, leading the model to establish a direct subject-to-answer association. From an empirical perspective, the performance of standard GPT-2 models aligns closely with simple Emb--MLP models across varying levels of problem complexity. Finally, analyses of fine-tuned mainstream LLMs indicate that correct two-hop predictions consistently coincide with the establishment of a subject-to-answer relationship, extending our findings to realistic settings.

Large language models (LLMs) have shown remarkable capabilities in natural language processing. However, in knowledge graph question answering tasks (KGQA), there remains the issue of answering questions that require multi-hop reasoning. Existing methods rely on entity vector matching, but the purpose of the question is abstract and difficult to match with specific entities. As a result, it is difficult to establish reasoning paths to the purpose, which leads to information loss and redundancy. To address this issue, inspired by human reverse thinking, we propose Ontology-Guided Reverse Thinking (ORT), a novel framework that constructs reasoning paths from purposes back to conditions. ORT operates in three key phases: (1) using LLM to extract purpose labels and condition labels, (2) constructing label reasoning paths based on the KG ontology, and (3) using the label reasoning paths to guide knowledge retrieval. Experiments on the WebQSP and CWQ datasets show that ORT achieves state-of-the-art performance and significantly enhances the capability of LLMs for KGQA.

Complex query answering (CQA) on knowledge graphs (KGs) is gaining momentum as a challenging reasoning task. In this paper, we show that the current benchmarks for CQA might not be as complex as we think, as the way they are built distorts our perception of progress in this field. For example, we find that in these benchmarks, most queries (up to 98% for some query types) can be reduced to simpler problems, e.g., link prediction, where only one link needs to be predicted. The performance of state-of-the-art CQA models decreases significantly when such models are evaluated on queries that cannot be reduced to easier types. Thus, we propose a set of more challenging benchmarks composed of queries that require models to reason over multiple hops and better reflect the construction of real-world KGs. In a systematic empirical investigation, the new benchmarks show that current methods leave much to be desired from current CQA methods.

Causal video question answering (QA) has garnered increasing interest, yet existing datasets often lack depth in causal reasoning. To address this gap, we capitalize on the unique properties of cartoons and construct CausalChaos!, a novel, challenging causal Why-QA dataset built upon the iconic "Tom and Jerry" cartoon series. Cartoons use the principles of animation that allow animators to create expressive, unambiguous causal relationships between events to form a coherent storyline. Utilizing these properties, along with thought-provoking questions and multi-level answers (answer and detailed causal explanation), our questions involve causal chains that interconnect multiple dynamic interactions between characters and visual scenes. These factors demand models to solve more challenging, yet well-defined causal relationships. We also introduce hard incorrect answer mining, including a causally confusing version that is even more challenging. While models perform well, there is much room for improvement, especially, on open-ended answers. We identify more advanced/explicit causal relationship modeling & joint modeling of vision and language as the immediate areas for future efforts to focus upon. Along with the other complementary datasets, our new challenging dataset will pave the way for these developments in the field. Project Page: https://github.com/LUNAProject22/CausalChaos