Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly--producing correct answers without explicitly verbalizing intermediate steps--but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a threestage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

Retrieval-augmented generation (RAG) has proven effective in integrating knowledge into large language models (LLMs). However, conventional RAGs struggle to capture complex relationships between pieces of knowledge, limiting their performance in intricate reasoning that requires integrating knowledge from multiple sources. Recently, graph-enhanced retrieval augmented generation (GraphRAG) builds graph structure to explicitly model these relationships, enabling more effective and efficient retrievers. Nevertheless, its performance is still hindered by the noise and incompleteness within the graph structure. To address this, we introduce GFM-RAG, a novel graph foundation model (GFM) for retrieval augmented generation. GFM-RAG is powered by an innovative graph neural network that reasons over graph structure to capture complex query-knowledge relationships.

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Query embedding (QE)---which aims to embed entities and first-order logical (FOL) queries in low-dimensional spaces---has shown great power in multi-hop reasoning over knowledge graphs. Recently, embedding entities and queries with geometric shapes becomes a promising direction, as geometric shapes can naturally represent answer sets of queries and logical relationships among them. However, existing geometry-based models have difficulty in modeling queries with negation, which significantly limits their applicability. To address this challenge, we propose a novel query embedding model, namely \textbf{Con}e \textbf{E}mbeddings (ConE), which is the first geometry-based QE model that can handle all the FOL operations, including conjunction, disjunction, and negation. Specifically, ConE represents entities and queries as Cartesian products of two-dimensional cones, where the intersection and union of cones naturally model the conjunction and disjunction operations. By further noticing that the closure of complement of cones remains cones, we design geometric complement operators in the embedding space for the negation operations. Experiments demonstrate that ConE significantly outperforms existing state-of-the-art methods on benchmark datasets.

RAG (Retrieval-Augmented Generation) systems and web agents are increasingly evaluated on multi-hop deep search tasks, yet current practice suffers from two major limitations. First, most benchmarks leak the reasoning path in the question text, allowing models to follow surface cues rather than discover reasoning chains autonomously. Second, evaluation is typically reduced to a single pass rate, which collapses diverse behaviours into one score and obscures whether failures stem from inadequate search, poor knowledge use, or inappropriate refusal. To address these issues, we present WebDetective, a benchmark of hint-free multi-hop questions paired with a controlled Wikipedia sandbox that ensures full traceability of model actions, and a holistic evaluation framework that separates search sufficiency, knowledge utilisation, and refusal behaviour. Our evaluation of 25 state-of-the-art models reveals systematic weaknesses across all architectures: models struggle with knowledge utilisation despite having sufficient evidence and demonstrate near-absent appropriate refusal when evidence is lacking. These patterns expose a fundamental gap: today's systems excel at executing given reasoning paths but fail when required to discover them. We develop an agentic workflow, EvidenceLoop, that explicitly targets the challenges our benchmark identifies, incorporating verification loops and systematic evidence tracking that improve both search and synthesis capabilities. This baseline demonstrates that WebDetective's diagnostic framework can guide concrete architectural improvements, establishing our benchmark as a critical tool for developing genuinely autonomous reasoning systems rather than pattern-following agents.

Abstract--Multi-hop question answering over knowledge graphs remains computationally challenging due to the combinatorial explosion of possible reasoning paths. Recent approaches rely on expensive Large Language Model (LLM) inference for both entity linking and path ranking, limiting their practical deployment. Additionally, LLM-generated answers often lack verifiable grounding in structured knowledge. We present two complementary hybrid algorithms that address both efficiency and verifiability: (1) LLM-Guided Planning that uses a single LLM call to predict relation sequences executed via breadth-first search, achieving near-perfect accuracy (micro-F1 > 0.90) while ensuring all answers are grounded in the knowledge graph, and (2) Embedding-Guided Neural Search that eliminates LLM calls entirely by fusing text and graph embeddings through a lightweight 6.7M-parameter edge scorer, achieving over 100 speedup with competitive accuracy. Through knowledge distillation, we compress planning capability into a 4B-parameter model that matches large-model performance at zero API cost. Evaluation on MetaQA demonstrates that grounded reasoning consistently outperforms ungrounded generation, with structured planning proving more transferable than direct answer generation. Our results show that verifiable multi-hop reasoning does not require massive models at inference time, but rather the right architectural inductive biases combining symbolic structure with learned representations. Knowledge graphs (KGs) have emerged as powerful structures for representing domain-specific, structured information that supports verifiable, multi-hop reasoning. Meanwhile, large language models (LLMs) trained on vast web-scale corpora have achieved impressive fluency and generalization across a wide range of tasks.

Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly -- producing correct answers without explicitly verbalizing intermediate steps -- but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a three-stage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

Existing tabular reasoning benchmarks mostly test models on small, uniform tables, underrepresenting the complexity of real-world data and giving an incomplete view of Large Language Models' (LLMs) reasoning abilities. Real tables are long, heterogeneous, and domain-specific, mixing structured fields with free text and requiring multi-hop reasoning across thousands of tokens. To address this gap, we introduce RUST-BENCH, a benchmark of 7966 questions from 2031 real-world tables spanning two domains: i) RB-Science (NSF grant records) and ii) RB-Sports (NBA statistics). Unlike prior work, RUST-BENCH evaluates LLMs jointly across scale, heterogeneity, domain specificity, and reasoning complexity. Experiments with open-source and proprietary models show that LLMs struggle with heterogeneous schemas and complex multi-hop inference, revealing persistent weaknesses in current architectures and prompting strategies. RUST-BENCH establishes a challenging new testbed for advancing tabular reasoning research.

Large Language Models have been shown to contain extensive world knowledge in their parameters, enabling impressive performance on many knowledge intensive tasks. However, when deployed in novel settings, LLMs often encounter situations where they must integrate parametric knowledge with new or unfamiliar information. In this work, we explore whether LLMs can combine knowledge in-context with their parametric knowledge through the lens of counterfactual reasoning. Through synthetic and real experiments in multi-hop reasoning problems, we show that LLMs generally struggle with counterfactual reasoning, often resorting to exclusively using their parametric knowledge. Moreover, we show that simple post-hoc finetuning can struggle to instill counterfactual reasoning ability - often leading to degradation in stored parametric knowledge. Ultimately, our work reveals important limitations of current LLM's abilities to re-purpose parametric knowledge in novel settings. Benchmarks like NaturalQuestions and HotpotQA have driven progress on recall-based and multi-hop reasoning, but they primarily evaluate a model's ability to regurgitate stored facts or compose chains of parametric knowledge without new external inputs (Y ang et al., 2018; Kwiatkowski et al., 2019). In contrast, many real-world scenarios require LLMs to integrate their pretrained knowledge with novel or hypothetical information provided at inference time. For example, consider a counterfactual query: "If Paris were located in Italy, in which country would the Eiffel T ower stand?"