Knowledge Graphs

Knowledge Distillation (KD) can transfer the reasoning abilities of large models to smaller ones, which can reduce the costs to generate Chain-of-Thoughts for reasoning tasks. KD methods typically ask the student to mimic the teacher's distribution over the entire output. However, a student with limited capacity can be overwhelmed by such extensive supervision causing a distribution mismatch, especially in complex reasoning tasks. We propose Token-Selective Dual Knowledge Distillation (TSD-KD), a framework for student-centric distillation. TSD-KD focuses on distilling important tokens for reasoning and encourages the student to explain reasoning in its own words. TSD-KD combines indirect and direct distillation. \textit{Indirect} distillation uses a weak form of feedback based on preference ranking. The student proposes candidate responses generated on its own; the teacher re-ranks those candidates as indirect feedback without enforcing its entire distribution. \textit{Direct} distillation uses distribution matching; however, it selectively distills tokens based on the relative confidence between teacher and student. Finally, we add \textit{entropy regularization} to maintain the student's confidence during distillation. Overall, our method provides the student with targeted and indirect feedback to support its own reasoning process and to facilitate self-improvement. The experiments show the state-of-the-art performance of TSD-KD on 10 challenging reasoning benchmarks, outperforming the baseline and runner-up in accuracy by up to 54.4\% and 40.3\%, respectively. Notably, a student trained by TSD-KD even outperformed its own teacher model in four cases by up to 20.3\%. The source code is available at \href{https://github.com/kmswin1/TSD-KD}{https://github.com/kmswin1/TSD-KD}.

Knowledge editing and machine unlearning are two popular approaches for large language models (LLMs) to stay up-to-date. However, the knowledge updating mechanism of LLMs remains largely unexplored due to insufficient, isolated, and small-scale evaluation. For instance, are LLMs similar to humans in modifying certain knowledge? What differs editing and unlearning as training data increases? This paper proposes KnowledgeSmith, a unified framework to systematically understand the updating mechanism of LLMs. We first cast editing and unlearning as instances of one constrained optimization problem. Then, we propose an automatic dataset generator that provides structured interventions across multiple graph levels and data scales, enabling controlled studies of how different modification strategies propagate through model knowledge. Extensive experiments demonstrate nuanced insights over knowledge propagation, plasticity scaling, consistency, and robustness. For instance, our results show that LLMs do not exhibit similar updating as humans for different levels of knowledge, and there exists consistency-capacity trade-off. We hope our findings can offer suggestions to the design of more reliable and scalable strategies.

Retrieval-Augmented Generation (RAG) systems enhance large language models (LLMs) by incorporating external knowledge bases, but this may expose them to extraction attacks, leading to potential copyright and privacy risks. However, existing extraction methods typically rely on malicious inputs such as prompt injection or jailbreaking, making them easily detectable via input- or output-level detection. In this paper, we introduce **I**mplicit **K**nowledge **E**xtraction **A**ttack (**IKEA**), which conducts *Knowledge Extraction* on RAG systems through benign queries. Specifically, **IKEA** first leverages anchor concepts—keywords related to internal knowledge—to generate queries with a natural appearance, and then designs two mechanisms that lead anchor concepts to thoroughly "explore" the RAG's knowledge: (1) Experience Reflection Sampling, which samples anchor concepts based on past query-response histories, ensuring their relevance to the topic; (2) Trust Region Directed Mutation, which iteratively mutates anchor concepts under similarity constraints to further exploit the embedding space. Extensive experiments demonstrate **IKEA**'s effectiveness under various defenses, surpassing baselines by over 80% in extraction efficiency and 90\% in attack success rate. Moreover, the substitute RAG system built from **IKEA**'s extractions shows close performance to the original RAG and outperforms those based on baselines across multiple evaluation tasks, underscoring the stealthy copyright infringement risk in RAG systems.

This paper studies the problem of open-set graph anomaly detection, which aims to generalize a graph neural network (GNN) trained with a small number of both normal and abnormal nodes to detect unseen anomalies different from training anomalies during inference. This problem is highly challenging due to both the data scarcity of unseen anomalies and the label scarcity for training nodes. Towards this end, we propose a novel approach named Dynamic Multi-sample Mixup with Gradient Exploration (DEMO) for open-set graph anomaly detection. The core of our proposed DEMO is to leverage a dynamic framework to adapt the optimization procedure with high generalizability. In particular, our DEMO first adaptively fuses multiple seen nodes to simulate the unseen anomalies, which expands the decision boundary for the detection model with enhanced generalizability. Moreover, we dynamically adjust sample weights based on their energy gradients to prioritize uncertain and informative nodes, ensuring a robust optimization procedure. To further address both label scarcity and severe class imbalance, we maintain a memory bank of historical records to guide the pseudo-labeling process of unlabeled nodes. Extensive experiments on various benchmark datasets validate the superiority of the proposed DEMO in comparison to various baselines.

Large language models (LLMs) excel at complex reasoning but remain limited by static and incomplete parametric knowledge. Retrieval-augmented generation (RAG) mitigates this by incorporating external knowledge, yet existing RAGs struggle with knowledge-intensive tasks due to fragmented information and weak modeling of knowledge structure. Graphs offer a natural way to model relationships within knowledge, but LLMs are inherently unstructured and cannot effectively reason over graph-structured data. Recent graph-enhanced RAG (GraphRAG) attempts to bridge this gap by constructing tailored graphs and enabling LLMs to reason on them. However, these methods often depend on ad-hoc graph designs, heuristic search, or costly agent pipelines, which hinder scalability and generalization. To address these challenges, we present G-reasoner, a unified framework that integrates graph and language foundation models for scalable reasoning over diverse graph-structured knowledge. Central to our approach is QuadGraph, a standardized four-layer abstraction that unifies heterogeneous knowledge sources into a common graph representation. Building on this, we introduce a 34M-parameter graph foundation model (GFM) that jointly captures graph topology and textual semantics, and is integrated with LLMs to enhance reasoning in downstream applications. To ensure scalability and efficiency, mixed-precision training and distributed message-passing are implemented to scale GFM with more GPUs. Extensive experiments on six benchmarks show that G-reasoner consistently outperforms state-of-the-art baselines, significantly enhances LLM reasoning, and achieves strong efficiency and cross-graph generalization.

Complex networks model the structure and function of critical technological, biological, and communication systems. Network dismantling, the targeted removal of nodes to fragment a network, is essential for analyzing and improving system robustness. Existing dismantling methods suffer from key limitations: they depend on global structural knowledge, exhibit slow running times on large networks, and overlook the network’s latent geometry, a key feature known to govern the dynamics of complex systems. Motivated by these findings, we introduce Latent Geometry-Driven Network Automata (LGD-NA), a novel framework that leverages local network automata rules to approximate effective link distances between interacting nodes. LGD-NA is able to identify critical nodes and capture latent manifold information of a network for effective and efficient dismantling. We show that this latent geometry-driven approach outperforms all existing dismantling algorithms, including spectral Laplacian-based methods and machine learning ones such as graph neural networks and . We also find that a simple common-neighbor-based network automata rule achieves near state-of-the-art performance, highlighting the effectiveness of minimal local information for dismantling. LGD-NA is extensively validated on the largest and most diverse collection of real-world networks to date (1,475 real-world networks across 32 complex systems domains) and scales efficiently to large networks via GPU acceleration. Finally, we leverage the explainability of our common-neighbor approach to engineer network robustness, substantially increasing the resilience of real-world networks. We validate LGD-NA's practical utility on domain-specific functional metrics, spanning neuronal firing rates in the Drosophila Connectome, transport efficiency in flight maps, outbreak sizes in contact networks, and communication pathways in terrorist cells. Our results confirm latent geometry as a fundamental principle for understanding the robustness of real-world systems, adding dismantling to the growing set of processes that network geometry can explain.

While message-passing NNs (MPNNs) are naturally invariant on graphs, they are fundamentally limited in expressive power. Canonicalization offers a powerful alternative by mapping each graph to a unique, invariant representation on which expressive encoders can operate. However, existing approaches rely on a single canonical sequence, which flattens the structure, distorts graph distances, and restricts expressivity. To address these limitations, we introduce Canonical Tree Cover Neural Networks (CTNNs), which represent the graph with a canonical spanning tree cover, i.e., a small collection of canonical trees covering all edges. Each tree is then processed with an existing expressive tree encoder. Theoretically, tree covers better preserve graph distances than sequences, and on sparse graphs, the cover recovers all edges with a logarithmic number of trees in the graph size, making CTNNs strictly more expressive than sequence-based canonicalization pipelines. Empirically, CTNNs consistently outperform invariant GNNs, random samplers, and sequence canonicalizations across graph classification benchmarks. Overall, CTNNs advance graph learning by providing an efficient, invariant, and expressive representation learning framework via tree cover-based canonicalization.

Graph retrieval-augmented generation (GraphRAG) has effectively enhanced large language models in complex reasoning by organizing fragmented knowledge into explicitly structured graphs. Prior efforts have been made to improve either graph construction or graph retrieval in isolation, yielding suboptimal performance, especially when domain shifts occur. In this paper, we propose a vertically unified agentic paradigm, $\texttt{Youtu-GraphRAG}$, to jointly connect the entire framework as an intricate integration. Specifically, $(i)$ a seed graph schema is introduced to bound the automatic extraction agent with targeted entity types, relations and attribute types, also continuously expanded for scalability over unseen domains; $(ii)$ To obtain higher-level knowledge upon the schema, we develop novel dually-perceived community detection, fusing structural topology with subgraph semantics for comprehensive knowledge organization. This naturally yields a hierarchical knowledge tree that supports both top-down filtering and bottom-up reasoning with community summaries; $(iii)$ An agentic retriever is designed to interpret the same graph schema to transform complex queries into tractable and parallel sub-queries. It iteratively performs reflection for more advanced reasoning; $(iv)$ To alleviate the knowledge leaking problem in pre-trained LLM, we propose a tailored anonymous dataset and a novel 'Anonymity Reversion' task that deeply measures the real performance of the GraphRAG frameworks. Extensive experiments across six challenging benchmarks demonstrate the robustness of $\texttt{Youtu-GraphRAG}$, remarkably moving the Pareto frontier of performance and efficiency with up to 33.6% cost saving and 16.62% higher accuracy over state-of-the-art baselines. The results indicate our adaptability, allowing seamless domain transfer with minimal intervention on the schema.

Large language models (LLMs) are typically trained to acquire behaviours from demonstrations or experience, yet much of their training data consists of symbolic descriptions: instructions, rules, and strategies that specify procedures without examples. We investigate whether LLMs can learn to execute such behaviours directly from their abstract description, a process we term *Programming by Backprop* (PBB). We study this phenomenon in two domains: first, using source code as a canonical form of procedural description by comparing models finetuned on algorithms versus execution examples; and second, extending beyond code to abstract grammar rules, testing whether models learn to generate compliant text. Our findings show that PBB can be elicited through targeted finetuning, demonstrating that LLMs can acquire new behaviours from symbolic descriptions, albeit not yet with full reliability. Once elicited, PBB enables models to internalise reusable procedural abstractions - generalising across inputs, executing procedures implicitly in a forward pass, and benefiting further from chain-of-thought reasoning. These results position PBB as a distinct pathway through which LLMs acquire behavioural skills from symbolic descriptions, with implications for both more efficient capability acquisition and aligning models through formal specifications rather than demonstrations alone.

We introduce *TopoFormer*, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is *Topo-Scan*, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, *Topo-Scan* is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that *TopoFormer* matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Cross-capability transfer represents a key challenge in large language model (LLM) research, particularly in multi-task integration, model compression, and knowledge fusion. Recent works such as FuseLLM and FuseChat have shown the potential of transferring multiple model capabilities to lightweight models, thereby enhancing adaptability and efficiency. This motivates our investigation into more efficient methods for cross-capability transfer. However, existing merging approaches primarily focus on small, homogeneous models, limiting their applicability. For large, heterogeneous models, knowledge distillation with full-parameter fine-tuning often overlooks the student model’s inherent capability and risks catastrophic forgetting, while PEFT methods struggle to effectively absorb knowledge from source LLMs. To address these issues, we introduce **GraftLLM**, a novel grafting-based method that stores source model capabilities in a target model + SkillPack format. This approach preserves general capabilities, reduces parameter conflicts, and supports forget-free continual learning and model fusion. We employ a module-aware adaptive compression strategy for parameter updates, ensuring efficient storage while **preserving task-specific knowledge**. The resulting SkillPack serves as a compact and transferable knowledge carrier, ideal for **heterogeneous LLM fusion**. Experiments across various scenarios demonstrate that GraftLLM outperforms existing techniques in knowledge transfer, knowledge fusion, and forget-free learning, providing a scalable and efficient solution for cross-capability transfer.

Graph Neural Networks (GNNs) have demonstrated both empirical efficiency and universal expressivity for solving constrained optimization problems such as linear and quadratic programming. However, extending this paradigm to more general convex problems with universality guarantees, particularly Second-Order Cone Programs (SOCPs), remains largely unexplored. We address this challenge by proposing a novel graph representation that captures the inherent structure of conic constraints. We then establish a key universality theorem: *there exist GNNs that can provably approximate essential SOCP properties, including instance feasibility and optimal solutions*. We further derive the sample complexity for GNN generalization based on Rademacher complexity, filling an important gap for Weisfeiler-Lehman-based GNNs in learning-to-optimize paradigms. Our results provide a rigorous foundation linking GNN expressivity and generalization power to conic optimization structure, opening new avenues for scalable, data-driven SOCP solvers. The approach extends naturally to $p$-order cone programming for any $p \geq 1$ while preserving universal expressivity and requiring no structural modifications to the GNN architecture. Numerical experiments on randomly generated SOCPs and real-world power grid problems demonstrate the effectiveness of our approach, achieving superior prediction accuracy with significantly fewer parameters than fully connected neural networks.

Recovering missing flows on the edges of a network, while exactly respecting local conservation laws, is a fundamental inverse problem that arises in many systems such as transportation, energy, and mobility. We introduce FlowSymm, a novel architecture that combines (i) a group-action on divergence-free flows, (ii) a graph-attention encoder to learn feature-conditioned weights over these symmetry-preserving actions, and (iii) a lightweight Tikhonov refinement solved via implicit bilevel optimization. The method first anchors the given observation on a minimum-norm divergence-free completion. We then compute an orthonormal basis for all admissible group actions that leave the observed flows invariant and parameterize the valid solution subspace, which shows an Abelian group structure under vector addition. A stack of GATv2 layers then encodes the graph and its edge features into per-edge embeddings, which are pooled over the missing edges and produce per-basis attention weights. This attention-guided process selects a set of physics-aware group actions that preserve the observed flows. Finally, a scalar Tikhonov penalty refines the missing entries via a convex least-squares solver, with gradients propagated implicitly through Cholesky factorization. Across three real-world flow benchmarks (traffic, power, bike), FlowSymm substantially outperforms state-of-the-art baselines in RMSE, MAE and correlation metrics.

Graph structured data is commonly used to represent complex relationships such as transactions between accounts, communications between devices, and dependencies among machines or processes. Correspondingly, graph anomaly detection (GAD) plays a critical role in identifying anomalies across various domains, including finance, cybersecurity, manufacturing, etc. Facing the large-volume and multi-domain graph data, recent efforts aim to develop foundational generalist models capable of detecting anomalies in unseen graphs without retraining. To the best of our knowledge, the different feature semantics and dimensions of cross-domain graph structured data heavily hinders the development of graph foundation model, and leaves the further in-depth continual learning and inference capabilities in the evolving setting a quite nascent problem. To address these above challenges, we propose OWLEYE, a novel zero-shot GAD framework that learns transferable patterns of normal behavior from multiple graphs. Systematically, OWLEYE first introduces a cross-domain feature alignment module to harmonize feature distributions, which preserves domain-specific semantics during aligning more than the simple but widely-used Principle Component Analysis. Second, with aligned features, to enable method with continuous and scaling-up learning and inference capabilities, OWLEYE designs the multi-domain pattern dictionary learning to encode shared structural and attribute-based patterns. Third, for achieving the in-context learning ability, OWLEYE presents a truncated attention-based reconstruction module to robustly detect anomalies without requiring labeled data for unseen graph structured data. Extensive experiments on real-world datasets demonstrate that OWLEYE achieves superior performance and generalizability compared to state-of-the-art baselines, establishing a strong foundation for scalable and label-efficient anomaly detection.

The proliferation of Large Language Models (LLMs) in function calling is pivotal for creating advanced AI agents, yet their large scale hinders widespread adoption, necessitating transferring their capabilities into smaller ones. However, existing paradigms are often plagued by overfitting, training instability, ineffective binary rewards for multi-solution tasks, and the difficulty of synergizing techniques. We introduce STAR: Similarity-guided Teacher-Assisted Refinement, a novel holistic framework that effectively transfers LLMs' capabilities to super-tiny models. STAR consists of two core technical innovations: (1) Constrained Knowledge Distillation (CKD), a training objective that augments top-k forward KL divergence to suppress confidently incorrect predictions, ensuring training stability while preserving exploration capacity for downstream RL. STAR holistically synergizes these strategies within a cohesive training curriculum, enabling super-tiny models to achieve exceptional performance on complex function calling tasks; (2) Similarity-guided RL (Sim-RL), a RL mechanism that introduces a fine-grained, similarity-based reward. This provides a robust, continuous, and rich signal for better policy optimization by evaluating the similarity between generated outputs and the ground truth. Extensive experiments on challenging and renowned benchmarks demonstrate the effectiveness of our method. Our STAR models establish SOTA in their size classes, significantly outperforming baselines. Remarkably, our 0.6B STAR model achieves the best performance among all open models under 1B, surpassing even several well-known open models at a larger scale. STAR demonstrates a training framework that distills capabilities of LLMs into super-tiny models, paving the way for powerful, accessible, and efficient AI agents.

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution induced by a structural causal model, and additional data from (in the best case) *only two* environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.

Post-training algorithms such as Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT) are widely used to adapt multimodal large language models to downstream tasks. While effective at task adaptation, their impact on prior knowledge remains unclear. In this paper, we introduce jigsaw puzzles as a novel task absent from existing pretraining corpora and systematically study the behavior of SFT and RFT on open-source multimodal model, Qwen2.5-VL series. Our experiments reveal a sharp trade-off: SFT enables rapid task acquisition but leads to catastrophic forgetting, whereas RFT learns more slowly but maintains prior knowledge. We study this phenomenon through learning dynamics by examining both the magnitude and direction of how training data influence prior knowledge. Our analysis shows that RFT mainly reinforces correct samples naturally aligned with the base model’s probability landscape, leading to weaker interference with prior knowledge. Moreover, training on RFT-simulated rollouts, which exert a small magnitude of influence and are well aligned in direction to prior knowledge, allows SFT to preserve prior knowledge better while rapidly learning new tasks. These findings suggest that distribution of training data, rather than algorithmic differences, plays a central role in forgetting, and highlight RFT's potential for stable continual learning in multimodal large language models.

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs.

Role-playing dialogue presents unique challenges for large language models (LLMs): beyond producing coherent text, models must sustain character persona, integrate contextual knowledge, and convey emotional nuance. Despite strong reasoning abilities, current LLMs often generate dialogue that is literal, stylistically bland, and misaligned with character-specific traits. Existing approaches such as retrieval-augmented generation (RAG) or reinforcement learning (RL) with scalar rewards are insufficient, as they cannot capture nuanced preferences or adapt reliably to diverse character contexts. In this work, we introduce R4, a unified framework that equips both the reward model and the role-playing agent with reasoning and retrieval capabilities. Our reward model reformulates evaluation as structured reasoning: it integrates multi-step deliberation and retrieved knowledge to assess responses along multiple dimensions. This reward supervision is then used within reinforcement learning to train a dialogue agent with the same dual capabilities, enabling contextually grounded and persona-consistent generation. Experiments demonstrate that R4 substantially improves dialogue quality, particularly in persona fidelity, narrative coherence, and emotional expressiveness. Analysis of training dynamics and case studies further shows that R4 agents employ retrieval more effectively, engage in retrieval-informed self-reflection, and achieve emergent role-playing behaviors unattainable by prior methods.

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.279), which processes the entire proof at once, and step-proof formalization (0.046), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://anonymous.4open.science/r/ProofFlow-351E.