Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified latent space, modeling prediction tasks including classification and regression as a form of conditional generation. However, due to the non-Euclidean nature of graph data, features of different curvatures are entangled in the same latent space without releasing their geometric potential. To address this issue, we aim to construt an ideal Riemannian diffusion model to capture distinct manifold signatures of complex graph data and learn their distribution. This goal faces two challenges: numerical instability caused by exponential mapping during the encoding proces and manifold deviation during diffusion generation. To address these challenges, we propose GeoMancer: a novel Riemannian graph diffusion framework for both generation and prediction tasks. To mitigate numerical instability, we replace exponential mapping with an isometric-invariant Riemannian gyrokernel approach and decouple multi-level features onto their respective task-specific manifolds to learn optimal representations. To address manifold deviation, we introduce a manifold-constrained diffusion method and a self-guided strategy for unconditional generation, ensuring that the generated data remains aligned with the manifold signature. Extensive experiments validate the effectiveness of our approach, demonstrating superior performance across a variety of tasks.

Proxy Model-Guided Reinforcement Learning for Client Selection in Federated Recommendation

Federated recommender systems have emerged as a promising privacy-preserving paradigm, enabling personalized recommendation services without exposing users' raw data. By keeping data local and relying on a central server to coordinate training across distributed clients, FedRSs protect user privacy while collaboratively learning global models. However, most existing FedRS frameworks adopt fully random client selection strategy in each training round, overlooking the statistical heterogeneity of user data arising from diverse preferences and behavior patterns, thereby resulting in suboptimal model performance. While some client selection strategies have been proposed in the broader federated learning literature, these methods are typically designed for generic tasks and fail to address the unique challenges of recommendation scenarios, such as expensive contribution evaluation due to the large number of clients, and sparse updates resulting from long-tail item distributions. To bridge this gap, we propose ProxyRL-FRS, a proxy model-guided reinforcement learning framework tailored for client selection in federated recommendation. Specifically, we first introduce ProxyNCF, a dual-branch model deployed on each client, which augments standard Neural Collaborative Filtering with an additional proxy model branch that provides lightweight contribution estimation, thus eliminating the need for expensive per-round local training traditionally required to evaluate a client's contribution. Furthermore, we design a staleness-aware SA reinforcement learning agent that selects clients based on the proxy-estimated contribution, and is guided by a reward function balancing recommendation accuracy and embedding staleness, thereby enriching the update coverage of item embeddings. Experiments conducted on public recommendation datasets demonstrate the effectiveness of ProxyRL-FRS.

Invariant Graph Transformer for Out-of-Distribution Generalization

Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under distribution shifts. Graph invariant learning, aiming to capture generalizable graph structural patterns with labels under distribution shifts, is potentially a promising solution, but how to design attention mechanisms and positional and structural encodings (PSEs) based on graph invariant learning principles remains challenging. To solve these challenges, we introduce Graph Out-Of-Distribution generalized Transformer (GOODFormer), aiming to learn generalized graph representations by capturing invariant relationships between predictive graph structures and labels through jointly optimizing three modules. Specifically, we first develop a GT-based entropy-guided invariant subgraph disentangler to separate invariant and variant subgraphs while preserving the sharpness of the attention function. Next, we design an evolving subgraph positional and structural encoder to effectively and efficiently capture the encoding information of dynamically changing subgraphs during training. Finally, we propose an invariant learning module utilizing subgraph node representations and encodings to derive generalizable graph representations that can to unseen graphs. We also provide theoretical justifications for our method. Extensive experiments on benchmark datasets demonstrate the superiority of our method over state-of-the-art baselines under distribution shifts.

GraphRAG-R1: Graph Retrieval-Augmented Generation with Process-Constrained Reinforcement Learning

Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of LLMs by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However, existing GraphRAG methods still face significant bottlenecks when handling complex problems that require multi-hop reasoning, as their query and retrieval phases are largely based on pre-defined heuristics and do not fully utilize the reasoning potentials of LLMs. To address this problem, we propose GraphRAG-R1, an adaptive GraphRAG framework by training LLMs with process-constrained outcome-based reinforcement learning (RL) to enhance the multi-hop reasoning ability. Our method can decompose complex problems, autonomously invoke retrieval tools to acquire necessary information, and perform effective reasoning. Specifically, we utilize a modified version of Group Relative Policy Optimization (GRPO) that supports rollout-with-thinking capability. Next, we design two process-constrained reward functions. To handle the shallow retrieval problem, we design a Progressive Retrieval Attenuation (PRA) reward to encourage essential retrievals. Then, to handle the over-thinking problem, we design Cost-Aware F1 (CAF) reward to balance the model performance with computational costs. We further design a phase-dependent training strategy, containing three training stages corresponding to cold start and these two rewards. Lastly, our method adopts a hybrid graph-textual retrieval to improve the reasoning capacity. Extensive experimental results demonstrate that GraphRAG-R1 boosts LLM capabilities in solving complex reasoning problems compared to state-of-the-art GraphRAG methods on both in-domain and out-of-domain datasets. Furthermore, our framework can be flexibly integrated with various existing retrieval methods, consistently delivering performance improvements.

Improving Subgraph Matching by Combining Algorithms and Graph Neural Networks

Homomorphism is a key mapping technique between graphs that preserves their structure. Given a graph and a pattern, the subgraph homomorphism problem involves finding a mapping from the pattern to the graph, ensuring that adjacent vertices in the pattern are mapped to adjacent vertices in the graph. Unlike subgraph isomorphism, which requires a one-to-one mapping, homomorphism allows multiple vertices in the pattern to map to the same vertex in the graph, making it more complex. We propose HFrame, the first graph neural network-based framework for subgraph homomorphism, which integrates traditional algorithms with machine learning techniques. We demonstrate that HFrame outperforms standard graph neural networks by being able to distinguish more graph pairs where the pattern is not homomorphic to the graph. Additionally, we provide a generalization error bound for HFrame. Through experiments on both real-world and synthetic graphs, we show that HFrame is up to 101.91 times faster than exact matching algorithms and achieves an average accuracy of 0.962.

Towards Objective Fine-tuning: How LLMs' Prior Knowledge Causes Potential Poor Calibration?

Fine-tuned Large Language Models (LLMs) often demonstrate poor calibration, with their confidence scores misaligned with actual performance. While calibration has been extensively studied in models trained from scratch, the impact of LLMs' prior knowledge on calibration during fine-tuning remains understudied. Our research reveals that LLMs' prior knowledge causes potential poor calibration due to the ubiquitous presence of known data in real-world fine-tuning, which appears harmful for calibration. Specifically, data aligned with LLMs' prior knowledge would induce overconfidence, while new knowledge improves calibration. Our findings expose a tension: LLMs' encyclopedic knowledge, while enabling task versatility, undermines calibration through unavoidable knowledge overlaps. To address this, we propose CogCalib, a cognition-aware framework that applies targeted learning strategies according to the model's prior knowledge. Experiments across 7 tasks using 3 LLM families prove that CogCalib significantly improves calibration while maintaining performance, achieving an average 57\% reduction in ECE compared to standard fine-tuning in Llama3-8B. These improvements generalize well to out-of-domain tasks, enhancing the objectivity and reliability of domain-specific LLMs, and making them more trustworthy for critical human-AI interaction applications.

Controllable Logical Hypothesis Generation for Abductive Reasoning in Knowledge Graphs

Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis oversensitivity. To address these challenges, we propose CtrlHGen, a Controllable logcial Hypothesis Generation framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning. To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines.

FreqMoE: Dynamic Frequency Enhancement for Neural PDE Solvers

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the sparsity of high-frequency signals limits computational efficiency for high-dimensional inputs, and fixed-pattern truncation often causes high-frequency signal loss, reducing performance in scenarios such as high-resolution inputs or long-term predictions. To address these challenges, we propose FreqMoE, an efficient and progressive training framework that exploits the dependency of high-frequency signals on low-frequency components. The model first learns low-frequency weights and then applies a sparse upward-cycling strategy to construct a mixture of experts (MoE) in the frequency domain, effectively extending the learned weights to high-frequency regions. Experiments on both regular and irregular grid PDEs demonstrate that FreqMoE achieves up to 16.6% accuracy improvement while using merely 2.1% parameters (47.32x reduction) compared to dense FNO. Furthermore, the approach demonstrates remarkable stability in long-term predictions and generalizes seamlessly to various FNO variants and grid structures, establishing a new ``Low frequency Pretraining, High frequency Fine-tuning'' paradigm for solving PDEs.

Sparsification Under Siege: Defending Against Poisoning Attacks in Communication-Efficient Federated Learning

Federated Learning (FL) enables collaborative model training across distributed clients while preserving data privacy, yet it faces significant challenges in communication efficiency and vulnerability to poisoning attacks. While sparsification techniques mitigate communication overhead by transmitting only critical model parameters, they inadvertently amplify security risks: adversarial clients can exploit sparse updates to evade detection and degrade model performance. Existing defense mechanisms, designed for standard FL communication scenarios, are ineffective in addressing these vulnerabilities within sparsified FL. To bridge this gap, we propose FLARE, a novel federated learning framework that integrates sparse index mask inspection and model update sign similarity analysis to detect and mitigate poisoning attacks in sparsified FL. Extensive experiments across multiple datasets and adversarial scenarios demonstrate that FLARE significantly outperforms existing defense strategies, effectively securing sparsified FL against poisoning attacks while maintaining communication efficiency.

Privacy-Preserving Federated Embedding Learning for Localized Retrieval-Augmented Generation

Retrieval-Augmented Generation (RAG) has recently emerged as a promising solution for enhancing the accuracy and credibility of Large Language Models (LLMs), particularly in Question & Answer tasks. This is achieved by incorporating proprietary and private data from integrated databases. However, private RAG systems face significant challenges due to the scarcity of private domain data and critical data privacy issues. These obstacles impede the deployment of private RAG systems, as developing privacy-preserving RAG systems requires a delicate balance between data security and data availability. To address these challenges, we regard federated learning (FL) as a highly promising technology for privacy-preserving RAG services. We propose a novel framework called Federated Retrieval-Augmented Generation (FedE4RAG). This framework facilitates collaborative training of client-side RAG retrieval models. The parameters of these models are aggregated and distributed on a central-server, ensuring data privacy without direct sharing of raw data. In FedE4RAG, knowledge distillation is employed for communication between the server and client models. This technique improves the generalization of local RAG retrievers during the federated learning process. Additionally, we apply homomorphic encryption within federated learning to safeguard model parameters and mitigate concerns related to data leakage. Extensive experiments conducted on the real-world dataset have validated the effectiveness of FedE4RAG. The results demonstrate that our proposed framework can markedly enhance the performance of private RAG systems while maintaining robust data privacy protection.