Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence

Graphs provide a natural description of the complex relationships among objects, and play a pivotal role in communications, transportation, social computing, the life sciences, etc. Currently, there is strong agreement that Graph Foundation Models (GFMs) are essential for advancing graph learning, yet considerable disagreement persists on how to build a powerful, general-purpose GFM analogous to Large Language Models (LLMs). Graph Neural Networks (GNNs) exhibit limitations in memory retention and principled interpretability when confronted with multi-domain pretraining and adaptation. The challenge of graph serialization hinders the direct application of LLMs, as the words struggle to capture the structural complexity and diversity inherent in graphs. In contrast, Riemannian geometry offers an elegant mathematical framework for modeling structures, while remaining compatible with graph semantic learning, even with LLMs. In this paper, we argue that, for graphs, Riemannian geometry speaks louder than words, and lay out the foundational principles for GFM. Reimagining with Riemannian geometry, we introduce a blue sky idea-Riemannian Foundation Model (RFM)-that opens a new pathway for capturing complex structural patterns and uncovering cross-domain generalities. RFM emphasizes intrinsic graph geometry and embodies endogenous capacities for structural inference and generation, moving beyond mere representation-space switching. Accordingly, we outline a progressive agenda that begins with universal structural understanding through intrinsic geometry, and then rebuilds LLM with a Riemannian engine for general-purpose graph modeling and beyond. Thus, RFM enables a paradigm shift from designing graph models to solving graph-structured applications with RFM agents, unlocking the next-generation graph intelligence.

Cognitive Mismatch in Multimodal Large Language Models for Discrete Symbol Understanding

While Multimodal Large Language Models (MLLMs) have achieved remarkable success in interpreting natural scenes, their ability to process discrete symbols -- the fundamental building blocks of human cognition -- remains a critical open question. Unlike continuous visual data, symbols such as mathematical formulas, chemical structures, and linguistic characters require precise, deeper interpretation. This paper introduces a comprehensive benchmark to evaluate how top-tier MLLMs navigate these "discrete semantic spaces" across five domains: language, culture, mathematics, physics, and chemistry. Our investigation uncovers a counterintuitive phenomenon: models often fail at basic symbol recognition yet succeed in complex reasoning tasks, suggesting they rely on linguistic probability rather than true visual perception. By exposing this "cognitive mismatch", we highlight a significant gap in current AI capabilities: the struggle to truly perceive and understand the symbolic languages that underpin scientific discovery and abstract thought. This work offers a roadmap for developing more rigorous, human-aligned intelligent systems.

Learning to Explore: Policy-Guided Outlier Synthesis for Graph Out-of-Distribution Detection

Detecting out-of-distribution (OOD) graphs is crucial for ensuring the safety and reliability of Graph Neural Networks. In unsupervised graph-level OOD detection, models are typically trained using only in-distribution (ID) data, resulting in incomplete feature space characterization and weak decision boundaries. Although synthesizing outliers offers a promising solution, existing approaches rely on fixed, non-adaptive sampling heuristics (e.g., distance- or density-based), limiting their ability to explore informative OOD regions. We propose a Policy-Guided Outlier Synthesis (PGOS) framework that replaces static heuristics with a learned exploration strategy. Specifically, PGOS trains a reinforcement learning agent to navigate low-density regions in a structured latent space and sample representations that most effectively refine the OOD decision boundary. These representations are then decoded into high-quality pseudo-OOD graphs to improve detector robustness. Extensive experiments demonstrate that PGOS achieves state-of-the-art performance on multiple graph OOD and anomaly detection benchmarks.

Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

Actor-Curator: Co-adaptive Curriculum Learning via Policy-Improvement Bandits for RL Post-Training

Post-training large foundation models with reinforcement learning typically relies on massive and heterogeneous datasets, making effective curriculum learning both critical and challenging. In this work, we propose ACTOR-CURATOR, a scalable and fully automated curriculum learning framework for reinforcement learning post-training of large language models (LLMs). ACTOR-CURATOR learns a neural curator that dynamically selects training problems from large problem banks by directly optimizing for expected policy performance improvement. We formulate problem selection as a non-stationary stochastic bandit problem, derive a principled loss function based on online stochastic mirror descent, and establish regret guarantees under partial feedback. Empirically, ACTOR-CURATOR consistently outperforms uniform sampling and strong curriculum baselines across a wide range of challenging reasoning benchmarks, demonstrating improved training stability and efficiency. Notably, it achieves relative gains of 28.6% on AIME2024 and 30.5% on ARC-1D over the strongest baseline and up to 80% speedup. These results suggest that ACTOR-CURATOR is a powerful and practical approach for scalable LLM post-training.

Unlocking Multimodal Document Intelligence: From Current Triumphs to Future Frontiers of Visual Document Retrieval

With the rapid proliferation of multimodal information, Visual Document Retrieval (VDR) has emerged as a critical frontier in bridging the gap between unstructured visually rich data and precise information acquisition. Unlike traditional natural image retrieval, visual documents exhibit unique characteristics defined by dense textual content, intricate layouts, and fine-grained semantic dependencies. This paper presents the first comprehensive survey of the VDR landscape, specifically through the lens of the Multimodal Large Language Model (MLLM) era. We begin by examining the benchmark landscape, and subsequently dive into the methodological evolution, categorizing approaches into three primary aspects: multimodal embedding models, multimodal reranker models, and the integration of Retrieval-Augmented Generation (RAG) and Agentic systems for complex document intelligence. Finally, we identify persistent challenges and outline promising future directions, aiming to provide a clear roadmap for future multimodal document intelligence.

Pedagogically-Inspired Data Synthesis for Language Model Knowledge Distillation

Knowledge distillation from Large Language Models (LLMs) to smaller models has emerged as a critical technique for deploying efficient AI systems. However, current methods for distillation via synthetic data lack pedagogical awareness, treating knowledge transfer as a one-off data synthesis and training task rather than a systematic learning process. In this paper, we propose a novel pedagogically-inspired framework for LLM knowledge distillation that draws from fundamental educational principles. Our approach introduces a three-stage pipeline -- Knowledge Identifier, Organizer, and Adapter (IOA) -- that systematically identifies knowledge deficiencies in student models, organizes knowledge delivery through progressive curricula, and adapts representations to match the cognitive capacity of student models. We integrate Bloom's Mastery Learning Principles and Vygotsky's Zone of Proximal Development to create a dynamic distillation process where student models approach teacher model's performance on prerequisite knowledge before advancing, and new knowledge is introduced with controlled, gradual difficulty increments. Extensive experiments using LLaMA-3.1/3.2 and Qwen2.5 as student models demonstrate that IOA achieves significant improvements over baseline distillation methods, with student models retaining 94.7% of teacher performance on DollyEval while using less than 1/10th of the parameters. Our framework particularly excels in complex reasoning tasks, showing 19.2% improvement on MATH and 22.3% on HumanEval compared with state-of-the-art baselines.

The Devil Behind Moltbook: Anthropic Safety is Always Vanishing in Self-Evolving AI Societies

The emergence of multi-agent systems built from large language models (LLMs) offers a promising paradigm for scalable collective intelligence and self-evolution. Ideally, such systems would achieve continuous self-improvement in a fully closed loop while maintaining robust safety alignment--a combination we term the self-evolution trilemma. However, we demonstrate both theoretically and empirically that an agent society satisfying continuous self-evolution, complete isolation, and safety invariance is impossible. Drawing on an information-theoretic framework, we formalize safety as the divergence degree from anthropic value distributions. We theoretically demonstrate that isolated self-evolution induces statistical blind spots, leading to the irreversible degradation of the system's safety alignment. Empirical and qualitative results from an open-ended agent community (Moltbook) and two closed self-evolving systems reveal phenomena that align with our theoretical prediction of inevitable safety erosion. We further propose several solution directions to alleviate the identified safety concern. Our work establishes a fundamental limit on the self-evolving AI societies and shifts the discourse from symptom-driven safety patches to a principled understanding of intrinsic dynamical risks, highlighting the need for external oversight or novel safety-preserving mechanisms.

RiemannGL: Riemannian Geometry Changes Graph Deep Learning

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean structure with complex interactions among the objects. This paper argues that Riemannian geometry provides a principled and necessary foundation for graph representation learning, and that Riemannian graph learning should be viewed as a unifying paradigm rather than a collection of isolated techniques. While recent studies have explored the integration of graph learning and Riemannian geometry, most existing approaches are limited to a narrow class of manifolds, particularly hyperbolic spaces, and often adopt extrinsic manifold formulations. We contend that the central mission of Riemannian graph learning is to endow graph neural networks with intrinsic manifold structures, which remains underexplored. To advance this perspective, we identify key conceptual and methodological gaps in existing approaches and outline a structured research agenda along three dimensions: manifold type, neural architecture, and learning paradigm. We further discuss open challenges, theoretical foundations, and promising directions that are critical for unlocking the full potential of Riemannian graph learning. This paper aims to provide a coherent viewpoint and to stimulate broader exploration of Riemannian geometry as a foundational framework for future graph learning research.

NanoNet: Parameter-Efficient Learning with Label-Scarce Supervision for Lightweight Text Mining Model

The lightweight semi-supervised learning (LSL) strategy provides an effective approach of conserving labeled samples and minimizing model inference costs. Prior research has effectively applied knowledge transfer learning and co-training regularization from large to small models in LSL. However, such training strategies are computationally intensive and prone to local optima, thereby increasing the difficulty of finding the optimal solution. This has prompted us to investigate the feasibility of integrating three low-cost scenarios for text mining tasks: limited labeled supervision, lightweight fine-tuning, and rapid-inference small models. We propose NanoNet, a novel framework for lightweight text mining that implements parameter-efficient learning with limited supervision. It employs online knowledge distillation to generate multiple small models and enhances their performance through mutual learning regularization. The entire process leverages parameter-efficient learning, reducing training costs and minimizing supervision requirements, ultimately yielding a lightweight model for downstream inference.