Xinyu Fu

While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit-framework, datasets, and benchmark-to unlock complex, human-like visual-aided reasoning in LMMs.

Existing multimodal browsing benchmarks often fail to require genuine multimodal reasoning, as many tasks can be solved with text-only heuristics without vision-in-the-loop verification. We introduce MMSearch-Plus, a 311-task benchmark that enforces multimodal understanding by requiring extraction and propagation of fine-grained visual cues through iterative image-text retrieval and cross-validation under retrieval noise. Our curation procedure seeds questions whose answers require extrapolating from spatial cues and temporal traces to out-of-image facts such as events, dates, and venues. Beyond the dataset, we provide a model-agnostic agent framework with standard browsing tools and a set-of-mark (SoM) module, which lets the agent place marks, crop subregions, and launch targeted image/text searches. SoM enables provenance-aware zoom-and-retrieve and improves robustness in multi-step reasoning. We evaluated closed- and open-source MLLMs in this framework. The strongest system achieves an end-to-end accuracy of 36.0%, and integrating SoM produces consistent gains in multiple settings, with improvements up to +3.9 points. From failure analysis, we observe recurring errors in locating relevant webpages and distinguishing between visually similar events. These results underscore the challenges of real-world multimodal search and establish MMSearch-Plus as a rigorous benchmark for advancing agentic MLLMs.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model’s current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model’s reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

Heterogeneous graph neural networks (HGNNs) were proposed for representation learning on structural data with multiple types of nodes and edges. To deal with the performance degradation issue when HGNNs become deep, researchers combine metapaths into HGNNs to associate nodes closely related in semantics but far apart in the graph. However, existing metapath-based models suffer from either information loss or high computation costs. To address these problems, we present a novel Metapath Context Convolution-based Heterogeneous Graph Neural Network (MECCH). MECCH leverages metapath contexts, a new kind of graph structure that facilitates lossless node information aggregation while avoiding any redundancy. Specifically, MECCH applies three novel components after feature preprocessing to extract comprehensive information from the input graph efficiently: (1) metapath context construction, (2) metapath context encoder, and (3) convolutional metapath fusion. Experiments on five real-world heterogeneous graph datasets for node classification and link prediction show that MECCH achieves superior prediction accuracy compared with state-of-the-art baselines with improved computational efficiency.

Heterogeneous graph neural networks (HGNNs) can learn from typed and relational graph data more effectively than conventional GNNs. With larger parameter spaces, HGNNs may require more training data, which is often scarce in real-world applications due to privacy regulations (e.g., GDPR). Federated graph learning (FGL) enables multiple clients to train a GNN collaboratively without sharing their local data. However, existing FGL methods mainly focus on homogeneous GNNs or knowledge graph embeddings; few have considered heterogeneous graphs and HGNNs. In federated heterogeneous graph learning, clients may have private graph schemas. Conventional FL/FGL methods attempting to define a global HGNN model would violate schema privacy. To address these challenges, we propose FedHGN, a novel and general FGL framework for HGNNs. FedHGN adopts schema-weight decoupling to enable schema-agnostic knowledge sharing and employs coefficients alignment to stabilize the training process and improve HGNN performance. With better privacy preservation, FedHGN consistently outperforms local training and conventional FL methods on three widely adopted heterogeneous graph datasets with varying client numbers.

A large number of real-world graphs or networks are inherently heterogeneous, involving a diversity of node types and relation types. Heterogeneous graph embedding is to embed rich structural and semantic information of a heterogeneous graph into low-dimensional node representations. Existing models usually define multiple metapaths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models either omit node content features, discard intermediate nodes along the metapath, or only consider one metapath. To address these three limitations, we propose a new model named Metapath Aggregated Graph Neural Network (MAGNN) to boost the final performance. Specifically, MAGNN employs three major components, i.e., the node content transformation to encapsulate input node attributes, the intra-metapath aggregation to incorporate intermediate semantic nodes, and the inter-metapath aggregation to combine messages from multiple metapaths. Extensive experiments on three real-world heterogeneous graph datasets for node classification, node clustering, and link prediction show that MAGNN achieves more accurate prediction results than state-of-the-art baselines.