A Scalable Pretraining Framework for Link Prediction with Efficient Adaptation

Link Prediction (LP) is a critical task in graph machine learning. While Graph Neural Networks (GNNs) have significantly advanced LP performance recently, existing methods face key challenges including limited supervision from sparse connectivity, sensitivity to initialization, and poor generalization under distribution shifts. We explore pretraining as a solution to address these challenges. Unlike node classification, LP is inherently a pairwise task, which requires the integration of both node- and edge-level information. In this work, we present the first systematic study on the transferability of these distinct modules and propose a late fusion strategy to effectively combine their outputs for improved performance. To handle the diversity of pretraining data and avoid negative transfer, we introduce a Mixture-of-Experts (MoE) framework that captures distinct patterns in separate experts, facilitating seamless application of the pretrained model on diverse downstream datasets. For fast adaptation, we develop a parameter-efficient tuning strategy that allows the pretrained model to adapt to unseen datasets with minimal computational overhead. Experiments on 16 datasets across two domains demonstrate the effectiveness of our approach, achieving state-of-the-art performance on low-resource link prediction while obtaining competitive results compared to end-to-end trained methods, with over 10,000x lower computational overhead.

SSEmb: A Joint Structural and Semantic Embedding Framework for Mathematical Formula Retrieval

Formula retrieval is an important topic in Mathematical Information Retrieval. We propose SSEmb, a novel embedding framework capable of capturing both structural and semantic features of mathematical formulas. Structurally, we employ Graph Contrastive Learning to encode formulas represented as Operator Graphs. To enhance structural diversity while preserving mathematical validity of these formula graphs, we introduce a novel graph data augmentation approach through a substitution strategy. Semantically, we utilize Sentence-BERT to encode the surrounding text of formulas. Finally, for each query and its candidates, structural and semantic similarities are calculated separately and then fused through a weighted scheme. In the ARQMath-3 formula retrieval task, SSEmb outperforms existing embedding-based methods by over 5 percentage points on P'@10 and nDCG'@10. Furthermore, SSEmb enhances the performance of all runs of other methods and achieves state-of-the-art results when combined with Approach0.

The Ubiquitous Sparse Matrix-Matrix Products

Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected neural networks, graph neural networks, clustering, and many-to-many comparisons of biological sequencing data. In many application scenarios, the matrix multiplication takes places on an arbitrary algebraic semiring where the scalar operations are overloaded with user-defined functions with certain properties or a more general heterogenous algebra where even the domains of the input matrices can be different. Here, we provide a unifying treatment of the sparse matrix-matrix operation and its rich application space including machine learning, computational biology and chemistry, graph algorithms, and scientific computing.

GraphProp: Training the Graph Foundation Models using Graph Properties

This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different domains. We discover that graph structures provide more consistent cross-domain information compared to node features and graph labels. However, traditional GFMs primarily focus on transferring node features from various domains into a unified representation space but often lack structural cross-domain generalization. To address this, we introduce GraphProp, which emphasizes structural generalization. The training process of GraphProp consists of two main phases. First, we train a structural GFM by predicting graph invariants. Since graph invariants are properties of graphs that depend only on the abstract structure, not on particular labellings or drawings of the graph, this structural GFM has a strong ability to capture the abstract structural information and provide discriminative graph representations comparable across diverse domains. In the second phase, we use the representations given by the structural GFM as positional encodings to train a comprehensive GFM. This phase utilizes domain-specific node attributes and graph labels to further improve cross-domain node feature generalization. Our experiments demonstrate that GraphProp significantly outperforms the competitors in supervised learning and few-shot learning, especially in handling graphs without node attributes.

A Comparative Survey of PyTorch vs TensorFlow for Deep Learning: Usability, Performance, and Deployment Trade-offs

This paper presents a comprehensive comparative survey of TensorFlow and PyTorch, the two leading deep learning frameworks, focusing on their usability, performance, and deployment trade-offs. We review each framework's programming paradigm and developer experience, contrasting TensorFlow's graph-based (now optionally eager) approach with PyTorch's dynamic, Pythonic style. We then compare model training speeds and inference performance across multiple tasks and data regimes, drawing on recent benchmarks and studies. Deployment flexibility is examined in depth - from TensorFlow's mature ecosystem (TensorFlow Lite for mobile/embedded, TensorFlow Serving, and JavaScript support) to PyTorch's newer production tools (TorchScript compilation, ONNX export, and TorchServe). We also survey ecosystem and community support, including library integrations, industry adoption, and research trends (e.g., PyTorch's dominance in recent research publications versus TensorFlow's broader tooling in enterprise). Applications in computer vision, natural language processing, and other domains are discussed to illustrate how each framework is used in practice. Finally, we outline future directions and open challenges in deep learning framework design, such as unifying eager and graph execution, improving cross-framework interoperability, and integrating compiler optimizations (XLA, JIT) for improved speed. Our findings indicate that while both frameworks are highly capable for state-of-the-art deep learning, they exhibit distinct trade-offs: PyTorch offers simplicity and flexibility favored in research, whereas TensorFlow provides a fuller production-ready ecosystem - understanding these trade-offs is key for practitioners selecting the appropriate tool. We include charts, code snippets, and more than 20 references to academic papers and official documentation to support this comparative analysis

Circuit-Aware SAT Solving: Guiding CDCL via Conditional Probabilities

Circuit Satisfiability (CSAT) plays a pivotal role in Electronic Design Automation. The standard workflow for solving CSAT problems converts circuits into Conjunctive Normal Form (CNF) and employs generic SAT solvers powered by Conflict-Driven Clause Learning (CDCL). However, this process inherently discards rich structural and functional information, leading to suboptimal solver performance. To address this limitation, we introduce CASCAD, a novel circuit-aware SAT solving framework that directly leverages circuit-level conditional probabilities computed via Graph Neural Networks (GNNs). By explicitly modeling gate-level conditional probabilities, CASCAD dynamically guides two critical CDCL heuristics -- variable phase selection and clause managementto significantly enhance solver efficiency. Extensive evaluations on challenging real-world Logical Equivalence Checking (LEC) benchmarks demonstrate that CASCAD reduces solving times by up to 10x compared to state-of-the-art CNF-based approaches, achieving an additional 23.5% runtime reduction via our probability-guided clause filtering strategy. Our results underscore the importance of preserving circuit-level structural insights within SAT solvers, providing a robust foundation for future improvements in SAT-solving efficiency and EDA tool design.

Benefit from Rich: Tackling Search Interaction Sparsity in Search Enhanced Recommendation

In modern online platforms, search and recommendation (S&R) often coexist, offering opportunities for performance improvement through search-enhanced approaches. Existing studies show that incorporating search signals boosts recommendation performance. However, the effectiveness of these methods relies heavily on rich search interactions. They primarily benefit a small subset of users with abundant search behavior, while offering limited improvements for the majority of users who exhibit only sparse search activity. To address the problem of sparse search data in search-enhanced recommendation, we face two key challenges: (1) how to learn useful search features for users with sparse search interactions, and (2) how to design effective training objectives under sparse conditions. Our idea is to leverage the features of users with rich search interactions to enhance those of users with sparse search interactions. Based on this idea, we propose GSERec, a method that utilizes message passing on the User-Code Graphs to alleviate data sparsity in Search-Enhanced Recommendation. Specifically, we utilize Large Language Models (LLMs) with vector quantization to generate discrete codes, which connect similar users and thereby construct the graph. Through message passing on this graph, embeddings of users with rich search data are propagated to enhance the embeddings of users with sparse interactions. To further ensure that the message passing captures meaningful information from truly similar users, we introduce a contrastive loss to better model user similarities. The enhanced user representations are then integrated into downstream search-enhanced recommendation models. Experiments on three real-world datasets show that GSERec consistently outperforms baselines, especially for users with sparse search behaviors.

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.

Nested Graph Pseudo-Label Refinement for Noisy Label Domain Adaptation Learning

Graph Domain Adaptation (GDA) facilitates knowledge transfer from labeled source graphs to unlabeled target graphs by learning domain-invariant representations, which is essential in applications such as molecular property prediction and social network analysis. However, most existing GDA methods rely on the assumption of clean source labels, which rarely holds in real-world scenarios where annotation noise is pervasive. This label noise severely impairs feature alignment and degrades adaptation performance under domain shifts. To address this challenge, we propose Nested Graph Pseudo-Label Refinement (NeGPR), a novel framework tailored for graph-level domain adaptation with noisy labels. NeGPR first pretrains dual branches, i.e., semantic and topology branches, by enforcing neighborhood consistency in the feature space, thereby reducing the influence of noisy supervision. To bridge domain gaps, NeGPR employs a nested refinement mechanism in which one branch selects high-confidence target samples to guide the adaptation of the other, enabling progressive cross-domain learning. Furthermore, since pseudo-labels may still contain noise and the pre-trained branches are already overfitted to the noisy labels in the source domain, NeGPR incorporates a noise-aware regularization strategy. This regularization is theoretically proven to mitigate the adverse effects of pseudo-label noise, even under the presence of source overfitting, thus enhancing the robustness of the adaptation process. Extensive experiments on benchmark datasets demonstrate that NeGPR consistently outperforms state-of-the-art methods under severe label noise, achieving gains of up to 12.7% in accuracy.

Neighbor-Sampling Based Momentum Stochastic Methods for Training Graph Neural Networks

Graph convolutional networks (GCNs) are a powerful tool for graph representation learning. Due to the recursive neighborhood aggregations employed by GCNs, efficient training methods suffer from a lack of theoretical guarantees or are missing important practical elements from modern deep learning algorithms, such as adaptivity and momentum. In this paper, we present several neighbor-sampling (NS) based Adam-type stochastic methods for solving a nonconvex GCN training problem. We utilize the control variate technique proposed by [1] to reduce the stochastic error caused by neighbor sampling. Under standard assumptions for Adam-type methods, we show that our methods enjoy the optimal convergence rate. In addition, we conduct extensive numerical experiments on node classification tasks with several benchmark datasets. The results demonstrate superior performance of our methods over classic NS-based SGD that also uses the control-variate technique, especially for large-scale graph datasets. Our code is available at https://github.com/RPI-OPT/CV-ADAM-GNN .