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1. Modeling Transitivity and Cyclicity in Directed Graphs via Binary Code Box Embeddings

   Zhang, Dongxu; Boratko, Michael; Musco, Cameron N; McCallum, Andrew (October 2022, Neural Information Processing Systems)

   Modeling directed graphs with differentiable representations is a fundamental requirement for performing machine learning on graph-structured data. Geometric embedding models (e.g. hyperbolic, cone, and box embeddings) excel at this task, exhibiting useful inductive biases for directed graphs. However, modeling directed graphs that both contain cycles and some element of transitivity, two properties common in real-world settings, is challenging. Box embeddings, which can be thought of as representing the graph as an intersection over some learned super-graphs, have a natural inductive bias toward modeling transitivity, but (as we prove) cannot model cycles. To this end, we propose binary code box embeddings, where a learned binary code selects a subset of graphs for intersection. We explore several variants, including global binary codes (amounting to a union over intersections) and per-vertex binary codes (allowing greater flexibility) as well as methods of regularization. Theoretical and empirical results show that the proposed models not only preserve a useful inductive bias of transitivity but also have sufficient representational capacity to model arbitrary graphs, including graphs with cycles. 

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2. Capacity and Bias of Learned Geometric Embeddings for Directed Graphs

   Boratko, Michael; Zhang, Dongxu; Monath, Nicholas; Vilnis, Luke; Clarkson, Kenneth L; McCallum, Andrew (January 2021, NeurIPS 2021)

   A wide variety of machine learning tasks such as knowledge base completion, ontology alignment, and multi-label classification can benefit from incorporating into learning differentiable representations of graphs or taxonomies. While vectors in Euclidean space can theoretically represent any graph, much recent work shows that alternatives such as complex, hyperbolic, order, or box embeddings have geometric properties better suited to modeling real-world graphs. Experimentally these gains are seen only in lower dimensions, however, with performance benefits diminishing in higher dimensions. In this work, we introduce a novel variant of box embeddings that uses a learned smoothing parameter to achieve better representational capacity than vector models in low dimensions, while also avoiding performance saturation common to other geometric models in high dimensions. Further, we present theoretical results that prove box embeddings can represent any DAG. We perform rigorous empirical evaluations of vector, hyperbolic, and region-based geometric representations on several families of synthetic and real-world directed graphs. Analysis of these results exposes correlations between different families of graphs, graph characteristics, model size, and embedding geometry, providing useful insights into the inductive biases of various differentiable graph representations. 

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3. ATP: Directed Graph Embedding with Asymmetric Transitivity Preservation

   https://doi.org/10.1609/aaai.v33i01.3301265  

   Sun, Jiankai; Bandyopadhyay, Bortik; Bashizade, Armin; Liang, Jiongqian; Sadayappan, P.; Parthasarathy, Srinivasan (July 2019, Proceedings of the AAAI Conference on Artificial Intelligence)

   Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential property of directed graphs, since it can play an important role in downstream graph inference and analysis. Question difficulty and user expertise follow the characteristic of asymmetric transitivity. Maintaining such properties, while reducing the graph to a lower dimensional vector embedding space, has been the focus of much recent research. In this paper, we tackle the challenge of directed graph embedding with asymmetric transitivity preservation and then leverage the proposed embedding method to solve a fundamental task in CQAs: how to appropriately route and assign newly posted questions to users with the suitable expertise and interest in CQAs. The technique incorporates graph hierarchy and reachability information naturally by relying on a nonlinear transformation that operates on the core reachability and implicit hierarchy within such graphs. Subsequently, the methodology levers a factorization-based approach to generate two embedding vectors for each node within the graph, to capture the asymmetric transitivity. Extensive experiments show that our framework consistently and significantly outperforms the state-of-the-art baselines on three diverse realworld tasks: link prediction, and question difficulty estimation and expert finding in online forums like Stack Exchange. Particularly, our framework can support inductive embedding learning for newly posted questions (unseen nodes during training), and therefore can properly route and assign these kinds of questions to experts in CQAs. 

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4. Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals

   Dan, T; Ding, J; Wei, Z; Kovalsky, S; Kim, M; Kim, WH; Wu, G (September 2023, Advances in Neural Information Processing Systems 36 (NeurIPS 2023))

   Graphs are ubiquitous in various domains, such as social networks and biological systems. Despite the great successes of graph neural networks (GNNs) in modeling and analyzing complex graph data, the inductive bias of locality assumption, which involves exchanging information only within neighboring connected nodes, restricts GNNs in capturing long-range dependencies and global patterns in graphs. Inspired by the classic Brachistochrone problem, we seek how to devise a new inductive bias for cutting-edge graph application and present a general framework through the lens of variational analysis. The backbone of our framework is a two-way mapping between the discrete GNN model and continuous diffusion functional, which allows us to design application-specific objective function in the continuous domain and engineer discrete deep model with mathematical guarantees. First, we address over-smoothing in current GNNs. Specifically, our inference reveals that the existing layer-by-layer models of graph embedding learning are equivalent to a ℓ 2 -norm integral functional of graph gradients, which is the underlying cause of the over-smoothing problem. Similar to edge-preserving filters in image denoising, we introduce the total variation (TV) to promote alignment of the graph diffusion pattern with the global information present in community topologies. On top of this, we devise a new selective mechanism for inductive bias that can be easily integrated into existing GNNs and effectively address the trade-off between model depth and over-smoothing. Second, we devise a novel generative adversarial network (GAN) to predict the spreading flows in the graph through a neural transport equation. To avoid the potential issue of vanishing flows, we tailor the objective function to minimize the transportation within each community while maximizing the inter-community flows. Our new GNN models achieve state-of-the-art (SOTA) performance on graph learning benchmarks such as Cora, Citeseer, and Pubmed. 

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5. A Progressive Transformer for Unifying Binary Code Embedding and Knowledge Transfer

   Lu, Hanxiao; Cai, Hongyu; Liang, Yiming; Bianchi, Antonio; Celik, Z Berkay (March 2025, Proceedings of the IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER))

   Language model approaches have recently been integrated into binary analysis tasks, such as function similarity detection and function signature recovery. These models typically employ a two-stage training process: pre-training via Masked Language Modeling (MLM) on machine code and fine-tuning for specific tasks. While MLM helps to understand binary code struc- tures, it ignores essential code characteristics, including control and data flow, which negatively affect model generalization. Recent work leverages domain-specific features (e.g., control flow graphs and dynamic execution traces) in transformer-based approaches to improve binary code semantic understanding. However, this approach involves complex feature engineering, a cumbersome and time-consuming process that can introduce predictive uncertainty when dealing with stripped or obfuscated code, leading to a performance drop. In this paper, we introduce PROTST, a novel transformer-based methodology for binary code embedding. PROTST employs a hierarchical training process based on a unique tree-like structure, where knowledge progressively flows from fundamental tasks at the root to more specialized tasks at the leaves. This progressive teacher-student paradigm allows the model to build upon previously learned knowledge, resulting in high-quality embeddings that can be effectively leveraged for diverse downstream binary analysis tasks. The effectiveness of PROTST is evaluated in seven binary analysis tasks, and the results show that PROTST yields an average validation score (F1, MRR, and Recall@1) improvement of 14.8% compared to traditional two-stage training and an average validation score of 10.7% compared to multimodal two-stage frameworks. 

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