Zuoyu Yan

Zuoyu Yan, Junru Zhou, Liangcai Gao et al. · pku

We investigate the enhancement of graph neural networks' (GNNs) representation power through their ability in substructure counting. Recent advances have seen the adoption of subgraph GNNs, which partition an input graph into numerous subgraphs, subsequently applying GNNs to each to augment the graph's overall representation. Despite their ability to identify various substructures, subgraph GNNs are hindered by significant computational and memory costs. In this paper, we tackle a critical question: Is it possible for GNNs to count substructures both \textbf{efficiently} and \textbf{provably}? Our approach begins with a theoretical demonstration that the distance to rooted nodes in subgraphs is key to boosting the counting power of subgraph GNNs. To avoid the need for repetitively applying GNN across all subgraphs, we introduce precomputed structural embeddings that encapsulate this crucial distance information. Experiments validate that our proposed model retains the counting power of subgraph GNNs while achieving significantly faster performance.

Zuoyu Yan, Tengfei Ma, Liangcai Gao et al.

Cycles are fundamental elements in graph-structured data and have demonstrated their effectiveness in enhancing graph learning models. To encode such information into a graph learning framework, prior works often extract a summary quantity, ranging from the number of cycles to the more sophisticated persistence diagram summaries. However, more detailed information, such as which edges are encoded in a cycle, has not yet been used in graph neural networks. In this paper, we make one step towards addressing this gap, and propose a structure encoding module, called CycleNet, that encodes cycle information via edge structure encoding in a permutation invariant manner. To efficiently encode the space of all cycles, we start with a cycle basis (i.e., a minimal set of cycles generating the cycle space) which we compute via the kernel of the 1-dimensional Hodge Laplacian of the input graph. To guarantee the encoding is invariant w.r.t. the choice of cycle basis, we encode the cycle information via the orthogonal projector of the cycle basis, which is inspired by BasisNet proposed by Lim et al. We also develop a more efficient variant which however requires that the input graph has a unique shortest cycle basis. To demonstrate the effectiveness of the proposed module, we provide some theoretical understandings of its expressive power. Moreover, we show via a range of experiments that networks enhanced by our CycleNet module perform better in various benchmarks compared to several existing SOTA models.

Xingjian Hu, Zuoyu Yan, Jianhua Zhu et al.

Current research on distributed multi-modal learning typically assumes that clients can access complete information across all modalities, which may not hold in practice. In this paper, we explore patchwork learning, in which the modalities available to different clients vary, and the objective is to impute the missing modalities for each client in an unsupervised manner. Existing methods are shown not to fully utilize the modality information as they tend to rely on only a subset of the observed modalities. To address this issue, we propose GraphPL, which combines graph neural networks with patchwork learning to flexibly integrate all observed modalities and remains robust with noisy inputs. Experimental results show that GraphPL achieves SOTA performance on benchmark datasets. Our results on real-world distributed electronic health record dataset show GraphPL learns strong downstream features and enables tasks like disease prediction via superior modality imputation.

Zuoyu Yan, Qi Zhao, Ze Ye et al.

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.

Zuoyu Yan, Tengfei Ma, Liangcai Gao et al.

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.

Zuoyu Yan, Tengfei Ma, Liangcai Gao et al.

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel solution for inductive relation prediction, an important learning task for knowledge graph completion. To predict the relation between two entities, one can use the existence of rules, namely a sequence of relations. Previous works view rules as paths and primarily focus on the searching of paths between entities. The space of rules is huge, and one has to sacrifice either efficiency or accuracy. In this paper, we consider rules as cycles and show that the space of cycles has a unique structure based on the mathematics of algebraic topology. By exploring the linear structure of the cycle space, we can improve the searching efficiency of rules. We propose to collect cycle bases that span the space of cycles. We build a novel GNN framework on the collected cycles to learn the representations of cycles, and to predict the existence/non-existence of a relation. Our method achieves state-of-the-art performance on benchmarks.

Wenqi Zhao, Liangcai Gao, Zuoyu Yan et al.

Encoder-decoder models have made great progress on handwritten mathematical expression recognition recently. However, it is still a challenge for existing methods to assign attention to image features accurately. Moreover, those encoder-decoder models usually adopt RNN-based models in their decoder part, which makes them inefficient in processing long $\LaTeX{}$ sequences. In this paper, a transformer-based decoder is employed to replace RNN-based ones, which makes the whole model architecture very concise. Furthermore, a novel training strategy is introduced to fully exploit the potential of the transformer in bidirectional language modeling. Compared to several methods that do not use data augmentation, experiments demonstrate that our model improves the ExpRate of current state-of-the-art methods on CROHME 2014 by 2.23%. Similarly, on CROHME 2016 and CROHME 2019, we improve the ExpRate by 1.92% and 2.28% respectively.

Ke Yuan, Zuoyu Yan, Yibo Li et al.

Math expressions are important parts of scientific and educational documents, but some of them may be challenging for junior scholars or students to understand. Nevertheless, constructing textual descriptions for math expressions is nontrivial. In this paper, we explore the feasibility to automatically construct descriptions for math expressions. But there are two challenges that need to be addressed: 1) finding relevant documents since a math equation understanding usually requires several topics, but these topics are often explained in different documents. 2) the sparsity of the collected relevant documents making it difficult to extract reasonable descriptions. Different documents mainly focus on different topics which makes model hard to extract salient information and organize them to form a description of math expressions. To address these issues, we propose a hybrid model (MathDes) which contains two important modules: Selector and Summarizer. In the Selector, a Topic Relation Graph (TRG) is proposed to obtain the relevant documents which contain the comprehensive information of math expressions. TRG is a graph built according to the citations between expressions. In the Summarizer, a summarization model under the Integer Linear Programming (ILP) framework is proposed. This module constructs the final description with the help of a timeline that is extracted from TRG. The experimental results demonstrate that our methods are promising for this task and outperform the baselines in all aspects.

Zuoyu Yan, Tengfei Ma, Liangcai Gao et al.

Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent homology, encodes rich structural information regarding the multi-hop paths connecting nodes. Based on this feature, we propose a graph neural network method that outperforms state-of-the-arts on different benchmarks. As another contribution, we propose a novel algorithm to more efficiently compute the extended persistence diagrams for graphs. This algorithm can be generally applied to accelerate many other topological methods for graph learning tasks.

Zuoyu Yan, Xiaode Zhang, Liangcai Gao et al.

Despite the recent advances in optical character recognition (OCR), mathematical expressions still face a great challenge to recognize due to their two-dimensional graphical layout. In this paper, we propose a convolutional sequence modeling network, ConvMath, which converts the mathematical expression description in an image into a LaTeX sequence in an end-to-end way. The network combines an image encoder for feature extraction and a convolutional decoder for sequence generation. Compared with other Long Short Term Memory(LSTM) based encoder-decoder models, ConvMath is entirely based on convolution, thus it is easy to perform parallel computation. Besides, the network adopts multi-layer attention mechanism in the decoder, which allows the model to align output symbols with source feature vectors automatically, and alleviates the problem of lacking coverage while training the model. The performance of ConvMath is evaluated on an open dataset named IM2LATEX-100K, including 103556 samples. The experimental results demonstrate that the proposed network achieves state-of-the-art accuracy and much better efficiency than previous methods.

Liangcai Gao, Zhuoren Jiang, Yue Yin et al.

While neural network approaches are achieving breakthrough performance in the natural language related fields, there have been few similar attempts at mathematical language related tasks. In this study, we explore the potential of applying neural representation techniques to Mathematical Information Retrieval (MIR) tasks. In more detail, we first briefly analyze the characteristic differences between natural language and mathematical language. Then we design a "symbol2vec" method to learn the vector representations of formula symbols (numbers, variables, operators, functions, etc.) Finally, we propose a "formula2vec" based MIR approach and evaluate its performance. Preliminary experiment results show that there is a promising potential for applying formula embedding models to mathematical language representation and MIR tasks.