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.

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 efficiently and 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.

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.

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.

Infantile hemangioma(IH) is one of the most common skin and soft tissue tumors in children. From the appearance, it is very easy to be confused with vascular malformation. As a result, the misdiagnosis between them often occurs. To help doctors screen and identify hemangioma patients, we employed image recognition technology based on deep learning to recognize photos of patients. At first, we process and sort out the existing medical image to establish and release an infantile hemangioma dataset named IH-2021. Then we do classification experiments and obtain the baseline results on it. However, the number of medical images is usually rather small, directly leading to the overfitting of deep learning methods. To further improve the performance of image classification, we constructed a new neural network for image classification of infantile hemangioma, in which we introduced data augmentation approaches based on generative adversarial network and active learning. It has achieved better results on IH-2021 compared with other state-of-the-art models for this task.

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.

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.

A number of people are infected with functional disorders of the pelvic floor such as pelvic organ prolapse and defecation dysfunction. For radiologists, to discern anatomical structures from tomographic images is an important way to find such diseases. However, it is a challenge to recognize the anatomical structures from pelvic MR (magnetic resonance) images, since the same pelvic organs usually are with various shapes and different organs sometimes are with similar appearance in MR images. To address this problem, we introduce a non-local module in the deep neural networks so that both the local features and the global features could be fused to segment organs. Moreover, for the very small quantities of the open pelvic MR images, we have built up a fine-grained MR image segmentation dataset annotated by professional medical researchers, and proposed a data augmentation strategy that is especially suitable for our dataset. In the primary experiments on the dataset, the proposed method in this paper is compared with state-of-the-art image segmentation methods and achieves better performance.

In practice, PDF files may be generated by different tools and their character information quality could be different. As a result, the approaches to detecting formulae from PDF documents usually have much different performance on different PDF files. To address this problem, in this paper we combine and refine the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) model to detect formulae according to both their character and vision features. Based on the characteristic of PDF documents, we propose a series of strategies to train and optimize deep networks, such as the implicit class down-sampling strategy which can reduce the unbalancedness between formulae and other page elements (e.g., text paragraphs, tables, figures, etc.). The region proposal method is also redesigned to generate moderate formula candidates through combining the bottom-up and top-down layout analysis. The experimental results show that the combination of CNN and RNN can increase the robustness of our proposed detection method. Furthermore, the proposed method outperforms the existing formula detection methods on both a ground-truth dataset and a larger self-built dataset, which would be released and available for research purposes.