A survey on handwritten mathematical expression recognition: The rise of encoder-decoder and GNN models

This paper presents the competition on Offline Recognition and Spotting of Handwritten Mathematical Expressions (OffRaSHME) held at the 17th International Conference on Frontiers in Handwriting Recognition (ICFHR 2020). Handwritten Mathematical Expression Recognition (HMER) has wide potential applications and is capturing increasing attention in recent years. Previous HMER competitions mainly focused on online datasets or offline datasets that are converted from online data. In this competition, we have collected a dataset of offline handwritten mathematical expressions by scanning papers that contain expressions. Moreover, we labeled the offline dataset at symbol level, i.e., the bounding boxes of each symbol are also provided, to facilitate the research of HMER. At last, 19,749 offline handwritten mathematical expressions are collected for training, and 2,000 ones are provided for evaluating the participating systems. In the competition, 7 teams submitted 8 systems for the task of offline HMER, among which 5 systems only use the provided datasets without any extra data while 3 systems use extra data. The winner team achieved a recognition accuracy of 79.85% (without extra data) and 81.85% (with extra data) on the offline formula recognition task.

Handwritten mathematical expression recognition (HMER) is a challenging task due to the complex two-dimensional structure of mathematical expressions and the similarity of handwritten texts. Most existing methods for HMER only consider single-scale features while ignoring multi-scale features that are very important to HMER. Few works have explored the fusion of multi-scale features in HMER, but exhibited an extra branch that brings more parameters and computation. In this paper, we propose an end-to-end method to integrate multi-scale features using a unified model. Specifically, we customized the Dense Atrous Spatial Pyramid Pooling (DenseASPP) to our backbone network to capture the multi-scale features of the input image meanwhile expanding the receptive fields. Moreover, we added a symbol classifier using focal loss to better discriminate and recognize similar symbols, to further improve the performance of HMER. Experiments on the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2014, 2016 and 2019 shows that the proposed method achieves superior performance to most state-of-the-art methods, demonstrating the effectiveness of the proposed method.

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.

We present a temporal classification constraint as an auxiliary learning method for improving the recognition of Handwritten Mathematical Expression (HME). Connectionist temporal classification (CTC) is used to learn the temporal alignment of the input feature sequence and corresponding symbol label sequence. The CTC alignment is trained with the encoder-decoder alignment through a combination of CTC loss and encoder-decoder loss to improve the feature learning of the encoder in the encoder-decoder model. We show the effectiveness of the approach in improving symbol classification and expression recognition on the CROHME datasets.

Developing fast and accurate computational models to simulate intricate physical phenomena has been a persistent research challenge. Recent studies have demonstrated remarkable capabilities in predicting various physical outcomes through machine learning-assisted approaches. However, it remains challenging to generalize current methods, usually crafted for a specific problem, to other more complex or broader scenarios. To address this challenge, we developed graph neural network (GNN) models with enhanced generalizability derived from the distinct GNN architecture and neural operator techniques. As a proof of concept, we employ our GNN models to predict finite element (FE) simulation results for three-dimensional solid mechanics problems with varying boundary conditions. Results show that our GNN model achieves accurate and robust performance in predicting the stress and deformation profiles of structures compared with FE simulations. Furthermore, the neural operator embedded GNN approach enables learning and predicting various solid mechanics problems in a generalizable fashion, making it a promising approach for surrogate modeling.

Sex classification is a major benchmark of previous work in learning on the structural connectome, a naturally occurring brain graph that has proven useful for studying cognitive function and impairment. While graph neural networks (GNNs), specifically graph convolutional networks (GCNs), have gained popularity lately for their effectiveness in learning on graph data, achieving strong performance in adult sex classification tasks, their application to pediatric populations remains unexplored. We seek to characterize the capacity for GNN models to learn connectomic patterns on pediatric data through an exploration of training techniques and architectural design choices. Two datasets comprising an adult BRIGHT dataset (N = 147 Hodgkin's lymphoma survivors and N = 162 age similar controls) and a pediatric Human Connectome Project in Development (HCP-D) dataset (N = 135 healthy subjects) were utilized. Two GNN models (GCN simple and GCN residual), a deep neural network (multi-layer perceptron), and two standard machine learning models (random forest and support vector machine) were trained. Architecture exploration experiments were conducted to evaluate the impact of network depth, pooling techniques, and skip connections on the ability of GNN models to capture connectomic patterns. Models were assessed across a range of metrics including accuracy, AUC score, and adversarial robustness. GNNs outperformed other models across both populations. Notably, adult GNN models achieved 85.1% accuracy in sex classification on unseen adult participants, consistent with prior studies. The extension of the adult models to the pediatric dataset and training on the smaller pediatric dataset were sub-optimal in their performance. Using adult data to augment pediatric models, the best GNN achieved comparable accuracy across unseen pediatric (83.0%) and adult (81.3%) participants. Adversarial sensitivity experiments showed that the simple GCN remained the most robust to perturbations, followed by the multi-layer perceptron and the residual GCN. These findings underscore the potential of GNNs in advancing our understanding of sex-specific neurological development and disorders and highlight the importance of data augmentation in overcoming challenges associated with small pediatric datasets. Further, they highlight relevant tradeoffs in the design landscape of connectomic GNNs. For example, while the simpler GNN model tested exhibits marginally worse accuracy and AUC scores in comparison to the more complex residual GNN, it demonstrates a higher degree of adversarial robustness.

Collecting handwritten mathematical expressions (HMEs) generally requires a lot of time and effort for data preparation, data collection, annotation and so on. In this paper, we present a method for generating realistic HMEs in a wide variety of structures and styles from a LaTeX sequence or a MathML script using online isolated symbol patterns. Our method firstly positions all symbols in a symbol relation tree constructed from the input LaTeX or MathML script. Then, it places normalized online symbol patterns into the corresponding locations. A questionnaire-based experiment shows that the synthetic patterns are as clear and natural as the real patterns. Therefore, we can use the generated synthetic HME patterns for research on HME recognition and clustering.

Deep learning has led to major advances in fields like natural language processing, computer vision, and other Euclidean data domains. Yet, many important fields have data defined on irregular domains, requiring graphs to be explicitly modeled. One such application is drug discovery. Recently, research has found that using graph neural network (GNN) models, given enough data, can perform better than using human-engineered fingerprints or descriptors in predicting molecular properties of potential antibiotics.We explore these state-of-the-art AI models on predicting desirable molecular properties for drugs that can inhibit SARS-CoV-2. We build upon the GNN models with ideas from recent breakthroughs in geometric deep learning, inspired by the topologies of the molecules. In this poster paper, we present an overview of the drug discovery framework, drug-target interaction framework, and GNNs. Preliminary results on two COVID-19 related datasets are encouraging, achieving a ROC-AUC of 0.72 for FDA-approved chemical library screened against SARS-CoV-2 in vitro.

We present a technique based on stroke order normalization for improving recognition of online handwritten mathematical expressions (ME). The stroke order dependent system has less time complexity than the stroke order free system, but it must incorporate special grammar rules to cope with stroke order variations. The stroke order normalization technique solves this problem and also the problem of unexpected stroke order variations without increasing the time complexity of ME recognition. In order to normalize stroke order, the X–Y cut method is modified since its original form causes problems when structural components in ME overlap. First, vertically ordered strokes are located by detecting vertical symbols and their upper/lower components, which are treated as MEs and reordered recursively. Second, unordered strokes on the left side of the vertical symbols are reordered as horizontally ordered strokes. Third, the remaining strokes are reordered recursively. The horizontally ordered strokes are reordered from left to right, and the vertically ordered strokes are reordered from top to bottom. Finally, the proposed stroke order normalization is combined with the stroke order dependent ME recognition system. The evaluations on the CROHME 2014 database show that the ME recognition system incorporating the stroke order normalization outperforms all other systems that use only CROHME 2014 for training while the processing time is kept low.

Graph Neural Networks (GNNs) have become indispensable tools for learning from graph-structured data, catering to various applications such as social network analysis and fraud detection for financial services. At the heart of these networks are the edges, which are crucial in guiding GNN models' predictions. In many scenarios, these edges represent sensitive information, such as personal associations or financial dealings, which require privacy assurance. However, their contributions to GNN model predictions may, in turn, be exploited by the adversary to compromise their privacy. Motivated by these conflicting requirements, this paper investigates edge privacy in contexts where adversaries possess only black-box access to the target GNN model, restricted further by access controls, preventing direct insights into arbitrary node outputs. Moreover, we are the first to extensively examine situations where the target graph continuously evolves—a common trait of many real-world graphs. In this setting, we present a range of attacks that leverage the message-passing mechanism of GNNs. We evaluated the effectiveness of our attacks using nine real-world datasets, encompassing both static and dynamic graphs, across four different GNN architectures. The results demonstrate that our attack outperforms existing methods across various GNN architectures, consistently achieving an F1 score of at least 0.8 in static scenarios. Furthermore, our attack retains robustness in dynamic graph scenarios, maintaining F1 scores up to 0.8, unlike previous methods that only achieve F1 scores around 0.2.

Past events have revealed that widespread blackouts are mostly a result of cascading failures in the power grid. Understanding the underlining mechanisms of cascading failures can help in developing strategies to minimize the risk of such events. Moreover, a real-time detection of precursors to cascading failures will help operators take measures to prevent their propagation. Currently, the well-established probabilistic and physics-based models of cascading failures offer low computational efficiency, hindering them to be used only as offline tools. In this work, we develop a data-driven methodology for online estimation of the risk of cascading failures. We utilize a physics-based cascading failure model to generate a cascading failure dataset considering different operating conditions and failure scenarios, thus obtaining a sample space covering a large set of power grid states that are labeled as safe or unsafe. We use the synthetic data to train deep learning architectures, namely Feed-forward Neural Networks (FNN) and Graph Neural Networks (GNN). With the development of GNNs, improved performance is achieved with graph-structured data, and GNNs can generalize to graphs of diverse sizes. A comparison between FNN and GNN is made and the GNNs inductive capability is demonstrated via test grids. Furthermore, we apply transfer learning to improve the performance of a pre-trained GNN model on power grids not seen in the training process. The GNN model shows accuracy and balanced accuracy above 96% on selected test datasets not used in the training. Conversely, the FNN shows accuracy above 85% and balanced accuracy above 81% on test datasets unseen during training. Overall, the GNN model is successful in determining, if one or several simultaneous outages result in a critical grid state, under specific grid operating conditions.

Most distribution system operators may not accurately record or completely maintain the phase connections for the numerous LV customers. Different consumer phase identification (CPI) approaches based on voltages, powers or other measurements are proposed in the literature. Due to the technical challenges in collecting voltage measurements, power measurement based approaches are preferable. Hence, this paper proposes a novel power based CPI methodology applying Graph Neural Networks (GNNs). The CPI methodology generates synthetic transformer power profiles assuming random combinations of phases for the measured load profiles, which are used altogether to train the GNN model. The GNN model is then tested using measured transformer and load power profiles. The performance of the methodology is evaluated in a test low voltage grid of 55 loads under various conditions of Photovoltaic penetration, Photovoltaics under maintenance, measurement errors, unmetered consumption, uncertain grid asset parameters and inaccurate phase connections. Further tests on a real low voltage grid with 111 loads prove the scalability of the methodology. The attained results show that the GNN model can achieve accuracy above 90% in most cases, outperforming various state-of-the-art methods. • The Graph Neural Network identifies the phase labels with accuracy higher than 90%. • Under noisy or unmetered demand, the Graph Neural Network achieves accuracy over 90%. • Under various Photovoltaic cases, the Graph Neural Network yields accuracy over 90%. • The Graph Neural Network yields accuracy of 92% in case of multi-phase connections. • The grid losses and uncertain assets’ parameters have minor impact on model accuracy.

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

Drug response prediction is an essential part of precision medicine, which assesses the efficacy of drugs in specific cancer cell lines. Recently, numerous deep learning models have been developed for drug response prediction. The ability to effectively represent complicated interactions within a network makes Graph Neural Network (GNN) models a prominent area of exploration. To exploit the diverse capabilities of different GNN models, the proposed model uses an ensemble approach that combines results from Graph Convolutional Network (GCN), Graph SAmple and aggreGatE Network (GraphSAGE) and Graph Attention Network (GAT)-based models for drug response prediction. The proposed ensemble GNN model is used to predict the efficacy of drugs in treating leukemia. The model outperformed individual models when evaluated with the GDSC1000 dataset, with lower root mean squared error, higher Pearson’s correlation coefficient, higher coefficient of determination and higher Spearman’s correlation coefficient. Furthermore, most of the drugs identified by the model as potential candidates for the treatment of leukemia are currently in clinical trials or have supporting evidence in the PubMed literature database.

Graph Neural Networks (GNNs) are the current state-of-the-art models in learning node representations for many predictive tasks on graphs. Typically, GNNs reuses the same set of model parameters across all nodes in the graph to improve the training efficiency and exploit the translationally-invariant properties in many datasets. However, the parameter sharing scheme prevents GNNs from distinguishing two nodes that are isomorphic and that the translation invariance property may not exhibit in real-world graphs. In this paper, we present Graph Representation Learning with Adaptive Mixtures (GRAM), a novel approach for learning node representations in a graph by introducing multiple independent GNN models and a trainable mixture distribution for each node. GRAM is a general framework that can be readily embedded into existing models for enhancing representation learning. It allows for adaptive node clustering with mixtures and joint optimization of all GNN models simultaneously. To achieve this, we develop an Expectation-Maximization algorithm with stochastic gradient descent in a scalable manner. Specifically, in the E-Step, we approximate the posterior probability distribution of the latent cluster membership based on the k-th independent GNN models in the last iteration. In the M-step, we update all GNN models and the mixture parameters based on the refined latent cluster membership for downstream tasks, e.g., node classification. To fully exploit the graph structural information, we further implement a regularization term on unlabeled nodes, which encourages adjacent nodes to have the same mixture distribution. By jointly optimizing the model in an end-to-end manner, GRAM learns to capture different abstract patterns on graphs for different node clusters, which yields discriminative representation for each node. We evaluate GRAM on five benchmark datasets with extensive experiments. GRAM is demonstrated to consistently boost state-of-the-art GNN variants in node classification tasks.