Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure. However, processes in real-world applications often exhibit non-Gaussianity and nonstationarity. Moreover, likelihood-based inference for GPs is computationally expensive and thus prohibitive for large datasets. In this paper we propose a deep neural network (DNN) based two-stage model for spatio-temporal interpolation and forecasting. Interpolation is performed in the first step, which utilizes a dependent DNN with the embedding layer constructed with spatio-temporal basis functions. For the second stage, we use Long-Short Term Memory (LSTM) and convolutional LSTM to forecast future observations at a given location. We adopt the quantile-based loss function in the DNN to provide probabilistic forecasting. Compared to Kriging, the proposed method does not require specifying covariance functions or making stationarity assumption, and is computationally efficient. Therefore, it is suitable for large-scale prediction of complex spatio-temporal processes. We apply our method to monthly $PM_{2.5}$ data at more than $200,000$ space-time locations from January 1999 to December 2022 for fast imputation of missing values and forecasts with uncertainties.

Recently, ChatGPT, a representative large language model (LLM), has gained considerable attention due to its powerful emergent abilities. Some researchers suggest that LLMs could potentially replace structured knowledge bases like knowledge graphs (KGs) and function as parameterized knowledge bases. However, while LLMs are proficient at learning probabilistic language patterns based on large corpus and engaging in conversations with humans, they, like previous smaller pre-trained language models (PLMs), still have difficulty in recalling facts while generating knowledge-grounded contents. To overcome these limitations, researchers have proposed enhancing data-driven PLMs with knowledge-based KGs to incorporate explicit factual knowledge into PLMs, thus improving their performance to generate texts requiring factual knowledge and providing more informed responses to user queries. This paper reviews the studies on enhancing PLMs with KGs, detailing existing knowledge graph enhanced pre-trained language models (KGPLMs) as well as their applications. Inspired by existing studies on KGPLM, this paper proposes to enhance LLMs with KGs by developing knowledge graph-enhanced large language models (KGLLMs). KGLLM provides a solution to enhance LLMs' factual reasoning ability, opening up new avenues for LLM research.

Recently, deep learning has revolutionized the field of natural language processing, with neural language models proving to be very effective for next-word prediction. However, a rigorous theoretical explanation for their success in the context of formal language theory has not yet been developed, as it is unclear why neural language models can learn the combinatorial rules that govern the next-word prediction task. In this paper, we study a class of formal languages that can be used to model real-world examples of English sentences. We construct neural language models can solve the next-word prediction task in this context with zero error. Our proof highlights the different roles of the embedding layer and the fully connected component within the neural language model.

Downsampling layers, including pooling and strided convolutions, are crucial components of the convolutional neural network architecture that determine both the granularity/scale of image feature analysis as well as the receptive field size of a given layer. To fully understand this problem, we analyse the performance of models independently trained with each pooling configurations on CIFAR10, using a ResNet20 network, and show that the position of the downsampling layers can highly influence the performance of a network and predefined downsampling configurations are not optimal. Network Architecture Search (NAS) might be used to optimize downsampling configurations as an hyperparameter. However, we find that common one-shot NAS based on a single SuperNet does not work for this problem. We argue that this is because a SuperNet trained for finding the optimal pooling configuration fully shares its parameters among all pooling configurations. This makes its training hard, because learning some configurations can harm the performance of others. Therefore, we propose a balanced mixture of SuperNets that automatically associates pooling configurations to different weight models and helps to reduce the weight-sharing and inter-influence of pooling configurations on the SuperNet parameters. We evaluate our proposed approach on CIFAR10, CIFAR100, as well as Food101 and show that in all cases, our model outperforms other approaches and improves over the default pooling configurations.

Machine learning (ML) is a focal element of digitization that affects many areas of modern society: besides driving a plethora of physical and virtual products already woven into our daily lives, such as smartphones and social media platforms, ML techniques can be leveraged to power a wide range of business applications [1, 2]. Although ML as an umbrella term comprises various techniques, some of which are aimed at different purposes, most ML algorithms are designed to calculate empirical predictions based on given data [2]. This prediction-oriented approach to ML is widely referred to as supervised learning, predictive analytics, or predictive modeling, and initially requires at least two data sets: one for model training and one for testing [2, 3]. While the former allows a given ML algorithm to "learn" patterns that connect the model input and output, the latter serves to evaluate the predictive accuracy of a trained model. In practice, if a corresponding ML model is attributed to possess a sufficient degree of predictive power, it may be deployed in a productive environment to compute real-world predictions, e.g., to support managerial decision making. The application of supervised learning in business contexts is highly relevant as it may drive applications in the fields of predictive maintenance, financial fraud detection, personalized product recommendation, and more. Consequently, the global ML market size was valued at US$ 34.56 billion in 2021 and is expected to grow to US$ 74.99 billion by 2028 at a compound annual growth rate of 25.7% [4]. Given the enormous business potential of ML, a considerable number of companies have already begun to launch data analytics initiatives to automate their processes or support their decision making over the last years.

Objectives: Graph representation learning (GRL) has emerged as a pivotal field that has contributed significantly to breakthroughs in various fields, including biomedicine. The objective of this survey is to review the latest advancements in GRL methods and their applications in the biomedical field. We also highlight key challenges currently faced by GRL and outline potential directions for future research. Methods: We conducted a comprehensive search of multiple databases, including PubMed, Web of Science, IEEE Xplore, and Google Scholar, to collect relevant publications from the past two years (2021-2022). The studies selected for review were based on their relevance to the topic and the publication quality.

Malware is a significant threat to the security of computer systems and networks which requires sophisticated techniques to analyze the behavior and functionality for detection. Traditional signature-based malware detection methods have become ineffective in detecting new and unknown malware due to their rapid evolution. One of the most promising techniques that can overcome the limitations of signature-based detection is to use control flow graphs (CFGs). CFGs leverage the structural information of a program to represent the possible paths of execution as a graph, where nodes represent instructions and edges represent control flow dependencies. Machine learning (ML) algorithms are being used to extract these features from CFGs and classify them as malicious or benign. In this survey, we aim to review some state-of-the-art methods for malware detection through CFGs using ML, focusing on the different ways of extracting, representing, and classifying. Specifically, we present a comprehensive overview of different types of CFG features that have been used as well as different ML algorithms that have been applied to CFG-based malware detection. We provide an in-depth analysis of the challenges and limitations of these approaches, as well as suggest potential solutions to address some open problems and promising future directions for research in this field.

Autonomous driving systems have witnessed a significant development during the past years thanks to the advance in machine learning-enabled sensing and decision-making algorithms. One critical challenge for their massive deployment in the real world is their safety evaluation. Most existing driving systems are still trained and evaluated on naturalistic scenarios collected from daily life or heuristically-generated adversarial ones. However, the large population of cars, in general, leads to an extremely low collision rate, indicating that the safety-critical scenarios are rare in the collected real-world data. Thus, methods to artificially generate scenarios become crucial to measure the risk and reduce the cost. In this survey, we focus on the algorithms of safety-critical scenario generation in autonomous driving. We first provide a comprehensive taxonomy of existing algorithms by dividing them into three categories: data-driven generation, adversarial generation, and knowledge-based generation. Then, we discuss useful tools for scenario generation, including simulation platforms and packages. Finally, we extend our discussion to five main challenges of current works -- fidelity, efficiency, diversity, transferability, controllability -- and research opportunities lighted up by these challenges.

Recently, speech-to-text translation has attracted more and more attention and many studies have emerged rapidly. In this paper, we present a comprehensive survey on direct speech translation aiming to summarize the current state-of-the-art techniques. First, we categorize the existing research work into three directions based on the main challenges -- modeling burden, data scarcity, and application issues. To tackle the problem of modeling burden, two main structures have been proposed, encoder-decoder framework (Transformer and the variants) and multitask frameworks. For the challenge of data scarcity, recent work resorts to many sophisticated techniques, such as data augmentation, pre-training, knowledge distillation, and multilingual modeling. We analyze and summarize the application issues, which include real-time, segmentation, named entity, gender bias, and code-switching. Finally, we discuss some promising directions for future work.