Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where deep learning algorithms are used to solve problems in mathematics. The latter has popularised the field of scientific machine learning where deep learning is applied to problems in scientific computing. Specifically, more and more neural network architectures have been developed to solve specific classes of partial differential equations (PDEs). Such methods exploit properties that are inherent to PDEs and thus solve the PDEs better than standard feed-forward neural networks, recurrent neural networks, or convolutional neural networks. This has had a great impact in the area of mathematical modeling where parametric PDEs are widely used to model most natural and physical processes arising in science and engineering. In this work, we review such methods as well as their extensions for parametric studies and for solving the related inverse problems. We equally proceed to show their relevance in some industrial applications.
Understanding deep learning model behavior is critical to accepting machine learning-based decision support systems in the medical community. Previous research has shown that jointly using clinical notes with electronic health record (EHR) data improved predictive performance for patient monitoring in the intensive care unit (ICU). In this work, we explore the underlying reasons for these improvements. While relying on a basic attention-based model to allow for interpretability, we first confirm that performance significantly improves over state-of-the-art EHR data models when combining EHR data and clinical notes. We then provide an analysis showing improvements arise almost exclusively from a subset of notes containing broader context on patient state rather than clinician notes. We believe such findings highlight deep learning models for EHR data to be more limited by partially-descriptive data than by modeling choice, motivating a more data-centric approach in the field.
Deep learning-based weather prediction models have advanced significantly in recent years. However, data-driven models based on deep learning are difficult to apply to real-world applications because they are vulnerable to spatial-temporal shifts. A weather prediction task is especially susceptible to spatial-temporal shifts when the model is overfitted to locality and seasonality. In this paper, we propose a training strategy to make the weather prediction model robust to spatial-temporal shifts. We first analyze the effect of hyperparameters and augmentations of the existing training strategy on the spatial-temporal shift robustness of the model. Next, we propose an optimal combination of hyperparameters and augmentation based on the analysis results and a test-time augmentation. We performed all experiments on the W4C22 Transfer dataset and achieved the 1st performance.
Traditional weather forecasting relies on domain expertise and computationally intensive numerical simulation systems. Recently, with the development of a data-driven approach, weather forecasting based on deep learning has been receiving attention. Deep learning-based weather forecasting has made stunning progress, from various backbone studies using CNN, RNN, and Transformer to training strategies using weather observations datasets with auxiliary inputs. All of this progress has contributed to the field of weather forecasting; however, many elements and complex structures of deep learning models prevent us from reaching physical interpretations. This paper proposes a SImple baseline with a spatiotemporal context Aggregation Network (SIANet) that achieved state-of-the-art in 4 parts of 5 benchmarks of W4C22. This simple but efficient structure uses only satellite images and CNNs in an end-to-end fashion without using a multi-model ensemble or fine-tuning. This simplicity of SIANet can be used as a solid baseline that can be easily applied in weather forecasting using deep learning.
Class-Incremental Learning is a challenging problem in machine learning that aims to extend previously trained neural networks with new classes. This is especially useful if the system is able to classify new objects despite the original training data being unavailable. While the semantic segmentation problem has received less attention than classification, it poses distinct problems and challenges since previous and future target classes can be unlabeled in the images of a single increment. In this case, the background, past and future classes are correlated and there exist a background-shift. In this paper, we address the problem of how to model unlabeled classes while avoiding spurious feature clustering of future uncorrelated classes. We propose to use Evidential Deep Learning to model the evidence of the classes as a Dirichlet distribution. Our method factorizes the problem into a separate foreground class probability, calculated by the expected value of the Dirichlet distribution, and an unknown class (background) probability corresponding to the uncertainty of the estimate. In our novel formulation, the background probability is implicitly modeled, avoiding the feature space clustering that comes from forcing the model to output a high background score for pixels that are not labeled as objects. Experiments on the incremental Pascal VOC, and ADE20k benchmarks show that our method is superior to state-of-the-art, especially when repeatedly learning new classes with increasing number of increments.
Computer vision and machine learning are playing an increasingly important role in computer-assisted diagnosis; however, the application of deep learning to medical imaging has challenges in data availability and data imbalance, and it is especially important that models for medical imaging are built to be trustworthy. Therefore, we propose TRUDLMIA, a trustworthy deep learning framework for medical image analysis, which adopts a modular design, leverages self-supervised pre-training, and utilizes a novel surrogate loss function. Experimental evaluations indicate that models generated from the framework are both trustworthy and high-performing. It is anticipated that the framework will support researchers and clinicians in advancing the use of deep learning for dealing with public health crises including COVID-19.
Scenario-based probabilistic forecasts have become vital for decision-makers in handling intermittent renewable energies. This paper presents a recent promising deep learning generative approach called denoising diffusion probabilistic models. It is a class of latent variable models which have recently demonstrated impressive results in the computer vision community. However, to our knowledge, there has yet to be a demonstration that they can generate high-quality samples of load, PV, or wind power time series, crucial elements to face the new challenges in power systems applications. Thus, we propose the first implementation of this model for energy forecasting using the open data of the Global Energy Forecasting Competition 2014. The results demonstrate this approach is competitive with other state-of-the-art deep learning generative models, including generative adversarial networks, variational autoencoders, and normalizing flows.
The proliferation of deep learning techniques led to a wide range of advanced analytics applications in important business areas such as predictive maintenance or product recommendation. However, as the effectiveness of advanced analytics naturally depends on the availability of sufficient data, an organization's ability to exploit the benefits might be restricted by limited data or likewise data access. These challenges could force organizations to spend substantial amounts of money on data, accept constrained analytics capacities, or even turn into a showstopper for analytics projects. Against this backdrop, recent advances in deep learning to generate synthetic data may help to overcome these barriers. Despite its great potential, however, synthetic data are rarely employed. Therefore, we present a taxonomy highlighting the various facets of deploying synthetic data for advanced analytics systems. Furthermore, we identify typical application scenarios for synthetic data to assess the current state of adoption and thereby unveil missed opportunities to pave the way for further research.
Stochastic gradients closely relate to both optimization and generalization of deep neural networks (DNNs). Some works attempted to explain the success of stochastic optimization for deep learning by the arguably heavy-tail properties of gradient noise, while other works presented theoretical and empirical evidence against the heavy-tail hypothesis on gradient noise. Unfortunately, formal statistical tests for analyzing the structure and heavy tails of stochastic gradients in deep learning are still under-explored. In this paper, we mainly make two contributions. First, we conduct formal statistical tests on the distribution of stochastic gradients and gradient noise across both parameters and iterations. Our statistical tests reveal that dimension-wise gradients usually exhibit power-law heavy tails, while iteration-wise gradients and stochastic gradient noise caused by minibatch training usually do not exhibit power-law heavy tails. Second, we further discover that the covariance spectra of stochastic gradients have the power-law structures overlooked by previous studies and present its theoretical implications for training of DNNs. While previous studies believed that the anisotropic structure of stochastic gradients matters to deep learning, they did not expect the gradient covariance can have such an elegant mathematical structure. Our work challenges the existing belief and provides novel insights on the structure of stochastic gradients in deep learning.
We examined multiple deep neural network (DNN) architectures for suitability in predicting neurotransmitter concentrations from labeled in vitro fast scan cyclic voltammetry (FSCV) data collected on carbon fiber electrodes. Suitability is determined by the predictive performance in the "out-of-probe" case, the response to artificially induced electrical noise, and the ability to predict when the model will be errant for a given probe. This work extends prior comparisons of time series classification models by focusing on this specific task. It extends previous applications of machine learning to FSCV task by using a much larger data set and by incorporating recent advancements in deep neural networks. The InceptionTime architecture, a deep convolutional neural network, has the best absolute predictive performance of the models tested but was more susceptible to noise. A naive multilayer perceptron architecture had the second lowest prediction error and was less affected by the artificial noise, suggesting that convolutions may not be as important for this task as one might suspect.
In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information transmission and representation. While considerable efforts are concentrated on realizing optimal channel properties during network optimization, we study a frequently overlooked possibility that neural networks can be initialized toward optimal channels. Our theory, consistent with experimental validation, identifies primary mechanics underlying this unknown possibility and suggests intrinsic connections between statistical physics and deep learning. Unlike the conventional theories that characterize neural networks applying the classic mean-filed approximation, we offer analytic proof that this extensively applied simplification scheme is not valid in studying neural networks as information channels. To fill this gap, we develop a corrected mean-field framework applicable for characterizing the limiting behaviors of information propagation in neural networks without strong assumptions on inputs. Based on it, we propose an analytic theory to prove that mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry, a case where information transmits via norm-preserving mappings. These theoretical predictions are validated by experiments on real neural networks, suggesting the robustness of our theory against finite-size effects. Finally, we analyze our findings with information bottleneck theory to confirm the precise relations among dynamic isometry, mutual information maximization, and optimal channel properties in deep learning.
A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin
A unidirectional imager would only permit image formation along one direction, from an input field-of-view (FOV) A to an output FOV B, and in the reverse path, the image formation would be blocked. Here, we report the first demonstration of unidirectional imagers, presenting polarization-insensitive and broadband unidirectional imaging based on successive diffractive layers that are linear and isotropic. These diffractive layers are optimized using deep learning and consist of hundreds of thousands of diffractive phase features, which collectively modulate the incoming fields and project an intensity image of the input onto an output FOV, while blocking the image formation in the reverse direction. After their deep learning-based training, the resulting diffractive layers are fabricated to form a unidirectional imager. As a reciprocal device, the diffractive unidirectional imager has asymmetric mode processing capabilities in the forward and backward directions, where the optical modes from B to A are selectively guided/scattered to miss the output FOV, whereas for the forward direction such modal losses are minimized, yielding an ideal imaging system between the input and output FOVs. Although trained using monochromatic illumination, the diffractive unidirectional imager maintains its functionality over a large spectral band and works under broadband illumination. We experimentally validated this unidirectional imager using terahertz radiation, very well matching our numerical results. Using the same deep learning-based design strategy, we also created a wavelength-selective unidirectional imager, where two unidirectional imaging operations, in reverse directions, are multiplexed through different illumination wavelengths. Diffractive unidirectional imaging using structured materials will have numerous applications in e.g., security, defense, telecommunications and privacy protection.
Deep learning models that leverage large datasets are often the state of the art for modelling molecular properties. When the datasets are smaller (< 2000 molecules), it is not clear that deep learning approaches are the right modelling tool. In this work we perform an extensive study of the calibration and generalizability of probabilistic machine learning models on small chemical datasets. Using different molecular representations and models, we analyse the quality of their predictions and uncertainties in a variety of tasks (binary, regression) and datasets. We also introduce two simulated experiments that evaluate their performance: (1) Bayesian optimization guided molecular design, (2) inference on out-of-distribution data via ablated cluster splits. We offer practical insights into model and feature choice for modelling small chemical datasets, a common scenario in new chemical experiments. We have packaged our analysis into the DIONYSUS repository, which is open sourced to aid in reproducibility and extension to new datasets.
The identification of vulnerabilities is an important element in the software development life cycle to ensure the security of software. While vulnerability identification based on the source code is a well studied field, the identification of vulnerabilities on basis of a binary executable without the corresponding source code is more challenging. Recent research [1] has shown, how such detection can be achieved by deep learning methods. However, that particular approach is limited to the identification of only 4 types of vulnerabilities. Subsequently, we analyze to what extent we could cover the identification of a larger variety of vulnerabilities. Therefore, a supervised deep learning approach using recurrent neural networks for the application of vulnerability detection based on binary executables is used. The underlying basis is a dataset with 50,651 samples of vulnerable code in the form of a standardized LLVM Intermediate Representation. The vectorised features of a Word2Vec model are used to train different variations of three basic architectures of recurrent neural networks (GRU, LSTM, SRNN). A binary classification was established for detecting the presence of an arbitrary vulnerability, and a multi-class model was trained for the identification of the exact vulnerability, which achieved an out-of-sample accuracy of 88% and 77%, respectively. Differences in the detection of different vulnerabilities were also observed, with non-vulnerable samples being detected with a particularly high precision of over 98%. Thus, the methodology presented allows an accurate detection of 23 (compared to 4 [1]) vulnerabilities.
Community Question Answering is the field of computational linguistics that deals with problems derived from the questions and answers posted to websites such as Quora or Stack Overflow. Among some of these problems we find the issue of ranking the multiple answers posted in reply to each question by how informative they are in the attempt to solve the original question. This work tries to advance the state of the art on answer ranking for community Question Answering by proceeding with a deep learning approach. We started off by creating a large data set of questions and answers posted to the Stack Overflow website. We then leveraged the natural language processing capabilities of dense embeddings and LSTM networks to produce a prediction for the accepted answer attribute, and present the answers in a ranked form ordered by how likely they are to be marked as accepted by the question asker. We also produced a set of numerical features to assist with the answer ranking task. These numerical features were either extracted from metadata found in the Stack Overflow posts or derived from the questions and answers texts. We compared the performance of our deep learning models against a set of forest and boosted trees ensemble methods and found that our models could not improve the best baseline results. We speculate that this lack of performance improvement versus the baseline models may be caused by the large number of out of vocabulary words present in the programming code snippets found in the questions and answers text. We conclude that while a deep learning approach may be helpful in answer ranking problems new methods should be developed to assist with the large number of out of vocabulary words present in the programming code snippets
Interoperability issue is a significant problem in Building Information Modeling (BIM). Object type, as a kind of critical semantic information needed in multiple BIM applications like scan-to-BIM and code compliance checking, also suffers when exchanging BIM data or creating models using software of other domains. It can be supplemented using deep learning. Current deep learning methods mainly learn from the shape information of BIM objects for classification, leaving relational information inherent in the BIM context unused. To address this issue, we introduce a two-branch geometric-relational deep learning framework. It boosts previous geometric classification methods with relational information. We also present a BIM object dataset IFCNet++, which contains both geometric and relational information about the objects. Experiments show that our framework can be flexibly adapted to different geometric methods. And relational features do act as a bonus to general geometric learning methods, obviously improving their classification performance, thus reducing the manual labor of checking models and improving the practical value of enriched BIM models.
Causal deep learning (CDL) is a new and important research area in the larger field of machine learning. With CDL, researchers aim to structure and encode causal knowledge in the extremely flexible representation space of deep learning models. Doing so will lead to more informed, robust, and general predictions and inference -- which is important! However, CDL is still in its infancy. For example, it is not clear how we ought to compare different methods as they are so different in their output, the way they encode causal knowledge, or even how they represent this knowledge. This is a living paper that categorises methods in causal deep learning beyond Pearl's ladder of causation. We refine the rungs in Pearl's ladder, while also adding a separate dimension that categorises the parametric assumptions of both input and representation, arriving at the map of causal deep learning. Our map covers machine learning disciplines such as supervised learning, reinforcement learning, generative modelling and beyond. Our paradigm is a tool which helps researchers to: find benchmarks, compare methods, and most importantly: identify research gaps. With this work we aim to structure the avalanche of papers being published on causal deep learning. While papers on the topic are being published daily, our map remains fixed. We open-source our map for others to use as they see fit: perhaps to offer guidance in a related works section, or to better highlight the contribution of their paper.
Recently, there has been a growing interest in applying machine learning methods to problems in engineering mechanics. In particular, there has been significant interest in applying deep learning techniques to predicting the mechanical behavior of heterogeneous materials and structures. Researchers have shown that deep learning methods are able to effectively predict mechanical behavior with low error for systems ranging from engineered composites, to geometrically complex metamaterials, to heterogeneous biological tissue. However, there has been comparatively little attention paid to deep learning model calibration, i.e., the match between predicted probabilities of outcomes and the true probabilities of outcomes. In this work, we perform a comprehensive investigation into ML model calibration across seven open access engineering mechanics datasets that cover three distinct types of mechanical problems. Specifically, we evaluate both model and model calibration error for multiple machine learning methods, and investigate the influence of ensemble averaging and post hoc model calibration via temperature scaling. Overall, we find that ensemble averaging of deep neural networks is both an effective and consistent tool for improving model calibration, while temperature scaling has comparatively limited benefits. Looking forward, we anticipate that this investigation will lay the foundation for future work in developing mechanics specific approaches to deep learning model calibration.
Cyber intrusion attacks that compromise the users' critical and sensitive data are escalating in volume and intensity, especially with the growing connections between our daily life and the Internet. The large volume and high complexity of such intrusion attacks have impeded the effectiveness of most traditional defence techniques. While at the same time, the remarkable performance of the machine learning methods, especially deep learning, in computer vision, had garnered research interests from the cyber security community to further enhance and automate intrusion detections. However, the expensive data labeling and limitation of anomalous data make it challenging to train an intrusion detector in a fully supervised manner. Therefore, intrusion detection based on unsupervised anomaly detection is an important feature too. In this paper, we propose a three-stage deep learning anomaly detection based network intrusion attack detection framework. The framework comprises an integration of unsupervised (K-means clustering), semi-supervised (GANomaly) and supervised learning (CNN) algorithms. We then evaluated and showed the performance of our implemented framework on three benchmark datasets: NSL-KDD, CIC-IDS2018, and TON_IoT.