NeuPPS: Neural Piecewise Parametric Surfaces

In this expository paper, we want to give a brief introduction, with few key references for further reading, to the inner functioning of the new and successful algorithms of Deep Learning and Geometric Deep Learning with a focus on Graph Neural Networks. We go over the key ingredients for these algorithms: the score and loss function and we explain the main steps for the training of a model. We do not aim to give a complete and exhaustive treatment, but we isolate few concepts to give a fast introduction to the subject. We provide some appendices to complement our treatment discussing Kullback–Leibler divergence, regression, Multi-layer Perceptrons and the Universal Approximation theorem.

Computational Methods in Neural Modeling

Multilayer perceptron for nonlinear programming

Online hate is a growing concern on many social media platforms, making them unwelcoming and unsafe. To combat this, technology companies are increasingly developing techniques to automatically identify and sanction hateful users. However, accurate detection of such users remains a challenge due to the contextual nature of speech, whose meaning depends on the social setting in which it is used. This contextual nature of speech has also led to minoritized users, especially African–Americans, to be unfairly detected as ‘hateful’ by the very algorithms designed to protect them. To resolve this problem of inaccurate and unfair hate detection, research has focused on developing machine learning (ML) systems that better understand textual context. Incorporating social networks of hateful users has not received as much attention, despite social science research suggesting it provides rich contextual information. We present a system for more accurately and fairly detecting hateful users by incorporating social network information through geometric deep learning. Geometric deep learning is a ML technique that dynamically learns information-rich network representations. We make two main contributions: first, we demonstrate that adding network information with geometric deep learning produces a more accurate classifier compared with other techniques that either exclude network information entirely or incorporate it through manual feature engineering. Our best performing model achieves an AUC score of 90.8% on a previously released hateful user dataset. Second, we show that such information also leads to fairer outcomes: using the ‘predictive equality’ fairness criteria, we compare the false positive rates of our geometric learning algorithm to other ML techniques and find that our best-performing classifier has no false positives among a subset of African–American users. A neural network without network information has the largest number of false positives at 26, while a neural network incorporating manual network features has 13 false positives among African–American users. The system we present highlights the importance of effectively incorporating social network features in automated hateful user detection, raising new opportunities to improve how online hate is tackled.

In recent years, more and more attention has been devoted to geometric deep learning (GDL) and its applications to various problems in medical imaging. Unlike convolutional neural networks (CNNs) limited to 2-D/3-D grid-structured data, GDL can handle non-Euclidean data (i.e., graphs and manifolds) and is hence well-suited for medical imaging data such as structure-function connectivity networks, imaging genetics and omics, spatio-temporal anatomical representations, physics-informed GDL for optimal imaging sampling and acquisition, GDL in imaging inverse problems, etc. However, despite recent advances in GDL research, questions remain on how best to learn representations of non-Euclidean medical imaging data; how to convolve effectively on graphs; how to perform graph pooling/unpooling; how to handle heterogeneous data; and how to improve the interpretability of GDL. After discussing many other domain experts, we identify the need for a special issue that brings to the attention of the medical imaging community these interesting topics.

In this paper, a neural approach is applied to determine the switching angles for a uniform step asymmetrical multilevel inverter by eliminating specified higher-order harmonics while maintaining the required fundamental voltage. A Multi-Layer Perceptron (MLP) neural network is used to approximate the function between the modulation rate and the required switching angles. After learning, the artificial neural network is able to determine the appropriate switching angles for the inverter. This leads to a low-computational-cost neural controller which is therefore well suited for real-time applications. This technique can be applied to multilevel inverters with any number of levels. As an example, a nine-level inverter and an eleven-level inverter are considered and the optimum switching angles are calculated on-line. The neural approach is compared to the well-known sinusoidal Pulse-Width Modulation (PWM) strategy. Simulation results demonstrate the better performances and technical advantages of the neural controller in feeding an asynchronous machine. Indeed, the harmonic distortions are efficiently cancelled providing thus an optimized control signal for the asynchronous machine. Moreover, the technique presented here substantially reduces the torque undulations.

BackgroundThe automatic medical image segmentation of liver and tumor plays a pivotal role in the clinical diagnosis of liver diseases. A number of effective methods based on deep neural networks, including convolutional neural networks (CNNs) and vision transformer (ViT) have been developed. However, these networks primarily focus on enhancing segmentation accuracy while often overlooking the segmentation speed, which is vital for rapid diagnosis in clinical settings. Therefore, we aimed to develop an automatic computed tomography (CT) image segmentation method for liver tumors that reduces inference time while maintaining accuracy, as rigorously validated through experimental studies.MethodsWe developed a U-shaped network enhanced by a multiscale attention module and attention gates, aimed at efficient CT image segmentation of liver tumors. In this network, a modified tokenized multilayer perceptron (MLP) block is first leveraged to reduce the feature dimensions and facilitate information interaction between adjacent patches so that the network can learn the key features of tumors with less computational complexity. Second, attention gates are added into the skip connections between the encoder and decoder, emphasizing feature expression in relevant regions and enabling the network to focus more on liver tumor features. Finally, a multiscale attention mechanism autonomously adjusts weights for each scale, allowing the network to adapt effectively to varying sizes of liver tumors. Our methodology was validated via the Liver Tumor Segmentation 2017 (LiTS17) public dataset. The data from this database are from seven global clinical sites. All data are anonymized, and the images have been prescreened to ensure the absence of personal identifiers. Standard metrics were used to evaluate the performance of the model.ResultsThe 21 cases were included for testing. The proposed network attained a Dice score of 0.713 [95% confidence interval (CI): 0.592–0.834], a volumetric overlap error of 0.39 (95% CI: 0.17–0.61), a relative volume difference score of 0.19 (95% CI: −0.37 to 0.31), an average symmetric surface distance of 2.04 mm (95% CI: 0.89–4.19), a maximum surface distance of 9.42 mm (95% CI: 6.97–19.87), and an inference time of 26 ms on average for liver tumor segmentation.ConclusionsThe proposed network demonstrated efficient liver tumor segmentation performance with less inference time. Our findings contribute to the application of neural networks in rapid clinical diagnosis and treatment.

Effective prediction of drug – target interaction on HIV using deep graph neural networks

Geometric deep learning (GDL) is based on neural network architectures that incorporate and process symmetry information. GDL bears promise for molecular modelling applications that rely on molecular representations with different symmetry properties and levels of abstraction. This Review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction and quantum chemistry. It contains an introduction to the principles of GDL, as well as relevant molecular representations, such as molecular graphs, grids, surfaces and strings, and their respective properties. The current challenges for GDL in the molecular sciences are discussed, and a forecast of future opportunities is attempted.

An accurate and fast wavelength demodulation method for fiber Bragg grating (FBG) reflected spectrum based on multilayer perceptron (MLP) neural network is presented. The wavelength demodulation is treated as a supervised regression problem and different MLP models are trained by ideal reflected spectrum of FBG under different spectral resolution. The simulation and experimental results show that the algorithm proposed has higher precision and stronger robustness to spectral resolution compared with correlation and bandwidth middle-point (BMP). Moreover, MLP can still achieve an accuracy below 10 pm even when the spectral resolution is 100 pm, which is about 10 pm higher than the BMP method and about 20 pm higher than the correlation method. Meanwhile, well-trained MLP can achieve µs-level fast demodulation for per reflected spectrum. Therefore, the MLP can be considered as an attractive method to extract wavelength for FBG reflected spectrum, especially at coarse sampling, which can achieve fast demodulation in large-scale distributed FBG sensor networks.

In this paper, two different adaptive strategies are presented for continuous time uncertain nonlinear systems with unknown disturbances and faults. In first strategy, a sliding mode control based adaptive neural observer approach is anticipated for estimation of unknown disturbances and faults by using the multi-layer perceptron, the weight parameters are updated by using the sliding mode online learning strategy. Conventionally, gradient descent back-propagation adaptation methods are used for neural networks training, within these adaptation methods a new theory of sliding mode control is added to conventional gradient descent back-propagation procedure. In this nonlinear control concept, the Sliding Mode Control is employed as a learning strategy, in which the neural network is considered as a control process and computes the stable and dynamic learning rates of neural network. By considering the unknown faults approximation and reconstruction, this online learning strategy shows a rapid sensor fault detection, approximation, and reconstruction with high preciseness and rapidness compared to conventional strategy and algorithms presented in literature. Approaches used in literature do not have much higher preciseness and fast response to fault occurrence compared to the strategy proposed in this study. In second strategy, the neural network controller strategy is proposed with concept of filtered error scheme. Online weight updating strategy comprise of additional term to back-propagation, plus an additional robustifying term, assures the stability and rapid convergence of the faulty system. The stability analysis of the proposed fault tolerance control is also provided. While considering stability of system, this robust online adaptive fault tolerance control shows a fast convergence in the presence of unknown disturbances and faults. The robust adaptive neural controller is compared with the conventional gradient descent based controller in the existence of various sensor faults and failures. The proposed strategies are validated on Boeing 747 100/200 aircraft, results show the efficiency, preciseness and robustness of strategies compared to the algorithm presented in literature.

Abstract: Geometric Deep Learning (GDL) extends traditional neural network paradigms to non-Euclidean data structures, enabling the effective processing of data that lies on manifolds or graphs. Among GDL techniques, Graph Neural Networks (GNNs) have emerged as powerful tools for modelling relational data by leveraging principles from graph theory and algebraic topology. This paper explores GNNs through the lens of mathematics, focusing on how geometric and topological insights drive the architecture and functionality of these networks. By framing GNNs in terms of graph signal processing and spectral theory, we illuminate how GNNs capture dependencies across nodes and edges, offering a structured approach to learning on graph-structured data. We further examine the theoretical underpinnings that make GNNs particularly suited for applications in social networks, molecular biology, and recommendation systems. In doing so, this study provides a mathematical perspective on the capabilities and limitations of GNNs, underscoring the role of invariance, equivariance, and generalization within graph-based learning models.

A geometric deep learning model for display and prediction of potential drug-virus interactions against SARS-CoV-2

A learning rule for very simple universal approximators consisting of a single layer of perceptrons

While current neural networks (NNs) are becoming good at deriving single types of abstractions for a small set of phenomena, for example, using a single NN to predict a flow velocity field, NNs are not good at composing large systems as compositions of small phenomena and reasoning about their interactions. We want to study how NNs build both the abstraction and composition of phenomena when a single NN model cannot suffice. Rather than a single NN that learns one physical or social phenomenon, we want a group of NNs that learn to abstract, compose, reason, and correct the behaviors of different parts in a system. In this paper, we investigate the joint use of Physics-Informed (Navier-Stokes equations) Deep Neural Networks (i.e., Deconvolutional Neural Networks) as well as Geometric Deep Learning (i.e., Graph Neural Networks) to learn and compose fluid component behavior. Our models successfully predict the fluid flows and their composition behaviors (i.e., velocity fields) with an accuracy of about 99%.