The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and spatio-temporal modelling. There are many introductions to transformers, but most do not contain precise mathematical descriptions of the architecture and the intuitions behind the design choices are often also missing. Moreover, as research takes a winding path, the explanations for the components of the transformer can be idiosyncratic. In this note we aim for a mathematically precise, intuitive, and clean description of the transformer architecture. We will not discuss training as this is rather standard. We assume that the reader is familiar with fundamental topics in machine learning including multi-layer perceptrons, linear transformations, softmax functions and basic probability.

The large increase in the number of Internet of Things (IoT) devices have revolutionised the way data is processed, which added to the current trend from cloud to edge computing has resulted in the need for efficient and reliable data processing near the data sources using energy-efficient devices. Two methods based on low-cost edge-IoT architectures are proposed to implement lightweight Machine Learning (ML) models that estimate indoor environmental quality (IEQ) parameters, such as Artificial Neural Networks of Multilayer Perceptron type. Their implementation is based on centralised and distributed parallel IoT architectures, connected via wireless, which share commercial off-the-self modules for data acquisition and sensing, such as sensors for temperature, humidity, illuminance, CO2, and other gases. The centralised method uses a Graphics Processing Unit and the Message Queuing Telemetry Transport protocol, but the distributed method utilises low performance ARM-based devices and the Message Passing Interface protocol. Although multiple IEQ parameters are measured, the training and testing of ML models is accomplished with experiments focused on small temperature and illuminance datasets to reduce data processing load, obtained from sudden spikes, square profiles and sawteeth test cases. The results show a high estimation performance with F-score and Accuracy values close to 0.95, and an almost theorical Speedup with a reduction in power consumption close to 37% in the distributed parallel approach. In addition, similar or slightly better performance is achieved compared to equivalent IoT architectures from related research, but error reduction of 35 to 76% is accomplished with an adequate balance between performance and energy efficiency.

Trust plays an essential role in an individual's decision-making. Traditional trust prediction models rely on pairwise correlations to infer potential relationships between users. However, in the real world, interactions between users are usually complicated rather than pairwise only. Hypergraphs offer a flexible approach to modeling these complex high-order correlations (not just pairwise connections), since hypergraphs can leverage hyperedeges to link more than two nodes. However, most hypergraph-based methods are generic and cannot be well applied to the trust prediction task. In this paper, we propose an Adaptive Hypergraph Network for Trust Prediction (AHNTP), a novel approach that improves trust prediction accuracy by using higher-order correlations. AHNTP utilizes Motif-based PageRank to capture high-order social influence information. In addition, it constructs hypergroups from both node-level and structure-level attributes to incorporate complex correlation information. Furthermore, AHNTP leverages adaptive hypergraph Graph Convolutional Network (GCN) layers and multilayer perceptrons (MLPs) to generate comprehensive user embeddings, facilitating trust relationship prediction. To enhance model generalization and robustness, we introduce a novel supervised contrastive learning loss for optimization. Extensive experiments demonstrate the superiority of our model over the state-of-the-art approaches in terms of trust prediction accuracy. The source code of this work can be accessed via https://github.com/Sherry-XU1995/AHNTP.

Hypergraph Neural Networks (HGNNs) have recently attracted much attention and exhibited satisfactory performance due to their superiority in high-order correlation modeling. However, it is noticed that the high-order modeling capability of hypergraph also brings increased computation complexity, which hinders its practical industrial deployment. In practice, we find that one key barrier to the efficient deployment of HGNNs is the high-order structural dependencies during inference. In this paper, we propose to bridge the gap between the HGNNs and inference-efficient Multi-Layer Perceptron (MLPs) to eliminate the hypergraph dependency of HGNNs and thus reduce computational complexity as well as improve inference speed. Experiments on eight hypergraph datasets demonstrate that even without hypergraph dependency, the proposed LightHGNNs can still achieve competitive or even better performance than HGNNs and outperform vanilla MLPs by 16.3 on average. Extensive experiments on three graph datasets further show the average best performance of our LightHGNNs compared with all other methods. Experiments on synthetic hypergraphs with 5.5w vertices indicate LightHGNNs can run 100 faster than HGNNs, showcasing their ability for latency-sensitive deployments. Compared to the graph with pair-wise correlation, the hypergraph is composed of degree-free hyperedges, which have an inherent superior modeling ability to represent those more complex high-order correlations. However, for large-scale industrial applications, especially for those big-data, small-memory, and high-speed demand environments, the Multi-Layer Perceptrons (MLPs) remain the primary workhorse. The main reason for such an academic-industrial gap for HGNNs is the dependence on the hypergraph structure in inference, which requires large memories in practice.

BLDC motor applications require precise position and speed measurements, traditionally obtained with sensors. This article presents a method for estimating those measurements without position sensors using terminal phase voltages with attenuated spurious, acquired with a FPGA that also operates a PWM-controlled inverter. Voltages are labelled with electrical and virtual rotor states using an encoder that provides training and testing data for two three-layer ANNs with perceptron-based cascade topology. The first ANN estimates the position from features of voltages with incremental timestamps, and the second ANN estimates the speed from features of position differentials considering timestamps in an acquisition window. Sensor-based training and sensorless testing at 125 to 1,500 rpm with a loaded 8-pole-pair motor obtained absolute errors of 0.8 electrical degrees and 22 rpm. Results conclude that the overall position estimation significantly improved conventional and advanced methods, and the speed estimation slightly improved conventional methods, but was worse than in advanced ones.

Printed Electronics (PE) stands out as a promisingtechnology for widespread computing due to its distinct attributes, such as low costs and flexible manufacturing. Unlike traditional silicon-based technologies, PE enables stretchable, conformal,and non-toxic hardware. However, PE are constrained by larger feature sizes, making it challenging to implement complex circuits such as machine learning (ML) classifiers. Approximate computing has been proven to reduce the hardware cost of ML circuits such as Multilayer Perceptrons (MLPs). In this paper, we maximize the benefits of approximate computing by integrating hardware approximation into the MLP training process. Due to the discrete nature of hardware approximation, we propose and implement a genetic-based, approximate, hardware-aware training approach specifically designed for printed MLPs. For a 5% accuracy loss, our MLPs achieve over 5x area and power reduction compared to the baseline while outperforming state of-the-art approximate and stochastic printed MLPs.

Printed Electronics (PE) feature distinct and remarkable characteristics that make them a prominent technology for achieving true ubiquitous computing. This is particularly relevant in application domains that require conformal and ultra-low cost solutions, which have experienced limited penetration of computing until now. Unlike silicon-based technologies, PE offer unparalleled features such as non-recurring engineering costs, ultra-low manufacturing cost, and on-demand fabrication of conformal, flexible, non-toxic, and stretchable hardware. However, PE face certain limitations due to their large feature sizes, that impede the realization of complex circuits, such as machine learning classifiers. In this work, we address these limitations by leveraging the principles of Approximate Computing and Bespoke (fully-customized) design. We propose an automated framework for designing ultra-low power Multilayer Perceptron (MLP) classifiers which employs, for the first time, a holistic approach to approximate all functions of the MLP's neurons: multiplication, accumulation, and activation. Through comprehensive evaluation across various MLPs of varying size, our framework demonstrates the ability to enable battery-powered operation of even the most intricate MLP architecture examined, significantly surpassing the current state of the art.

In this paper, we introduce a new class of parameterized controllers, drawing inspiration from Model Predictive Control (MPC). The controller resembles a Quadratic Programming (QP) solver of a linear MPC problem, with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. This approach addresses the limitations of common controllers with Multi-Layer Perceptron (MLP) or other general neural network architecture used in DRL, in terms of verifiability and performance guarantees, and the learned controllers possess verifiable properties like persistent feasibility and asymptotic stability akin to MPC. On the other hand, numerical examples illustrate that the proposed controller empirically matches MPC and MLP controllers in terms of control performance and has superior robustness against modeling uncertainty and noises. Furthermore, the proposed controller is significantly more computationally efficient compared to MPC and requires fewer parameters to learn than MLP controllers. Real-world experiments on vehicle drift maneuvering task demonstrate the potential of these controllers for robotics and other demanding control tasks.

This paper introduces the Orthogonal Polynomials Quadrature Algorithm for Survival Analysis (OPSurv), a new method providing time-continuous functional outputs for both single and competing risks scenarios in survival analysis. OPSurv utilizes the initial zero condition of the Cumulative Incidence function and a unique decomposition of probability densities using orthogonal polynomials, allowing it to learn functional approximation coefficients for each risk event and construct Cumulative Incidence Function estimates via Gauss--Legendre quadrature. This approach effectively counters overfitting, particularly in competing risks scenarios, enhancing model expressiveness and control. The paper further details empirical validations and theoretical justifications of OPSurv, highlighting its robust performance as an advancement in survival analysis with competing risks.

Long-term time series forecasting (LTSF) represents a critical frontier in time series analysis, distinguished by its focus on extensive input sequences, in contrast to the constrained lengths typical of traditional approaches. While longer sequences inherently convey richer information, potentially enhancing predictive precision, prevailing techniques often respond by escalating model complexity. These intricate models can inflate into millions of parameters, incorporating parameter-intensive elements like positional encodings, feed-forward networks and self-attention mechanisms. This complexity, however, leads to prohibitive model scale, particularly given the time series data's semantic simplicity. Motivated by the pursuit of parsimony, our research employs conditional correlation and auto-correlation as investigative tools, revealing significant redundancies within the input data. Leveraging these insights, we introduce the HDformer, a lightweight Transformer variant enhanced with hierarchical decomposition. This novel architecture not only inverts the prevailing trend toward model expansion but also accomplishes precise forecasting with drastically fewer computations and parameters. Remarkably, HDformer outperforms existing state-of-the-art LTSF models, while requiring over 99\% fewer parameters. Through this work, we advocate a paradigm shift in LTSF, emphasizing the importance to tailor the model to the inherent dynamics of time series data-a timely reminder that in the realm of LTSF, bigger is not invariably better.