Deep learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when DL is used for financial time series forecasting tasks, where the nonstationary and multimodal nature of the data pose significant challenges and severely affect the performance of DL models. In this brief, a simple, yet effective, neural layer that is capable of adaptively normalizing the input time series, while taking into account the distribution of the data, is proposed. The proposed layer is trained in an end-to-end fashion using backpropagation and leads to significant performance improvements compared to other evaluated normalization schemes. The proposed method differs from traditional normalization methods since it learns how to perform normalization for a given task instead of using a fixed normalization scheme. At the same time, it can be directly applied to any new time series without requiring retraining. The effectiveness of the proposed method is demonstrated using a large-scale limit order book data set, as well as a load forecasting data set.

Knowledge-transfer (KT) methods allow for transferring the knowledge contained in a large deep learning model into a more lightweight and faster model. However, the vast majority of existing KT approaches are designed to handle mainly classification and detection tasks. This limits their performance on other tasks, such as representation/metric learning. To overcome this limitation, a novel probabilistic KT (PKT) method is proposed in this article. PKT is capable of transferring the knowledge into a smaller student model by keeping as much information as possible, as expressed through the teacher model. The ability of the proposed method to use different kernels for estimating the probability distribution of the teacher and student models, along with the different divergence metrics that can be used for transferring the knowledge, allows for easily adapting the proposed method to different applications. PKT outperforms several existing state-of-the-art KT techniques, while it is capable of providing new insights into KT by enabling several novel applications, as it is demonstrated through extensive experiments on several challenging data sets.

The recent explosive compute growth, mainly fueled by the boost of artificial intelligence (AI) and deep neural networks (DNNs), is currently instigating the demand for a novel computing paradigm that can overcome the insurmountable barriers imposed by conventional electronic computing architectures. Photonic neural networks (PNNs) implemented on silicon integration platforms stand out as a promising candidate to endow neural network (NN) hardware, offering the potential for energy efficient and ultra-fast computations through the utilization of the unique primitives of photonics, i.e., energy efficiency, THz bandwidth, and low-latency. Thus far, several demonstrations have revealed the huge potential of PNNs in performing both linear and non-linear NN operations at unparalleled speed and energy consumption metrics. Transforming this potential into a tangible reality for deep learning (DL) applications requires, however, a deep understanding of the basic PNN principles, requirements, and challenges across all constituent architectural, technological, and training aspects. In this Tutorial, we, initially, review the principles of DNNs along with their fundamental building blocks, analyzing also the key mathematical operations needed for their computation in photonic hardware. Then, we investigate, through an intuitive mathematical analysis, the interdependence of bit precision and energy efficiency in analog photonic circuitry, discussing the opportunities and challenges of PNNs. Followingly, a performance overview of PNN architectures, weight technologies, and activation functions is presented, summarizing their impact in speed, scalability, and power consumption. Finally, we provide a holistic overview of the optics-informed NN training framework that incorporates the physical properties of photonic building blocks into the training process in order to improve the NN classification accuracy and effectively elevate neuromorphic photonic hardware into high-performance DL computational settings.

Photonic artificial neural networks have garnered enormous attention due to their potential to perform multiply-accumulate (MAC) operations at much higher clock rates and consuming significantly lower power and chip real-estate compared to digital electronic alternatives. Herein, we present a comprehensive power consumption analysis of photonic neurons, taking into account global design parameters and concluding to analytical expressions for the neuron's energy- and footprint efficiencies. We identify the optimal design-space and analyze the performance plateaus and their dependence on a range of physical parameters, highlighting the existence of an optimal data-rate for maximizing the energy efficiency. Following a survey of the best-in-class integrated photonic devices, including on-chip lasers, photodetectors, modulators and weighting elements, the mathematically calculated energy and footprint efficiencies are mapped into real photonic neuron deployment scenarios. We reveal that silicon photonics can compete with the best-performing currently available digital electronic neural network engines, reaching ${\rm{TMAC/s/mm^{2}}}$ footprint- and sub-pJ/MAC energy efficiencies. Simultaneously, neuromorphic plasmonics, plasmo-photonics and sub-wavelength photonics hold the credentials for 1 to 3 orders of magnitude improvements even when the laser requirements and a reasonable waveguide pitch are accounted for, promising performance at a few fJ/MAC and up to a few ${\rm{TMAC/s/mm^{2}}}$ .