Related papers: On the Computational Complexities of Complex-value…
Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we introduce the quaternion-valued recurrent projection neural networks (QRPNNs). Briefly,…
The dominant approach for many NLP tasks are recurrent neural networks, in particular LSTMs, and convolutional neural networks. However, these architectures are rather shallow in comparison to the deep convolutional networks which have…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
Since their first applications, Convolutional Neural Networks (CNNs) have solved problems that have advanced the state-of-the-art in several domains. CNNs represent information using real numbers. Despite encouraging results, theoretical…
The rapid development of Convolutional Neural Networks (CNNs) in recent years has triggered significant breakthroughs in many machine learning (ML) applications. The ability to understand and compare various CNN models available is thus…
Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we present the quaternion-valued recurrent projection neural networks (QRPNNs). Briefly,…
Convolutional Neural Networks (CNNs) are the state-of-the-art algorithms for the processing of images. However the configuration and training of these networks is a complex task requiring deep domain knowledge, experience and much trial and…
Autonomous driving highly depends on capable sensors to perceive the environment and to deliver reliable information to the vehicles' control systems. To increase its robustness, a diversified set of sensors is used, including radar…
We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights…
Bayesian neural networks (BNN) can estimate the uncertainty in predictions, as opposed to non-Bayesian neural networks (NNs). However, BNNs have been far less widely used than non-Bayesian NNs in practice since they need iterative NN…
Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…
Convolutional neural networks (CNN) play a major role in image processing tasks like image classification, object detection, semantic segmentation. Very often CNN networks have from several to hundred stacked layers with several megabytes…
Convolutional neural network (CNN) is widely used in computer vision applications. In the networks that deal with images, CNNs are the most time-consuming layer of the networks. Usually, the solution to address the computation cost is to…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
Deep Neural Networks are widely used in academy as well as corporate and public applications, including safety critical applications such as health care and autonomous driving. The ability to explain their output is critical for safety…
In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands.…
Complex-valued neural networks (CVNNs) are particularly suitable for handling phase-sensitive signals, including electrocardiography (ECG), radar/sonar, and wireless in-phase/quadrature (I/Q) streams. Nevertheless, their…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
The complexity of deep neural network algorithms for hardware implementation can be much lowered by optimizing the word-length of weights and signals. Direct quantization of floating-point weights, however, does not show good performance…
In this paper, we provide a systematic approach for assessing and comparing the computational complexity of neural network layers in digital signal processing. We provide and link four software-to-hardware complexity measures, defining how…