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Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…

We present a general framework for training deep neural networks without backpropagation. This substantially decreases training time and also allows for construction of deep networks with many sorts of learners, including networks whose…

The vanishing gradient problem was a major obstacle for the success of deep learning. In recent years it was gradually alleviated through multiple different techniques. However the problem was not really overcome in a fundamental way, since…

Deep neural network training involves both forward propagation (from features through logits to loss) and backward propagation (from loss through gradients to parameter updates). While perturbations along the forward chain, including…

The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward…

The problem of vanishing and exploding gradients has been a long-standing obstacle that hinders the effective training of neural networks. Despite various tricks and techniques that have been employed to alleviate the problem in practice,…

We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete versions of the model, and we rigorously prove the convergence…

This paper reveal the selective rotation in the CNNs' forward processing. It elucidates the activation function as a discerning mechanism that unifies and quantizes the rotational aspects of the input data. Experiments show how this defined…

Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…

Stochastic neurons can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic neurons, i.e.,…

Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. Training such networks with backpropagation through time is a…

This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a…

Threshold activation functions are highly preferable in neural networks due to their efficiency in hardware implementations. Moreover, their mode of operation is more interpretable and resembles that of biological neurons. However,…

Catastrophic forgetting has remained a significant challenge for efficient reinforcement learning for decades (Ring 1994, Rivest and Precup 2003). While recent works have proposed effective methods to mitigate this issue, they mainly focus…

Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based…

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural…

Activation functions are critical to the performance of deep neural networks, particularly in domains such as functional near-infrared spectroscopy (fNIRS), where nonlinearity, low signal-to-noise ratio (SNR), and signal variability poses…