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We introduce stochastic activations. This novel strategy randomly selects between several non-linear functions in the feed-forward layer of a large language model. In particular, we choose between SILU or RELU depending on a Bernoulli draw.…

ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

In our previous work [Ma and Chan (2023)], we presented a feedforward unitary equivariant neural network. We proposed three distinct activation functions tailored for this network: a softsign function with a small residue, an identity…

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of…

This work studies the expressivity of ReLU neural networks with a focus on their depth. A sequence of previous works showed that $\lceil \log_2(n+1) \rceil$ hidden layers are sufficient to compute all continuous piecewise linear (CPWL)…

The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network…

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…

Rectified Linear Units (ReLUs) are among the most widely used activation function in a broad variety of tasks in vision. Recent theoretical results suggest that despite their excellent practical performance, in various cases, a substitution…

We present a greedy-based approach to construct an efficient single hidden layer neural network with the ReLU activation that approximates a target function. In our approach we obtain a shallow network by utilizing a greedy algorithm with…

The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture,…

We introduce LL-RNNs (Log-Linear RNNs), an extension of Recurrent Neural Networks that replaces the softmax output layer by a log-linear output layer, of which the softmax is a special case. This conceptually simple move has two main…

This document proposes a parametric activation function (ac.f.) aimed at improving multidimensional nonlinear data regression. It is a established knowledge that nonlinear ac.f's are required for learning nonlinear datasets. This work shows…

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we…

Artificial Neural Networks (ANN) have been employed for a range of modelling and prediction tasks using financial data. However, evidence on their predictive performance, especially for time-series data, has been mixed. Whereas some…

Lipschitz-constrained neural networks have many applications in machine learning. Since designing and training expressive Lipschitz-constrained networks is very challenging, there is a need for improved methods and a better theoretical…

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear…

Activation functions are essential to introduce nonlinearity into neural networks, with the Rectified Linear Unit (ReLU) often favored for its simplicity and effectiveness. Motivated by the structural similarity between a shallow…

Element-wise activation functions play a critical role in deep neural networks via affecting the expressivity power and the learning dynamics. Learning-based activation functions have recently gained increasing attention and success. We…

Activation functions are essential to deep learning networks. Popular and versatile activation functions are mostly monotonic functions, some non-monotonic activation functions are being explored and show promising performance. But by…