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Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When…

Multilayer networks have seen a resurgence under the umbrella of deep learning. Current deep learning algorithms train the layers of the network sequentially, improving algorithmic performance as well as providing some regularization. We…

Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

Emulator embedded neural networks, which are a type of physics informed neural network, leverage multi-fidelity data sources for efficient design exploration of aerospace engineering systems. Multiple realizations of the neural network…

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…

Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neural network (RNN) with identity…

In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in…

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian…

Spatial Transformer Networks (STNs) estimate image transformations that can improve downstream tasks by `zooming in' on relevant regions in an image. However, STNs are hard to train and sensitive to mis-predictions of transformations. To…

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without…

Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the…

The process of training feedforward neural networks (FFNNs) can benefit from an automated process where the best heuristic to train the network is sought out automatically by means of a high-level probabilistic-based heuristic. This…

On the one hand, artificial neural networks have many successful applications in the field of machine learning and optimization. On the other hand, interferometers are integral parts of any field that deals with waves such as optics,…

How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly…