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A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…

Deep neural networks (DNNs) transform stimuli across multiple processing stages to produce representations that can be used to solve complex tasks, such as object recognition in images. However, a full understanding of how they achieve this…

We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…

Deep neural networks have achieved success across a wide range of applications, including as models of human behavior and neural representations in vision tasks. However, neural network training and human learning differ in fundamental…

Logical relations widely exist in human activities. Human use them for making judgement and decision according to various conditions, which are embodied in the form of \emph{if-then} rules. As an important kind of cognitive intelligence, it…

Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to…

Humans represent scenes and objects in rich feature spaces, carrying information that allows us to generalise about category memberships and abstract functions with few examples. What determines whether a neural network model generalises…

Visual object recognition -- the behavioral ability to rapidly and accurately categorize many visually encountered objects -- is core to primate cognition. This behavioral capability is algorithmically impressive because of the myriad…

Artificial neural networks (ANNs) have evolved from the 1940s primitive models of brain function to become tools for artificial intelligence. They comprise many units, artificial neurons, interlinked through weighted connections. ANNs are…

Convolutional neural networks (CNN) have become one of the most popular machine learning tools and are being applied in various tasks, however, CNN models are vulnerable to universal perturbations, which are usually human-imperceptible but…

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…

Neural ordinary differential equations (NODEs) is an invertible neural network architecture promising for its free-form Jacobian and the availability of a tractable Jacobian determinant estimator. Recently, the representation power of NODEs…

Autoregressive Neural Networks (ANN) have been recently proposed as a mechanism to improve the efficiency of Monte Carlo algorithms for several spin systems. The idea relies on the fact that the total probability of a configuration can be…

Artificial neural networks are being proposed as models of parts of the brain. The networks are compared to recordings of biological neurons, and good performance in reproducing neural responses is considered to support the model's…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

We argue that representations in AI models, particularly deep networks, are converging. First, we survey many examples of convergence in the literature: over time and across multiple domains, the ways by which different neural networks…

Deep neural networks (DNNs) once showed increasing alignment with primate perception and neural responses as they improved on vision benchmarks, raising hopes that advances in AI would yield better models of biological vision. However, we…

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of…

After four decades of research there still exists a Classification accuracy gap of about 20% between our best Unsupervisedly Learned Representations methods and the accuracy rates achieved by intelligent animals. It thus may well be that we…

One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…