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Today, intelligent systems that offer artificial intelligence capabilities often rely on machine learning. Machine learning describes the capacity of systems to learn from problem-specific training data to automate the process of analytical…

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may…

Evolution has resulted in highly developed abilities in many natural intelligences to quickly and accurately predict mechanical phenomena. Humans have successfully developed laws of physics to abstract and model such mechanical phenomena.…

Differentiable neural computers extend artificial neural networks with an explicit memory without interference, thus enabling the model to perform classic computation tasks such as graph traversal. However, such models are difficult to…

Modelling dynamical systems is an integral component for understanding the natural world. To this end, neural networks are becoming an increasingly popular candidate owing to their ability to learn complex functions from large amounts of…

Deep learning has been proven to yield reliably generalizable answers to numerous classification and decision tasks. Here, we demonstrate for the first time, to our knowledge, that deep neural networks (DNNs) can be trained to solve inverse…

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…

Mathematical expressions were generated, evaluated and used to train neural network models based on the transformer architecture. The expressions and their targets were analyzed as a character-level sequence transduction task in which the…

Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is…

Convolutional Neural Networks define an exceptionally powerful class of models, but are still limited by the lack of ability to be spatially invariant to the input data in a computationally and parameter efficient manner. In this work we…

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt…

Transformers demonstrate significant advantages as the building block of modern LLMs. In this work, we study the capacities of Transformers in performing unsupervised learning. We show that multi-layered Transformers, given a sufficiently…

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…