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Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical…
Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…
Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, previous studies have…
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…
Human visual perception carves a scene at its physical joints, decomposing the world into objects, which are selectively attended, tracked, and predicted as we engage our surroundings. Object representations emancipate perception from the…
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,…
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…
As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…
It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…
Recent work has argued that neural networks can be understood theoretically by taking the number of channels to infinity, at which point the outputs become Gaussian process (GP) distributed. However, we note that infinite Bayesian neural…
How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? And how much can these fundamentals help while devising new pruning techniques? A lot, it turns out. Neural network pruning has…
Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…
Recurrent neurons, or "simulated" qubits, can store simultaneous true and false with probabilistic behaviors usually reserved for the qubits of quantum physics. Although possible to construct artificially, simulated qubits are intended to…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…
Deep neural networks and brains both learn and share superficial similarities: processing nodes are likened to neurons and adjustable weights are likened to modifiable synapses. But can a unified theoretical framework be found to underlie…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…