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A common issue for companies is that the volume of product orders may at times exceed the production capacity. We formally introduce two novel problems dealing with the question which orders to discard or postpone in order to meet certain…
This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of the result in the previous paper "Complete controllability of continuous-time recurrent neural networks" (Sontag and…
Deep neural networks are highly expressive models that have recently achieved state of the art performance on speech and visual recognition tasks. While their expressiveness is the reason they succeed, it also causes them to learn…
The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…
We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is…
Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…
The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs. The presence of dependence in the inputs…
Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted,…
The success of neural networks builds to a large extent on their ability to create internal knowledge representations from real-world high-dimensional data, such as images, sound, or text. Approaches to extract and present these…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
We investigate the problem of weight uncertainty originally proposed by [Blundell et al. (2015). Weight uncertainty in neural networks. In International conference on machine learning, 1613-1622, PMLR.] in the context of neural networks…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
Recurrent Neural Networks (RNNs) are frequently used to model aspects of brain function and structure. In this work, we trained small fully-connected RNNs to perform temporal and flow control tasks with time-varying stimuli. Our results…
Deep Neural Networks (DNNs) have achieved state of the art results and even outperformed human accuracy in many challenging tasks, leading to DNNs adoption in a variety of fields including natural language processing, pattern recognition,…
Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…
Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…
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…
Recent advances have shown how deep neural networks can be extremely effective at super-resolving remote sensing imagery, starting from a multitemporal collection of low-resolution images. However, existing models have neglected the issue…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…