Related papers: Interpreting Neural Network Judgments via Minimal,…

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a…

We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected…

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…

Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting…

We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural…

Over the last decade, Neural Networks (NNs) have been widely used in numerous applications including safety-critical ones such as autonomous systems. Despite their emerging adoption, it is well known that NNs are susceptible to Adversarial…

This work investigates if the current neural architectures are adequate for learning symbolic rewriting. Two kinds of data sets are proposed for this research -- one based on automated proofs and the other being a synthetic set of…

Neural networks have to capture mathematical relationships in order to learn various tasks. They approximate these relations implicitly and therefore often do not generalize well. The recently proposed Neural Arithmetic Logic Unit (NALU) is…

Algorithmic stability is a classical framework for analyzing the generalization error of learning algorithms. It predicts that an algorithm has small generalization error if it is insensitive to small perturbations in the training set such…

There is great interest in using formal methods to guarantee the reliability of deep neural networks. However, these techniques may also be used to implant carefully selected input-output pairs. We present initial results on a novel…

*Minimal sufficient reasons* represent a prevalent form of explanation - the smallest subset of input features which, when held constant at their corresponding values, ensure that the prediction remains unchanged. Previous *post-hoc*…

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…

Neural networks have proved an effective means of learning control policies for autonomous systems, but these learned policies are difficult to understand due to the black-box nature of neural networks. This lack of interpretability makes…

Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal…

Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…

We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given…

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…

Complementarity problems, a class of mathematical optimization problems with orthogonality constraints, are widely used in many robotics tasks, such as locomotion and manipulation, due to their ability to model non-smooth phenomena (e.g.,…