Related papers: Norm-Based Capacity Control in Neural Networks

Neural networks have shown great success in many machine learning related tasks, due to their ability to act as general function approximators. Recent work has demonstrated the effectiveness of neural networks in control systems (known as…

We present techniques for automatically inferring formal properties of feed-forward neural networks. We observe that a significant part (if not all) of the logic of feed forward networks is captured in the activation status ('on' or 'off')…

We study the problem of explaining a rich class of behavioral properties of deep neural networks. Distinctively, our influence-directed explanations approach this problem by peering inside the network to identify neurons with high influence…

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…

Traditional approaches to understanding the brain's resilience to neuropathology have identified neurophysiological variables, often described as brain or cognitive 'reserve,' associated with better outcomes. However, mechanisms of function…

Neural networks (NNs) have emerged as powerful tools for solving high-dimensional optimal control problems. In particular, their compositional structure has been shown to enable efficient approximation of high-dimensional functions, helping…

A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…

This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and…

We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…

Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in…

Convolutional Neural Networks (CNNs) are a class of artificial neural networks whose computational blocks use convolution, together with other linear and non-linear operations, to perform classification or regression. This paper explores…

We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based…

We present a new framework to measure the intrinsic properties of (deep) neural networks. While we focus on convolutional networks, our framework can be extrapolated to any network architecture. In particular, we evaluate two network…

Despite the significant advances in identifying the driver nodes and energy requiring in network control, a framework that incorporates more complicated dynamics remains challenging. Here, we consider the conformity behavior into network…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

Despite having high accuracy, neural nets have been shown to be susceptible to adversarial examples, where a small perturbation to an input can cause it to become mislabeled. We propose metrics for measuring the robustness of a neural net…

A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…

Today's networks are controlled assuming pre-compressed and packetized data. For video, this assumption of data packets abstracts out one of the key aspects - the lossy compression problem. Therefore, first, this paper develops a framework…