相关论文: Reachability analysis of neural networks using mix…

Flexible optical network is a promising technology to accommodate high-capacity demands in next-generation networks. To ensure uninterrupted communication, existing lightpath provisioning schemes are mainly done with the assumption of…

Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…

ReLU is widely seen as the default choice for activation functions in neural networks. However, there are cases where more complicated functions are required. In particular, recurrent neural networks (such as LSTMs) make extensive use of…

In this paper, we explain the universal approximation capabilities of deep residual neural networks through geometric nonlinear control. Inspired by recent work establishing links between residual networks and control systems, we provide a…

Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power,…

Deep neural networks have achieved impressive performance on a variety of tasks, but their brittleness to distributional shifts remains a significant barrier to real-world deployment. In this paper, we propose a framework to analyse and…

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes…

As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…

While it is well-known that neural networks enjoy excellent approximation capabilities, it remains a big challenge to compute such approximations from point samples. Based on tools from Information-based complexity, recent work by Grohs and…

This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and diminished control authority, given an a priori computed reachable set for…

We study optimization problems where the objective function is modeled through feedforward neural networks with rectified linear unit (ReLU) activation. Recent literature has explored the use of a single neural network to model either…

The function or performance of a network is strongly dependent on its robustness, quantifying the ability of the network to continue functioning under perturbations. While a wide variety of robustness metrics have been proposed, they have…

This study explores the number of neurons required for a Rectified Linear Unit (ReLU) neural network to approximate multivariate monomials. We establish an exponential lower bound on the complexity of any shallow network approximating the…

Simultaneous behavioral and electrophysiological recordings call for new methods to reveal the interactions between neural activity and behavior. A milestone would be an interpretable model of the co-variability of spiking activity and…

Recently, formal verification of deep neural networks (DNNs) has garnered considerable attention, and over-approximation based methods have become popular due to their effectiveness and efficiency. However, these strategies face challenges…

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work…

This paper focuses on the multi-agent synchronization problem with an open-loop unstable leader and followers under the switching topologies. For this issue, the typical approach is intermittent communication (including a spanning tree…

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While…