Related papers: Open- and Closed-Loop Neural Network Verification …

Automatic segmentation of neuronal topology is critical for handling large scale neuroimaging data, as it can greatly accelerate neuron annotation and analysis. However, the intricate morphology of neuronal branches and the occlusions among…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

This paper presents a new mathematical framework to analyze the loss functions of deep neural networks with ReLU functions. Furthermore, as as application of this theory, we prove that the loss functions can reconstruct the inputs of the…

We study the expressivity of deep neural networks. Measuring a network's complexity by its number of connections or by its number of neurons, we consider the class of functions for which the error of best approximation with networks of a…

This paper studies the expressive power of artificial neural networks with rectified linear units. In order to study them as a model of real-valued computation, we introduce the concept of Max-Affine Arithmetic Programs and show equivalence…

Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…

This paper presents a new reachability analysis approach to compute interval over-approximations of the output set of feedforward neural networks with input uncertainty. We adapt to neural networks an existing mixed-monotonicity method for…

Neural networks with piecewise linear activation functions, such as rectified linear units (ReLU) or maxout, are among the most fundamental models in modern machine learning. We make a step towards proving lower bounds on the size of such…

Recent work has shown that purely quadratic functions can replace MLPs in transformers with no significant loss in performance, while enabling new methods of interpretability based on linear algebra. In this work, we theoretically derive…

A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural networks. So far, either theoretical or empirical studies on…

Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding,…

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…

A wide range of verification methods have been proposed to verify the safety properties of deep neural networks ensuring that the networks function correctly in critical applications. However, many well-known verification tools still…

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network…

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…

In this paper, we propose a framework for performing state space exploration of closed loop control systems. Our approach involves approximating sensitivity and a newly introduced notion of inverse sensitivity by a neural network. We show…

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer…

Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for…

In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both…

Rectified Linear Units (ReLU) are the default choice for activation functions in deep neural networks. While they demonstrate excellent empirical performance, ReLU activations can fall victim to the dead neuron problem. In these cases, the…