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The robustness of deep neural networks has received significant interest recently, especially when being deployed in safety-critical systems, as it is important to analyze how sensitive the model output is under input perturbations. While…

Control barrier functions are a popular method of ensuring system safety, and these functions can be used to enforce invariance of a set under the dynamics of a system. A control barrier function must have certain properties, and one must…

There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks,…

The threat of adversarial examples has motivated work on training certifiably robust neural networks to facilitate efficient verification of local robustness at inference time. We formalize a notion of global robustness, which captures the…

The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…

In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such…

This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate…

We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

Neural networks serve as effective controllers in a variety of complex settings due to their ability to represent expressive policies. The complex nature of neural networks, however, makes their output difficult to verify and predict, which…

The outstanding problem of controlling complex networks is relevant to many areas of science and engineering, and has the potential to generate technological breakthroughs as well. We address the physically important issue of the energy…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…

Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…

Deep learning models excel at capturing complex representations through sequential layers of linear and non-linear transformations, yet their inherent black-box nature and multi-modal training landscape raise critical concerns about…

Deep Neural Networks (DNNs) have become key components of many safety-critical applications such as autonomous driving and medical diagnosis. However, DNNs have been shown suffering from poor robustness because of their susceptibility to…

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…

Deep clustering, a method for partitioning complex, high-dimensional data using deep neural networks, presents unique evaluation challenges. Traditional clustering validation measures, designed for low-dimensional spaces, are problematic…