Related papers: Comparative Analysis of Interval Reachability for …
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
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…
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…
This paper introduces an Interpretable Neural Network (INN) incorporating spatial information to tackle the opaque parameterization process of random weighted neural networks. The INN leverages spatial information to elucidate the…
Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation properties of INNs have also been established recently.…
Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
Implicit Neural Representations (INRs) encode discrete signals in a continuous manner using neural networks, demonstrating significant value across various multimedia applications. However, the vulnerability of INRs presents a critical…
Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…
Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…
System identification (SysID) is critical for modeling dynamical systems from experimental data, yet traditional approaches often fail to capture nonlinear behaviors. While deep learning offers powerful tools for modeling such dynamics,…
We investigate the topics of sensitivity and robustness in feedforward and convolutional neural networks. Combining energy landscape techniques developed in computational chemistry with tools drawn from formal methods, we produce empirical…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
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…
While the interaction of ultra-intense ultra-short laser pulses with near- and overcritical plasmas cannot be directly observed, experimentally accessible quantities (observables) often only indirectly give information about the underlying…
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…
Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…