Related papers: Performance Bounds for Neural Network Estimators: …
The last decade has witnessed the breakthrough of deep neural networks (DNNs) in many fields. With the increasing depth of DNNs, hundreds of millions of multiply-and-accumulate (MAC) operations need to be executed. To accelerate such…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…
We evaluate the uncertainty quality in neural networks using anomaly detection. We extract uncertainty measures (e.g. entropy) from the predictions of candidate models, use those measures as features for an anomaly detector, and gauge how…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
Anomaly detection in surveillance videos is attracting an increasing amount of attention. Despite the competitive performance of recent methods, they lack theoretical performance analysis, particularly due to the complex deep neural network…
Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…
Modern neural networks are very powerful predictive models, but they are often incapable of recognizing when their predictions may be wrong. Closely related to this is the task of out-of-distribution detection, where a network must…
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…
With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…
For given system dynamics, observer structure, and observer-based fault/attack detection procedure, we provide mathematical tools -- in terms of Linear Matrix Inequalities (LMIs) -- for computing outer ellipsoidal bounds on the set of…
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial input uncertainty, but researchers…
Randomized artificial neural networks such as extreme learning machines provide an attractive and efficient method for supervised learning under limited computing ressources and green machine learning. This especially applies when equipping…
We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive…
Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a…
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…
The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…
Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…