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The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important…
Collider bias is a harmful form of sample selection bias that neural networks are ill-equipped to handle. This bias manifests itself when the underlying causal signal is strongly correlated with other confounding signals due to the training…
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…
LiDAR point clouds collected from a moving vehicle are functions of its trajectories, because the sensor motion needs to be compensated to avoid distortions. When autonomous vehicles are sending LiDAR point clouds to deep networks for…
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…
Estimation of the parameters of a 2-dimensional sinusoidal model is a fundamental problem in digital signal processing and time series analysis. In this paper, we propose a robust least absolute deviation (LAD) estimators for parameter…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Adversarial training is one of the most effective methods for enhancing model robustness. Recent approaches incorporate adversarial distillation in adversarial training architectures. However, we notice two scenarios of defense methods that…
Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…
In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike…
The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the…
In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…
This paper proposes a resilient state estimator for LTI discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a…
The nonuniform and growing impact of adversarial noise across the layers of deep neural networks has been used in the literature, without a formal mathematical justification, to detect adversarial inputs and improve robustness. In this…
The vulnerability of Deep Neural Networks to Adversarial Attacks has fuelled research towards building robust models. While most Adversarial Training algorithms aim at defending attacks constrained within low magnitude Lp norm bounds,…
In this work, we consider model robustness of deep neural networks against adversarial attacks from a global manifold perspective. Leveraging both the local and global latent information, we propose a novel adversarial training method…
Deep models are highly susceptible to adversarial attacks. Such attacks are carefully crafted imperceptible noises that can fool the network and can cause severe consequences when deployed. To encounter them, the model requires training…
Adversarial attacks add perturbations to the input features with the intent of changing the classification produced by a machine learning system. Small perturbations can yield adversarial examples which are misclassified despite being…
The fact that deep neural networks are susceptible to crafted perturbations severely impacts the use of deep learning in certain domains of application. Among many developed defense models against such attacks, adversarial training emerges…
We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…