Related papers: Robustness of infinite frames and Besselian struct…
Vision-Language Models (VLMs) can perform zero-shot classification but are susceptible to adversarial attacks. While robust fine-tuning improves their robustness, existing approaches align fixed text embeddings with an image embedding,…
For a finite Blaschke product $B$ and for an isometry $V$ on an infinite-dimensional separable complex Hilbert space $\mathcal{H}$ we study a sequence $(b_m)_{m=1}^\infty$ of vectors in $\mathcal{H}$, defined by $b_m = B(V^*)e_m$, where…
Controlled $\ast$-K-fusion frames are generalization of controlled fusion frames in frame theory. In this paper, we propose the notion of controlled $\ast$-k-fusions frames on Hilbert $C^{\ast}$-modules. We give some caraterizations and…
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…
We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm. In a first part, we obtain these results in the i.i.d. setup under subgaussian…
In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact…
Recurrent Neural Networks (RNNs) yield attractive properties for constructing Intrusion Detection Systems (IDSs) for network data. With the rise of ubiquitous Machine Learning (ML) systems, malicious actors have been catching up quickly to…
The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks…
In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
To explain predictions made by complex machine learning models, many feature attribution methods have been developed that assign importance scores to input features. Some recent work challenges the robustness of these methods by showing…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…
The paper studies finite extensions of Bessel sequences in infinite-dimensional Hilbert spaces. We provide a characterization of Bessel sequences that can be extended to frames by adding finitely many vectors. We also characterize frames…
Object-centric representation learning offers the potential to overcome limitations of image-level representations by explicitly parsing image scenes into their constituent components. While image-level representations typically lack…
This paper aims to provide a thorough study on the effectiveness of the transformation-based ensemble defence for image classification and its reasons. It has been empirically shown that they can enhance the robustness against evasion…
Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
This initial version of this document was written back in 2014 for the sole purpose of providing fundamentals of reliability theory as well as to identify the theoretical types of machinery for the prediction of durability/availability of…