Related papers: The General Adversary Bound: A Survey

Generalization to unseen instances is our eternal pursuit for all data-driven models. However, for realistic task like machine translation, the traditional approach measuring generalization in an average sense provides poor understanding…

Process mining algorithms discover a process model from an event log. The resulting process model is supposed to describe all possible event sequences of the underlying system. Generalization is a process model quality dimension of…

Given a graph $G$, we define ${\bf bcg}(G)$ as the minimum $k$ for which $G$ can be contracted to the uniformly triangulated grid $\Gamma_{k}$. A graph class ${\cal G}$ has the SQG${\bf C}$ property if every graph $G\in{\cal G}$ has…

The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of…

Deep neural networks are vulnerable to adversarial attacks. Ideally, a robust model shall perform well on both the perturbed training data and the unseen perturbed test data. It is found empirically that fitting perturbed training data is…

Privacy concerns have led to the development of privacy-preserving approaches for learning models from sensitive data. Yet, in practice, even models learned with privacy guarantees can inadvertently memorize unique training examples or leak…

We prove the lower bound R(M_m) \geq 3/2 m^2 - 2 on the border rank of m x m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of the geometric complexity theory (GCT) program. While…

We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target…

For Riemannian manifolds with a measure $(M,g, e^{-f} dvol_g)$ we prove mean curvature and volume comparison results when the $\infty$-Bakry-Emery Ricci tensor is bounded from below and $f$ is bounded or $\partial_r f$ is bounded from…

Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…

We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.

Adversarial examples are inevitable on the road of pervasive applications of deep neural networks (DNN). Imperceptible perturbations applied on natural samples can lead DNN-based classifiers to output wrong prediction with fair confidence…

For an infinite class of finite graphs of unbounded size, we define a limit object, to be called a $\textit{wide limit}$, relative to some computationally restricted class of functions. The limit object is a first order Boolean-valued…

We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high…

A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more…

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance $\varepsilon$, using tools from variational analysis. In particular, we describe necessary conditions associated…

One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance…

Given a black-box classification model and an unlabeled evaluation dataset from some application domain, efficient strategies need to be developed to evaluate the model. Random sampling allows a user to estimate metrics like accuracy,…

In a manner analogous to their classical counterparts, quantum classifiers are vulnerable to adversarial attacks that perturb their inputs. A promising countermeasure is to train the quantum classifier by adopting an attack-aware, or…

We derive bounds for a notion of adversarial risk, designed to characterize the robustness of linear and neural network classifiers to adversarial perturbations. Specifically, we introduce a new class of function transformations with the…