Related papers: Adversarial Barrier in Uniform Class Separation
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
We propose a framework for adversarial training that relies on a sample rather than a single sample point as the fundamental unit of discrimination. Inspired by discrepancy measures and two-sample tests between probability distributions, we…
Abstaining classifiers have the option to refrain from providing a prediction for instances that are difficult to classify. The abstention mechanism is designed to trade off the classifier's performance on the accepted data while ensuring a…
Deep neural networks are known to be vulnerable to small adversarial perturbations in test data. To defend against adversarial attacks, probabilistic classifiers have been proposed as an alternative to deterministic ones. However,…
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…
We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
This work investigates adversarial training in the context of margin-based linear classifiers in the high-dimensional regime where the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha = n / d$. We introduce…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the…
Text classifiers are vulnerable to adversarial examples -- correctly-classified examples that are deliberately transformed to be misclassified while satisfying acceptability constraints. The conventional approach to finding adversarial…
Adversarial examples have attracted significant attention in machine learning, but the reasons for their existence and pervasiveness remain unclear. We demonstrate that adversarial examples can be directly attributed to the presence of…
Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating…
We study adversarial perturbations when the instances are uniformly distributed over $\{0,1\}^n$. We study both "inherent" bounds that apply to any problem and any classifier for such a problem as well as bounds that apply to specific…
Deciding the amalgamation property for a given class of finite structures is an important subroutine in classifying countable finitely homogeneous structures. We study the computational complexity of the amalgamation decision problem for…
A standard introductory result is that Hausdorff spaces have the property US, that is, each convergent sequence has a unique limit. This paper explores several existing and new characterizations of separation axioms that are strictly weaker…
Adversarial attacks dramatically change the output of an otherwise accurate learning system using a seemingly inconsequential modification to a piece of input data. Paradoxically, empirical evidence indicates that even systems which are…
Despite the widespread use of machine learning algorithms to solve problems of technological, economic, and social relevance, provable guarantees on the performance of these data-driven algorithms are critically lacking, especially when the…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…