English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study adversarial perturbations when the instances are uniformlydistributed over $\{0,1\}^n$. We study both "inherent" bounds that apply to anyproblem and any classifier for such a problem as well as bounds that apply tospecific problems and specific hypothesis classes.  As the current literature contains multiple definitions of adversarial riskand robustness, we start by giving a taxonomy for these definitions based ontheir goals, we identify one of them as the one guaranteeing misclassificationby pushing the instances to the error region. We then study some classicalgorithms for learning monotone conjunctions and compare their adversarialrisk and robustness under different definitions by attacking the hypothesesusing instances drawn from the uniform distribution. We observe that sometimesthese definitions lead to significantly different bounds. Thus, this studyadvocates for the use of the error-region definition, even though otherdefinitions, in other contexts, may coincide with the error-region definition.  Using the error-region definition of adversarial perturbations, we then studyinherent bounds on risk and robustness of any classifier for any classificationproblem whose instances are uniformly distributed over $\{0,1\}^n$. Using theisoperimetric inequality for the Boolean hypercube, we show that for initialerror $0.01$, there always exists an adversarial perturbation that changes$O(\sqrt{n})$ bits of the instances to increase the risk to $0.5$, makingclassifier's decisions meaningless. Furthermore, by also using the centrallimit theorem we show that when $n\to \infty$, at most $c \cdot \sqrt{n}$ bitsof perturbations, for a universal constant $c< 1.17$, suffice for increasingthe risk to $0.5$, and the same $c \cdot \sqrt{n} $ bits of perturbations onaverage suffice to increase the risk to $1$, hence bounding the robustness by$c \cdot \sqrt{n}$.

Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution