Related papers: The General Adversary Bound: A Survey
We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption…
We introduce two new complexity measures for Boolean functions, or more generally for functions of the form f:S->T. We call these measures sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query…
Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial…
Obtaining deep networks that are robust against adversarial examples and generalize well is an open problem. A recent hypothesis even states that both robust and accurate models are impossible, i.e., adversarial robustness and…
In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function $f$ on $n$ variables that only depends on $k$ variables, and, when restricted to them, equals some predefined…
Adversarial robustness of machine learning models is critical to ensuring reliable performance under data perturbations. Recent progress has been on point estimators, and this paper considers distributional predictors. First, using the link…
The degree of a polynomial representing (or approximating) a function f is a lower bound for the number of quantum queries needed to compute f. This observation has been a source of many lower bounds on quantum algorithms. It has been an…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…
We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
Harry Buhrman et al gave an Omega(sqrt n) lower bound for monotone graph properties in the adjacency matrix query model. Their proof is based on the polynomial method. However for some properties stronger lower bounds exist. We give an…
Applying Baaz's Generalization Method and a new technique to, respectively, proofs and denumerable simple graphs, diverse arithmetical patterns are observed. In particular, sufficient conditions for a number to be a divisor of a Fermat…
The paper presents a generalization bound for quantum neural networks based on a dynamical Lie algebra. Using covering numbers derived from a dynamical Lie algebra, the Rademacher complexity is derived to calculate the generalization bound.…
In our recent work (Bubeck, Price, Razenshteyn, arXiv:1805.10204) we argued that adversarial examples in machine learning might be due to an inherent computational hardness of the problem. More precisely, we constructed a binary…
End-to-end (geometric) deep learning has seen first successes in approximating the solution of combinatorial optimization problems. However, generating data in the realm of NP-hard/-complete tasks brings practical and theoretical…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…