30,086 research outputs found
Procedural Noise Adversarial Examples for Black-Box Attacks on Deep Convolutional Networks
Deep Convolutional Networks (DCNs) have been shown to be vulnerable to
adversarial examples---perturbed inputs specifically designed to produce
intentional errors in the learning algorithms at test time. Existing
input-agnostic adversarial perturbations exhibit interesting visual patterns
that are currently unexplained. In this paper, we introduce a structured
approach for generating Universal Adversarial Perturbations (UAPs) with
procedural noise functions. Our approach unveils the systemic vulnerability of
popular DCN models like Inception v3 and YOLO v3, with single noise patterns
able to fool a model on up to 90% of the dataset. Procedural noise allows us to
generate a distribution of UAPs with high universal evasion rates using only a
few parameters. Additionally, we propose Bayesian optimization to efficiently
learn procedural noise parameters to construct inexpensive untargeted black-box
attacks. We demonstrate that it can achieve an average of less than 10 queries
per successful attack, a 100-fold improvement on existing methods. We further
motivate the use of input-agnostic defences to increase the stability of models
to adversarial perturbations. The universality of our attacks suggests that DCN
models may be sensitive to aggregations of low-level class-agnostic features.
These findings give insight on the nature of some universal adversarial
perturbations and how they could be generated in other applications.Comment: 16 pages, 10 figures. In Proceedings of the 2019 ACM SIGSAC
Conference on Computer and Communications Security (CCS '19
Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation
We study the compressed sensing (CS) signal estimation problem where an input
signal is measured via a linear matrix multiplication under additive noise.
While this setup usually assumes sparsity or compressibility in the input
signal during recovery, the signal structure that can be leveraged is often not
known a priori. In this paper, we consider universal CS recovery, where the
statistics of a stationary ergodic signal source are estimated simultaneously
with the signal itself. Inspired by Kolmogorov complexity and minimum
description length, we focus on a maximum a posteriori (MAP) estimation
framework that leverages universal priors to match the complexity of the
source. Our framework can also be applied to general linear inverse problems
where more measurements than in CS might be needed. We provide theoretical
results that support the algorithmic feasibility of universal MAP estimation
using a Markov chain Monte Carlo implementation, which is computationally
challenging. We incorporate some techniques to accelerate the algorithm while
providing comparable and in many cases better reconstruction quality than
existing algorithms. Experimental results show the promise of universality in
CS, particularly for low-complexity sources that do not exhibit standard
sparsity or compressibility.Comment: 29 pages, 8 figure
Approximate resilience, monotonicity, and the complexity of agnostic learning
A function is -resilient if all its Fourier coefficients of degree at
most are zero, i.e., is uncorrelated with all low-degree parities. We
study the notion of of Boolean
functions, where we say that is -approximately -resilient if
is -close to a -valued -resilient function in
distance. We show that approximate resilience essentially characterizes the
complexity of agnostic learning of a concept class over the uniform
distribution. Roughly speaking, if all functions in a class are far from
being -resilient then can be learned agnostically in time and
conversely, if contains a function close to being -resilient then
agnostic learning of in the statistical query (SQ) framework of Kearns has
complexity of at least . This characterization is based on the
duality between approximation by degree- polynomials and
approximate -resilience that we establish. In particular, it implies that
approximation by low-degree polynomials, known to be sufficient for
agnostic learning over product distributions, is in fact necessary.
Focusing on monotone Boolean functions, we exhibit the existence of
near-optimal -approximately
-resilient monotone functions for all
. Prior to our work, it was conceivable even that every monotone
function is -far from any -resilient function. Furthermore, we
construct simple, explicit monotone functions based on and that are close to highly resilient functions. Our constructions are
based on a fairly general resilience analysis and amplification. These
structural results, together with the characterization, imply nearly optimal
lower bounds for agnostic learning of monotone juntas
On the hardness of learning sparse parities
This work investigates the hardness of computing sparse solutions to systems
of linear equations over F_2. Consider the k-EvenSet problem: given a
homogeneous system of linear equations over F_2 on n variables, decide if there
exists a nonzero solution of Hamming weight at most k (i.e. a k-sparse
solution). While there is a simple O(n^{k/2})-time algorithm for it,
establishing fixed parameter intractability for k-EvenSet has been a notorious
open problem. Towards this goal, we show that unless k-Clique can be solved in
n^{o(k)} time, k-EvenSet has no poly(n)2^{o(sqrt{k})} time algorithm and no
polynomial time algorithm when k = (log n)^{2+eta} for any eta > 0.
Our work also shows that the non-homogeneous generalization of the problem --
which we call k-VectorSum -- is W[1]-hard on instances where the number of
equations is O(k log n), improving on previous reductions which produced
Omega(n) equations. We also show that for any constant eps > 0, given a system
of O(exp(O(k))log n) linear equations, it is W[1]-hard to decide if there is a
k-sparse linear form satisfying all the equations or if every function on at
most k-variables (k-junta) satisfies at most (1/2 + eps)-fraction of the
equations. In the setting of computational learning, this shows hardness of
approximate non-proper learning of k-parities. In a similar vein, we use the
hardness of k-EvenSet to show that that for any constant d, unless k-Clique can
be solved in n^{o(k)} time there is no poly(m, n)2^{o(sqrt{k}) time algorithm
to decide whether a given set of m points in F_2^n satisfies: (i) there exists
a non-trivial k-sparse homogeneous linear form evaluating to 0 on all the
points, or (ii) any non-trivial degree d polynomial P supported on at most k
variables evaluates to zero on approx. Pr_{F_2^n}[P(z) = 0] fraction of the
points i.e., P is fooled by the set of points
A composition theorem for the Fourier Entropy-Influence conjecture
The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96]
seeks to relate two fundamental measures of Boolean function complexity: it
states that holds for every Boolean function , where
denotes the spectral entropy of , is its total influence,
and is a universal constant. Despite significant interest in the
conjecture it has only been shown to hold for a few classes of Boolean
functions.
Our main result is a composition theorem for the FEI conjecture. We show that
if are functions over disjoint sets of variables satisfying the
conjecture, and if the Fourier transform of taken with respect to the
product distribution with biases satisfies the conjecture,
then their composition satisfies the conjecture. As
an application we show that the FEI conjecture holds for read-once formulas
over arbitrary gates of bounded arity, extending a recent result [OWZ11] which
proved it for read-once decision trees. Our techniques also yield an explicit
function with the largest known ratio of between and
, improving on the previous lower bound of 4.615
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