740 research outputs found
ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation
Deep neural networks are vulnerable to adversarial attacks. The literature is
rich with algorithms that can easily craft successful adversarial examples. In
contrast, the performance of defense techniques still lags behind. This paper
proposes ME-Net, a defense method that leverages matrix estimation (ME). In
ME-Net, images are preprocessed using two steps: first pixels are randomly
dropped from the image; then, the image is reconstructed using ME. We show that
this process destroys the adversarial structure of the noise, while
re-enforcing the global structure in the original image. Since humans typically
rely on such global structures in classifying images, the process makes the
network mode compatible with human perception. We conduct comprehensive
experiments on prevailing benchmarks such as MNIST, CIFAR-10, SVHN, and
Tiny-ImageNet. Comparing ME-Net with state-of-the-art defense mechanisms shows
that ME-Net consistently outperforms prior techniques, improving robustness
against both black-box and white-box attacks.Comment: ICML 201
Multireference Alignment using Semidefinite Programming
The multireference alignment problem consists of estimating a signal from
multiple noisy shifted observations. Inspired by existing Unique-Games
approximation algorithms, we provide a semidefinite program (SDP) based
relaxation which approximates the maximum likelihood estimator (MLE) for the
multireference alignment problem. Although we show that the MLE problem is
Unique-Games hard to approximate within any constant, we observe that our
poly-time approximation algorithm for the MLE appears to perform quite well in
typical instances, outperforming existing methods. In an attempt to explain
this behavior we provide stability guarantees for our SDP under a random noise
model on the observations. This case is more challenging to analyze than
traditional semi-random instances of Unique-Games: the noise model is on
vertices of a graph and translates into dependent noise on the edges.
Interestingly, we show that if certain positivity constraints in the SDP are
dropped, its solution becomes equivalent to performing phase correlation, a
popular method used for pairwise alignment in imaging applications. Finally, we
show how symmetry reduction techniques from matrix representation theory can
simplify the analysis and computation of the SDP, greatly decreasing its
computational cost
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