2,243 research outputs found
PhaseMax: Convex Phase Retrieval via Basis Pursuit
We consider the recovery of a (real- or complex-valued) signal from
magnitude-only measurements, known as phase retrieval. We formulate phase
retrieval as a convex optimization problem, which we call PhaseMax. Unlike
other convex methods that use semidefinite relaxation and lift the phase
retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation
that operates in the original signal dimension. We show that the dual problem
to PhaseMax is Basis Pursuit, which implies that phase retrieval can be
performed using algorithms initially designed for sparse signal recovery. We
develop sharp lower bounds on the success probability of PhaseMax for a broad
range of random measurement ensembles, and we analyze the impact of measurement
noise on the solution accuracy. We use numerical results to demonstrate the
accuracy of our recovery guarantees, and we showcase the efficacy and limits of
PhaseMax in practice
Adversarially Robust Distillation
Knowledge distillation is effective for producing small, high-performance
neural networks for classification, but these small networks are vulnerable to
adversarial attacks. This paper studies how adversarial robustness transfers
from teacher to student during knowledge distillation. We find that a large
amount of robustness may be inherited by the student even when distilled on
only clean images. Second, we introduce Adversarially Robust Distillation (ARD)
for distilling robustness onto student networks. In addition to producing small
models with high test accuracy like conventional distillation, ARD also passes
the superior robustness of large networks onto the student. In our experiments,
we find that ARD student models decisively outperform adversarially trained
networks of identical architecture in terms of robust accuracy, surpassing
state-of-the-art methods on standard robustness benchmarks. Finally, we adapt
recent fast adversarial training methods to ARD for accelerated robust
distillation.Comment: Accepted to AAAI Conference on Artificial Intelligence, 202
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