DeformRS: Certifying Input Deformations with Randomized Smoothing

Randomized Smoothing for Stochastic Optimization

We analyze convergence rates of stochastic optimization algorithms for nonsmooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic optimization procedures, both in expectation and with high probability, that have optimal dependence on the variance of the gradient estimates. To the best of our k...

ScrewBox: a Randomized Certifying Graph-Non-Isomorphism Algorithm

We present a novel randomized approach to the graph isomorphism problem. Our algorithm aims at solving difficult instances by producing randomized certificates for non-isomorphism. We compare our implementation to the de facto standard nauty. On many of the hardest known instances, the incidence graphs of finite projective planes, our program is considerably faster than nauty. However, it is in...

Certifying algorithms

Investigating Type-Certifying Compilation with Isabelle

This paper presents a type certifying compiler for a subset of Java and proves the type correctness of the bytecode it generates in the proof assistant Isabelle. The proof is performed by defining a type compiler that emits a type certificate and by showing a correspondence between bytecode and the certificate which entails well-typing.

Certifying the Fast Fourier Transform with Coq

We program the Fast Fourier Transform in type theory, using the tool Coq. We prove its correctness and the correctness of the Inverse Fourier Transform. A type of trees representing vectors with interleaved elements is defined to facilitate the definition of the transform by structural recursion. We define several operations and proof tools for this data structure, leading to a simple proof of ...