Related papers: Galois Slicing as Automatic Differentiation
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
Masking is a widely-used effective countermeasure against power side-channel attacks for implementing cryptographic algorithms. Surprisingly, few formal verification techniques have addressed a fundamental question, i.e., whether the masked…
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their…
Machine learning models make mistakes, yet sometimes it is difficult to identify the systematic problems behind the mistakes. Practitioners engage in various activities, including error analysis, testing, auditing, and red-teaming, to form…
Given a value computed within a program, an idempotent backward slice with respect to this value is a maximal subprogram that computes it. An informal notion of an idempotent slice has previously been used by Guimaraes et al. to transform…
In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through…
Using the action of the Galois group of a normal extension of number fields, we generalize and symmetrize various fundamental statements in algebra and algebraic number theory concerning splitting types of prime ideals, factorization types…
This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative…
In embedded control systems, the potential risks of software defects have been increasing because of software complexity which leads to, for example, timing related problems. These defects are rarely found by tests or simulations. To detect…
Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We propose a new method, that we coined the ``morphism-trick'', to integrate custom implementations of vector-Jacobian products in automatic differentiation softwares, applicable to a wide range of semiring-based computations. Our approach…
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…
Dataset distillation is an effective technique for reducing the cost and complexity of model training while maintaining performance by compressing large datasets into smaller, more efficient versions. In this paper, we present a novel…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
We describe a system that simplifies the process of debugging programs produced by computer-aided parallelization tools. The system uses relative debugging techniques to compare serial and parallel executions in order to show where the…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of…
We give a gentle introduction to using various software tools for automatic differentiation (AD). Ready-to-use examples are discussed, and links to further information are presented. Our target audience includes all those who are looking…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to…