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In recent years, formal methods of privacy protection such as differential privacy (DP), capable of deployment to data-driven tasks such as machine learning (ML), have emerged. Reconciling large-scale ML with the closed-form reasoning…
We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
Anomaly detection (AD) plays a crucial role in various domains, including cybersecurity, finance, and healthcare, by identifying patterns or events that deviate from normal behaviour. In recent years, significant progress has been made in…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
Image anomaly detection (IAD) is an emerging and vital computer vision task in industrial manufacturing (IM). Recently, many advanced algorithms have been reported, but their performance deviates considerably with various IM settings. We…
Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably,…
Multi-objective optimization problems, which require the simultaneous optimization of multiple objectives, are prevalent across numerous applications. Existing multi-objective optimization methods often rely on manually-tuned aggregation…
RooFit is a toolkit for statistical modeling and fitting used by most experiments in particle physics. Just as data sets from next-generation experiments grow, processing requirements for physics analysis become more computationally…
Classical reverse-mode automatic differentiation (AD) imposes only a small constant-factor overhead in operation count over the original computation, but has storage requirements that grow, in the worst case, in proportion to the time…
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…
Algebraic differentiators have attracted much interest in recent years. Their simple implementation as classical finite impulse response digital filters and systematic tuning guidelines may help to solve challenging problems, including, but…
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…
A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
Anomaly detection (AD) is a critical task across domains such as cybersecurity and healthcare. In the unsupervised setting, an effective and theoretically-grounded principle is to train classifiers to distinguish normal data from…
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…
A natural and often used strategy when testing software is to use input values at boundaries, i.e. where behavior is expected to change the most, an approach often called boundary value testing or analysis (BVA). Even though this has been a…
Anomaly detection (AD) is an important machine learning task with applications in fraud detection, content moderation, and user behavior analysis. However, AD is relatively understudied in a natural language processing (NLP) context,…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…