Related papers: Automatic differentiation of hybrid models Illustr…

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular…

The auto differentiable simulation is a type of simulation that outputs of the simulation include not only the simulation result itself, but also their derivatives with respect to various input parameters. It provides an efficient method to…

During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…

Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the…

Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…

Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to…

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…

Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

Hybrid parallelism techniques are essential for efficiently training large language models (LLMs). Nevertheless, current automatic parallel planning frameworks often overlook the simultaneous consideration of node heterogeneity and dynamic…

Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is…

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…

Diffusion models have achieved remarkable success in image and video generation. However, their inherently multiple step inference process imposes substantial computational overhead, hindering real-world deployment. Accelerating diffusion…

The ability for a human to understand an Artificial Intelligence (AI) model's decision-making process is critical in enabling stakeholders to visualize model behavior, perform model debugging, promote trust in AI models, and assist in…

Conventional document layout analysis (DLA) traditionally depends on empirical priors or a fixed set of learnable queries executed in a single forward pass. While sufficient for early-generation documents with a small, predetermined number…

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…

Changes, planned or unexpected, are common during the execution of real-life processes. Detecting these changes is a must for optimizing the performance of organizations running such processes. Most of the algorithms present in the…

Automatic parallelization remains a challenging problem in software engineering, particularly in identifying code regions where loops can be safely executed in parallel on modern multi-core architectures. Traditional static analysis…

Recent data-driven image colorization methods have enabled automatic or reference-based colorization, while still suffering from unsatisfactory and inaccurate object-level color control. To address these issues, we propose a new method…