Related papers: Automatic Differentiation using Constraint Handlin…
In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it…
We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive…
Automatic differentiation has become an important tool for optimization problems in computational science, and it has been applied to the Hartree-Fock method. Although the reverse-mode automatic differentiation is more efficient than the…
We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…
This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…
Automatic differentiation (AD) is a set of techniques that systematically applies the chain rule to compute the gradients of functions without requiring human intervention. Although the fundamentals of this technology were established…
An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and…
Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is often determined \emph{adaptively} by the algorithm based…
This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
We introduce a technique that can automatically tune the parameters of a rule-based computer vision system comprised of thresholds, combinational logic, and time constants. This lets us retain the flexibility and perspicacity of a…
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…
The performance of deep neural networks is well-known to be sensitive to the setting of their hyperparameters. Recent advances in reverse-mode automatic differentiation allow for optimizing hyperparameters with gradients. The standard way…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
Runtime repeated recursion unfolding was recently introduced as a just-in-time program transformation strategy that can achieve super-linear speedup. So far, the method was restricted to single linear direct recursive rules in the…
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
PRholog is an experimental extension of logic programming with strategic conditional transformation rules, combining Prolog with Rholog calculus. The rules perform nondeterministic transformations on hedges. Queries may have several results…
Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…
Grammars written as Constraint Handling Rules (CHR) can be executed as efficient and robust bottom-up parsers that provide a straightforward, non-backtracking treatment of ambiguity. Abduction with integrity constraints as well as other…
Constraint Handling Rules (CHR) is a declarative rule-based formalism and language. Concurrency is inherent as rules can be applied to subsets of constraints in parallel. Parallel implementations of CHR, be it in software, be it in…
Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual…