Related papers: A Language for Evaluating Derivatives of Functiona…
We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
We consider the problem of computing optimal generalised policies for relational Markov decision processes. We describe an approach combining some of the benefits of purely inductive techniques with those of symbolic dynamic programming…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
We present a computational framework for piecewise constant functions (PCFs) and use this for several types of computations that are useful in statistics, e.g., averages, similarity matrices, and so on. We give a linear-time,…
This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no…
The purpose of this survey is a comprehensive study of operator Lip\-schitz functions. A continuous function $f$ on the real line ${\Bbb R}$ os called operator Lipschitz if $\|f(A)-f(B)\|\le\operatorname{const}\|A-B\|$ for arbitrary…
We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…
We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
This report presents the Dafny language and verifier, with a focus on describing the main features of the language, including pre- and postconditions, assertions, loop invariants, termination metrics, quantifiers, predicates and frames.…
The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg, in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by…
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…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But…
In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length…