Related papers: Fast and General Automatic Differentiation for Fin…
Due to the superiority of quantum computing, traditional cryptography is facing severe threat. This makes the security evaluation of cryptographic systems in quantum attack models significant and urgent. For symmetric ciphers, the security…
In this paper we establish an abstraction of on-the-fly determinization of finite-state automata using transition monoids and demonstrate how it can be applied to bound the asymptotics. We present algebraic and combinatorial properties that…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD)…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the…
Fair classification is a critical challenge that has gained increasing importance due to international regulations and its growing use in high-stakes decision-making settings. Existing methods often rely on adversarial learning or…
We establish a translation between a formalism for dynamic programming over hypergraphs and the computation of semiring-based provenance for Datalog programs. The benefit of this translation is a new method for computing provenance for a…
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental…
Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…
Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due…
Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…
Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial…
The core challenge in designing an effective static program analysis is to find a good program abstraction -- one that retains only details relevant to a given query. In this paper, we present a new approach for automatically finding such…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…