Related papers: Adjoints and Automatic (Algorithmic) Differentiati…
Automatic Differentiation (AD) allows to determine exactly the Taylor series of any function truncated at any order. Here we propose to use AD techniques for Monte Carlo data analysis. We discuss how to estimate errors of a general function…
We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Adversarial Optimization (AO) provides a reliable, practical way to match two implicitly defined distributions, one of which is usually represented by a sample of real data, and the other is defined by a generator. Typically, AO involves…
We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
The ambiguity function is fundamental to radar waveform design, characterizing range and Doppler resolution capabilities. However, its traditional formulation involves non-differentiable operations, preventing integration with…
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…
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…
The computation of Greeks is a fundamental task for risk managing of financial instruments. The standard approach to their numerical evaluation is via finite differences. Most exotic derivatives are priced via Monte Carlo simulation: in…
Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…
The field of algorithms with predictions incorporates machine learning advice in the design of online algorithms to improve real-world performance. A central consideration is the extent to which predictions can be trusted -- while existing…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavior: AD sometimes disagrees with the true derivative of a…
The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a…
Differentiable economics, which uses neural networks as function approximators and gradient-based optimization in automated mechanism design (AMD), marked a significant breakthrough with the introduction of RegretNet…
Calibration is a basic property for prediction systems, and algorithms for achieving it are well-studied in both statistics and machine learning. In many applications, however, the predictions are used to make decisions that select which…
The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes…
A recent approach to automated mechanism design, differentiable economics, represents auctions by rich function approximators and optimizes their performance by gradient descent. The ideal auction architecture for differentiable economics…