相关论文: Automatic Differentiation in PCF

This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…

Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…

In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…

We consider the use of machine learning for hypothesis testing with an emphasis on target detection. Classical model-based solutions rely on comparing likelihoods. These are sensitive to imperfect models and are often computationally…

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…

The Cheap Gradient Principle (Griewank 2008) --- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of $5$) as that of simply computing the function itself --- is of…

Algorithmic Differentiation (AD) can be used to automate the generation of derivatives in arbitrary software projects. This will generate maintainable derivatives, that are always consistent with the computation of the software. If a domain…

We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…

We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…

Multiple lines of evidence suggest that predictive models may benefit from algorithmic triage. Under algorithmic triage, a predictive model does not predict all instances but instead defers some of them to human experts. However, the…

The extraction of the model parameters is as important as the development of compact model itself because simulation accuracy is fully determined by the accuracy of the parameters used. This study proposes an efficient model-parameter…

The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods…

To derive a program for a given specification R means to find an artifact P that satisfies two conditions: P is executable in some programming language; and P is correct with respect to R. Refinement-based program derivation achieves this…

We study the problem of automated mechanism design with partial verification, where each type can (mis)report only a restricted set of types (rather than any other type), induced by the principal's limited verification power. We prove…

Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent G\"odel…

Machine learning can provide predictions with disparate outcomes, in which subgroups of the population (e.g., defined by age, gender, or other sensitive attributes) are systematically disadvantaged. In order to comply with upcoming…

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…

The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…

The performance of gradient-based optimization methods, such as standard gradient descent (GD), greatly depends on the choice of learning rate. However, it can require a non-trivial amount of user tuning effort to select an appropriate…