Related papers: Implementing an Automatic Differentiator in ACL2
We present the classical coordinate-free formalism for forward and backward mode ad in the real and complex setting. We show how to formally derive the forward and backward formulae for a number of matrix functions starting from basic…
Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of…
For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
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…
ACL2(ml) is an extension for the Emacs interface of ACL2. This tool uses machine-learning to help the ACL2 user during the proof-development. Namely, ACL2(ml) gives hints to the user in the form of families of similar theorems, and…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
Automatic differentiation is a tool for numerically calculating derivatives of a given function up to machine precision. This tool is useful for quantum chemistry methods, which require the calculation of gradients either for the…
We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive…
In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how…
Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…
Automatic Curriculum Learning (ACL) has become a cornerstone of recent successes in Deep Reinforcement Learning (DRL).These methods shape the learning trajectories of agents by challenging them with tasks adapted to their capacities. In…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations…
In this paper we take a look at Automatic Differentiation through the eyes of Tensor and Operational Calculus. This work is best consumed as supplementary material for learning tensor and operational calculus by those already familiar with…
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…
Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in…