Related papers: Implementing an Automatic Differentiator in ACL2

ACL2 provides a systems programming capability that allows one to write code that uses and extends ACL2 inside of ACL2. However, for soundness reasons, ACL2 bars the unrestricted use of certain kinds of programming constructs, like…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

We present a minimal control-based continuation algorithm designed to track branches of limit cycles in autonomous systems. The controller can be viewed as three sub-controllers: (i) a derivative feedback controller that is used to…

Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…

Despite the remarkable code generation abilities of large language models LLMs, they still face challenges in complex task handling. Robot development, a highly intricate field, inherently demands human involvement in task allocation and…

This document investigates the integration of adaptive distinguishing sequences into the process of active automata learning (AAL). A novel AAL algorithm "ADT" (adaptive discrimination tree) is developed and presented. Since the submission…

In-context learning (ICL) has emerged as a powerful paradigm for easily adapting Large Language Models (LLMs) to various tasks. However, our understanding of how ICL works remains limited. We explore a simple model of ICL in a controlled…

Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…

Differentiation lies at the core of many machine-learning algorithms, and is well-supported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable…

This paper presents the ReXCL tool, which automates the extraction and classification processes in requirement engineering, enhancing the software development lifecycle. The tool features two main modules: Extraction, which processes raw…

Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis.…

The ACL2 Workshop series is the major technical forum for users of the ACL2 theorem proving system to present research related to the ACL2 theorem prover and its applications. ACL2 is an industrial-strength automated reasoning system, the…

In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement…

If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A…

We want to obtain derivatives in discontinuous program code, where default Algorithmic Differentiation may not perform well. Specifically, we consider discontinuities induced by control flow statements, where meaningful derivatives should…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition…

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…

Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives…

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…