相关论文: JAX Autodiff from a Linear Logic Perspective (Exte…

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)…

It is common to reject undesired outputs of Large Language Models (LLMs); however, current methods to do so require an excessive amount of computation to re-sample after a rejection, or distort the distribution of outputs by constraining…

We present a differentiable extension of the VEROS ocean model, enabling automatic differentiation through its dynamical core. We describe the key modifications required to make the model fully compatible with JAX autodifferentiation…

In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…

Self-play with large language models has emerged as a promising paradigm for achieving self-improving artificial intelligence. However, existing self-play frameworks often suffer from optimization instability, due to (i) non-stationary…

This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…

Tools for algorithmic differentiation (AD) provide accurate derivatives of computer-implemented functions for use in, e. g., optimization and machine learning (ML). However, they often require the source code of the function to be available…

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…

This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid…

We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…

Large Language Models (LLMs) have reshaped natural language processing, powering applications from multi-hop retrieval and question answering to autonomous agent workflows. Yet, prompt engineering -- the task of crafting textual inputs to…

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…

This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…

Machine learning and deep learning-based decision making has become part of today's software. The goal of this work is to ensure that machine learning and deep learning-based systems are as trusted as traditional software. Traditional…

We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…

We combine quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with temporal logic for reasoning about the temporal behavior during their operation. Our logic supports…

This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…

We present ADerrors.jl, a software for linear error propagation and analysis of Monte Carlo data. Although the focus is in data analysis in Lattice QCD, where estimates of the observables have to be computed from Monte Carlo samples, the…

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…

We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the…