Related papers: Implementing an Automatic Differentiator in ACL2

This paper presents a method for learning logical task specifications and cost functions from demonstrations. Constructing specifications by hand is challenging for complex objectives and constraints in autonomous systems. Instead, we…

Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…

The application of Deep Reinforcement Learning (DRL) to inventory management is an emerging field. However, traditional DRL algorithms, originally developed for diverse domains such as game-playing and robotics, may not be well-suited for…

Reinforcement learning (RL) tasks are challenging to implement, execute and test due to algorithmic instability, hyper-parameter sensitivity, and heterogeneous distributed communication patterns. We argue for the separation of logical…

In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the…

Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…

Offline reinforcement learning (RL) defines the task of learning from a fixed batch of data. Due to errors in value estimation from out-of-distribution actions, most offline RL algorithms take the approach of constraining or regularizing…

Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…

This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of…

In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…

Reverse differentiation is an essential operation for automatic differentiation. Cartesian reverse differential categories axiomatize reverse differentiation in a categorical framework, where one of the primary axioms is the reverse chain…

A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the…

A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…

To be practically useful, modern static analyzers must precisely model the effect of both, statements in the programming language as well as frameworks used by the program under analysis. While important, manually addressing these…

The framework of deep reinforcement learning (DRL) provides a powerful and widely applicable mathematical formalization for sequential decision-making. This paper present a novel DRL framework, termed \emph{$f$-Divergence Reinforcement…