An Exact Bitwise Reversible Integrator

TL;DR

This paper introduces a novel exact bitwise reversible integrator that preserves time-reversibility at the discrete computational level, enabling precise forward and backward simulations for applications in optimization and machine learning.

Contribution

It presents a new integrator that maintains exact reversibility using mixed arithmetic, improving the accuracy of reverse computations in simulations and backpropagation.

Findings

Simulations can be run forward and backward with exact bitwise consistency.

The integrator enhances reverse step efficiency in the adjoint method.

Potential applications include differential simulations and machine learning backpropagation.

Abstract

At a fundamental level most physical equations are time reversible. In this paper we propose an integrator that preserves this property at the discrete computational level. Our simulations can be run forward and backwards and trace the same path exactly bitwise. We achieve this by implementing theoretically reversible integrators using a mix of fixed and floating point arithmetic. Our main application is in efficiently implementing the reverse step in the adjoint method used in optimization. Our integrator has applications in differential simulations and machine learning (backpropagation).