An Exact Bitwise Reversible Integrator
This work addresses the need for exact reversibility in simulations for efficient optimization and backpropagation, though it appears incremental as it builds on theoretically reversible integrators.
The authors tackled the problem of preserving time reversibility in physical simulations at the discrete computational level by proposing an integrator that allows simulations to run forward and backward exactly bitwise, using a mix of fixed and floating point arithmetic, with applications in optimization and machine learning.
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).