# An Exact Bitwise Reversible Integrator

arXiv: https://arxiv.org/abs/2207.07695 · HTML: https://mlsanity.com/paper/2207.07695/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 15 Jul 2022.

## Builds on (most cited first, 1 of 1)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)

## Built on by (most cited first, 1 of 1)

- [On Exact Bit-level Reversible Transformers Without Changing Architectures](https://mlsanity.com/paper/2407.09093/) (2024)

## Abstract (arXiv)

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).