# A note on the adjoint method for neural ordinary differential equation network

arXiv: https://arxiv.org/abs/2402.15141 · HTML: https://mlsanity.com/paper/2402.15141/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 6 references that are in the map.
- First posted on arXiv 23 Feb 2024.

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

- [Revealing hidden dynamics from time-series data by ODENet](https://mlsanity.com/paper/2005.04849/) (2020)

## Abstract (arXiv)

Perturbation and operator adjoint method are used to give the right adjoint form rigourously. From the derivation, we can have following results: 1) The loss gradient is not an ODE, it is an integral and we shows the reason; 2) The traditional adjoint form is not equivalent with the back propagation results. 3) The adjoint operator analysis shows that if and only if the discrete adjoint has the same scheme with the discrete neural ODE, the adjoint form would give the same results as BP does.