# Symplectic Methods in Deep Learning

arXiv: https://arxiv.org/abs/2406.04104 · HTML: https://mlsanity.com/paper/2406.04104/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2024.

## Built on by (most cited first, 3 of 3)

- [Symplectic Neural Networks Based on Dynamical Systems](https://mlsanity.com/paper/2408.09821/) (2024)
- [Learning Generalized Hamiltonians using fully Symplectic Mappings](https://mlsanity.com/paper/2409.11138/) (2024)
- [Deep Network Trainability via Persistent Subspace Orthogonality](https://mlsanity.com/paper/2508.02882/) (2025)

## Abstract (arXiv)

Deep learning is widely used in tasks including image recognition and generation, in learning dynamical systems from data and many more. It is important to construct learning architectures with theoretical guarantees to permit safety in the applications. There has been considerable progress in this direction lately. In particular, symplectic networks were shown to have the non vanishing gradient property, essential for numerical stability. On the other hand, architectures based on higher order numerical methods were shown to be efficient in many tasks where the learned function has an underlying dynamical structure. In this work we construct symplectic networks based on higher order explicit methods with non vanishing gradient property and test their efficiency on various examples.