# Deep Signature: Characterization of Large-Scale Molecular Dynamics

arXiv: https://arxiv.org/abs/2410.02847 · HTML: https://mlsanity.com/paper/2410.02847/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [Graph Neural Rough Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2303.10909/) (2023)
- [Graph Neural Network Based Coarse-Grained Mapping Prediction](https://mlsanity.com/paper/2007.04921/) (2020)
- [Rotation invariants of two dimensional curves based on iterated integrals](https://mlsanity.com/paper/1305.6883/) (2013)
- [Growing ecosystem of deep learning methods for modeling proteinunicodex2013protein interactions](https://mlsanity.com/paper/2310.06725/) (2023)

## Abstract (arXiv)

Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose significant challenge for existing computational techniques. In this paper, we approach this problem for the first time by introducing Deep Signature, a novel computationally tractable framework that characterizes complex dynamics and interatomic interactions based on their evolving trajectories. Specifically, our approach incorporates soft spectral clustering that locally aggregates cooperative dynamics to reduce the size of the system, as well as signature transform that collects iterated integrals to provide a global characterization of the non-smooth interactive dynamics. Theoretical analysis demonstrates that Deep Signature exhibits several desirable properties, including invariance to translation, near invariance to rotation, equivariance to permutation of atomic coordinates, and invariance under time reparameterization. Furthermore, experimental results on three benchmarks of biological processes verify that our approach can achieve superior performance compared to baseline methods.