# Grassmannian Geometry Meets Dynamic Mode Decomposition in DMD-GEN: A New Metric for Mode Collapse in Time Series Generative Models

arXiv: https://arxiv.org/abs/2412.11292 · HTML: https://mlsanity.com/paper/2412.11292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Increasing Diversity While Maintaining Accuracy: Text Data Generation with Large Language Models and Human Interventions](https://mlsanity.com/paper/2306.04140/) (2023)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)
- [Beyond Scale: The Diversity Coefficient as a Data Quality Metric for Variability in Natural Language Data](https://mlsanity.com/paper/2306.13840/) (2023)
- [A Survey on Generative Modeling with Limited Data, Few Shots, and Zero Shot](https://mlsanity.com/paper/2307.14397/) (2023)
- [Measuring Diversity in Co-creative Image Generation](https://mlsanity.com/paper/2403.13826/) (2024)
- [Sample weighting as an explanation for mode collapse in generative adversarial networks](https://mlsanity.com/paper/2010.02035/) (2020)
- [Evaluating the diversity and utility of materials proposed by generative models](https://mlsanity.com/paper/2309.12323/) (2023)

## Abstract (arXiv)

Generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) often fail to capture the full diversity of their training data, leading to mode collapse. While this issue is well-explored in image generation, it remains underinvestigated for time series data. We introduce a new definition of mode collapse specific to time series and propose a novel metric, DMD-GEN, to quantify its severity. Our metric utilizes Dynamic Mode Decomposition (DMD), a data-driven technique for identifying coherent spatiotemporal patterns, and employs Optimal Transport between DMD eigenvectors to assess discrepancies between the underlying dynamics of the original and generated data. This approach not only quantifies the preservation of essential dynamic characteristics but also provides interpretability by pinpointing which modes have collapsed. We validate DMD-GEN on both synthetic and real-world datasets using various generative models, including TimeGAN, TimeVAE, and DiffusionTS. The results demonstrate that DMD-GEN correlates well with traditional evaluation metrics for static data while offering the advantage of applicability to dynamic data. This work offers for the first time a definition of mode collapse for time series, improving understanding, and forming the basis of our tool for assessing and improving generative models in the time series domain.