A Stability Analysis of Neural Networks and Its Application to Tsunami Early Warning
by D. Rim, S. Suri, S. Hong, K. Lee, and R.J. LeVeque Journal of Geophysical Research: Machine Learning and Computation 1 (2024) e2024JH000223. DOI 10.1029/2024JH000223

Abstract. Neural networks (NNs) enable precise modeling of complicated geophysical phenomena but are sensitive to small input changes. In this work, we present a new method for analyzing this instability in NNs. We focus our analysis on adversarial examples, test-time inputs with carefully-crafted human-imperceptible perturbations that expose the worst-case instability in a model's predictions. Our stability analysis is based on alow-rank expansion of NNs on a fixed input, and we apply our analysis to a NN model for tsunami early warning which takes geodetic measurements as the input and fore-casts tsunami waveforms. The result is an improved description of local stability that explains adversarial examples generated by a standard gradient-based algorithm, and allows the generation of even worse examples. Our analysis can predict whether noise in the geodetic input will produce an unstable output, and identifies a simple approach to filtering the input that enables more robust forecasting from noisy input.

Key Points.

• Neural networks suffer from local instabilities which makes it difficult to deploy in safety-critical applicationslike natural hazard warning.

• We derive a low-rank expansion for feedforward neural networks, writing it as the sum of a input-independent linear map and a input-dependent low-rank linear map.

• We are able to reduce the instabilities by performing a component analysis of the low-rank map and using projection-based filtering techniques.

Journal: DOI 10.1029/2024JH000223

EarthArXiv Preprint

bibtex entry:

@article{rim_stability_2024,
  author="D. Rim and S. Suri and S. Hong and K. Lee and R.J. LeVeque",
  title="A Stability Analysis of Neural Networks andIts Application to
    Tsunami Early Warning",
  volume = {1},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1029/2024JH000223},
  doi = {10.1029/2024JH000223},
  journal = {Journal of Geophysical Research: Machine Learning and Computation},
  year = {2024},
  pages = {e2024JH000223},
}   

@misc{RimSuri2023,
  author="D. Rim and S. Suri and S. Hong and K. Lee and R.J. LeVeque",
  title="A Stability Analysis of Neural Networks andIts Application to
    Tsunami Early Warning",
  howpublished="EarthArXiv Preprint,
    \url{https://eartharxiv.org/repository/view/5381/}",
  year="2023"
}