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 submitted, 2023.

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.

EarthArXiv Preprint

bibtex entry:

@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"
}