# Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise

arXiv: https://arxiv.org/abs/2409.13470 · HTML: https://mlsanity.com/paper/2409.13470/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Learning Natural Language Inference with LSTM](https://mlsanity.com/paper/1512.08849/) (2015)
- [Dense Associative Memory is Robust to Adversarial Inputs](https://mlsanity.com/paper/1701.00939/) (2017)
- [Machine learning in spectral domain](https://mlsanity.com/paper/2005.14436/) (2020)
- [Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes](https://mlsanity.com/paper/2012.07747/) (2020)
- [Defense Methods Against Adversarial Examples for Recurrent Neural Networks](https://mlsanity.com/paper/1901.09963/) (2019)
- [How a student becomes a teacher: learning and forgetting through Spectral methods](https://mlsanity.com/paper/2310.12612/) (2023)
- [Stable Attractors for Neural networks classification via Ordinary Differential Equations (SA-nODE)](https://mlsanity.com/paper/2311.10387/) (2023)
- [Complex Recurrent Spectral Network](https://mlsanity.com/paper/2312.07296/) (2023)
- [Training neural networks with structured noise improves classification and generalization](https://mlsanity.com/paper/2302.13417/) (2023)
- [Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach](https://mlsanity.com/paper/2406.01183/) (2024)

## Built on by (most cited first, 4 of 4)

- [Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality](https://mlsanity.com/paper/2605.10613/) (2026)
- [Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes](https://mlsanity.com/paper/2606.23550/) (2026)
- [Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds](https://mlsanity.com/paper/2607.19042/) (2026)
- [Multiplicity of Stable Attractors in Disordered Neural Models](https://mlsanity.com/paper/2607.22047/) (2026)

## Abstract (arXiv)

The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as a veritable dynamically assisted classifier. To this end the model is supplied with a set of planted attractors which are self-consistently embedded in the inter-nodes coupling matrix, via its spectral decomposition. Learning to classify amounts to sculp the basin of attraction of the imposed equilibria, directing different items towards the corresponding destination target, which reflects the class of respective pertinence. A stochastic variant of the CVFR model is also studied and found to be robust to aversarial random attacks, which corrupt the items to be classified. This remarkable finding is one of the very many surprising effects which arise when noise and dynamical attributes are made to mutually resonate.