The butterfly effect in neural networks: Unveiling hyperbolic chaos through parameter sensitivity

Area of Science:

• Artificial Intelligence
• Dynamical Systems Theory

Background:

• Neural networks demonstrate strong performance on short-term predictions.
• Long-term reliability of neural networks remains a significant challenge.

Purpose of the Study:

• To investigate the causes of long-term forecasting instability in neural networks.
• To explore the relationship between parameter perturbations and chaotic behavior.
• To propose methods for enhancing the global robustness of neural networks.

Main Methods:

• Analysis of neural network architectures using concepts from classical dynamical systems.
• Examination of Lyapunov exponents and structural stability.
• Simulation of parameter perturbations and their impact on forecasting.
• Introduction of a 'pinning' strategy to mitigate instability.

Main Results:

• Minimal neural network architectures can exhibit hyperbolic chaotic behavior after small parameter perturbations.
• Borderline-zero Lyapunov exponents do not guarantee multi-step forecast stability without structural stability.
• Weight changes as small as 10^-3 can drastically affect long-horizon forecasting.
• A 'pinning' strategy can help constrain runaway expansions, but borderline orbits persist.

Conclusions:

• Short-horizon validation is insufficient for detecting critical multi-step vulnerabilities in neural networks.
• Genuine structural stability is crucial for reliable long-term forecasting.
• Global diagnostics are essential for assessing and ensuring the robustness of neural networks.