arXiv:2606.04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training. When the coupled Jacobian is block-triangular, asymptotic stability is governed by the spectral radii of the diagonal blocks, yet transient amplification before convergence can be arbitrarily large due to non-normality. We develop a sharp pseudospectral theory for such block-triangular Jacobians, proving that the Kreiss constant satisfies $K(J) \leq 2/(1-\gamma) +
The continuous evolution of AI and machine learning algorithms necessitates deeper theoretical understanding of their optimization dynamics to improve performance and stability.
Understanding transient amplification in coupled gradient descent is crucial for developing more robust and efficient AI models, especially in complex applications like bilevel optimization and adversarial training.
This theoretical work provides new insights into the stability and convergence properties of advanced optimization techniques, potentially leading to more reliable and predictable AI system behavior.
- · AI researchers
- · Machine learning engineers
- · Sectors using complex AI models
- · Developers of unstable AI models
- · Researchers relying on ad-hoc optimization fixes
Improved stability and predictability of complex AI optimization algorithms.
Faster development and deployment of advanced AI applications due to reduced training instability.
Enhanced trust and broader adoption of AI systems that are known to converge reliably under various conditions.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG