Author

Andrew Gracyk

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Preprint Aug 2026

K\"ahler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold

We study landscapes for complex-parameterized networks. Our approach is motivated with an information-theoretic manifold perspective of the parameter and via classical optimization guarantees although of complex geometric variety such as through Dolbeault asymptotics. The descent path admits a K\"ahler information metr...

Andrew Gracyk · 0 citations

#machine learning Preprint Aug 2026

K\"ahler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold

It has been discovered that negative curvature subverts the loss landscape, specifically sectional curvature, so it has been discovered that negative curvature subverts the loss landscape, so this work expands on this and draw interconnections to negative-definite Ricci curvature.

Andrew Gracyk · 0 citations

#machine learning Apr 2025

Observability conditions for neural state-space models with eigenvalues and their roots of unity

We operate through the lens of ordinary differential equations and control theory to study the concept of observability in the context of neural state-space models and the Mamba architecture. We develop strategies to enforce observability, which are tailored to a learning context, specifically where the hidden states a...

Andrew Gracyk · arXiv.org · 0 citations