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

arXiv:2608.19584 · cs.LG, math.DG, stat.ML · Submitted 2026-08-20 · Read on arXiv

cs.LG, math.DG, stat.ML

Submitted: 2026-08-20

Updated: 2026-10-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 25× in this paper · explained in 2 episodes
• Regret — 9× in this paper · explained in 3 episodes
• Regularization — 8× in this paper · explained in 3 episodes
• Loss Function — 6× in this paper · explained in 2 episodes
• Gradient Flow — 5× in this paper · explained in 2 episodes
• Neural Tangent Kernel — 5× in this paper
• Spectral Gap — 4× in this paper · explained in 5 episodes
• Failure Modes — 3× in this paper · explained in 3 episodes
• Cosine Similarity — 2× in this paper · explained in 3 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Theoretical Guarantees — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Anisotropy — 1× in this paper · explained in 3 episodes
• Commentary — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Riemannian optimization — 1× in this paper · explained in 2 episodes

Sources

• On the asymptotics of wide networks with polynomial activations
• Alexandrov geometry: foundations
• Asymptotics of Wide Convolutional Neural Networks
• AKSZ Descent on Manifolds with Ordinary Corners
• Local Information Operators for Spatial Identifiability in Distributed-Parameter Inverse Problems in Computational Mechanics
• Extra-fine sheaves and interaction decompositions
• A Riemannian Optimization Perspective of the Gauss-Newton Method for Feedforward Neural Networks
• Genus expansion for non-linear random matrix ensembles with applications to neural networks
• Efficient displacement convex optimization with particle gradient descent
• Quotient Geometry, Effective Curvature, and Implicit Bias in Simple Shallow Neural Networks
• Navigating Potholes with Geometry-Aware Sharpness Minimization
• Asymptotics of Wide Networks from Feynman Diagrams
• Laplacian comparison theorems on complete K\"ahler manifolds and applications
• Construction of Exponential Families from Statistical Manifolds
• Finite-Width Neural Tangent Kernels from Feynman Diagrams
• Random Fully Connected Neural Networks as Perturbatively Solvable Hierarchies
• Dynamics of Deep Neural Networks and Neural Tangent Hierarchy
• Statistical Neurodynamics of Deep Networks: Geometry of Signal Spaces
• Analysis of a Two-Layer Neural Network via Displacement Convexity
• Adam: A Method for Stochastic Optimization

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