The Geometry of Anisotropic Dilation for Optimal Regularization

arXiv:2610.09310 · math.OC, math.MG, math.ST, stat.ML, stat.TH · Submitted 2026-10-07 · Read on arXiv

math.OC, math.MG, math.ST, stat.ML, stat.TH

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Regularization — 39× in this paper · explained in 3 episodes
• Inverse Problem — 27× in this paper · explained in 2 episodes
• Homogeneity — 9× in this paper · explained in 2 episodes
• Generalization — 7× in this paper · explained in 13 episodes
• Optimal Transport — 6× in this paper · explained in 5 episodes
• Wasserstein Distance — 6× in this paper · explained in 4 episodes
• Sparsity — 5× in this paper · explained in 4 episodes
• Flow Matching — 4× in this paper · explained in 8 episodes
• Generative Model — 3× in this paper · explained in 2 episodes
• Generative Models — 3× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Bayesian Inference — 2× in this paper · explained in 5 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• Generalization Bounds — 2× in this paper · explained in 2 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Normalizing Flow — 2× in this paper · explained in 3 episodes
• Rectified Flow — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• 2-Wasserstein Distance — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Alternating Minimization — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• On Optimal Regularization Parameters via Bilevel Learning
• Learning Regularization Functionals for Inverse Problems: A Comparative Study
• Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraints
• Rectified Flow: A Marginal Preserving Approach to Optimal Transport
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
• Learned convex regularizers for inverse problems
• Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation
• Towards optimal algorithms for the recovery of low-dimensional models with linear rates
• Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees

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