Geometry ideas

Research ideas extracted from mathematics papers, categorized as Geometry.

2 ideas found

Category: Geometry Solves: Sample efficiency Math: Statistics Clear all

Unverified 2026

Median-Normalized Weak Pushforward Potential Training

Represent the quadratic OT potential with a strongly convex input-convex neural network and train it by matching the distribution of its gradient pushforward to the target distribution in a weak dual metric. Median-center the potential on every minibatch so that optimization does not waste capacity or suffer instability from the additive constant ambiguity. The paper's stability inequality predicts that this can produce a more stable potential estimate than directly optimizing a transport-map…

Useful6/10

Difficulty6/10

Novelty6/10

Geometry Stability Sample efficiency Accuracy

Paper: Empirical optimal transport potentials: fast rates and a functional central limit theorem arXiv:2608.00649

Unverified 2026

Fisher-Width-Balanced Sparse Fine-Tuning

Select the coordinates of a sparse adapter or sparse fine-tuning mask using both Fisher width and inverse-Fisher width. The mask should avoid parameter subsets that are cheap in the Fisher geometry but extremely large in the inverse-Fisher geometry, or vice versa, thereby controlling both prediction sensitivity and estimator-like uncertainty.

Useful6/10

Difficulty5/10

Novelty6/10

Geometry Stability Sample efficiency Memory

Paper: Fisher Widths: Local Learning Geometry and Anisotropic Recovery arXiv:2607.20578