DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses

arXiv:2510.17072 · stat.ML, cs.LG, stat.ME · Submitted 2025-10-20 · Read on arXiv

stat.ML, cs.LG, stat.ME

Submitted: 2025-10-20

Updated: 2026-09-08

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

Terminology

• Regularization — 11× in this paper · explained in 3 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Representation Learning — 3× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Federal Reserve Economic Data — 2× in this paper
• Neural Network Approximation — 2× in this paper · explained in 2 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• European Conference on Computer Vision — 1× in this paper
• Intrinsic Dimension — 1× in this paper · explained in 2 episodes
• Model-Agnostic — 1× in this paper · explained in 2 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes

Sources

• Sliced Wasserstein Regression
• Transportation of Measure Regression in Higher Dimensions
• Nonparametric forecasting of multivariate probability density functions
• Distribution-on-Distribution Regression with Wasserstein Metric: Multivariate Gaussian Case
• Nonparametric Regression in Nonstandard Spaces
• End-to-End Deep Learning for Predicting Metric Space-Valued Outputs

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