# Geometric Dataset Distances via Optimal Transport

arXiv: https://arxiv.org/abs/2002.02923 · HTML: https://mlsanity.com/paper/2002.02923/

## Key facts

- Cited by 158 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 30 of 158)

- [Narcissus: A Practical Clean-Label Backdoor Attack with Limited Information](https://mlsanity.com/paper/2204.05255/) (2022)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Benchmarking Distribution Shift in Tabular Data with TableShift](https://mlsanity.com/paper/2312.07577/) (2023)
- [OTCE: A Transferability Metric for Cross-Domain Cross-Task Representations](https://mlsanity.com/paper/2103.13843/) (2021)
- [InsCL: A Data-efficient Continual Learning Paradigm for Fine-tuning Large Language Models with Instructions](https://mlsanity.com/paper/2403.11435/) (2024)
- [Transferability Estimation using Bhattacharyya Class Separability](https://mlsanity.com/paper/2111.12780/) (2021)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [Improved Fine-Tuning by Better Leveraging Pre-Training Data](https://mlsanity.com/paper/2111.12292/) (2021)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [Cross-Modal Fine-Tuning: Align then Refine](https://mlsanity.com/paper/2302.05738/) (2023)
- [Model Spider: Learning to Rank Pre-Trained Models Efficiently](https://mlsanity.com/paper/2306.03900/) (2023)
- [How stable are Transferability Metrics evaluations?](https://mlsanity.com/paper/2204.01403/) (2022)
- [DISCO: Distilling Counterfactuals with Large Language Models](https://mlsanity.com/paper/2212.10534/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Probing transfer learning with a model of synthetic correlated datasets](https://mlsanity.com/paper/2106.05418/) (2021)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Controllable and Guided Face Synthesis for Unconstrained Face Recognition](https://mlsanity.com/paper/2207.10180/) (2022)
- [Lifelong Reinforcement Learning with Modulating Masks](https://mlsanity.com/paper/2212.11110/) (2022)
- [Characterizing Out-of-Distribution Error via Optimal Transport](https://mlsanity.com/paper/2305.15640/) (2023)
- [SyntheWorld: A Large-Scale Synthetic Dataset for Land Cover Mapping and Building Change Detection](https://mlsanity.com/paper/2309.01907/) (2023)
- [FedAWA: Adaptive Optimization of Aggregation Weights in Federated Learning Using Client Vectors](https://mlsanity.com/paper/2503.15842/) (2025)
- [Align then Adapt: Rethinking Parameter-Efficient Transfer Learning in 4D Perception](https://mlsanity.com/paper/2602.23069/) (2026)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [OT-VP: Optimal Transport-guided Visual Prompting for Test-Time Adaptation](https://mlsanity.com/paper/2407.09498/) (2024)
- [Choosing Public Datasets for Private Machine Learning via Gradient Subspace Distance](https://mlsanity.com/paper/2303.01256/) (2023)
- [Performance Scaling via Optimal Transport: Enabling Data Selection from Partially Revealed Sources](https://mlsanity.com/paper/2307.02460/) (2023)
- [Neural Optimal Transport with Lagrangian Costs](https://mlsanity.com/paper/2406.00288/) (2024)
- [Transferability-Guided Cross-Domain Cross-Task Transfer Learning](https://mlsanity.com/paper/2207.05510/) (2022)

## Abstract (arXiv)

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameters (e.g., require training a model on each dataset). In this work we propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.