# Disentangling Marginal Capacity from Geometry in Optimal-Transport Label Transfer

arXiv: https://arxiv.org/abs/2610.14853 · HTML: https://mlsanity.com/paper/2610.14853/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 22 of 22)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [The Shape of Learning Curves: a Review](https://mlsanity.com/paper/2103.10948/) (2021)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [DeepSMOTE: Fusing Deep Learning and SMOTE for Imbalanced Data](https://mlsanity.com/paper/2105.02340/) (2021)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Benchmarking Transcriptomics Foundation Models for Perturbation Analysis : one PCA still rules them all](https://mlsanity.com/paper/2410.13956/) (2024)
- [Label Propagation Through Optimal Transport](https://mlsanity.com/paper/2110.01446/) (2021)

## Abstract (arXiv)

Optimal transport (OT) is widely used to align distributions and transfer labels between unpaired source and target data, but source-target composition shifts can cause rare classes to be systematically under-predicted even with high transport confidence. We identify a source of this failure in the transport marginal: under the standard uniform weighting of source points, each class has transport capacity proportional to its source frequency, which can be insufficient to meet its target demand even when separated well in the embedding space. We show that displaced mass is preferentially absorbed by high-capacity classes rather than geometrically similar classes, producing confident errors that are difficult to detect from the transport plan. Downstream read-outs, entropic smoothing, and marginal relaxation provide limited recovery, whereas matching the transport marginal to the target composition substantially improves label transfer. On single-cell data, the oracle composition-matched marginal raises macro-F1 from 0.322 to 0.623, and the best deployable estimator closes 69% of the oracle gap. Correcting the marginal also separates a coverage-dependent component of error from residual error associated with class separability, showing that transport capacity and representation geometry are distinct sources of transfer error.