# Beyond Pooling: Matching for Robust Generalization under Data Heterogeneity

arXiv: https://arxiv.org/abs/2602.07154 · HTML: https://mlsanity.com/paper/2602.07154/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [Unified Deep Supervised Domain Adaptation and Generalization](https://mlsanity.com/paper/1709.10190/) (2017)
- [WinCLIP: Zero-/Few-Shot Anomaly Classification and Segmentation](https://mlsanity.com/paper/2303.14814/) (2023)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [AnomalyCLIP: Object-agnostic Prompt Learning for Zero-shot Anomaly Detection](https://mlsanity.com/paper/2310.18961/) (2023)
- [A Unified Model for Multi-class Anomaly Detection](https://mlsanity.com/paper/2206.03687/) (2022)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [APRIL-GAN: A Zero-/Few-Shot Anomaly Classification and Segmentation Method for CVPR 2023 VAND Workshop Challenge Tracks 1&2: 1st Place on Zero-shot AD and 4th Place on Few-shot AD](https://mlsanity.com/paper/2305.17382/) (2023)
- [AdaCLIP: Adapting CLIP with Hybrid Learnable Prompts for Zero-Shot Anomaly Detection](https://mlsanity.com/paper/2407.15795/) (2024)
- [BMAD: Benchmarks for Medical Anomaly Detection](https://mlsanity.com/paper/2306.11876/) (2023)
- [The Double-Ellipsoid Geometry of CLIP](https://mlsanity.com/paper/2411.14517/) (2024)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [The Data Addition Dilemma](https://mlsanity.com/paper/2408.04154/) (2024)
- [Multi-scale Cross-restoration Framework for Electrocardiogram Anomaly Detection](https://mlsanity.com/paper/2308.01639/) (2023)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Equivariance Allows Handling Multiple Nuisance Variables When Analyzing Pooled Neuroimaging Datasets](https://mlsanity.com/paper/2203.15234/) (2022)
- [Memory-Statistics Tradeoff in Continual Learning with Structural Regularization](https://mlsanity.com/paper/2504.04039/) (2025)
- [Matching for causal effects via multimarginal unbalanced optimal transport](https://mlsanity.com/paper/2112.04398/) (2021)

## Abstract (arXiv)

Pooling heterogeneous datasets across domains is a common strategy in representation learning, but naive pooling can amplify distributional asymmetries and yield biased estimators, especially in settings where zero-shot generalization is required. We propose a matching framework that selects samples relative to an adaptive centroid and iteratively refines the representation distribution. The double robustness and the propensity score matching for the inclusion of data domains make matching more robust than naive pooling and uniform subsampling by filtering out the confounding domains (the main cause of heterogeneity). Theoretical and empirical analyses show that, unlike naive pooling or uniform subsampling, matching achieves better results under asymmetric meta-distributions, which are also extended to non-Gaussian and multimodal real-world settings. Most importantly, we show that these improvements translate to zero-shot medical anomaly detection, one of the extreme forms of data heterogeneity and asymmetry. The code is available on https://github.com/AyushRoy2001/Beyond-Pooling.