# Le Cam Distortion: A Decision-Theoretic Framework for Robust Transfer Learning

arXiv: https://arxiv.org/abs/2512.23617 · HTML: https://mlsanity.com/paper/2512.23617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Likelihood-Preserving Embeddings for Statistical Inference](https://mlsanity.com/paper/2512.22638/) (2025)

## Abstract (arXiv)

Distribution shift is the defining challenge of real-world machine learning. The dominant paradigm--Unsupervised Domain Adaptation (UDA)--enforces feature invariance, aligning source and target representations via symmetric divergence minimization [Ganin et al., 2016]. We demonstrate that this approach is fundamentally flawed: when domains are unequally informative (e.g., high-quality vs degraded sensors), strict invariance necessitates information destruction, causing "negative transfer" that can be catastrophic in safety-critical applications [Wang et al., 2019]. We propose a decision-theoretic framework grounded in Le Cam's theory of statistical experiments [Le Cam, 1986], using constructive approximations to replace symmetric invariance with directional simulability. We introduce Le Cam Distortion, quantified by the Deficiency Distance δ(E1, E2), as a rigorous upper bound for transfer risk conditional on simulability. Our framework enables transfer without source degradation by learning a kernel that simulates the target from the source. Across five experiments (genomics, vision, reinforcement learning), Le Cam Distortion achieves: (1) near-perfect frequency estimation in HLA genomics (correlation r=0.999, matching classical methods), (2) zero source utility loss in CIFAR-10 image classification (81.2% accuracy preserved vs 34.7% drop for CycleGAN), and (3) safe policy transfer in RL control where invariance-based methods suffer catastrophic collapse. Le Cam Distortion provides the first principled framework for risk-controlled transfer learning in domains where negative transfer is unacceptable: medical imaging, autonomous systems, and precision medicine.