[Paper] Le Cam Distortion: A Decision-Theoretic Framework for Robust Transfer Learning

Source: arXiv - 2512.23617v1

Overview

The paper introduces Le Cam Distortion, a decision‑theoretic framework that replaces the common “make source and target features look the same” mindset of unsupervised domain adaptation with a directional notion of simulability. By measuring how well a source experiment can simulate a target experiment using Le Cam’s deficiency distance, the authors derive a provable upper bound on the transfer risk and show how to avoid the dreaded “negative transfer” that can cripple safety‑critical systems.

Key Contributions

• Decision‑theoretic reformulation of transfer learning based on Le Cam’s statistical experiments, moving from symmetric invariance to directional simulability.
• Le Cam Distortion metric (deficiency distance δ) that quantifies the worst‑case risk increase when transferring from source to target.
• Constructive kernel‑learning algorithm that learns a mapping from source to target data while explicitly minimizing the deficiency distance.
• Comprehensive empirical validation on five heterogeneous benchmarks (genomics, image classification, reinforcement learning), demonstrating near‑perfect performance preservation and elimination of negative transfer.
• Practical safety guarantees for domains where any degradation of source utility is unacceptable (e.g., medical imaging, autonomous driving).

Methodology

1. Statistical experiment view – Treat the source and target data‑generating processes as statistical experiments (E_S) and (E_T).
2. Deficiency distance – Use Le Cam’s deficiency (δ(E_S, E_T)) to capture how well a simulator (a measurable transformation) can turn observations from (E_S) into observations that are statistically indistinguishable from those of (E_T).
3. Directional simulability – Unlike classic UDA, which forces bidirectional feature alignment, the framework only requires a one‑way simulation from source to target, preserving information that is unique to the source.
4. Kernel learning – Parameterize the simulator as a kernel (k_\theta) (e.g., a neural network with a reproducing‑kernel‑Hilbert‑space regularizer). The training objective jointly minimizes:
   • Empirical deficiency estimate (via a variational bound).
   • Source task loss (to keep source performance intact).
5. Risk bound – Prove that the target risk is bounded by the source risk plus a term proportional to (δ(E_S, E_T)), giving a concrete guarantee that transfer will not increase error beyond the measured distortion.

Results & Findings

The deficiency distance estimated during training correlates tightly with the observed transfer risk, confirming the theoretical bound’s practical relevance.

Practical Implications

• Safer model deployment – Engineers can quantify the worst‑case performance loss before pushing a model to a new sensor or environment, crucial for autonomous vehicles, drones, and medical devices.
• Zero‑degradation transfer – Existing high‑performing models can be repurposed for new domains without sacrificing the original task, saving costly retraining cycles.
• Plug‑and‑play kernel module – The proposed simulator can be wrapped as a lightweight preprocessing layer (e.g., a TorchScript module) that sits between raw sensor data and any downstream model, making integration straightforward.
• Regulatory compliance – The explicit risk bound aligns with emerging AI safety standards that demand provable guarantees for model updates in regulated sectors.
• Tooling opportunities – The deficiency‑distance estimator can be exposed as a diagnostic metric in MLOps platforms, enabling automated alerts when a proposed transfer exceeds a predefined risk budget.

Limitations & Future Work

• Computational overhead – Estimating the deficiency distance and training the simulator adds extra epochs compared with vanilla UDA; scaling to massive datasets may require more efficient variational approximations.
• Assumption of simulability – The framework presumes that a measurable transformation from source to target exists; in cases of completely disjoint feature spaces, the bound may be loose.
• Limited to unsupervised target – While the theory extends to semi‑supervised settings, the current experiments focus on fully unlabeled targets.
• Future directions suggested by the authors include: (1) tighter variational bounds for δ, (2) extending the approach to multi‑source transfer, and (3) integrating causal reasoning to handle shifts that are not purely statistical but stem from underlying mechanism changes.

Authors

• Deniz Akdemir

Paper Information

• arXiv ID: 2512.23617v1
• Categories: cs.LG, cs.AI, math.ST, stat.ME, stat.ML
• Published: December 29, 2025
• PDF: Download PDF