Correcting Sensor-Induced Distribution Drift with Wasserstein Adversarial Learning

Technical Summary: Correcting Sensor-Induced Distribution Drift with Wasserstein Adversarial Learning

Problem Statement
The integrity of data-driven analysis in high energy physics (HEP) relies on the stability of sensor systems. However, sensor motion, environmental conditions, and long-term material aging introduce systematic distortions that degrade detector performance. While traditional calibration and alignment procedures exist, they are often resource-intensive and require explicit event-level correspondences or labeled degradation targets, which are frequently unavailable in realistic scenarios. The core challenge is to infer physically interpretable transformation parameters (e.g., geometric offsets or attenuation coefficients) that map a changed detector response distribution back to a nominal reference distribution, without relying on supervised targets or explicit likelihood models. This problem is framed as a distribution shift (or domain shift) issue where the data-generating distributions differ between nominal and degraded conditions.

Methodology
The authors propose a novel, unsupervised framework based on Wasserstein Generative Adversarial Networks (WGANs) to recover these transformation parameters. Unlike standard generative modeling where a generator synthesizes new data samples, this approach reinterprets the generator as a deterministic, learnable calibration transformation.

• Architecture: The system consists of two main components:
  1. The Generator ($T_\theta$): A parameterized transformation applied directly to observed data. Its trainable weights $\theta$ represent the physical parameters to be inferred (e.g., a spatial shift $\Delta x$ for tracking or cell-wise attenuation coefficients $\alpha_i$ for calorimetry).
  2. The Critic ($C_\phi$): A neural network constrained to be 1-Lipschitz, trained to estimate the Wasserstein-1 distance between the reference (nominal) distribution and the transformed (changed) distribution.
• Objective: The framework employs a minimax optimization. The critic is trained to maximize the estimated Wasserstein distance between the reference data and the transformed data, while the transformation parameters $\theta$ are updated to minimize this distance. By driving the transformed distribution to statistically align with the reference distribution, the model implicitly learns the physical parameters responsible for the shift.
• Key Distinction: No event-level correspondence between reference and changed samples is assumed. The inference is driven entirely by population-level distributional agreement.

Experimental Validation
The method was validated in two distinct settings:

1. Tracker Toy Model: A simplified simulation of a tracking detector with three layers. A known geometric misalignment (a shift $\Delta x_2$ in the second plane) was injected. The framework successfully recovered the shift parameter by aligning the hit coordinate distributions. The study demonstrated that the method remains accurate for low-to-moderate noise levels but degrades as measurement noise approaches the magnitude of the injected shift, consistent with the loss of identifiable geometric information.
2. Calorimeter Aging: A high-granularity Geant4-simulated calorimeter was subjected to cell-wise signal attenuation to emulate radiation damage. The generator was configured as a learnable 3D tensor of calibration coefficients ($\alpha_i$) to rescale cell-wise energy deposits.
   • Results: The inferred aging coefficients showed a strong positive correlation with the ground truth ($R^2 \approx 0.896$).
   • Performance: The proposed method achieved a Root Mean Square Error (RMSE) of $0.0176$, significantly outperforming a simple baseline that estimated aging based solely on the ratio of mean cell responses (RMSE $0.0562$).
   • Distribution Alignment: Applying the learned coefficients to the damaged data successfully restored the global energy-sum distribution to match the undamaged reference.
   • Noise Sensitivity: The study confirmed that as stochastic cell-to-cell variations (noise) increase, the identifiability of individual parameters decreases, as multiple coefficient configurations can yield similar aggregate statistics.

Key Contributions and Significance
The paper positions detector calibration and alignment within the broader class of distribution-shift problems. Its primary contributions are:

• Paradigm Shift: It redefines the role of the generator in adversarial learning from data synthesis to parameter recovery, using trainable weights to represent physical calibration constants.
• Unsupervised Inference: The method enables the recovery of interpretable physical parameters without labeled degradation targets or event-level matching, addressing a key bottleneck in detector operations where comprehensive recalibration is often infeasible.
• Data-Driven Calibration: It demonstrates that adversarial distribution matching can serve as a viable, data-driven component of calibration strategies, particularly in settings where direct labels for degradation parameters are unavailable.

Limitations and Scope
The authors maintain a modest stance regarding the method's capabilities. They note that while the approach effectively recovers dominant systematic trends (e.g., global aging trends or geometric shifts), it faces limitations in resolving fine-grained, per-cell stochastic fluctuations when channel-to-channel noise is high. The paper concludes that this adversarial calibration should be viewed as a complementary technique to reduce reliance on supervision, rather than a complete replacement for established workflows. Future work is suggested to extend the framework to time-dependent degradation and hybrid strategies incorporating external reference signals.