Modeling Systematic Uncertainty Propagation in Contrastive Learning for Anomaly Detection

Despite the Standard Model’s success, outstanding questions still motivate searches for physics beyond the Standard Model (BSM) at the Large Hadron Collider. However, the lack of a dominant direction makes it challenging to explore theory models with traditional, signal-driven analysis. 

Machine-learning-based anomaly detection (AD) offers a promising, model-agnostic alternative to search for many signals. Recent AI advances in representation learning motivate the use of neural embeddings to map detector data into low-dimensional latent spaces, preserving critical features. However, the propagation of systematic uncertainty in embedded spaces remains poorly understood, severely limiting BSM signal detection in AD.

We address this gap with a machine learning strategy that uses a likelihood-based objective to structure the embedded space. Building on previous work using supervised contrastive learning for physics-aware embeddings, our approach further fine-tunes them with a downstream parameterized classification task that incorporates continuous uncertainties. This enables the latent space to covary predictably with systematic distortions.

Using simulated CMS level-1 trigger data, we show that our method successfully models continuous uncertainties in a 4D latent space, improving both interpretability and robustness for AD. This framework offers a general way to study and control systematic uncertainties in latent spaces and can be applied to other scientific domains and problems.