Training-Time Regularization for Inference-Time Monitoring-A Unified Framework for Self-Supervised World Models

<title>Abstract</title> <p> Self-supervised world models have emerged as a powerful paradigm for learning environment dynamics from high-dimensional observations. The Sketched Isotropic Gaussian Regularizer (SIGReg) has recently enabled stable end-to-end training of Joint-Embedding Predictive Architectures (JEPAs) by preventing representation collapse through marginal Gaussianization. However, we identify a fundamental and previously unrecognized dichotomy: <bold>the same regularization mechanism that guarantees training stability inherently suppresses the discriminative structure needed for reliable online monitoring.</bold> This tension what we term the regularization-monitoring dilemma is not a limitation of SIGReg alone but reflects a deep structural incompatibility between distributional regularization objectives and the geometric requirements of anomaly detection. </p>