Statistical anomaly detection empowered by AI is a subject of growing interest in high-energy physics and astrophysics. The unsupervised nature of the anomaly detection task combined with the highly complex nature of the LHC and astrophysical data give rise to a set of yet unaddressed challenges for AI. A particular challenge is the design of AI model architectures that are highly expressive, interpretable and incorporates physics knowledge. Under the assumption that the anomalous effects are mild perturbations of the nominal data distribution, sparse models represent an ideal family of functionals to learn interpretable models of the anomalies. In this work we propose a sparse model based on Gaussian kernels to construct a local representation of an anomaly score in semi supervised problems. Inspired by dictionary learning techniques we optimise the kernels’ location over the input data, triggering a competition mechanism that induces the model’s attention towards anomaly-enriched regions. We demonstrate the effectiveness using one-dimensional proof-of-concept numerical experiments and an application to gravitational wave anomaly detection.