SN-ABSTOPK: AN UNROLLED SPATIAL-NORMATIVE SPARSE AUTOENCODER FOR MEDICAL FOUNDATION MODELS

Sparse autoencoders (SAEs) decompose foundation model representations into monosemantic latents. However, applying independent per-token sparsity across image grids ignores spatial correlations, which causes feature fragmentation in medical imaging. We introduce Spatial-Normative AbsTopK (SN-AbsTopK), an unrolled sparse autoencoder that integrates spatial group support containment and normative reference centering into signed-magnitude dictionary learning. Rather than evaluating tokens independently, SN-AbsTopK operates via a two-stage se- lection mechanism across spatial token groups. This structure enables effective processing across continuous regions, such as contiguous histology tiles or vol- umetric MRI slice stacks. In the first stage, the model aggregates pre-activation column energies across all group tokens to rank dictionary atoms and establish a shared group candidate support. In the second stage, each individual token se- lects its active signed features strictly from within this shared group candidate pool. This guarantees that all token-level active features remain strict subsets of the group candidate set. To isolate disease-specific variations, an exponential moving average reference buffer first centers the input embeddings. This pro- cess forces the sparse latent codes to represent residual departures from base- line reference states. Evaluated across histopathology (BCSS with frozen UNI) and radiology (CheXpert and Duke Breast MRI with frozen BiomedCLIP), SN- AbsTopK substantially enhances structural continuity, increasing spatial autocor- relation by 2.9× on BCSS (Moran’s 0.244 vs. 0.084) and 3D adjacent-slice sup- port persistence by 60.7% on Duke MRI (Jaccard 0.614 vs. 0.382). Although strict candidate bounds increase reconstruction error and cause feature lock-out ( 80% dead atoms), raw reconstruction error proves decoupled from clinical de- codability. Consequently, SN-AbsTopK yields superior downstream linear probe performance (+0.085 macro-AUROC on CheXpert; +0.033 on Duke MRI).