Learning Sparse Semantic-Cortical Atoms for Multisubject Naturalistic fMRI Encoding

Naturalistic language encoding models based on large language model features can predict cortical responses well, but their learned representations remain difficult to interpret. Three challenges are central: semantic selectivity is fundamentally non-identifiable in high-dimensional correlated feature spaces, cortical organization remains implicit in voxelwise weight maps, and cross-subject structure is usually addressed only after model fitting. We introduce a multisubject coupled sparse autoencoder that jointly reconstructs language-model features and predicts subject-specific brain responses, learning a sparse basis of semantic-cortical atoms that makes semantic structure, cortical organization, and cross-subject correspondence explicit within a single model. In naturalistic story-listening fMRI, the model retains 88\% of matched dense-feature ridge brain prediction performance using 50 atoms and $k{=}5$ active atoms per TR. Relative to matched two-stage baselines, joint training yields the strongest overall tradeoff between prediction and interpretability. The learned atoms are semantically coherent and interpretable, recover more reproducible cross-subject brain maps than standard post hoc encoding-model analyses, align with large-scale cortical structure from Yeo~7 and Neurosynth, and transfer better than ridge to held-out subjects in the low-data regime. This framework provides a more interpretable basis for cognitive neuroscience analyses of semantic-to-brain encoding by linking semantic features to corresponding cortical response patterns across subjects.