Encoding models using word embeddings or artificial neural network (ANN) features reliably predict brain responses to naturalistic stimuli, yet interpreting these models remains challenging. A central limitation is superposition: distinct semantic features become entangled along correlated directions in dense embeddings when latent features outnumber embedding dimensions. This entanglement renders regression weights non-identifiable—different combinations of semantic directions can produce identical predictions, precluding principled interpretation of voxel selectivity. To address this, we introduce the Sparse Concept Encoding Model, which transforms dense embeddings into a higher-dimensional, sparse, non-negative space of learned concept atoms. This transformation yields an axis-aligned semantic basis where each dimension corresponds to an interpretable concept, enabling direct readout of conceptual selectivity from voxel weights. When applied to fMRI data collected during story listening, our model matches the prediction performance of conventional dense models while substantially enhancing interpretability. It enables novel neuroscientific analyses such as disentangling overlapping cortical representations of time, space, and number, and revealing structured similarity among distributed conceptual maps. This framework offers a scalable and interpretable bridge between ANN-derived features and human conceptual representations in the brain.