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We present a new method of deconstructing class activation tokens of vision transformers into a new, overcomplete basis, where each basis vector is “monosemantic” and affiliated with a single, human-compatible conceptual description. We achieve this through the use of a highly optimized and customized version of the K-SVD algorithm, which we call Double-Batch K-SVD (DBK-SVD). We demonstrate the efficacy of our approach on the sbucaptions dataset, using CLIP embeddings and comparing our results to a Sparse Autoencoder (SAE) baseline. Our method significantly outperforms SAE in terms of reconstruction loss, recovering approximately 2/3 of the original signal compared to 1/6 for SAE. We introduce novel metrics for evaluating explanation faithfulness and specificity, showing that DBK-SVD produces more diverse and specific concept descriptions. We therefore show empirically for the first time that disentangling of concepts arising in Vision Transformers is possible, a statement that has previously been questioned when applying an additional sparsity constraint. Our research opens new avenues for model interpretability, failure mitigation, and downstream task domain transfer in vision transformer models. An interactive demo showcasing our results can be found at https://disentangling-sbucaptions.xyz, and we make our DBK-SVD implementation openly available at https://github.com/RomeoV/KSVD.jl.