Abstract Motivation Motifs play a crucial role in computational biology, as they provide valuable information about the binding specificity of proteins. However, conventional motif discovery methods typically rely on simple combinatoric or probabilistic approaches, which can be biased by heuristics such as substring-masking for multiple motif discovery. In recent years, deep neural networks have become increasingly popular for motif discovery, as they are capable of capturing complex patterns in data. Nonetheless, inferring motifs from neural networks remains a challenging problem, both from a modeling and computational standpoint, despite the success of these networks in supervised learning tasks. Results We present a principled representation learning approach based on a hierarchical sparse representation for motif discovery. Our method effectively discovers gapped, long, or overlapping motifs that we show to commonly exist in next-generation sequencing datasets, in addition to the short and enriched primary binding sites. Our model is fully interpretable, fast, and capable of capturing motifs in a large number of DNA strings. A key concept emerged from our approach—enumerating at the image level—effectively overcomes the k-mers paradigm, enabling modest computational resources for capturing the long and varied but conserved patterns, in addition to capturing the primary binding sites. Availability and implementation Our method is available as a Julia package under the MIT license at https://github.com/kchu25/MOTIFs.jl, and the results on experimental data can be found at https://zenodo.org/record/7783033.