AnyBottle is a universal recipe for building compact, task‑specific concept bottleneck models (CBMs). CBMs route predictions through human‑interpretable concepts, making results inspectable and intervenable, but traditionally require extensive concept annotations. Annotation‑free variants remove this requirement yet usually rely on a static, large concept vocabulary, inflating the bottleneck beyond what any task needs and making inspection harder. AnyBottle assumes only a frozen backbone and an unsupervised concept pool (e.g., a sparse autoencoder) and leverages a black‑box teacher trained on the same backbone to guide selection. In each round the method adds the concept that best explains the current bottleneck failures, restricting candidates to regions where teacher and student disagree. Training with nested dropout over this selection order yields a bottleneck that can predict accurately from any concept prefix—few concepts are spent on confident inputs, more are allocated to hard cases. Because no stage is modality‑specific, adapting to a new domain only requires swapping the backbone and concept pool. Across six vision and two text datasets and two teacher paradigms, AnyBottle achieves bottlenecks with fewer concepts and higher concept consistency than annotation‑free baselines while staying close to the black‑box reference. Overall, the work shows that going annotation‑free does not have to mean going large: a small, discovered vocabulary can be as expressive as a much larger, fixed one.
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