Feedback-Efficient Antibody Design within Discrete CDR Shape Space

Antibody design is typically performed in a joint space of discrete residue identities and continuous atomic coordinates. Yet complementarity-determining regions (CDR) backbones recur within a few canonical conformations, suggesting that explicitly leveraging these structural patterns could make antibody design more efficient. We therefore formulate antibody design in a discrete CDR shape space constructed by clustering experimental CDR conformations by type, length and backbone similarity ($n=772$ shapes). Over this discrete space we train a controllable generative model that, conditioned on a target epitope and a combination of six CDR shapes, produces antibodies that bind the specified epitope while realizing the prescribed conformations. We then perform feedback-guided Bayesian optimization over CDR-shape combinations at test time. Compared to direct generation with test-time scaling in continuous space, our method reduces the CDR structural deviation by $1.87\times$ under the same budget, while matching its performance with $13\times$ fewer evaluations. In short, a compact, biologically grounded search space preserves design capacity while making antibody optimization substantially more feedback-efficient.