Task-Aware Certified Block Frames for Exact Latent Recovery

Most block-erasure designs optimize reconstruction stability. With erasure locations known at decoding, every full-column-rank survivor frame recovers the same latent representation in the zero-noise case. Under bounded observation noise, however, survivor geometry determines the amplification of each class-pair score difference. We exploit this remaining design freedom to reduce decision uncertainty while preserving exact recovery of the full latent representation at zero noise. For a linear head and a total ${\ell }_2$ observation-noise budget, we derive the worst-case pairwise score uncertainty and the largest radius that preserves the multiclass prediction over all survivor sets; an explicit perturbation reaches its boundary. The resulting certificate identifies the decision directions that the block design must protect. Task-Aware Certified Block Frames (TACBF) combines closed-form task-subspace allocation with learned rank-constrained block geometry. Across held-out test sets from seven datasets, TACBF improves both grid-based and continuous-radius measures of the area under the certified-accuracy curve (AUC) relative to a fixed-factor control paired by training seed. Continuous-radius AUC improves for every paired seed on all seven datasets, and TACBF has the highest mean grid AUC among seven methods on every dataset. The method preserves exact zero-noise recovery, transmitted width, and trace without changing the inference procedure; dataset-level mean clean accuracy differs by at most $0.25$ percentage points.