SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Thus, for each  $q \in \mathcal{T}$ , the overall data structure will answer accurately with failure probability  $e^{-\Omega(M)}$ . For  $M = O(d\log(dR/r))$ , we have that  $|\mathcal{T}| \leq e^{\Omega(M)}$ , so by a union bound, the data structure will answer any query  $q \in \mathcal{T}$  accurately. Therefore, even adaptive queries can be answered accurately, since even any adaptive query can be assumed WLOG to be in  $\mathcal{T}$ .