During inference for a span prediction task, the optimal answer span, represented by the start index $\hat{j}_1$ and end index $\hat{j}_2$, is found by selecting the pair of indices that maximizes the sum of the log-probabilities for the start and end positions. The search is constrained such that the start index must not come after the end index. The formula is: $(\hat{j}_1, \hat{j}_2) = \operatorname*{argmax}_{1 \le j_1 \le j_2 \le n} \big( \log p_{j_1}^{\mathrm{beg}} + \log p_{j_2}^{\mathrm{end}} \big)$ Where: - $p_{j_1}^{\mathrm{beg}}$ is the probability that token $j_1$ is the start of the span. - $p_{j_2}^{\mathrm{end}}$ is the probability that token $j_2$ is the end of the span. - $n$ is the number of tokens in the context.