Batch Diversity under Distortion Constraints for Language Models

A batch of responses to one prompt is more useful when the responses differ and each response stays close in distribution to the model. We introduce batch diversity, which quantifies the spread of responses within a batch, and distortion, which quantifies the deviation of the batch's average feature distribution from the model's. We characterize the maximum diversity at every distortion bound. Release selects a batch from a pool of independent responses under the bound, and Release diversity converges to the supremum on the support of the model's features as the pool grows and the optimization error vanishes. Diversity-Adaptive Release (DAR) chooses the number of additional responses from a pilot and keeps the bound. On two language models, Release has higher diversity than independent sampling at zero distortion, and DAR has lower generation cost than Release. Larger distortion bounds tend to raise utility and answer coverage and lower the constant-reward fraction, majority accuracy, and response accuracy.