Arithmetic Sampling: Parallel Diverse Decoding for Large Language Models

TL;DR

This paper introduces Arithmetic Sampling, a novel decoding framework for large language models that balances diversity and parallelism, offering guarantees on output diversity while maintaining efficiency and unbiasedness.

Contribution

It proposes a new sampling method compatible with existing variations, providing provable diversity and parallelism, and demonstrates significant improvements in machine translation evaluation.

Findings

Halves the standard deviation in BLEU score estimation.

Reduces the BLEU score gap between independent sampling and beam search by up to 63%.

Provides a theoretically grounded sampling framework with practical benefits.

Abstract

Decoding methods for large language models often trade-off between diversity of outputs and parallelism of computation. Methods such as beam search and Gumbel top-k sampling can guarantee a different output for each element of the beam, but are not easy to parallelize. Alternatively, methods such as temperature sampling and its modifications (top-k sampling, nucleus sampling, typical decoding, and others), are embarrassingly parallel, but have no guarantees about duplicate samples. We present a framework for sampling according to an arithmetic code book implicitly defined by a large language model, compatible with common sampling variations, with provable beam diversity under certain conditions, as well as being embarrassingly parallel and providing unbiased and consistent expectations from the original model. We demonstrate the effectiveness of our approach on WMT machine translation, more than halving the standard deviation when estimating expected BLEU score reward, and closing the BLEU score gap between independent sampling and beam search by up to 63%.