Multi-Draft Speculative Sampling: Canonical Architectures and Theoretical Limits

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios. The transformer architecture (Vaswani et al., 2017) has revolutionized the field of natural language processing and deep learning. One of the key factors contributing to the success story of transformers, as opposed to prior recurrent-based architectures (Hochreiter and Schmidhuber, 1997; Chung et al., 2014), is their inherent train-time parallelization due to the attention mechanism. This allows for massive scaling and lead to the development of state-of-the-art Large Language Models (LLMs) (Touvron et al., 2023; Achiam et al., 2023; Brown et al., 2020; Chowdhery et al., 2023) which have demonstrated remarkable performance across a wide range of tasks.