Title: Speculative Speculative Decoding
Primary area: foundation or frontier models, including LLMs
Keywords: inference, large language models, speculative decoding

Abstract: Autoregressive decoding is bottlenecked by its *sequential* nature. Speculative decoding has become a standard way to accelerate inference by using a fast *draft model* to predict upcoming tokens from a slower *target model*, and then verifying them *in parallel* with a single target model forward pass. However, speculative decoding itself relies on a *sequential* dependence between speculation and verification. We introduce *speculative speculative decoding* (SSD) to parallelize these operations. While a verification is ongoing, the draft model *predicts* likely verification outcomes and prepares speculations pre-emptively for them. If the actual verification outcome is then in the predicted set, a speculation can be returned immediately, thereby eliminating all speculation overhead.  We identify three key challenges presented by speculative speculative decoding, and put forth principled methods to solve each after theoretical analysis. The result is **Saguaro**, an optimized SSD algorithm which is up to twice as fast as optimized speculative decoding baselines and up to 5× faster than autoregressive decoding with open source inference engines.  **Saguaro** can be combined with existing methods like EAGLE and token tree speculation for further gains, and permits scaling draft compute to better predict verification outcomes, introducing new tradeoffs between compute and latency.

TL;DR: We introduce an asynchronous speculative decoding algorithm wherein the draft model continuously speculates on top of anticipated verification outcomes, thus hiding drafting latency entirely.