Inference with modern Large Language Models (LLMs) is expensive and time-consuming, and speculative sampling has proven to be an effective solution. Most speculative sampling methods such as EAGLE use a static draft tree, implicitly assuming that the acceptance rate of draft tokens depends only on their position. Interestingly, we found that the acceptance rate of draft tokens is also context-dependent. In this paper, building upon EAGLE, we propose EAGLE-2, which introduces a new technique of context-aware dynamic draft tree into drafting modeling. This improvement leverages the fact that the draft model of EAGLE is well-calibrated: the confidence scores from the draft model approximate acceptance rates with small errors. We conducted extensive evaluations on three series of LLMs and six tasks, with EAGLE-2 achieving speedup ratios of up to **5x**, which is 1.3x that of EAGLE. EAGLE-2 also ensures that the distribution of the generated text remains unchanged, making it a **lossless** acceleration algorithm.

In information retrieval (IR), candidate set pruning has been commonly used to speed up two-stage relevance ranking. However, such an approach lacks accurate error control and often trades accuracy against computational efficiency in an empirical fashion, missing theoretical guarantees. In this paper, we propose the concept of certified error control of candidate set pruning for relevance ranking, which means that the test error after pruning is guaranteed to be controlled under a user-specified threshold with high probability. Both in-domain and out-of-domain experiments show that our method successfully prunes the first-stage retrieved candidate sets to improve the second-stage reranking speed while satisfying the pre-specified accuracy constraints in both settings. For example, on MS MARCO Passage v1, our method reduces the average candidate set size from 1000 to 27, increasing reranking speed by about 37 times, while keeping MRR@10 greater than a pre-specified value of 0.38 with about 90% empirical coverage. In contrast, empirical baselines fail to meet such requirements. Code and data are available at: https://github.com/alexlimh/CEC-Ranking.