마팅게일 이론 및 응용에 대한 고찰

Variational Speculative Decoding: Rethinking Draft Training from Token Likelihood to Sequence Acceptance

본 논문에서는 마팅게일의 핵심 속성을 조사하며, 조건부 기댓값의 측정론적 표현, 마팅게일 변환, 그리고 업크로싱 정리를 강조합니다. 이러한 결과는 마팅게일 수렴 정리로 이어지며, 이 정리를 사용하여 갈톤-왓슨 분기 과정에서의 소멸 행동을 연구합니다.

Speculative decoding accelerates inference for (M)LLMs, yet a training-decoding discrepancy persists: while existing methods optimize single greedy trajectories, decoding involves verifying and ranking multiple sampled draft paths. We propose Variational Speculative Decoding (VSD), formulating draft training as variational inference over latent proposals (draft paths). VSD maximizes the marginal probability of target-model acceptance, yielding an ELBO that promotes high-quality latent proposals while minimizing divergence from the target distribution. To enhance quality and reduce variance, we incorporate a path-level utility and optimize via an Expectation-Maximization procedure. The E-step draws Monte Carlo samples from an oracle-filtered posterior, while the M-step maximizes weighted likelihood using Adaptive Rejection Weighting (ARW) and Confidence-Aware Regularization (CAR). Theoretical analysis confirms that VSD increases expected acceptance length and speedup. Extensive experiments across LLMs and MLLMs show that VSD achieves up to a 9.6% speedup over EAGLE-3 and 7.9% over ViSpec, significantly improving decoding efficiency.