# Polybasic Speculative Decoding Through a Theoretical Perspective

arXiv: https://arxiv.org/abs/2510.26527 · HTML: https://mlsanity.com/paper/2510.26527/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 40 of its 46 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 40)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Abstractive Text Summarization Using Sequence-to-Sequence RNNs and Beyond](https://mlsanity.com/paper/1602.06023/) (2016)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [Speculative Decoding: Exploiting Speculative Execution for Accelerating Seq2seq Generation](https://mlsanity.com/paper/2203.16487/) (2022)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning](https://mlsanity.com/paper/2401.01325/) (2024)
- [Hydra: Sequentially-Dependent Draft Heads for Medusa Decoding](https://mlsanity.com/paper/2402.05109/) (2024)
- [TriForce: Lossless Acceleration of Long Sequence Generation with Hierarchical Speculative Decoding](https://mlsanity.com/paper/2404.11912/) (2024)
- [MagicDec: Breaking the Latency-Throughput Tradeoff for Long Context Generation with Speculative Decoding](https://mlsanity.com/paper/2408.11049/) (2024)
- [PEARL: Parallel Speculative Decoding with Adaptive Draft Length](https://mlsanity.com/paper/2408.11850/) (2024)
- [Cascade Speculative Drafting for Even Faster LLM Inference](https://mlsanity.com/paper/2312.11462/) (2023)
- [GliDe with a CaPE: A Low-Hassle Method to Accelerate Speculative Decoding](https://mlsanity.com/paper/2402.02082/) (2024)
- [Accelerating Auto-regressive Text-to-Image Generation with Training-free Speculative Jacobi Decoding](https://mlsanity.com/paper/2410.01699/) (2024)
- [Judge Decoding: Faster Speculative Sampling Requires Going Beyond Model Alignment](https://mlsanity.com/paper/2501.19309/) (2025)
- [SpecExec: Massively Parallel Speculative Decoding for Interactive LLM Inference on Consumer Devices](https://mlsanity.com/paper/2406.02532/) (2024)
- [Lookahead: An Inference Acceleration Framework for Large Language Model with Lossless Generation Accuracy](https://mlsanity.com/paper/2312.12728/) (2023)
- [A Theoretical Perspective for Speculative Decoding Algorithm](https://mlsanity.com/paper/2411.00841/) (2024)
- [AdaEDL: Early Draft Stopping for Speculative Decoding of Large Language Models via an Entropy-based Lower Bound on Token Acceptance Probability](https://mlsanity.com/paper/2410.18351/) (2024)
- [Generation Meets Verification: Accelerating Large Language Model Inference with Smart Parallel Auto-Correct Decoding](https://mlsanity.com/paper/2402.11809/) (2024)

## Built on by (most cited first, 1 of 1)

- [Approximate Speculative Decoding](https://mlsanity.com/paper/2608.03447/) (2026)

## Abstract (arXiv)

Inference latency stands as a critical bottleneck in the large-scale deployment of Large Language Models (LLMs). Speculative decoding methods have recently shown promise in accelerating inference without compromising the output distribution. However, existing work typically relies on a dualistic draft-verify framework and lacks rigorous theoretical grounding. In this paper, we introduce a novel polybasic speculative decoding framework, underpinned by a comprehensive theoretical analysis. Specifically, we prove a fundamental theorem that characterizes the optimal inference time for multi-model speculative decoding systems, shedding light on how to extend beyond the dualistic approach to a more general polybasic paradigm. Through our theoretical investigation of multi-model token generation, we expose and optimize the interplay between model capabilities, acceptance lengths, and overall computational cost. Our framework supports both standalone implementation and integration with existing speculative techniques, leading to accelerated performance in practice. Experimental results across multiple model families demonstrate that our approach yields speedup ratios ranging from 3.31× to 4.01× for LLaMA2-Chat 7B, up to 3.87 × for LLaMA3-8B, up to 4.43 × for Vicuna-7B and up to 3.85 × for Qwen2-7B -- all while preserving the original output distribution. We release our theoretical proofs and implementation code to facilitate further investigation into polybasic speculative decoding.