# Hydra: Sequentially-Dependent Draft Heads for Medusa Decoding

arXiv: https://arxiv.org/abs/2402.05109 · HTML: https://mlsanity.com/paper/2402.05109/

## Key facts

- Cited by 117 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 20 of its 33 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [Break the Sequential Dependency of LLM Inference Using Lookahead Decoding](https://mlsanity.com/paper/2402.02057/) (2024)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023)
- [Accelerating LLM Inference with Staged Speculative Decoding](https://mlsanity.com/paper/2308.04623/) (2023)
- [NEFTune: Noisy Embeddings Improve Instruction Finetuning](https://mlsanity.com/paper/2310.05914/) (2023)

## Built on by (most cited first, 30 of 117)

- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [TriForce: Lossless Acceleration of Long Sequence Generation with Hierarchical Speculative Decoding](https://mlsanity.com/paper/2404.11912/) (2024)
- [SWIFT: On-the-Fly Self-Speculative Decoding for LLM Inference Acceleration](https://mlsanity.com/paper/2410.06916/) (2024)
- [Judge Decoding: Faster Speculative Sampling Requires Going Beyond Model Alignment](https://mlsanity.com/paper/2501.19309/) (2025)
- [Kangaroo: Lossless Self-Speculative Decoding via Double Early Exiting](https://mlsanity.com/paper/2404.18911/) (2024)
- [LANTERN: Accelerating Visual Autoregressive Models with Relaxed Speculative Decoding](https://mlsanity.com/paper/2410.03355/) (2024)
- [Your LLM Knows the Future: Uncovering Its Multi-Token Prediction Potential](https://mlsanity.com/paper/2507.11851/) (2025)
- [DiffuSpec: Unlocking Diffusion Language Models for Speculative Decoding](https://mlsanity.com/paper/2510.02358/) (2025)
- [Speculative Streaming: Fast LLM Inference without Auxiliary Models](https://mlsanity.com/paper/2402.11131/) (2024)
- [d3LLM: Ultra-Fast Diffusion LLM using Pseudo-Trajectory Distillation](https://mlsanity.com/paper/2601.07568/) (2026)
- [A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Models](https://mlsanity.com/paper/2508.08712/) (2025)
- [PARD: Accelerating LLM Inference with Low-Cost PARallel Draft Model Adaptation](https://mlsanity.com/paper/2504.18583/) (2025)
- [Learning to Keep a Promise: Scaling Language Model Decoding Parallelism with Learned Asynchronous Decoding](https://mlsanity.com/paper/2502.11517/) (2025)
- [SpecDiff-2: Scaling Diffusion Drafter Alignment For Faster Speculative Decoding](https://mlsanity.com/paper/2511.00606/) (2025)
- [Speculative Decoding and Beyond: An In-Depth Survey of Techniques](https://mlsanity.com/paper/2502.19732/) (2025)
- [ReSpec: Towards Optimizing Speculative Decoding in Reinforcement Learning Systems](https://mlsanity.com/paper/2510.26475/) (2025)
- [Mixture of Attentions For Speculative Decoding](https://mlsanity.com/paper/2410.03804/) (2024)
- [D-PACE: Dynamic Position-Aware Cross-Entropy for Parallel Speculative Drafting](https://mlsanity.com/paper/2605.18810/) (2026)
- [GRIFFIN: Effective Token Alignment for Faster Speculative Decoding](https://mlsanity.com/paper/2502.11018/) (2025)
- [Speculative Decoding with CTC-based Draft Model for LLM Inference Acceleration](https://mlsanity.com/paper/2412.00061/) (2024)
- [Reviving Any-Subset Autoregressive Models with Principled Parallel Sampling and Speculative Decoding](https://mlsanity.com/paper/2504.20456/) (2025)
- [L-MTP: Leap Multi-Token Prediction Beyond Adjacent Context for Large Language Models](https://mlsanity.com/paper/2505.17505/) (2025)
- [DREAM: Drafting with Refined Target Features and Entropy-Adaptive Cross-Attention Fusion for Multimodal Speculative Decoding](https://mlsanity.com/paper/2505.19201/) (2025)
- [LogitSpec: Accelerating Retrieval-based Speculative Decoding via Next Next Token Speculation](https://mlsanity.com/paper/2507.01449/) (2025)
- [AutoJudge: Judge Decoding Without Manual Annotation](https://mlsanity.com/paper/2504.20039/) (2025)
- [Scaling Speculative Decoding with Lookahead Reasoning](https://mlsanity.com/paper/2506.19830/) (2025)
- [ECHO: Elastic Speculative Decoding with Sparse Gating for High-Concurrency Scenarios](https://mlsanity.com/paper/2604.09603/) (2026)
- [A Survey on Parallel Reasoning](https://mlsanity.com/paper/2510.12164/) (2025)
- [Boosting Lossless Speculative Decoding via Feature Sampling and Partial Alignment Distillation](https://mlsanity.com/paper/2408.15562/) (2024)

## Abstract (arXiv)

To combat the memory bandwidth-bound nature of autoregressive LLM inference, previous research has proposed the speculative decoding frame-work. To perform speculative decoding, a small draft model proposes candidate continuations of the input sequence that are then verified in parallel by the base model. One way to specify the draft model, as used in the recent Medusa decoding framework, is as a collection of lightweight heads, called draft heads, that operate on the base model's hidden states. To date, all existing draft heads have been sequentially independent, meaning that they speculate tokens in the candidate continuation independently of any preceding tokens in the candidate continuation. In this work, we propose Hydra heads: a sequentially-dependent drop-in replacement for standard draft heads that significantly improves the accuracy of draft head speculation. We further explore the design space of Hydra head training objectives and architectures, and propose a carefully tuned Hydra head recipe, which we call Hydra++, that improves decoding throughput by up to 1.31x and 2.70x compared to Medusa decoding and autoregressive de-coding respectively. Overall, Hydra heads are a simple and well-motivated intervention on standard draft heads that significantly improve the end-to-end speed of draft head-based speculative decoding. We make our code publicly available at https://github.com/zankner/Hydra.