# Goose: Anisotropic Speculation Trees for Training-Free Speculative Decoding

arXiv: https://arxiv.org/abs/2604.02047 · HTML: https://mlsanity.com/paper/2604.02047/

## Key facts

- Cited by 2 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 24 of its 28 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [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)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [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)
- [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)
- [ClassEval: A Manually-Crafted Benchmark for Evaluating LLMs on Class-level Code Generation](https://mlsanity.com/paper/2308.01861/) (2023)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [REST: Retrieval-Based Speculative Decoding](https://mlsanity.com/paper/2311.08252/) (2023)
- [Inference with Reference: Lossless Acceleration of Large Language Models](https://mlsanity.com/paper/2304.04487/) (2023)
- [Turning Trash into Treasure: Accelerating Inference of Large Language Models with Token Recycling](https://mlsanity.com/paper/2408.08696/) (2024)
- [SuffixDecoding: Extreme Speculative Decoding for Emerging AI Applications](https://mlsanity.com/paper/2411.04975/) (2024)
- [PLD+: Accelerating LLM inference by leveraging Language Model Artifacts](https://mlsanity.com/paper/2412.01447/) (2024)

## Built on by (most cited first, 2 of 2)

- [Cost-Aware Diffusion Draft Trees for Speculative Decoding](https://mlsanity.com/paper/2606.01813/) (2026)
- [Oilbird: Training-Free Speculative Decoding with Keys the Verifier Already Computes](https://mlsanity.com/paper/2608.03839/) (2026)

## Abstract (arXiv)

Speculative decoding accelerates large language model inference by drafting multiple candidate tokens and verifying them in a single forward pass. Candidates are organized as a tree: deeper trees accept more tokens per step, but adding depth requires sacrificing breadth (fallback options) under a fixed verification budget. Existing training-free methods draft from a single token source and shape their trees without distinguishing candidate quality across origins. We observe that two common training-free token sources -- n-gram matches copied from the input context, and statistical predictions from prior forward passes -- differ sharply in acceptance rate (~6x median gap, range 2-18x across five models and five benchmarks). We prove that when such a quality gap exists, the optimal tree is anisotropic (asymmetric): reliable tokens should form a deep chain while unreliable tokens spread as wide branches, raising the depth ceiling of balanced trees. We realize this structure in GOOSE, a training-free framework that builds an adaptive spine tree: a deep chain of high-acceptance context-matched tokens with wide branches of low-acceptance alternatives at each node. The resulting tree provably accepts at least as many tokens per step as either source alone. On five LLMs (7B-33B) and five benchmarks, GOOSE achieves 1.9-4.3x lossless speedup, outperforming balanced-tree baselines by 12-33% under the same budget.