Research map / Probabilistic and scientific modeling / Variational and generative sampling
Accelerated Speculative Sampling Based on Tree Monte Carlo
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Proposes Tree Monte Carlo (TMC), a framework for sampling over tree-structured spaces with sub-distributions and sub-sampler convergence, and applies it to derive Accelerated Speculative Sampling (ASpS), which accepts more tokens per step than speculative sampling while preserving the target distribution.
Problem
Speculative sampling applies maximum coupling token-by-token, which is suboptimal for multi-token reference strings because the LLM output space is a tree of token strings, not a product of token spaces.
Approach
Treat LLM generation as a tree distribution and define sub-distributions and prefix sub-samplers whose composition converges to the target; ASpS builds a global coupling over the reference token tree that accepts more reference tokens than SpS while keeping the target distribution.
Key results
- ASpS matches SpS at n=1 (1.284 accepted tokens per step) and improves with more reference tokens, reaching 1.522 vs 1.468 at n=10 on WMT16 with LLaMa-7b/68m (about 3.7% improvement).
- On open-ended generation with OPT-13b/OPT-125m, ASpS improves accepted tokens per step by up to 11.8% at n=10 (2.898 vs 2.591).
- With GPT-Neo-2.7B/GPT-2 and GPT-2-xl/GPT-2 pairs, ASpS gains reach roughly 14% in accepted tokens per step at n=10.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ASpS instead of SpS with one reference token | Speculative sampling with LLaMa-7B target and LLaMa-68M reference · WMT16 translation, n=1 reference token | ATN: 1.284 ± 0.001 -> 1.284 ± 0.001 | No clear effect |
| Use ASpS instead of SpS with multiple reference tokens | Speculative sampling with LLaMa-7B target and LLaMa-68M reference · WMT16 translation, n=10 reference tokens | ATN: 1.468 ± 0.003 -> 1.522 ± 0.003 | Helped |
| Use ASpS instead of SpS | Speculative sampling with LLaMa-2-7B target and LLaMa-68M reference · Machine translation, n=10 reference tokens | ATN: 1.177 ± 0.001 -> 1.185 ± 0.001 | Helped |
| Use ASpS instead of SpS | Speculative sampling with LLaMa-2-7B target and LLaMa-68M reference · Text summarization, n=10 reference tokens | ATN: 1.874 ± 0.002 -> 1.889 ± 0.002 | Helped |
| Use ASpS instead of SpS | Speculative sampling with LLaMa-7B target and LLaMa-68M reference · Open-ended text generation, n=10 reference tokens | ATN: 2.003 ± 0.006 -> 2.187 ± 0.008 | Helped |
| Increase the number of reference tokens from 1 to more than 1 when using ASpS | Accelerated Speculative Sampling · Reported tasks and model configurations | ATN: +0.9 ± 0.2% to +14.3 ± 0.7% | Helped |
| Use ASpS instead of SpS | Speculative sampling across reported tasks and model configurations · Reported tasks and model configurations | PPL change (%): 0.0 ± 2.5% | No clear effect |
Surprising findings
- Gains of ASpS over SpS on the WMT16 translation task are small (about 1-4%) and for LLaMa-2 pairs are below 1%, suggesting the benefit depends strongly on model pair and task.
Limitations
- Wall-clock measurements may not reflect FLOP savings because the HuggingFace implementation is not inference-optimized.
- Gains over SpS are modest and vary by model pair and task; ASpS equals SpS when only one reference token is used.
Experimental setup
Datasets: WMT16
Benchmarks: WMT16 machine translation text summarization open-ended text generation
Metrics: accepted tokens per step per-token time improvement perplexity change
Baselines: Speculative Sampling (SpS)
Builds on: speculative sampling maximum coupling Markov chain Monte Carlo
Closest papers by meaning
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- TreeGraft: Adaptive Multi-Drafter Grafting for Tree-Based Speculative Decoding (NeurIPS 2026 · similarity 0.89)
- Accelerating LLM Inference with Lossless Speculative Decoding Algorithms for Heterogeneous Vocabularies (ICML 2025 · similarity 0.89)
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- Dynamic-Width Speculative Beam Decoding for LLM Inference (AAAI 2025 · similarity 0.88)
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