This is a MEDUSA draft model for Llama-3.1-8B-Instruct, trained from scratch using LK losses — training objectives that directly target acceptance rate rather than using KL divergence as a proxy.

Training Details

Base model: meta-llama/Llama-3.1-8B-Instruct
Draft architecture: MEDUSA
Training data: Infinity-Instruct-0625 with Llama-3.1-8B generated responses
Training objective: Hybrid LK loss with adaptive λ scheduling (η=10)
Training: 10 epochs from random initialization
Draft length: K = 6 speculative tokens

Performance

Average acceptance length (τ) measured across MT-bench, HumanEval, and GSM8K with K = 6:

Configuration	Temperature = 0	Temperature = 1
MEDUSA + KL	2.19	1.85
MEDUSA + LK (ours)	2.21	2.00

Note: Earlier vLLM versions sampled draft tokens greedily regardless of temperature, which underestimated acceptance rates at temperature > 0. Stochastic draft sampling was introduced in v0.18.0, and from v0.21.0 it can be enabled via speculative_config using rejection_sample_method and draft_sample_method. The acceptance metrics reported above were measured under standard rejection sampling and are reproducible with the configuration below.

Usage with vLLM

python

from vllm import LLM, SamplingParams

llm = LLM(
    model="meta-llama/Llama-3.1-8B-Instruct",
    speculative_config={
        "method": "medusa",
        "model": "nebius/MEDUSA-Llama-3.1-8B-Instruct",
        "num_speculative_tokens": 6,
        "rejection_sample_method": "standard",
        "draft_sample_method": "gumbel",
    },
)

sampling_params = SamplingParams(temperature=0.7)
outputs = llm.generate(["Explain speculative decoding in simple terms."], sampling_params)

License

CC BY 4.0

This model was trained using outputs from meta-llama/Llama-3.1-8B-Instruct. Use of this model is additionally subject to the Llama 3.1 Community License Agreement.

Citation

@misc{samarin2026lklosses,
  title     = {LK Losses: Direct Acceptance Rate Optimization for Speculative Decoding},
  author    = {Alexander Samarin and Sergei Krutikov and Anton Shevtsov and Sergei Skvortsov and Filipp Fisin and Alexander Golubev},
  year      = {2026},
  eprint    = {2602.23881},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url       = {https://arxiv.org/abs/2602.23881}
}