InfoDensity-DeepSeek-R1-Distill-Llama-8B

InfoDensity-DeepSeek-R1-Distill-Llama-8B

deepseek-ai/DeepSeek-R1-Distill-Llama-8B trained with InfoDensity, a reinforcement-learning reward that favours information-dense reasoning traces. The reward combines an entropy-trajectory quality term with a group-relative length scaling term, and is applied only to traces that reach a correct answer, so the model learns to reach the right answer with markedly less deliberation. Method details are in the paper.

• 📄 Paper: InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning (EMNLP 2026 Main)
• 💻 Code: https://github.com/amao0o0/InfoDensity
• 🧩 Base model: deepseek-ai/DeepSeek-R1-Distill-Llama-8B

Results

Accuracy (pass@1) and mean generated length averaged over AMC23, AIME24, MATH500 and GPQA-Diamond. AES is the Accuracy–Efficiency Score (α=1, β=3, γ=5).

Per benchmark (accuracy % / mean response tokens):

Both rows are scored with the released evaluation code, so a run of it reproduces these numbers.

Evaluation protocol

Greedy decoding, pass@1, generation capped at 16384 tokens, with the prompt

<question>

Please reason step by step, and put your final answer within \boxed{}

The evaluation scripts that produce these numbers are in the GitHub repository.

Usage

from transformers import AutoModelForCausalLM, AutoTokenizer

model_id = "amao0o0/InfoDensity-DeepSeek-R1-Distill-Llama-8B"
tokenizer = AutoTokenizer.from_pretrained(model_id)
model = AutoModelForCausalLM.from_pretrained(model_id, torch_dtype="bfloat16", device_map="auto")

question = "What is the smallest positive integer n such that n^2 + n + 41 is not prime?"
messages = [{"role": "user",
             "content": f"{question}\n\nPlease reason step by step, and put your final answer within \\boxed{{}}"}]
prompt = tokenizer.apply_chat_template(messages, add_generation_prompt=True, tokenize=False)

out = model.generate(**tokenizer(prompt, return_tensors="pt").to(model.device), max_new_tokens=16384)
print(tokenizer.decode(out[0], skip_special_tokens=True))

With vLLM:

from vllm import LLM, SamplingParams

llm = LLM(model="amao0o0/InfoDensity-DeepSeek-R1-Distill-Llama-8B")
print(llm.generate([prompt], SamplingParams(temperature=0, max_tokens=16384))[0].outputs[0].text)

License

Released under mit, inherited from the base model deepseek-ai/DeepSeek-R1-Distill-Llama-8B.

Citation

@inproceedings{wei2026infodensity,
  title     = {InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning},
  author    = {Wei, Chengwei and Kim, Jung-jae and Zhang, Longyin and Chen, Shengkai and Chen, Nancy F.},
  booktitle = {Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing},
  year      = {2026}
}