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).
| Model | Accuracy | Length | AES |
|---|---|---|---|
| DeepSeek-R1-Distill-Llama-8B | 47.6 | 9.4k | — |
| InfoDensity-DeepSeek-R1-Distill-Llama-8B | 58.4 | 6.5k | +0.99 |
Per benchmark (accuracy % / mean response tokens):
| Model | AMC23 | AIME24 | MATH500 | GPQA-D |
|---|---|---|---|---|
| DeepSeek-R1-Distill-Llama-8B | 65.0 / 8.5k | 23.3 / 13.3k | 78.8 / 5.2k | 23.2 / 10.7k |
| InfoDensity | 80.0 / 5.4k | 40.0 / 10.0k | 82.8 / 3.2k | 30.8 / 7.6k |
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}
}