Figure 1: Rho-1 is pre-trained with Selective Language Modeling (SLM). SLM improves average few-shot accuracy on GSM8k and MATH by over 16%, achieving the baseline performance 5-10x faster.

🔥 News

[2024/04/12] 🔥🔥🔥 Rho-Math-v0.1 models released at 🤗 HuggingFace!
- Rho-Math-1B and Rho-Math-7B achieve 15.6% and 31.0% few-shot accuracy on MATH dataset, respectively — matching DeepSeekMath with only 3% of the pretraining tokens.
- Rho-Math-1B-Interpreter is the first 1B LLM that achieves over 40% accuracy on MATH.
- Rho-Math-7B-Interpreter achieves 52% on MATH dataset, using only 69k samples for fine-tuning.
[2024/04/11] Rho-1 paper and repo released.

💡 Introduction

Rho-1 base models employ Selective Language Modeling (SLM) for pretraining, which selectively trains on clean and useful tokens that aligned with the desired distribution.

Selective Lanugage Modeling (SLM)

Figure 2: Upper: Even an extensively filtered pretraining corpus contains token-level noise. Left: Previous Causal Language Modeling (CLM) trains on all tokens. Right: Our proposed Selective Language Modeling (SLM) selectively applies loss on those useful and clean tokens.

Figure 3: The pipeline of Selective Language Modeling. SLM optimizes language model performance by concentrating on valuable, clean tokens during pre-training. It involves three steps: (Step 1) Initially, train a reference model on high-quality data. (Step 2) Then, score each token's loss in a corpus using the reference model. (Step 3) Finally, train the language model selectively on tokens that show higher excess loss compared to the reference loss.

Evaluation Results

Base models (Few-shot CoT):

Model	Size	Data	Uniq. Token	Train Token	GSM8K	MATH	MMLU STEM	SAT
1-2B Base Models
Qwen1.5	1.8B	-	-	-	36.1	6.8	31.3	40.6
Gemma	2.0B	-	-	-	18.8	11.4	34.4	50.0
DeepSeekMath	1.3B	-	120B	150B	23.8	13.6	33.1	56.3
Rho-Math-1B-v0.1	1.1B	OWM	14B	30B	36.2	15.6	23.3	28.1
>= 7B Base Models
Mistral	7B		-	-	41.2	11.6	49.5	59.4
Minerva	540B	-	39B	26B	58.8	33.6	63.9	-
LLemma	34B	PPile	55B	50B	54.2	23.0	54.7	68.8
InternLM2-Math	20B	-	31B	125B	65.4	30.0	53.1	71.9
DeepSeekMath	7B	-	120B	500B	64.1	34.2	56.4	84.4
Rho-Math-7B-v0.1	7B	OWM	14B	10.5B	66.9	31.0	54.6	84.4

Tool-integrated reasoning (Code Interpreter):

Model	Size	SFT Data	GSM8k	MATH	SVAMP	ASDiv	MAWPS	TabMWP	GSM-Hard	AVG
gpt4-early (pal)	-	-	94.2	51.8	94.8	92.6	97.7	95.9	77.6	86.4
gpt-4-turbo-2024-04-09 (cot)	-	-	-	73.4	-	-	-	-	-
Open-Source Small Models
MAmmoTH	70B	MI-260k	76.9	41.8	82.4	-	-	-	-	-
ToRA	7B	ToRA-69k	68.8	40.1	68.2	73.9	88.8	42.4	54.6	62.4
ToRA	70B	ToRA-69k	84.3	49.7	82.7	86.8	93.8	74.0	67.2	76.9
DeepSeekMath	7B	ToRA-69k	79.8	52.0	80.1	87.1	93.8	85.8	63.1	77.4
Rho-Math-1B-Interpreter-v0.1	1B	ToRA-69k	59.4	40.6	60.7	74.2	88.6	26.7	48.1	56.9
Rho-Math-7B-Interpreter-v0.1	7B	ToRA-69k	81.3	51.8	80.8	85.5	94.5	70.1	63.1	75.3

🚀 Quick Start

Evaluation

git clone git@github.com:microsoft/rho.git
cd rho-1/math-evaluation-harness

Base model few-shot evaluation:

bash scripts/run_eval.sh cot microsoft/rho-math-7b-v0.1

SFT model (code-interpreter) evaluation:

bash scripts/run_eval.sh tora microsoft/rho-math-7b-interpreter-v0.1

Our reproduced outputs are provided in rho-1/outputs.zip.

☕️ Citation

If you find this repository helpful, please consider citing our paper:

@misc{lin2024rho1,
      title={Rho-1: Not All Tokens Are What You Need}, 
      author={Zhenghao Lin and Zhibin Gou and Yeyun Gong and Xiao Liu and Yelong Shen and Ruochen Xu and Chen Lin and Yujiu Yang and Jian Jiao and Nan Duan and Weizhu Chen},
      year={2024},
      eprint={2404.07965},
      archivePrefix={arXiv},
      primaryClass={cs.CL}
}