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nvidia/
AceMath-72B-RM

Name: AceMath-72B-RM
Rating: 2.5 (164 reviews)

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Introduction

We introduce AceMath, a family of frontier models designed for mathematical reasoning. The models in AceMath family, including AceMath-1.5B/7B/72B-Instruct and AceMath-7B/72B-RM, are Improved using Qwen. The AceMath-1.5B/7B/72B-Instruct models excel at solving English mathematical problems using Chain-of-Thought (CoT) reasoning, while the AceMath-7B/72B-RM models, as outcome reward models, specialize in evaluating and scoring mathematical solutions.

The AceMath-7B/72B-RM models are developed from our AceMath-7B/72B-Instruct models and trained on AceMath-RM-Training-Data using Bradley-Terry loss. The architecture employs standard sequence classification with a linear layer on top of the language model, using the final token to output a scalar score.

For more information about AceMath, check our website and paper.

All Resources

Benchmark Results (AceMath-Instruct + AceMath-72B-RM)

We compare AceMath to leading proprietary and open-access math models in above Table. Our AceMath-7B-Instruct, largely outperforms the previous best-in-class Qwen2.5-Math-7B-Instruct (Average pass@1: 67.2 vs. 62.9) on a variety of math reasoning benchmarks, while coming close to the performance of 10× larger Qwen2.5-Math-72B-Instruct (67.2 vs. 68.2). Notably, our AceMath-72B-Instruct outperforms the state-of-the-art Qwen2.5-Math-72B-Instruct (71.8 vs. 68.2), GPT-4o (67.4) and Claude 3.5 Sonnet (65.6) by a margin. We also report the rm@8 accuracy (best of 8) achieved by our reward model, AceMath-72B-RM, which sets a new record on these reasoning benchmarks. This excludes OpenAI’s o1 model, which relies on scaled inference computation.

Reward Model Benchmark Results

Model	GSM8K	MATH500	Minerva Math	GaoKao 2023 En	Olympiad Bench	College Math	MMLU STEM	Avg.
majority@8	96.22	83.11	41.20	68.21	42.69	45.01	78.21	64.95
Skywork-o1-Open-PRM-Qwen-2.5-7B	96.92	86.64	41.00	72.34	46.50	46.30	74.01	66.24
Qwen2.5-Math-RM-72B	96.61	86.63	43.60	73.62	47.21	47.29	84.24	68.46
AceMath-7B-RM (Ours)	96.66	85.47	41.96	73.82	46.81	46.37	80.78	67.41
AceMath-72B-RM (Ours)	97.23	86.72	45.06	74.69	49.23	46.79	87.01	69.53

*Reward model evaluation on AceMath-RewardBench. The average results (rm@8) of reward models on math benchmarks, randomly sample 8 responses from 64 candidates with 100 random seeds. Response candidates are generated from a pool of 8 LLMs.

How to use

python

import torch
from transformers import AutoModelForSequenceClassification, AutoTokenizer

model_name = "nvidia/AceMath-72B-RM" # Path to the model
device = "auto" # the device to load the model onto

model = AutoModelForSequenceClassification.from_pretrained(
    model_name, 
    device_map=device, 
    num_labels=1,
    torch_dtype=torch.bfloat16,
    trust_remote_code=True,
).eval()

tokenizer = AutoTokenizer.from_pretrained(model_name, trust_remote_code=True)


prompt = """Compute
\[\sum_{n = 1}^\infty \frac{F_{n + 1}}{F_n F_{n + 2}},\]where $F_n$ denotes the $n$th Fibonacci number, so $F_0 = 0$ and $F_1 = 1.$"""

resp_1 = """To compute \[\sum_{n=1}^\infty \frac{F_{n+1}}{F_n F_{n+2}},\] where \( F_n \) is the \(n\)-th Fibonacci number, we will use the recurrence relation \( F_{n+2} = F_{n+1} + F_n \) and properties of Fibonacci numbers.\n\n---\n\n### Step 1: Simplify the General Term\n\nThe given term is\n\[\frac{F_{n+1}}{F_n F_{n+2}}.\]\n\nUsing the Fibonacci recurrence relation \( F_{n+2} = F_{n+1} + F_n \), we rewrite \( \frac{1}{F_{n+2}} \) as\n\[\frac{1}{F_{n+2}} = \frac{1}{F_{n+1} + F_n}.\]\n\nThus, the term becomes\n\[\frac{F_{n+1}}{F_n F_{n+2}} = \frac{F_{n+1}}{F_n (F_{n+1} + F_n)}.\]\n\nNow, separate the fraction into partial fractions:\n\[\frac{F_{n+1}}{F_n (F_{n+1} + F_n)} = \frac{1}{F_n} - \frac{1}{F_{n+1}}.\]\n\n---\n\n### Step 2: Write the Series\n\nThe series becomes\n\[\sum_{n=1}^\infty \frac{F_{n+1}}{F_n F_{n+2}} = \sum_{n=1}^\infty \left( \frac{1}{F_n} - \frac{1}{F_{n+1}} \right).\]\n\nThis is a **telescoping series**, where most terms cancel out. Writing the first few terms explicitly:\n\[\sum_{n=1}^\infty \left( \frac{1}{F_n} - \frac{1}{F_{n+1}} \right) = \left( \frac{1}{F_1} - \frac{1}{F_2} \right) + \left( \frac{1}{F_2} - \frac{1}{F_3} \right) + \left( \frac{1}{F_3} - \frac{1}{F_4} \right) + \cdots.\]\n\nAll intermediate terms cancel, leaving:\n\[\frac{1}{F_1} - \lim_{n \to \infty} \frac{1}{F_{n+1}}.\]\n\n---\n\n### Step 3: Evaluate the Remaining Terms\n\n- The first Fibonacci number \( F_1 = 1 \), so \( \frac{1}{F_1} = 1 \).\n- As \( n \to \infty \), \( F_{n+1} \to \infty \), so \( \frac{1}{F_{n+1}} \to 0 \).\n\nThus, the sum is:\n\[\sum_{n=1}^\infty \frac{F_{n+1}}{F_n F_{n+2}} = 1 - 0 = 1.\]\n\n---\n\n### Final Answer:\n\n\[\boxed{1}\]"""

chat = [
    {"role": "system", "content": "Please reason step by step, and check your final answer within \\boxed{}."},
    {"role": "user", "content": prompt},
    {"role": "assistant", "content": resp_1}
]


conversation_str = tokenizer.apply_chat_template(
    chat, 
    tokenize=False, 
    add_generation_prompt=False
)

input_ids = tokenizer.encode(
    conversation_str, 
    return_tensors="pt", 
    add_special_tokens=False
).to(model.device)

outputs = model(input_ids=input_ids)
print(outputs[0][0]) # 5.4375

Correspondence to

Zihan Liu (zihanl@nvidia.com), Yang Chen (yachen@nvidia.com), Wei Ping (wping@nvidia.com)

Citation

If you find our work helpful, we’d appreciate it if you could cite us.

@article{acemath2024, title={AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling}, author={Liu, Zihan and Chen, Yang and Shoeybi, Mohammad and Catanzaro, Bryan and Ping, Wei}, journal={arXiv preprint}, year={2024} }

License

All models in the AceMath family are for non-commercial use only, subject to Terms of Use of the data generated by OpenAI. We put the AceMath models under the license of Creative Commons Attribution: Non-Commercial 4.0 International.

nvidia/AceMath-72B-RM

Introduction

All Resources

AceMath Instruction Models

AceMath Reward Models

Evaluation & Training Data

General Instruction Models