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Model: hkust-nlp/dart-math-mistral-7b-prop2diff Source: Original Platform
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---
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language:
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- en
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license: apache-2.0
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library_name: transformers
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tags:
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- mathematics
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datasets:
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- hkust-nlp/dart-math-hard
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metrics:
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- accuracy
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pipeline_tag: text-generation
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base_model: mistralai/Mistral-7B-v0.1
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model-index:
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- name: dart-math-mistral-7b-prop2diff
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results:
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: hendrycks/competition_math
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name: MATH
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split: test
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 45.5
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: openai/gsm8k
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name: GSM8K
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config: main
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split: test
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 81.1
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: college-math
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name: CollegeMath
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 29.4
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: deepmind-mathematics
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name: DeepMind-Mathematics
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 45.1
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: Hothan/OlympiadBench
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name: OlympiadBench-OE_TO_maths_en_COMP
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config: OE_TO_maths_en_COMP
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split: train
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 14.7
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- task:
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type: text-generation
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name: Mathematical Problem-Solving
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dataset:
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type: TIGER-Lab/TheoremQA
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name: TheoremQA
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split: test
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metrics:
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- type: accuracy
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name: Pass@1 (0-shot CoT)
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value: 17.0
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---
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# DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
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📝 [Paper@arXiv](https://arxiv.org/abs/2407.13690) | 🤗 [Datasets&Models@HF](https://huggingface.co/collections/hkust-nlp/dart-math-665704599b35de59f8fdf6c1) | 🐱 [Code@GitHub](https://github.com/hkust-nlp/dart-math)
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🐦 [Thread@X(Twitter)](https://x.com/tongyx361/status/1811413243350454455) | 🐶 [中文博客@知乎](https://zhuanlan.zhihu.com/p/708371895) | 📊 [Leaderboard@PapersWithCode](https://paperswithcode.com/paper/dart-math-difficulty-aware-rejection-tuning#results) | 📑 [BibTeX](https://github.com/hkust-nlp/dart-math?tab=readme-ov-file#citation)
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## Models: `DART-Math`
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`DART-Math` models achieve performance **superior or competitive to previous SOTAs** on 2 in-domain and 4 challenging out-of-domain mathematical reasoning benchmarks, despite using **much smaller datasets** and **no proprietary model like GPT-4**.
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| Model | [MATH](https://huggingface.co/datasets/hendrycks/competition_math) | [GSM8K](https://huggingface.co/datasets/gsm8k) | [College](https://github.com/hkust-nlp/dart-math/tree/main/data/eval-dsets/mwpbench/college-math-test.jsonl) | [DM](https://github.com/hkust-nlp/dart-math/tree/main/data/eval-dsets/deepmind-mathematics.json) | [Olympiad](https://github.com/hkust-nlp/dart-math/tree/main/data/eval-dsets/olympiadbench/OE_TO_maths_en_COMP.json) | [Theorem](https://github.com/hkust-nlp/dart-math/tree/main/data/eval-dsets/theoremqa.json) | AVG |
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| :----------------------------------------------------------------------------------------------------- | -----------------------------------------------------------------: | ---------------------------------------------: | -----------------------------------------------------------------------------------------------------------: | -----------------------------------------------------------------------------------------------: | ------------------------------------------------------------------------------------------------------------------: | -----------------------------------------------------------------------------------------: | -------: |
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| GPT-4 (0314) | [52.6](https://arxiv.org/abs/2403.04706) | [94.7](https://arxiv.org/abs/2403.04706) | [24.4](https://arxiv.org/abs/2403.02884) | -- | -- | -- | -- |
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| Llama-3-70B-MetaMath | 44.9 | 88.0 | 31.9 | 53.2 | 11.6 | 21.9 | 41.9 |
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| [`DART-Math-Llama-3-70B` (Uniform)](https://huggingface.co/hkust-nlp/dart-math-llama3-70b-uniform) | 54.9 | **90.4** | **38.5** | **64.1** | 19.1 | 27.4 | 49.1 |
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| [`DART-Math-Llama-3-70B` (Prop2Diff)](https://huggingface.co/hkust-nlp/dart-math-llama3-70b-prop2diff) | **56.1** | 89.6 | 37.9 | **64.1** | **20.0** | **28.2** | **49.3** |
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| DeepSeekMath-7B-MetaMath | 43.7 | 81.8 | 33.7 | 53.0 | 13.6 | 23.2 | 41.5 |
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| [DeepSeekMath-7B-RL](https://huggingface.co/deepseek-ai/deepseek-math-7b-rl) | 53.1 | 88.4 | 41.3 | 58.3 | 18.7 | 35.9 | 49.3 |
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| [`DART-Math-DSMath-7B` (Uniform)](https://huggingface.co/hkust-nlp/dart-math-dsmath-7b-uniform) | 52.9 | **88.2** | 40.1 | 60.2 | 21.3 | **32.5** | 49.2 |
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| [`DART-Math-DSMath-7B` (Prop2Diff)](https://huggingface.co/hkust-nlp/dart-math-dsmath-7b-prop2diff) | **53.6** | 86.8 | **40.7** | **61.6** | **21.7** | 32.2 | **49.4** |
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| Mistral-7B-MetaMath | 29.8 | 76.5 | 19.3 | 28.0 | 5.9 | 14.0 | 28.9 |
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| [`DART-Math-Mistral-7B` (Uniform)](https://huggingface.co/hkust-nlp/dart-math-mistral-7b-uniform) | 43.5 | **82.6** | 26.9 | 42.0 | 13.2 | 16.4 | 27.4 |
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| [`DART-Math-Mistral-7B` (Prop2Diff)](https://huggingface.co/hkust-nlp/dart-math-mistral-7b-prop2diff) | **45.5** | 81.1 | **29.4** | **45.1** | **14.7** | **17.0** | **38.8** |
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| Llama-3-8B-MetaMath | 32.5 | 77.3 | 20.6 | 35.0 | 5.5 | 13.8 | 30.8 |
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| [`DART-Math-Llama-3-8B` (Uniform)](https://huggingface.co/hkust-nlp/dart-math-llama3-8b-uniform) | 45.3 | **82.5** | 27.1 | **48.2** | 13.6 | 15.4 | 38.7 |
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| [`DART-Math-Llama-3-8B` (Prop2Diff)](https://huggingface.co/hkust-nlp/dart-math-llama3-8b-prop2diff) | **46.6** | 81.1 | **28.8** | 48.0 | **14.5** | **19.4** | **39.7** |
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***Abbreviations**: College (CollegeMath), DM (DeepMind Mathematics), Olympiad (OlympiadBench-Math), Theorem (TheoremQA).
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**Bold** means the best score by SFT on the respective base model here.
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To reproduce our results, please refer to [the `DART-Math` GitHub repository](https://github.com/hkust-nlp/dart-math).*
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## Prompt Template
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All the `DART-Math` models use the [Alpaca](https://github.com/tatsu-lab/stanford_alpaca) prompt template:
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```
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Below is an instruction that describes a task. Write a response that appropriately completes the request.\n\n###Instruction:\n{query}\n\n### Response:\n
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```
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## Training Dataset
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We construct our traning datasets by applying **Difficulty-Aware Rejection Sampling** (`DARS`) to the **MATH and GSM8K** training sets.
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`DARS` tackle **severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries**, in previous datasets.
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These biases are primarily caused by vanilla rejection sampling, where **the same number of responses is
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sampled for each query**, yet the likelihood of obtaining correct responses for difficult queries is significantly lower, sometimes even zero.
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Please refer to [`DART-Math-Hard`](https://huggingface.co/datasets/hkust-nlp/dart-math-hard) / [`DART-Math-Uniform`](https://huggingface.co/datasets/hkust-nlp/dart-math-uniform) for more details.
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## Training Setup
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We perform standard instruction tuning to several base models including Llama3-8B & Mistral-7B & Llama3-70B as representatives of general models and DeepSeekMath-
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7B as the representative of math-specialized model
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on our synthetic datasets [`DART-Math-Hard`](https://huggingface.co/datasets/hkust-nlp/dart-math-hard) & [`DART-Math-Uniform`](https://huggingface.co/datasets/hkust-nlp/dart-math-uniform),
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leading to `DART-Math (Prop2Diff)` & `DART-Math (Uniform)` respectively.
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For simplicity, we keep most hyper-parameters the same across different models and datasets:
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- Model max length (of [packed](https://github.com/MeetKai/functionary/tree/main/functionary/train/packing) sequence): 4096
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- Batch size: 64
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- Warm-up ratio: 0.03
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- Learning rate scheduler: cosine
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- Prompt template: [Alpaca](https://github.com/tatsu-lab/stanford_alpaca)
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Several other key hyper-parameters are tuned as follow:
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| Base Model | Max. L.R. | # of Epochs | # of Grad. Acc. Steps | # of A100 GPUs |
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|:--------------- | ---------:| -----------:| ---------------------:| --------------:|
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| Mistral-7B | `1e-5` | 3 | 1 | 8 |
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| Llama3-8B | `5e-5` | 1 | 2 | 8 |
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| Llama3-70B | `2e-5` | 1 | 1 | 32 |
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| DeepSeekMath-7B | `5e-5` | 3 | 1 | 8 |
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- For **maximum learning rate**, we determine the values by **searching** through `1e-6,5e-6,1e-5,2e-5,5e-5,1e-4` according to the MATH performance after training on MMIQC for 1 epoch, except for Llama3-70B that is so expensive to search for that we derive from Llama3-8B’s learning rate in analogy to the relationship of (per-training) learning rates between [Llama2-7B](https://huggingface.co/meta-llama/Llama-2-7b-hf) and [Llama2-70B](https://huggingface.co/meta-llama/Llama-2-70b-hf) (\~2:1).
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- For **Llama3** models, preliminary experiments indicate that **training for 1 epoch consistently outperforms 3 epochs**.
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Please refer to [Appendix A.1 of our paper](https://tongyx361.github.io/assets/dart-math/paper-dart-math.pdf) for more details.
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## Other Details
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- For Mistral-7B-based models, we disable `sliding_window` by default following [the newest Mistral-7B-Instruct](https://huggingface.co/mistralai/Mistral-7B-Instruct-v0.3/blob/main/config.json) (Flash Attention 2 does not support `sliding_window` and XFormer backend in vLLM has throughput \~10% lower in our experiments.)
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## Citation
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If you find our data, model or code useful for your work, please kindly cite [our paper](https://arxiv.org/abs/2407.13690):
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```latex
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@article{tong2024dartmath,
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title={DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving},
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author={Yuxuan Tong and Xiwen Zhang and Rui Wang and Ruidong Wu and Junxian He},
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year={2024},
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eprint={2407.13690},
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archivePrefix={arXiv},
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primaryClass={cs.CL},
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url={https://arxiv.org/abs/2407.13690},
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}
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```
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||||
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|
||||
}
|
||||
}
|
||||
30
special_tokens_map.json
Normal file
30
special_tokens_map.json
Normal file
@@ -0,0 +1,30 @@
|
||||
{
|
||||
"bos_token": {
|
||||
"content": "<s>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
},
|
||||
"eos_token": {
|
||||
"content": "</s>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
},
|
||||
"pad_token": {
|
||||
"content": "[PAD]",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
},
|
||||
"unk_token": {
|
||||
"content": "<unk>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
}
|
||||
}
|
||||
91132
tokenizer.json
Normal file
91132
tokenizer.json
Normal file
File diff suppressed because it is too large
Load Diff
BIN
tokenizer.model
(Stored with Git LFS)
Normal file
BIN
tokenizer.model
(Stored with Git LFS)
Normal file
Binary file not shown.
51
tokenizer_config.json
Normal file
51
tokenizer_config.json
Normal file
@@ -0,0 +1,51 @@
|
||||
{
|
||||
"add_bos_token": true,
|
||||
"add_eos_token": false,
|
||||
"added_tokens_decoder": {
|
||||
"0": {
|
||||
"content": "<unk>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"1": {
|
||||
"content": "<s>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"2": {
|
||||
"content": "</s>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"32000": {
|
||||
"content": "[PAD]",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
}
|
||||
},
|
||||
"additional_special_tokens": [],
|
||||
"bos_token": "<s>",
|
||||
"clean_up_tokenization_spaces": false,
|
||||
"eos_token": "</s>",
|
||||
"legacy": true,
|
||||
"model_max_length": 4096,
|
||||
"pad_token": "[PAD]",
|
||||
"padding_side": "left",
|
||||
"sp_model_kwargs": {},
|
||||
"spaces_between_special_tokens": false,
|
||||
"tokenizer_class": "LlamaTokenizer",
|
||||
"unk_token": "<unk>",
|
||||
"use_default_system_prompt": false
|
||||
}
|
||||
Reference in New Issue
Block a user