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Model: hkust-nlp/dart-math-llama3-8b-uniform
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README.md

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+---
+language:
+- en
+license: llama3
+library_name: transformers
+tags:
+- mathematics
+datasets:
+- hkust-nlp/dart-math-uniform
+metrics:
+- accuracy
+pipeline_tag: text-generation
+base_model: meta-llama/Meta-Llama-3-8B
+model-index:
+  - name: dart-math-llama3-8b-uniform
+    results:
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: hendrycks/competition_math
+          name: MATH
+          split: test
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 45.3
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: openai/gsm8k
+          name: GSM8K
+          config: main
+          split: test
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 82.5
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: college-math
+          name: CollegeMath
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 27.1
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: deepmind-mathematics
+          name: DeepMind-Mathematics
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 48.2
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: Hothan/OlympiadBench
+          name: OlympiadBench-OE_TO_maths_en_COMP
+          config: OE_TO_maths_en_COMP
+          split: train
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 13.6
+      - task:
+          type: text-generation
+          name: Mathematical Problem-Solving
+        dataset:
+          type: TIGER-Lab/TheoremQA
+          name: TheoremQA
+          split: test
+        metrics:
+          - type: accuracy
+            name: Pass@1 (0-shot CoT)
+            value: 15.4
+---
+
+# DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
+
+📝 [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)
+
+🐦 [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)
+
+## Models: `DART-Math`
+
+`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**.
+
+| 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 |
+| :----------------------------------------------------------------------------------------------------- | -----------------------------------------------------------------: | ---------------------------------------------: | -----------------------------------------------------------------------------------------------------------: | -----------------------------------------------------------------------------------------------: | ------------------------------------------------------------------------------------------------------------------: | -----------------------------------------------------------------------------------------: | -------: |
+| 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) |                                                                                               -- |                                                                                                                  -- |                                                                                         -- |       -- |
+| Llama-3-70B-MetaMath                                                                                   |                                                               44.9 |                                           88.0 |                                                                                                         31.9 |                                                                                             53.2 |                                                                                                                11.6 |                                                                                       21.9 |     41.9 |
+| [`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 |
+| [`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** |
+| DeepSeekMath-7B-MetaMath                                                                               |                                                               43.7 |                                           81.8 |                                                                                                         33.7 |                                                                                             53.0 |                                                                                                                13.6 |                                                                                       23.2 |     41.5 |
+| [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 |
+| [`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 |
+| [`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** |
+| Mistral-7B-MetaMath                                                                                    |                                                               29.8 |                                           76.5 |                                                                                                         19.3 |                                                                                             28.0 |                                                                                                                 5.9 |                                                                                       14.0 |     28.9 |
+| [`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 |
+| [`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** |
+| Llama-3-8B-MetaMath                                                                                    |                                                               32.5 |                                           77.3 |                                                                                                         20.6 |                                                                                             35.0 |                                                                                                                 5.5 |                                                                                       13.8 |     30.8 |
+| [`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 |
+| [`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** |
+
+***Abbreviations**: College (CollegeMath), DM (DeepMind Mathematics), Olympiad (OlympiadBench-Math), Theorem (TheoremQA).
+**Bold** means the best score by SFT on the respective base model here.
+To reproduce our results, please refer to [the `DART-Math` GitHub repository](https://github.com/hkust-nlp/dart-math).*
+
+## Prompt Template
+
+All the `DART-Math` models use the [Alpaca](https://github.com/tatsu-lab/stanford_alpaca) prompt template:
+
+```
+
+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
+
+```
+
+## Training Dataset
+
+We construct our traning datasets by applying **Difficulty-Aware Rejection Sampling** (`DARS`) to the **MATH and GSM8K** training sets.
+
+`DARS` tackle **severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries**, in previous datasets.
+
+These biases are primarily caused by vanilla rejection sampling, where **the same number of responses is
+sampled for each query**, yet the likelihood of obtaining correct responses for difficult queries is significantly lower, sometimes even zero.
+
+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.
+
+## Training Setup
+
+We perform standard instruction tuning to several base models including Llama3-8B & Mistral-7B & Llama3-70B as representatives of general models and DeepSeekMath-
+7B as the representative of math-specialized model
+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),
+leading to `DART-Math (Prop2Diff)` & `DART-Math (Uniform)` respectively.
+
+For simplicity, we keep most hyper-parameters the same across different models and datasets:
+
+- Model max length (of [packed](https://github.com/MeetKai/functionary/tree/main/functionary/train/packing) sequence): 4096
+- Batch size: 64
+- Warm-up ratio: 0.03
+- Learning rate scheduler: cosine
+- Prompt template: [Alpaca](https://github.com/tatsu-lab/stanford_alpaca)
+
+Several other key hyper-parameters are tuned as follow:
+
+| Base Model      | Max. L.R. | # of Epochs | # of Grad. Acc. Steps | # of A100 GPUs |
+|:--------------- | ---------:| -----------:| ---------------------:| --------------:|
+| Mistral-7B      |    `1e-5` |           3 |                     1 |              8 |
+| Llama3-8B       |    `5e-5` |           1 |                     2 |              8 |
+| Llama3-70B      |    `2e-5` |           1 |                     1 |             32 |
+| DeepSeekMath-7B |    `5e-5` |           3 |                     1 |              8 |
+
+- 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).
+- For **Llama3** models, preliminary experiments indicate that **training for 1 epoch consistently outperforms 3 epochs**.
+
+Please refer to [Appendix A.1 of our paper](https://tongyx361.github.io/assets/dart-math/paper-dart-math.pdf) for more details.
+
+## Other Details
+
+- 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.)
+
+## Citation
+
+If you find our data, model or code useful for your work, please kindly cite [our paper](https://arxiv.org/abs/2407.13690):
+
+```latex
+@article{tong2024dartmath,
+  title={DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving},
+  author={Yuxuan Tong and Xiwen Zhang and Rui Wang and Ruidong Wu and Junxian He},
+  year={2024},
+  eprint={2407.13690},
+  archivePrefix={arXiv},
+  primaryClass={cs.CL},
+  url={https://arxiv.org/abs/2407.13690},
+}
+```

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+    "model.layers.8.self_attn.o_proj.weight": "model-00001-of-00004.safetensors",
+    "model.layers.8.self_attn.q_proj.weight": "model-00001-of-00004.safetensors",
+    "model.layers.8.self_attn.v_proj.weight": "model-00001-of-00004.safetensors",
+    "model.layers.9.input_layernorm.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.mlp.down_proj.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.mlp.gate_proj.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.mlp.up_proj.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.post_attention_layernorm.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.self_attn.k_proj.weight": "model-00002-of-00004.safetensors",
+    "model.layers.9.self_attn.o_proj.weight": "model-00002-of-00004.safetensors",
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+    "model.layers.9.self_attn.v_proj.weight": "model-00002-of-00004.safetensors",
+    "model.norm.weight": "model-00004-of-00004.safetensors"
+  }
+}

special_tokens_map.json

@@ -0,0 +1,30 @@
+{
+  "bos_token": {
+    "content": "<|begin_of_text|>",
+    "lstrip": false,
+    "normalized": false,
+    "rstrip": false,
+    "single_word": false
+  },
+  "eos_token": {
+    "content": "<|end_of_text|>",
+    "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
+  }
+}