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Model: uw-math-ai/gAPRIL-wo-exp Source: Original Platform
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190
README.md
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README.md
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---
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license: apache-2.0
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datasets:
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- uw-math-ai/APRIL
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tags:
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- lean4
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base_model:
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- Goedel-LM/Goedel-Prover-V2-8B
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pipeline_tag: text-generation
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library_name: transformers
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---
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# APRIL-Goedel-8B: Lean Proof Repair (Repair Only)
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This model is a LoRA finetune of [Goedel-Prover-V2-8B](https://huggingface.co/Goedel-LM/Goedel-Prover-V2-8B) on the [APRIL](https://huggingface.co/datasets/uw-math-ai/APRIL) dataset for **Lean 4 proof repair without explanation supervision**. Given an erroneous Lean proof and compiler feedback, the model directly produces a corrected proof. This variant maximizes single-shot repair accuracy by training exclusively on the repair objective.
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## Model Details
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- **Base model:** Goedel-Prover-V2-8B
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- **Method:** Supervised finetuning with LoRA (rank 32, α = 64)
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- **Training data:** APRIL — 260K paired erroneous/correct Lean proofs with compiler diagnostics (explanations excluded from supervision)
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- **Task:** Proof repair only
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- **Lean version:** 4.22.0-rc4
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## Results
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Single-shot proof repair accuracy (pass@1) on the APRIL test set (1,835 examples), evaluated by Lean compilation:
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| Error Type | This Model (w/o exp) | With Explanations | Base Goedel-8B | Goedel-32B |
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|---|---|---|---|---|
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| **Full** | **36.7%** | 34.6% | 15.5% | 26.8% |
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| Tactic | **48.5%** | 41.7% | 19.6% | 34.2% |
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| Line | **25.5%** | 18.5% | 20.0% | 28.5% |
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| Theorem | **37.5%** | 36.8% | 12.7% | 23.0% |
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| Multi-Line | **24.3%** | 20.8% | 19.4% | 32.6% |
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Training exclusively for repair (without explanation supervision) yields the highest pass@1 accuracy, gaining ~2% over the joint variant. However, this model does not produce human-interpretable diagnostics. See the [with-explanation variant](https://huggingface.co/uw-math-ai/gAPRIL-w-exp) for the trade-off discussion.
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## Model & Dataset Download
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| Resource | Description | Link |
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|---|---|---|
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| **APRIL Dataset** | 260K Lean proof-repair tuples with compiler diagnostics and explanations | [uw-math-ai/APRIL](https://huggingface.co/datasets/uw-math-ai/APRIL) |
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| **gAPRIL-w-exp** | Goedel-8B finetuned on APRIL with joint explanation supervision | [uw-math-ai/gAPRIL-w-exp](https://huggingface.co/uw-math-ai/gAPRIL-w-exp) |
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| **gAPRIL-wo-exp** | Goedel-8B finetuned on APRIL for repair only (no explanations) | [uw-math-ai/gAPRIL-wo-exp](https://huggingface.co/uw-math-ai/gAPRIL-wo-exp) |
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## Usage
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The model expects a chat-formatted prompt with the erroneous proof, goal state, error line, and compiler error message. The assistant response contains the corrected proof in a `lean` code block.
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**System:** `You are diagnosing a single failing proof`
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**User:**
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```
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Explain the error, suggest a fix, and provide the corrected proof based on the context:
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Incorrect Proof: <erroneous proof>
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State: <goal state before error from InfoView>
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Line at error: <error-occurred line of code>
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Lean error: <error messages from InfoView>
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```
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**Assistant** (model output):
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```
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Explanation: <explanation of error cause>
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Fix: <code manipulation fix suggestion>
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Corrected Proof: <corrected proof>
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```
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### Example Inference
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````python
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import re
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from transformers import AutoModelForCausalLM, AutoTokenizer
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import torch
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torch.manual_seed(42)
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def extract_proof_from_text(output):
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lean_codes = re.findall(r"```lean\s*(.*?)\s*```", output, re.DOTALL)
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if not lean_codes or len(lean_codes) == 0:
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lean_codes = re.findall(r"```lean4\s*(.*?)\s*```", output, re.DOTALL)
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words = ["by", ":="]
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for i in range(len(lean_codes)):
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lean_code = lean_codes[-i - 1]
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if all(word in lean_code for word in words):
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return lean_code
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return None
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model_id = "uw-math-ai/gAPRIL-wo-exp"
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tokenizer = AutoTokenizer.from_pretrained(model_id)
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model = AutoModelForCausalLM.from_pretrained(
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model_id, device_map="auto", torch_dtype=torch.bfloat16, trust_remote_code=True
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)
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system_prompt = (
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"You are a Lean 4 programmer diagnosing a single failing proof. "
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"Assume you only see the incorrect proof text, the infoview state"
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" near the failure, and Lean's error message."
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)
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# Context information for the incorrect proof
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incorrect_proof = """
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theorem lean_problem : IsLeast {x : ℕ | x > 0 ∧ (7 * x) % 100 = 29} 47 := by
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constructor
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· constructor
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· norm_num
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· norm_num
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· intro x ⟨hx_pos, hx_cong⟩
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by_contra h
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push_neg at h
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obtain ⟨h_le, h_ne⟩ := lt_iff_le_and_ne.mp h
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have h_lt := h_le
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revert x hx_pos hx_cong h_lt
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refine' Nat.le_induction _ _ 47 _ <;> intros x hx_lt hx_pos hx_cong
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· rfl
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· have : x < 47 := by omega
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interval_cases x
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all_goals try { norm_num at hx_cong; norm_num }
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""".strip()
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infoview_state = (
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"case right.intro.refine'_4 ⊢ ∀ (n : ℕ), sorry ≤ n → "
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"(∀ ⦃x : ℕ⦄, x > 0 → 7 * x % 100 = 29 → x < n → x ≤ n → x ≠ n → x ≤ n → False) → "
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"∀ ⦃x : ℕ⦄, x > 0 → 7 * x % 100 = 29 → x < n + 1 → x ≤ n + 1 → x ≠ n + 1 → x ≤ n + 1 → False"
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)
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line_at_error = "refine' Nat.le_induction _ _ 47 _ <;> intros x hx_lt hx_pos hx_cong"
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error_message = (
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"tactic 'introN' failed, insufficient number of binders\n"
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"case right.intro.refine'_1\n⊢ ℕ"
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)
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user_prompt = f"""
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**Instruction:** Provide the full corrected Lean 4 theorem/proof in a single ```lean``` code block.
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**Context:**
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Incorrect proof:
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```lean
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{incorrect_proof}
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```
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Infoview state:
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{infoview_state}
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Line at error:
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{line_at_error}
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Lean error:
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{error_message}
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""".strip()
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chat = [
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{"role": "system", "content": system_prompt},
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{"role": "user", "content": user_prompt},
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]
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inputs = tokenizer.apply_chat_template(
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chat, tokenize=True, add_generation_prompt=True, return_tensors="pt"
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).to(model.device)
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outputs = model.generate(inputs, max_new_tokens=8192)
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decoded_outputs = tokenizer.batch_decode(outputs)
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proof = extract_proof_from_text(decoded_outputs[0])
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print(proof)
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````
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## Citation
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```bibtex
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@article{wang2026repairlean,
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title = {Learning to Repair Lean Proofs from Compiler Feedback},
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author = {Wang, Evan and Chess, Simon and Lee, Daniel and Ge, Siyuan and Mallavarapu, Ajit and Ilin, Vasily},
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journal= {arXiv preprint arXiv:2602.02990},
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year = {2026},
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doi = {10.48550/arXiv.2602.02990},
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url = {https://arxiv.org/abs/2602.02990}
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}
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```
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## Acknowledgements
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Work by the Math AI Lab, University of Washington. Supported by UW eScience School, UW IT (AWS credits), UW Department of Applied Mathematics (GPU access), and Nebius (LLM cloud credits).
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added_tokens.json
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added_tokens.json
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{
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"</think>": 151668,
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"</tool_call>": 151658,
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"</tool_response>": 151666,
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"<think>": 151667,
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"<tool_call>": 151657,
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"<tool_response>": 151665,
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"<|box_end|>": 151649,
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"<|box_start|>": 151648,
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"<|endoftext|>": 151643,
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"<|file_sep|>": 151664,
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"<|fim_middle|>": 151660,
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"<|fim_pad|>": 151662,
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"<|fim_prefix|>": 151659,
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"<|fim_suffix|>": 151661,
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"<|im_end|>": 151645,
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"<|im_start|>": 151644,
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"<|image_pad|>": 151655,
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"<|object_ref_end|>": 151647,
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"<|object_ref_start|>": 151646,
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"<|quad_end|>": 151651,
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"<|quad_start|>": 151650,
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"<|repo_name|>": 151663,
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"<|video_pad|>": 151656,
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"<|vision_end|>": 151653,
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"<|vision_pad|>": 151654,
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"<|vision_start|>": 151652
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}
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chat_template.jinja
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chat_template.jinja
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{%- if tools %}
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{{- '<|im_start|>system\n' }}
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{%- if messages[0].role == 'system' %}
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{{- messages[0].content + '\n\n' }}
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{%- endif %}
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{{- "# Tools\n\nYou may call one or more functions to assist with the user query.\n\nYou are provided with function signatures within <tools></tools> XML tags:\n<tools>" }}
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{%- for tool in tools %}
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{{- "\n" }}
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{{- tool | tojson }}
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{%- endfor %}
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{{- "\n</tools>\n\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\n<tool_call>\n{\"name\": <function-name>, \"arguments\": <args-json-object>}\n</tool_call><|im_end|>\n" }}
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{%- else %}
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{%- if messages[0].role == 'system' %}
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{{- '<|im_start|>system\n' + messages[0].content + '<|im_end|>\n' }}
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{%- endif %}
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{%- endif %}
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{%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
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{%- for message in messages[::-1] %}
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{%- set index = (messages|length - 1) - loop.index0 %}
|
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{%- if ns.multi_step_tool and message.role == "user" and message.content is string and not(message.content.startswith('<tool_response>') and message.content.endswith('</tool_response>')) %}
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{%- set ns.multi_step_tool = false %}
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{%- set ns.last_query_index = index %}
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{%- endif %}
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{%- endfor %}
|
||||
{%- for message in messages %}
|
||||
{%- if message.content is string %}
|
||||
{%- set content = message.content %}
|
||||
{%- else %}
|
||||
{%- set content = '' %}
|
||||
{%- endif %}
|
||||
{%- if (message.role == "user") or (message.role == "system" and not loop.first) %}
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{{- '<|im_start|>' + message.role + '\n' + content + '<|im_end|>' + '\n' }}
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{%- elif message.role == "assistant" %}
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||||
{%- set reasoning_content = '' %}
|
||||
{%- if message.reasoning_content is string %}
|
||||
{%- set reasoning_content = message.reasoning_content %}
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{%- else %}
|
||||
{%- if '</think>' in content %}
|
||||
{%- set reasoning_content = content.split('</think>')[0].rstrip('\n').split('<think>')[-1].lstrip('\n') %}
|
||||
{%- set content = content.split('</think>')[-1].lstrip('\n') %}
|
||||
{%- endif %}
|
||||
{%- endif %}
|
||||
{%- if loop.index0 > ns.last_query_index %}
|
||||
{%- if loop.last or (not loop.last and reasoning_content) %}
|
||||
{{- '<|im_start|>' + message.role + '\n<think>\n' + reasoning_content.strip('\n') + '\n</think>\n\n' + content.lstrip('\n') }}
|
||||
{%- else %}
|
||||
{{- '<|im_start|>' + message.role + '\n' + content }}
|
||||
{%- endif %}
|
||||
{%- else %}
|
||||
{{- '<|im_start|>' + message.role + '\n' + content }}
|
||||
{%- endif %}
|
||||
{%- if message.tool_calls %}
|
||||
{%- for tool_call in message.tool_calls %}
|
||||
{%- if (loop.first and content) or (not loop.first) %}
|
||||
{{- '\n' }}
|
||||
{%- endif %}
|
||||
{%- if tool_call.function %}
|
||||
{%- set tool_call = tool_call.function %}
|
||||
{%- endif %}
|
||||
{{- '<tool_call>\n{"name": "' }}
|
||||
{{- tool_call.name }}
|
||||
{{- '", "arguments": ' }}
|
||||
{%- if tool_call.arguments is string %}
|
||||
{{- tool_call.arguments }}
|
||||
{%- else %}
|
||||
{{- tool_call.arguments | tojson }}
|
||||
{%- endif %}
|
||||
{{- '}\n</tool_call>' }}
|
||||
{%- endfor %}
|
||||
{%- endif %}
|
||||
{{- '<|im_end|>\n' }}
|
||||
{%- elif message.role == "tool" %}
|
||||
{%- if loop.first or (messages[loop.index0 - 1].role != "tool") %}
|
||||
{{- '<|im_start|>user' }}
|
||||
{%- endif %}
|
||||
{{- '\n<tool_response>\n' }}
|
||||
{{- content }}
|
||||
{{- '\n</tool_response>' }}
|
||||
{%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
|
||||
{{- '<|im_end|>\n' }}
|
||||
{%- endif %}
|
||||
{%- endif %}
|
||||
{%- endfor %}
|
||||
{%- if add_generation_prompt %}
|
||||
{{- '<|im_start|>assistant\n' }}
|
||||
{%- if enable_thinking is defined and enable_thinking is false %}
|
||||
{{- '<think>\n\n</think>\n\n' }}
|
||||
{%- endif %}
|
||||
{%- endif %}
|
||||
68
config.json
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config.json
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{
|
||||
"architectures": [
|
||||
"Qwen3ForCausalLM"
|
||||
],
|
||||
"attention_bias": false,
|
||||
"attention_dropout": 0.0,
|
||||
"bos_token_id": 151643,
|
||||
"dtype": "bfloat16",
|
||||
"eos_token_id": 151645,
|
||||
"head_dim": 128,
|
||||
"hidden_act": "silu",
|
||||
"hidden_size": 4096,
|
||||
"initializer_range": 0.02,
|
||||
"intermediate_size": 12288,
|
||||
"layer_types": [
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention",
|
||||
"full_attention"
|
||||
],
|
||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"model.layers.9.self_attn.q_proj.weight": "model-00001-of-00004.safetensors",
|
||||
"model.layers.9.self_attn.v_proj.weight": "model-00001-of-00004.safetensors",
|
||||
"model.norm.weight": "model-00004-of-00004.safetensors"
|
||||
}
|
||||
}
|
||||
31
special_tokens_map.json
Normal file
31
special_tokens_map.json
Normal file
@@ -0,0 +1,31 @@
|
||||
{
|
||||
"additional_special_tokens": [
|
||||
"<|im_start|>",
|
||||
"<|im_end|>",
|
||||
"<|object_ref_start|>",
|
||||
"<|object_ref_end|>",
|
||||
"<|box_start|>",
|
||||
"<|box_end|>",
|
||||
"<|quad_start|>",
|
||||
"<|quad_end|>",
|
||||
"<|vision_start|>",
|
||||
"<|vision_end|>",
|
||||
"<|vision_pad|>",
|
||||
"<|image_pad|>",
|
||||
"<|video_pad|>"
|
||||
],
|
||||
"eos_token": {
|
||||
"content": "<|im_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
},
|
||||
"pad_token": {
|
||||
"content": "<|endoftext|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
}
|
||||
}
|
||||
BIN
tokenizer.json
(Stored with Git LFS)
Normal file
BIN
tokenizer.json
(Stored with Git LFS)
Normal file
Binary file not shown.
240
tokenizer_config.json
Normal file
240
tokenizer_config.json
Normal file
@@ -0,0 +1,240 @@
|
||||
{
|
||||
"add_bos_token": false,
|
||||
"add_prefix_space": false,
|
||||
"added_tokens_decoder": {
|
||||
"151643": {
|
||||
"content": "<|endoftext|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151644": {
|
||||
"content": "<|im_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151645": {
|
||||
"content": "<|im_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151646": {
|
||||
"content": "<|object_ref_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151647": {
|
||||
"content": "<|object_ref_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151648": {
|
||||
"content": "<|box_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151649": {
|
||||
"content": "<|box_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151650": {
|
||||
"content": "<|quad_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151651": {
|
||||
"content": "<|quad_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151652": {
|
||||
"content": "<|vision_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151653": {
|
||||
"content": "<|vision_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151654": {
|
||||
"content": "<|vision_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151655": {
|
||||
"content": "<|image_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151656": {
|
||||
"content": "<|video_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151657": {
|
||||
"content": "<tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151658": {
|
||||
"content": "</tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151659": {
|
||||
"content": "<|fim_prefix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151660": {
|
||||
"content": "<|fim_middle|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151661": {
|
||||
"content": "<|fim_suffix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151662": {
|
||||
"content": "<|fim_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151663": {
|
||||
"content": "<|repo_name|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151664": {
|
||||
"content": "<|file_sep|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151665": {
|
||||
"content": "<tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151666": {
|
||||
"content": "</tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151667": {
|
||||
"content": "<think>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151668": {
|
||||
"content": "</think>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
}
|
||||
},
|
||||
"additional_special_tokens": [
|
||||
"<|im_start|>",
|
||||
"<|im_end|>",
|
||||
"<|object_ref_start|>",
|
||||
"<|object_ref_end|>",
|
||||
"<|box_start|>",
|
||||
"<|box_end|>",
|
||||
"<|quad_start|>",
|
||||
"<|quad_end|>",
|
||||
"<|vision_start|>",
|
||||
"<|vision_end|>",
|
||||
"<|vision_pad|>",
|
||||
"<|image_pad|>",
|
||||
"<|video_pad|>"
|
||||
],
|
||||
"bos_token": null,
|
||||
"clean_up_tokenization_spaces": false,
|
||||
"eos_token": "<|im_end|>",
|
||||
"errors": "replace",
|
||||
"extra_special_tokens": {},
|
||||
"model_max_length": 131072,
|
||||
"pad_token": "<|endoftext|>",
|
||||
"padding_side": "right",
|
||||
"split_special_tokens": false,
|
||||
"tokenizer_class": "Qwen2Tokenizer",
|
||||
"unk_token": null
|
||||
}
|
||||
1
vocab.json
Normal file
1
vocab.json
Normal file
File diff suppressed because one or more lines are too long
Reference in New Issue
Block a user