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Model: Edmon02/mathphd-plus-plus-0.5b 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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pipeline_tag: text-generation
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tags:
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- math
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- reasoning
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- chain-of-thought
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- qwen2
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- conversational
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- rlvr
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base_model: Qwen/Qwen2.5-0.5B-Instruct
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---
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# MathPhD++ 0.5B
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**MathPhD++** is a small (≈0.5B parameter) language model fine-tuned for **mathematical reasoning** in natural language. It is built on [Qwen2.5-0.5B-Instruct](https://huggingface.co/Qwen/Qwen2.5-0.5B-Instruct) and trained with the **MathPhD++** open-source pipeline (see linked code repository in your Hub “Model sources” if you publish it): supervised fine-tuning (SFT) on curated math instruction data with structured `<thinking>` / `<answer>` (and related) tags, optional process reward modeling (PRM), and reinforcement learning from verifiable rewards (GRPO) using SymPy-backed correctness checks.
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This Hub release is intended as a **reproducible checkpoint** for research and experimentation on math LLMs at the edge of what fits comfortably on a single consumer or Colab GPU.
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## Model summary
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| Attribute | Value |
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|-----------|--------|
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| **Architecture** | Qwen2 (causal LM), ~0.5B parameters |
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| **Precision** | FP16 (typical Hub export) |
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| **Chat format** | ChatML (`<|im_start|>` / `<|im_end|>`) — prefer `tokenizer.apply_chat_template` when available |
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| **Primary use** | Step-by-step math word problems, competition-style reasoning (informal proofs / chain-of-thought) |
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| **Developed by** | Edmon (Edmon02) — community research project |
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| **Finetuned from** | `Qwen/Qwen2.5-0.5B-Instruct` |
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## Training data (high level)
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SFT mixes multiple public sources (non-exhaustive; see project config for exact caps):
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- MetaMath-style QA
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- Competition MATH (train)
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- GSM8K (train)
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- OpenMathInstruct-2 (subset)
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- NuminaMath-CoT (subset)
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Examples are formatted in **ChatML** with structured assistant outputs (reasoning blocks and final answers) to encourage verifiable extraction and consistent formatting for downstream RL.
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## Evaluation (reported from project notebook run)
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Results below are **indicative** and used a **200-sample** cap per benchmark (`QUICK_TEST`-style eval). For publication-quality numbers, run full GSM8K test (1,319) and a standard MATH split with fixed protocol.
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| Benchmark | Subset / protocol | Accuracy |
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|-----------|-------------------|----------|
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| GSM8K | 200 / test | **18.5%** (37/200) |
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| MATH | 200 / MATH-500 | **6.0%** (12/200) |
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These scores reflect the **SFT-loaded** policy evaluated after the pipeline fix that loads fine-tuned weights from checkpoint storage (not the raw base model). A 0.5B model remains **capacity-limited** on MATH; GSM8K is the more informative “did SFT help?” signal at this scale.
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## How to use
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### Transformers (generate)
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```python
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from transformers import AutoModelForCausalLM, AutoTokenizer
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import torch
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model_id = "Edmon02/mathphd-plus-plus-0.5b"
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tokenizer = AutoTokenizer.from_pretrained(model_id, trust_remote_code=True)
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model = AutoModelForCausalLM.from_pretrained(
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model_id,
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torch_dtype=torch.float16,
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device_map="auto",
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trust_remote_code=True,
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)
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problem = "What is the sum of the first 100 positive integers?"
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prompt = (
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"<|im_start|>system\nYou are MathPhD++, an advanced mathematical reasoning assistant. "
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"Show your complete reasoning step-by-step.<|im_end|>\n"
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f"<|im_start|>user\n{problem}<|im_end|>\n"
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"<|im_start|>assistant\n"
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)
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inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
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outputs = model.generate(
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**inputs,
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max_new_tokens=512,
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do_sample=False,
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pad_token_id=tokenizer.pad_token_id,
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)
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print(tokenizer.decode(outputs[0][inputs["input_ids"].shape[1]:], skip_special_tokens=True))
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```
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Use **greedy or low temperature** for benchmarking; use sampling for exploratory interaction.
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## Limitations
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- **Small model:** Will underperform larger instruction models on hard competition math and long proofs.
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- **Informal reasoning:** Outputs are not formally verified unless you pair the model with an external proof checker or code execution sandbox.
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- **Data contamination:** Public math benchmarks overlap train/eval sources; treat leaderboard-style claims with care unless you hold out data strictly.
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- **Language:** Primarily English math text; mixed-language or non-math prompts are out of distribution.
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## Bias, safety, and responsible use
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This model inherits behaviors and limitations of the base Qwen2.5 model and the fine-tuning corpora. It may produce confident but incorrect mathematics. **Do not** use as a sole authority for safety-critical, financial, medical, or legal reasoning. Prefer human review and independent verification.
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## Environmental note
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If your Hub UI shows an unrelated arXiv paper (e.g. carbon footprint of ML), that is often an **automatic metadata artifact**. This model card is the authoritative description; consider removing incorrect `arxiv:` tags under model settings.
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## Links
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- **Checkpoints / artifacts (author):** [Google Drive — mathphd_checkpoints](https://drive.google.com/drive/folders/14T6zF9B_Zh0JbKUW2nFEWz7QrYtW_r85?usp=sharing) (SFT, PRM, GRPO, eval exports — access as permitted by owner)
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- **Base model:** [Qwen/Qwen2.5-0.5B-Instruct](https://huggingface.co/Qwen/Qwen2.5-0.5B-Instruct)
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## Citation
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If you use this model, cite the base model and this Hub repository as appropriate:
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```bibtex
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@misc{mathphd_plus_plus_05b,
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title = {MathPhD++ 0.5B: Math Reasoning Model (Qwen2.5-0.5B-Instruct fine-tune)},
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author = {Edmon02},
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year = {2026},
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howpublished = {\url{https://huggingface.co/Edmon02/mathphd-plus-plus-0.5b}},
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}
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```
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---
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*Model card written for professional Hub documentation. Update the GitHub URL and evaluation table when you publish full-benchmark runs.*
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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'] }}
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{%- else %}
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{{- 'You are Qwen, created by Alibaba Cloud. You are a helpful assistant.' }}
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{%- endif %}
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{{- "\n\n# 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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{%- else %}
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{{- '<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n' }}
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{%- endif %}
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{%- endif %}
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{%- for message in messages %}
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{%- if (message.role == "user") or (message.role == "system" and not loop.first) or (message.role == "assistant" and not message.tool_calls) %}
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{{- '<|im_start|>' + message.role + '\n' + message.content + '<|im_end|>' + '\n' }}
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{%- elif message.role == "assistant" %}
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{{- '<|im_start|>' + message.role }}
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{%- if message.content %}
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{{- '\n' + message.content }}
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{%- endif %}
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{%- for tool_call in message.tool_calls %}
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{%- if tool_call.function is defined %}
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{%- set tool_call = tool_call.function %}
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{%- endif %}
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{{- '\n<tool_call>\n{"name": "' }}
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{{- tool_call.name }}
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{{- '", "arguments": ' }}
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{{- tool_call.arguments | tojson }}
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{{- '}\n</tool_call>' }}
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{%- endfor %}
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{{- '<|im_end|>\n' }}
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{%- elif message.role == "tool" %}
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{%- if (loop.index0 == 0) or (messages[loop.index0 - 1].role != "tool") %}
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{{- '<|im_start|>user' }}
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{%- endif %}
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{{- '\n<tool_response>\n' }}
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{{- message.content }}
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{{- '\n</tool_response>' }}
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{%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
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{{- '<|im_end|>\n' }}
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{%- endif %}
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{%- endif %}
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{%- endfor %}
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{%- if add_generation_prompt %}
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{{- '<|im_start|>assistant\n' }}
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{%- endif %}
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config.json
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{
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"architectures": [
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"Qwen2ForCausalLM"
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],
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"attention_dropout": 0.0,
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"bos_token_id": 151643,
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"dtype": "float16",
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"eos_token_id": 151643,
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"hidden_act": "silu",
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"hidden_size": 896,
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"layer_types": [
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],
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"max_position_embeddings": 32768,
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"max_window_layers": 24,
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"model_type": "qwen2",
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"num_attention_heads": 14,
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"num_hidden_layers": 24,
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"num_key_value_heads": 2,
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"pad_token_id": null,
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"rms_norm_eps": 1e-06,
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"rope_parameters": {
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"rope_theta": 1000000.0,
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"rope_type": "default"
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"tie_word_embeddings": true,
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"transformers_version": "5.0.0",
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"use_cache": false,
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"use_mrope": false,
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"use_sliding_window": false,
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"vocab_size": 151936
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}
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generation_config.json
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{
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"bos_token_id": 151643,
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"do_sample": false,
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"max_new_tokens": 2048,
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"transformers_version": "5.0.0"
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}
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version https://git-lfs.github.com/spec/v1
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size 988097536
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tokenizer.json
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tokenizer.json
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version https://git-lfs.github.com/spec/v1
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oid sha256:a501836e7763df4123916b7ccab3f8be29c5afb8616bb5487aa741f1778a3019
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size 11424878
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tokenizer_config.json
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{
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"add_prefix_space": false,
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"backend": "tokenizers",
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"bos_token": null,
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"clean_up_tokenization_spaces": false,
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"eos_token": "<|im_end|>",
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"errors": "replace",
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"extra_special_tokens": [
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"<theorem>",
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"<proof>",
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"<definition>",
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"</definition>",
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"<lemma>",
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"</lemma>",
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"<thinking>",
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"</thinking>",
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"<answer>",
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"</answer>",
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"<verification>",
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"</verification>",
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"<step>",
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"</step>"
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],
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"is_local": false,
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"model_max_length": 131072,
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"pad_token": "<|endoftext|>",
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"padding_side": "right",
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"split_special_tokens": false,
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"tokenizer_class": "Qwen2Tokenizer",
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"unk_token": null
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}
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