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Model: Pythagoras-LM/Pythagoras-Prover-4B
Source: Original Platform

.gitattributes

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+*.pt filter=lfs diff=lfs merge=lfs -text
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+tokenizer.json filter=lfs diff=lfs merge=lfs -text

README.md

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+---
+license: apache-2.0
+base_model:
+- Qwen/Qwen3-4B
+pipeline_tag: text-generation
+library_name: transformers
+datasets:
+- Pythagoras-LM/SFT_Dataset
+---
+<div align="center">
+  <img src="https://github.com/Pythagoras-LM/Pythagoras-LM.github.io/blob/main/figures/pythagoras-without-background.png?raw=true" width="240" alt="Pythagoras-Prover logo"><br>
+  <h1>Pythagoras-Prover</h1>
+</div>
+
+<div align="center">
+  
+[![Website](https://img.shields.io/badge/%F0%9F%A4%96%20Homepage-Pythagoras-536af5?color=536af5&logoColor=white)](https://pythagoras-lm.github.io/)
+[![Paper](https://img.shields.io/badge/Paper-arXiv-b31b1b?logo=arxiv&logoColor=white)](https://arxiv.org/abs/XXXX.XXXXX)
+[![GitHub](https://img.shields.io/badge/GitHub-Code-black.svg?logo=github)](https://github.com/Pythagoras-LM/Pythagoras-Prover)
+[![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://opensource.org/licenses/Apache-2.0)
+
+</div>
+
+
+## 1. Introduction
+
+We introduce **Pythagoras-Prover**, a compute-efficient family of open-source large language models for formal theorem proving in Lean 4. The family comprises two autoregressive provers at 4B and 32B parameters, together with **Pythagoras-Prover-Diffusion**, the first diffusion-based theorem prover, which iteratively refines Lean proofs at inference time. All three models are artefacts of a single methodological approach: a scalable, Lean-verified synthetic data pipeline. At its centre is **Augmented Lean Formalisation** (ALF), a structured mutation scheme that expands a verified seed corpus into formal variants without per-instance Lean compilation, then re-uses them as a self-distillation signal during training. This design lets careful data construction stand in for raw scale, closing much of the gap between small open provers and their largest counterparts — without relying on inference-time self-correction.
+
+<div align="center">
+  <img src="https://github.com/Pythagoras-LM/Pythagoras-LM.github.io/blob/main/figures/prover_fig1_v2_hi.png?raw=true" alt="Pythagoras-Prover benchmark overview" width="90%">
+</div>
+
+
+## 2. Model Summary
+
+---
+
+**A Lean-Verified Synthetic Data Pipeline**
+
+- Natural-language problems from general-math and competition sources are autoformalised into Lean and gated on the type-checker using predominantly sub-30B open models, with an auto-informalisation and alignment step discarding faithful-but-wrong formalisations to yield a verified seed corpus partitioned into easy, medium, and hard tiers.
+- A rubric-guided distillation stage re-prompts on each rejected instance to target the specific Lean type-checker error responsible for its failure, lifting autoformalisation success and roughly doubling the verified training set.
+
+---
+
+**Model Training**
+
+- LoRA-only supervised fine-tuning of Qwen3-4B and Qwen3-32B under an 8K context, paired with a dynamic proof-reasoning filter and a difficulty-ordered easy→medium→hard curriculum, followed by reinforcement learning with a Lean-compilation reward and a final continued-SFT stage on the ALF corpus.
+
+---
+
+**Augmented Lean Formalisation**
+- ALF emits one structured variant per category — simplification, generalisation, lemma proposal, proof-step decomposition, and reformulation — for every seed statement, replacing per-instance Lean verification with a cheap statement-alignment check and expanding the seed corpus into roughly 2M formal variants.
+- The post-RL prover proves the mutations, and these self-distilled proofs form a corpus that trains both the autoregressive and diffusion provers from a single recipe.
+
+---
+
+**The Smallest Efficient Open-Source Lean Theorem Prover**
+
+- We train Pythagoras-Prover-4B, one of the smallest and most compute-efficient open-source Lean theorem provers to date, reaching 86.07% on MiniF2F-Test at Pass@32 and surpassing the prior state of the art at a fraction of its parameter count.
+- Pythagoras-Prover-Diffusion adapts a block-diffusion formulation with a tactic-based masking objective aligned to the discrete reasoning steps of Lean — to our knowledge the first demonstration that a diffusion language model can verifiably solve Lean theorems at non-trivial rates.
+
+---
+
+The resulting models set a new bar for compute-efficient formal proving. **Pythagoras-Prover-32B** achieves state-of-the-art performance among open-source provers, reaching **93.03%** on MiniF2F-Test and solving **93 of 672** problems on PutnamBench, while **Pythagoras-Prover-4B** outperforms DeepSeek-Prover-V2-671B on MiniF2F-Test despite being roughly **167× smaller** — with no self-correction or test-time reinforcement learning. We additionally release **MiniF2F-ALF**, an ALF-mutated companion benchmark on which every evaluated prover degrades.
+
+## 3. Benchmark Performance
+
+We evaluate Pythagoras-Prover on three Lean 4 benchmarks — MiniF2F-Test, PutnamBench, and the MiniF2F-ALF benchmark we introduce — under a single unified protocol (Lean 4.9.0-rc1, a 30,000-token generation limit, and a verbatim-statement pass criterion). Across all three, Pythagoras-Prover matches or exceeds open-source provers an order of magnitude larger, and does so **without** inference-time self-correction or test-time reinforcement learning.
+
+
+<div align="center">
+  <table style="margin: 0 auto;">
+    <thead>
+      <tr>
+        <th>Method</th>
+        <th>#Params</th>
+        <th>Pass@32</th>
+        <th>Pass@1024</th>
+        <th>Best (N)</th>
+      </tr>
+    </thead>
+    <tbody>
+      <tr><td>Goedel-Prover-SFT</td><td>7B</td><td>57.6</td><td>–</td><td>62.7 (3200)</td></tr>
+      <tr><td>STP</td><td>7B</td><td>–</td><td>–</td><td>67.6 (25600)</td></tr>
+      <tr><td>Kimina-Prover-Preview-72B</td><td>72B</td><td>68.85</td><td>–</td><td>80.74 (8192)</td></tr>
+      <tr><td>DeepSeek-Prover-V2-7B</td><td>7B</td><td>75.6</td><td>–</td><td>82.0 (8192)</td></tr>
+      <tr><td>DeepSeek-Prover-V2-671B</td><td>671B</td><td>82.4</td><td>–</td><td>88.9 (8192)</td></tr>
+      <tr><td>Kimina-Prover-8B-Distill</td><td>8B</td><td>77.86</td><td>–</td><td>–</td></tr>
+      <tr><td>Kimina-Prover-70B</td><td>70B</td><td>84.0</td><td>87.7</td><td>92.2 (TTRL)</td></tr>
+      <tr><td>Goedel-Prover-V2-8B</td><td>8B</td><td>84.6</td><td>87.9</td><td>90.2 (8192)</td></tr>
+      <tr><td>&nbsp;&nbsp;+ Self-Correction</td><td>8B</td><td>86.7</td><td>89.3</td><td>–</td></tr>
+      <tr><td>Goedel-Prover-V2-32B</td><td>32B</td><td>88.1</td><td>91.8</td><td>92.2 (8192)</td></tr>
+      <tr><td>&nbsp;&nbsp;+ Self-Correction</td><td>32B</td><td>90.4</td><td>92.6</td><td>–</td></tr>
+      <tr><td><strong>Pythagoras-Prover-4B</strong></td><td>4B</td><td><strong>86.07</strong></td><td><strong>88.11</strong></td><td><strong>89.75 (2048)</strong></td></tr>
+      <tr><td><strong>Pythagoras-Prover-32B</strong></td><td>32B</td><td><strong>89.75</strong></td><td><strong>92.62</strong></td><td><strong>93.03 (2048)</strong></td></tr>
+    </tbody>
+  </table>
+  <!-- table caption -->
+  <caption align="bottom"><strong>Table 1</strong>: <em>Pythagoras-Prover-4B exceeds DeepSeek-Prover-V2-671B's pass@8192 result (88.9%) at pass@2048 — a quarter of the budget and ~167× fewer parameters. Pythagoras-Prover-32B sets the strongest reported MiniF2F-Test pass rate without self-correction or test-time RL.</em></caption>
+</div>
+
+
+<br>
+
+<div align="center">
+  <table style="margin: 0 auto;">
+    <thead>
+      <tr>
+        <th>#</th>
+        <th>Model</th>
+        <th>num-solved</th>
+        <th>compute</th>
+      </tr>
+    </thead>
+    <tbody>
+      <tr><td>1</td><td><strong>Pythagoras-Prover-32B</strong></td><td><strong>93</strong></td><td><strong>Pass@2048</strong></td></tr>
+      <tr><td>1</td><td><strong>Pythagoras-Prover-32B</strong></td><td><strong>59</strong></td><td><strong>Pass@64</strong></td></tr>
+      <tr><td>1</td><td><strong>Pythagoras-Prover-32B</strong></td><td><strong>48</strong></td><td><strong>Pass@32</strong></td></tr>
+      <tr><td>2</td><td>Goedel-Prover-V2-32B (self-correction mode)</td><td>86</td><td>Pass@184</td></tr>
+      <tr><td>2</td><td>Goedel-Prover-V2-32B (self-correction mode)</td><td>57</td><td>Pass@32</td></tr>
+      <tr><td>2</td><td>Goedel-Prover-V2-32B</td><td>43</td><td>Pass@32</td></tr>
+      <tr><td>3</td><td>DeepSeek-Prover-V2-671B</td><td>47</td><td>Pass@1024</td></tr>
+      <tr><td>3</td><td>DeepSeek-Prover-V2-671B</td><td>22</td><td>Pass@32</td></tr>
+      <tr><td>4</td><td>DSP+</td><td>23</td><td>Pass@128</td></tr>
+      <tr><td>5</td><td>Bourbaki</td><td>14</td><td>Pass@512</td></tr>
+      <tr><td>6</td><td>Kimina-Prover-7B-Distill</td><td>10</td><td>Pass@192</td></tr>
+      <tr><td>7</td><td>Self-play Theorem Prover</td><td>8</td><td>Pass@3200</td></tr>
+      <tr><td>8</td><td>Goedel-Prover-SFT</td><td>7</td><td>Pass@512</td></tr>
+      <tr><td>9</td><td>ABEL (closed-source)</td><td>7</td><td>Pass@596</td></tr>
+    </tbody>
+  </table>
+  <!-- table caption -->
+  <caption align="bottom"><strong>Table 2</strong>: <em>PutnamBench leaderboard (problems solved out of 657). Pythagoras-Prover-32B takes the top rank, solving 93 problems at Pass@2048 — 7 more than the previous best (Goedel-Prover-V2-32B, 86 at Pass@184 in self-correction mode) and nearly double DeepSeek-Prover-V2-671B's 47 at Pass@1024, despite being roughly 20× smaller. Seed-Prover (331 solved) is omitted from the ranked rows as it is closed-source with undisclosed test-time compute.</em></caption>
+</div>
+
+<br>
+
+<div align="center">
+  <table style="margin: 0 auto;">
+    <thead>
+      <tr>
+        <th>Model</th>
+        <th>Pass@32</th>
+      </tr>
+    </thead>
+    <tbody>
+      <tr><td>DeepSeek-Prover-V2-671B</td><td>79.71</td></tr>
+      <tr><td>Goedel-Prover-V2-8B</td><td>82.58</td></tr>
+      <tr><td>Goedel-Prover-V2-32B</td><td>83.61</td></tr>
+      <tr><td><strong>Pythagoras-Prover-4B</strong></td><td><strong>83.19</strong></td></tr>
+      <tr><td><strong>Pythagoras-Prover-32B</strong></td><td><strong>85.04</strong></td></tr>
+    </tbody>
+  </table>
+  <!-- table caption -->
+  <caption align="bottom"><strong>Table 3</strong>: <em>Performance of current state-of-the-art provers on MiniF2F-ALF (Pass@32, %). As MiniF2F-ALF is introduced in this work, all results are evaluated by us under a unified setup.</em></caption>
+</div>
+
+## 4. Model & Dataset Downloads
+
+We release our Pythagoras-Prover models, the training dataset and the new MiniF2F-ALF benchmark for future future research.
+
+<div align="center">
+  
+| Model | Download |
+| -------- | -------- |
+|    Pythagoras-Prover-32B    |   Coming Soon   |
+|    Pythagoras-Prover-4B    |   [🤗Download](https://huggingface.co/Pythagoras-LM/Pythagoras-Prover-4B)    |
+|    Pythagoras-Prover-Diffusion-4B    |   [🤗Download](https://huggingface.co/Pythagoras-LM/Pythagoras-Prover-Diffusion-4B)   |
+
+</div>
+
+
+<div align="center">
+
+| Dataset | Download |
+| -------- | -------- |
+|   Pythagoras-Prover-SFT    |   [🤗Download](https://huggingface.co/datasets/Pythagoras-LM/SFT_Dataset)   |
+|   Pythagoras-Prover-Distill-4B    |   Coming Soon    |
+|    Pythagoras-Prover-Distill-32B    |   Coming Soon    |
+</div>
+
+## 5. Quick Start
+
+For model inference., <a href="https://github.com/huggingface/transformers" target="_blank" rel="noopener">Huggingface's Transformers</a> can directly be used
+
+```python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+import torch
+
+model_id = "Pythagoras-LM/Pythagoras-Prover-4B"
+tokenizer = AutoTokenizer.from_pretrained(model_id)
+model = AutoModelForCausalLM.from_pretrained(
+    model_id,
+    torch_dtype=torch.bfloat16,
+    device_map="auto",
+)
+
+formal_statement = """
+import Mathlib
+import Aesop
+
+set_option maxHeartbeats 0
+
+open BigOperators Real Nat Topology Rat
+
+/-- The volume of a cone is given by the formula $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume? Show that it is 65.-/
+theorem mathd_algebra_478 (b h v : ℝ) (h₀ : 0 < b ∧ 0 < h ∧ 0 < v) (h₁ : v = 1 / 3 * (b * h))
+(h₂ : b = 30) (h₃ : h = 13 / 2) : v = 65 := by
+  sorry
+""".strip()
+
+prompt = """
+Complete the following Lean 4 code:
+
+```lean4
+{}```
+
+Before producing the Lean 4 code to formally prove the given theorem, provide a detailed proof plan outlining the main proof steps and strategies.
+The plan should highlight key ideas, intermediate lemmas, and proof structures that will guide the construction of the final formal proof.
+""".strip()
+
+chat = [
+  {"role": "user", "content": prompt.format(formal_statement)},
+]
+
+model = AutoModelForCausalLM.from_pretrained(model_id, device_map="auto", torch_dtype=torch.bfloat16, trust_remote_code=True)
+inputs = tokenizer.apply_chat_template(chat, tokenize=True, add_generation_prompt=True, return_tensors="pt").to(model.device)
+
+import time
+start = time.time()
+outputs = model.generate(inputs, max_new_tokens=8192)
+print(tokenizer.batch_decode(outputs))
+print(time.time() - start)
+```
+
+# Cite
+```
+@article{leang2026pythagoras,
+  title={Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation},
+  author={Leang, Joshua Ong Jun and Zhao, Zheng and Stoian, Mihaela Catalina and Xu, Qiyuan and Li, Haonan and Li, Wenda and Cohen, Shay B. and Giunchiglia, Eleonora},
+  journal={arXiv preprint arXiv:2606.12594},
+  year={2026}
+}
+```

added_tokens.json

@@ -0,0 +1,28 @@
+{
+  "</think>": 151668,
+  "</tool_call>": 151658,
+  "</tool_response>": 151666,
+  "<think>": 151667,
+  "<tool_call>": 151657,
+  "<tool_response>": 151665,
+  "<|box_end|>": 151649,
+  "<|box_start|>": 151648,
+  "<|endoftext|>": 151643,
+  "<|file_sep|>": 151664,
+  "<|fim_middle|>": 151660,
+  "<|fim_pad|>": 151662,
+  "<|fim_prefix|>": 151659,
+  "<|fim_suffix|>": 151661,
+  "<|im_end|>": 151645,
+  "<|im_start|>": 151644,
+  "<|image_pad|>": 151655,
+  "<|object_ref_end|>": 151647,
+  "<|object_ref_start|>": 151646,
+  "<|quad_end|>": 151651,
+  "<|quad_start|>": 151650,
+  "<|repo_name|>": 151663,
+  "<|video_pad|>": 151656,
+  "<|vision_end|>": 151653,
+  "<|vision_pad|>": 151654,
+  "<|vision_start|>": 151652
+}

chat_template.jinja

@@ -0,0 +1,89 @@
+{%- if tools %}
+    {{- '<|im_start|>system\n' }}
+    {%- if messages[0].role == 'system' %}
+        {{- messages[0].content + '\n\n' }}
+    {%- endif %}
+    {{- "# 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>" }}
+    {%- for tool in tools %}
+        {{- "\n" }}
+        {{- tool | tojson }}
+    {%- endfor %}
+    {{- "\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" }}
+{%- else %}
+    {%- if messages[0].role == 'system' %}
+        {{- '<|im_start|>system\n' + messages[0].content + '<|im_end|>\n' }}
+    {%- endif %}
+{%- endif %}
+{%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
+{%- for message in messages[::-1] %}
+    {%- set index = (messages|length - 1) - loop.index0 %}
+    {%- 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>')) %}
+        {%- set ns.multi_step_tool = false %}
+        {%- set ns.last_query_index = index %}
+    {%- endif %}
+{%- 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) %}
+        {{- '<|im_start|>' + message.role + '\n' + content + '<|im_end|>' + '\n' }}
+    {%- elif message.role == "assistant" %}
+        {%- set reasoning_content = '' %}
+        {%- if message.reasoning_content is string %}
+            {%- set reasoning_content = message.reasoning_content %}
+        {%- 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 %}

config.json

@@ -0,0 +1,68 @@
+{
+  "architectures": [
+    "Qwen3ForCausalLM"
+  ],
+  "attention_bias": false,
+  "attention_dropout": 0.0,
+  "dtype": "bfloat16",
+  "eos_token_id": 151645,
+  "head_dim": 128,
+  "hidden_act": "silu",
+  "hidden_size": 2560,
+  "initializer_range": 0.02,
+  "intermediate_size": 9728,
+  "layer_types": [
+    "full_attention",
+    "full_attention",
+    "full_attention",
+    "full_attention",
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tokenizer_config.json

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