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.gitattributes CHANGED
@@ -33,3 +33,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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  *.zip filter=lfs diff=lfs merge=lfs -text
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  *.zst filter=lfs diff=lfs merge=lfs -text
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  *tfevents* filter=lfs diff=lfs merge=lfs -text
 
 
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  *.zip filter=lfs diff=lfs merge=lfs -text
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  *.zst filter=lfs diff=lfs merge=lfs -text
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  *tfevents* filter=lfs diff=lfs merge=lfs -text
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+ tokenizer.json filter=lfs diff=lfs merge=lfs -text
README.md ADDED
@@ -0,0 +1,210 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ ---
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+ library_name: transformers
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+ license: apache-2.0
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+ base_model: huihui-ai/Huihui-Qwen3.6-27B-abliterated
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+ pipeline_tag: image-text-to-text
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+ tags:
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+ - qwen3.6
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+ - nvfp4
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+ - quantized
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+ - compressed-tensors
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+ - blackwell
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+ - abliterated
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+ - vlm
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+ - vision-language-model
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+ language:
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+ - en
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+ - ja
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+ - zh
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+ - multilingual
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+ quantized_by: Lna-Lab
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+ ---
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+
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+ # Huihui-Qwen3.6-27B-abliterated-NVFP4
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+
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+ NVFP4 quantized version of [huihui-ai/Huihui-Qwen3.6-27B-abliterated](https://huggingface.co/huihui-ai/Huihui-Qwen3.6-27B-abliterated) — an abliterated (uncensored) variant of Qwen3.6-27B, the dense 27B VLM with Gated DeltaNet hybrid attention.
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+
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+ Quantized to **NVIDIA FP4** by [Lna-Lab](https://huggingface.co/sakamakismile) using custom Blackwell NVFP4 GEMM kernels ([lna-lab/blackwell-geforce-nvfp4-gemm](https://github.com/lna-lab/blackwell-geforce-nvfp4-gemm)).
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+
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+ **55.6 GB → 19.7 GB** (0.35x) — vision tower preserved in BF16. Runs on a single NVIDIA Blackwell GPU.
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+
31
+ ## Key Specs
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+
33
+ | | |
34
+ |---|---|
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+ | **Base model** | [huihui-ai/Huihui-Qwen3.6-27B-abliterated](https://huggingface.co/huihui-ai/Huihui-Qwen3.6-27B-abliterated) |
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+ | **Original** | [Qwen/Qwen3.6-27B](https://huggingface.co/Qwen/Qwen3.6-27B) |
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+ | **Architecture** | Dense 27B, Gated DeltaNet + Gated Attention hybrid, VLM |
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+ | **Quantization** | NVFP4 (W4A4 — weights FP4, activations FP4, scales FP8) |
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+ | **Format** | `compressed-tensors` (native vLLM support) |
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+ | **Tool** | [vllm-project/llm-compressor](https://github.com/vllm-project/llm-compressor) + [blackwell-geforce-nvfp4-gemm](https://github.com/lna-lab/blackwell-geforce-nvfp4-gemm) |
41
+ | **Size** | 19.7 GB |
42
+ | **Requires** | NVIDIA Blackwell GPU (SM 120), vLLM >= 0.19 |
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+
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+ ## Benchmark Results
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+
46
+ Tested on a single **NVIDIA RTX PRO 6000 Blackwell** (96 GB), vLLM 0.19.1+, 128K context, FP8 KV cache.
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+
48
+ | Task | Tokens | Speed (tok/s) | Status |
49
+ |------|--------|---------------|--------|
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+ | English reasoning | 1,024 | 56.2 | PASS |
51
+ | Japanese essay (方丈記) | 2,048 | 59.7 | PASS |
52
+ | Python code generation | 2,048 | 59.1 | PASS |
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+ | Contradictory instructions | 1,500 | 59.5 | PASS |
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+ | VLM image description | 947 | 58.1 | PASS |
55
+ | Math proof (√2 irrationality) | 1,024 | 59.3 | PASS |
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+
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+ **Sustained throughput: ~58 tok/s** (single GPU, 128K context, FP8 KV cache)
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+
59
+ ### VRAM Usage
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+
61
+ | State | GPU Memory |
62
+ |-------|-----------|
63
+ | After model load | 92,142 MiB |
64
+ | Peak (during inference) | 92,150 MiB |
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+
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+ ## Quick Start — From Scratch with Docker
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+
68
+ ### 1. Pull the model
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+
70
+ ```bash
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+ hf download sakamakismile/Huihui-Qwen3.6-27B-abliterated-NVFP4 \
72
+ --local-dir /models/Huihui-Qwen3.6-27B-abliterated-NVFP4
73
+ ```
74
+
75
+ ### 2. Run with Docker (128K context + FP8 KV cache)
76
+
77
+ ```bash
78
+ docker run -d --name huihui-qwen36-27b \
79
+ --gpus '"device=0"' \
80
+ --shm-size=16g \
81
+ -v /models/Huihui-Qwen3.6-27B-abliterated-NVFP4:/models/current:ro \
82
+ -p 8000:8000 \
83
+ -e MODEL_PATH=/models/current \
84
+ -e PORT=8000 \
85
+ -e TENSOR_PARALLEL_SIZE=1 \
86
+ -e MAX_MODEL_LEN=131072 \
87
+ -e MAX_NUM_SEQS=4 \
88
+ -e GPU_MEMORY_UTILIZATION=0.95 \
89
+ -e QUANTIZATION=auto \
90
+ lna-lab/gemma4-inference:latest \
91
+ --trust-remote-code --kv-cache-dtype fp8_e4m3
92
+ ```
93
+
94
+ ### 3. Run with vLLM directly
95
+
96
+ ```bash
97
+ vllm serve /models/Huihui-Qwen3.6-27B-abliterated-NVFP4 \
98
+ --max-model-len 131072 \
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+ --gpu-memory-utilization 0.95 \
100
+ --dtype auto \
101
+ --kv-cache-dtype fp8_e4m3 \
102
+ --trust-remote-code
103
+ ```
104
+
105
+ ### 4. Test inference
106
+
107
+ ```bash
108
+ # Text
109
+ curl -s http://localhost:8000/v1/chat/completions \
110
+ -H "Content-Type: application/json" \
111
+ -d '{
112
+ "model": "Huihui-Qwen3.6-27B-abliterated-NVFP4",
113
+ "messages": [{"role": "user", "content": "Write a haiku about quantization."}],
114
+ "max_tokens": 256,
115
+ "temperature": 0.0
116
+ }'
117
+ ```
118
+
119
+ ```python
120
+ # VLM (image input)
121
+ import base64, requests
122
+ from pathlib import Path
123
+
124
+ img_b64 = base64.b64encode(Path("photo.jpg").read_bytes()).decode()
125
+ resp = requests.post("http://localhost:8000/v1/chat/completions", json={
126
+ "model": "Huihui-Qwen3.6-27B-abliterated-NVFP4",
127
+ "messages": [{"role": "user", "content": [
128
+ {"type": "image_url", "image_url": {"url": f"data:image/jpeg;base64,{img_b64}"}},
129
+ {"type": "text", "text": "Describe this image."},
130
+ ]}],
131
+ "max_tokens": 1024,
132
+ })
133
+ print(resp.json()["choices"][0]["message"]["content"])
134
+ ```
135
+
136
+ ## Quantization Details
137
+
138
+ ### Recipe
139
+
140
+ ```yaml
141
+ QuantizationModifier:
142
+ targets: [Linear]
143
+ ignore: [lm_head, 're:.*visual.*', 're:.*mlp.gate$', 're:.*mlp.shared_expert_gate$']
144
+ scheme: NVFP4
145
+ ```
146
+
147
+ ### What's Quantized / What's Not
148
+
149
+ - **Quantized (NVFP4):** All `Linear` layers in the language model
150
+ - **Kept in BF16:** `lm_head`, all vision layers (`model.visual.*`), MLP gates
151
+
152
+ ### Reproduction
153
+
154
+ ```python
155
+ from transformers import AutoProcessor, Qwen3_5ForConditionalGeneration
156
+ from llmcompressor import oneshot
157
+ from llmcompressor.modifiers.quantization import QuantizationModifier
158
+ import torch
159
+
160
+ model = Qwen3_5ForConditionalGeneration.from_pretrained(
161
+ "huihui-ai/Huihui-Qwen3.6-27B-abliterated",
162
+ torch_dtype=torch.bfloat16, trust_remote_code=True,
163
+ )
164
+ processor = AutoProcessor.from_pretrained(
165
+ "huihui-ai/Huihui-Qwen3.6-27B-abliterated", trust_remote_code=True,
166
+ )
167
+
168
+ recipe = QuantizationModifier(
169
+ targets="Linear", scheme="NVFP4",
170
+ ignore=["lm_head", "re:.*visual.*", "re:.*mlp.gate$", "re:.*mlp.shared_expert_gate$"],
171
+ )
172
+
173
+ # Calibration with neuralmagic/calibration dataset (20 samples, 8192 seq len)
174
+ # ... (see quantization script in repo)
175
+
176
+ model.save_pretrained("output-NVFP4", save_compressed=True)
177
+ processor.save_pretrained("output-NVFP4")
178
+ ```
179
+
180
+ > **Note:** After saving, verify vision tower keys use `model.visual.*` prefix (not `model.language_model.visual.*`). See [this fix](https://huggingface.co/sakamakismile/Qwen3.6-27B-NVFP4/discussions/2) for details.
181
+
182
+ ### Tested Environment
183
+
184
+ | Component | Version |
185
+ |-----------|---------|
186
+ | vLLM | 0.19.1rc1+ (nightly) |
187
+ | Transformers | 5.5.4 |
188
+ | PyTorch | 2.11.0+cu130 |
189
+ | llm-compressor | 0.1.dev5 |
190
+ | CUDA | 13.0 |
191
+ | GPU | NVIDIA RTX PRO 6000 Blackwell (96 GB) |
192
+ | OS | Ubuntu 24.04, Linux 6.17 |
193
+
194
+ ## Credits
195
+
196
+ - **Original model:** [Qwen Team](https://huggingface.co/Qwen) (Alibaba Group) — [Qwen3.6-27B](https://huggingface.co/Qwen/Qwen3.6-27B)
197
+ - **Abliteration:** [huihui-ai](https://huggingface.co/huihui-ai) — [Huihui-Qwen3.6-27B-abliterated](https://huggingface.co/huihui-ai/Huihui-Qwen3.6-27B-abliterated)
198
+ - **NVFP4 quantization & benchmarking:** [Lna-Lab](https://huggingface.co/sakamakismile)
199
+ - **Blackwell NVFP4 GEMM kernels:** [lna-lab/blackwell-geforce-nvfp4-gemm](https://github.com/lna-lab/blackwell-geforce-nvfp4-gemm)
200
+ - **Quantization framework:** [vllm-project/llm-compressor](https://github.com/vllm-project/llm-compressor)
201
+
202
+ ## Support the Base Model Authors
203
+
204
+ If you find this model useful, please consider supporting:
205
+ - **huihui-ai** (abliteration): [Ko-fi](https://ko-fi.com/huihuiai) | BTC: `bc1qqnkhuchxw0zqjh2ku3lu4hq45hc6gy84uk70ge`
206
+ - **Qwen Team** (original model): Star the [Qwen repo](https://github.com/QwenLM/Qwen3)
207
+
208
+ ## License
209
+
210
+ This model inherits the [Apache 2.0 license](https://huggingface.co/Qwen/Qwen3.6-27B/blob/main/LICENSE).
chat_template.jinja ADDED
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+ {%- set image_count = namespace(value=0) %}
2
+ {%- set video_count = namespace(value=0) %}
3
+ {%- macro render_content(content, do_vision_count, is_system_content=false) %}
4
+ {%- if content is string %}
5
+ {{- content }}
6
+ {%- elif content is iterable and content is not mapping %}
7
+ {%- for item in content %}
8
+ {%- if 'image' in item or 'image_url' in item or item.type == 'image' %}
9
+ {%- if is_system_content %}
10
+ {{- raise_exception('System message cannot contain images.') }}
11
+ {%- endif %}
12
+ {%- if do_vision_count %}
13
+ {%- set image_count.value = image_count.value + 1 %}
14
+ {%- endif %}
15
+ {%- if add_vision_id %}
16
+ {{- 'Picture ' ~ image_count.value ~ ': ' }}
17
+ {%- endif %}
18
+ {{- '<|vision_start|><|image_pad|><|vision_end|>' }}
19
+ {%- elif 'video' in item or item.type == 'video' %}
20
+ {%- if is_system_content %}
21
+ {{- raise_exception('System message cannot contain videos.') }}
22
+ {%- endif %}
23
+ {%- if do_vision_count %}
24
+ {%- set video_count.value = video_count.value + 1 %}
25
+ {%- endif %}
26
+ {%- if add_vision_id %}
27
+ {{- 'Video ' ~ video_count.value ~ ': ' }}
28
+ {%- endif %}
29
+ {{- '<|vision_start|><|video_pad|><|vision_end|>' }}
30
+ {%- elif 'text' in item %}
31
+ {{- item.text }}
32
+ {%- else %}
33
+ {{- raise_exception('Unexpected item type in content.') }}
34
+ {%- endif %}
35
+ {%- endfor %}
36
+ {%- elif content is none or content is undefined %}
37
+ {{- '' }}
38
+ {%- else %}
39
+ {{- raise_exception('Unexpected content type.') }}
40
+ {%- endif %}
41
+ {%- endmacro %}
42
+ {%- if not messages %}
43
+ {{- raise_exception('No messages provided.') }}
44
+ {%- endif %}
45
+ {%- if tools and tools is iterable and tools is not mapping %}
46
+ {{- '<|im_start|>system\n' }}
47
+ {{- "# Tools\n\nYou have access to the following functions:\n\n<tools>" }}
48
+ {%- for tool in tools %}
49
+ {{- "\n" }}
50
+ {{- tool | tojson }}
51
+ {%- endfor %}
52
+ {{- "\n</tools>" }}
53
+ {{- '\n\nIf you choose to call a function ONLY reply in the following format with NO suffix:\n\n<tool_call>\n<function=example_function_name>\n<parameter=example_parameter_1>\nvalue_1\n</parameter>\n<parameter=example_parameter_2>\nThis is the value for the second parameter\nthat can span\nmultiple lines\n</parameter>\n</function>\n</tool_call>\n\n<IMPORTANT>\nReminder:\n- Function calls MUST follow the specified format: an inner <function=...></function> block must be nested within <tool_call></tool_call> XML tags\n- Required parameters MUST be specified\n- You may provide optional reasoning for your function call in natural language BEFORE the function call, but NOT after\n- If there is no function call available, answer the question like normal with your current knowledge and do not tell the user about function calls\n</IMPORTANT>' }}
54
+ {%- if messages[0].role == 'system' %}
55
+ {%- set content = render_content(messages[0].content, false, true)|trim %}
56
+ {%- if content %}
57
+ {{- '\n\n' + content }}
58
+ {%- endif %}
59
+ {%- endif %}
60
+ {{- '<|im_end|>\n' }}
61
+ {%- else %}
62
+ {%- if messages[0].role == 'system' %}
63
+ {%- set content = render_content(messages[0].content, false, true)|trim %}
64
+ {{- '<|im_start|>system\n' + content + '<|im_end|>\n' }}
65
+ {%- endif %}
66
+ {%- endif %}
67
+ {%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
68
+ {%- for message in messages[::-1] %}
69
+ {%- set index = (messages|length - 1) - loop.index0 %}
70
+ {%- if ns.multi_step_tool and message.role == "user" %}
71
+ {%- set content = render_content(message.content, false)|trim %}
72
+ {%- if not(content.startswith('<tool_response>') and content.endswith('</tool_response>')) %}
73
+ {%- set ns.multi_step_tool = false %}
74
+ {%- set ns.last_query_index = index %}
75
+ {%- endif %}
76
+ {%- endif %}
77
+ {%- endfor %}
78
+ {%- if ns.multi_step_tool %}
79
+ {{- raise_exception('No user query found in messages.') }}
80
+ {%- endif %}
81
+ {%- for message in messages %}
82
+ {%- set content = render_content(message.content, true)|trim %}
83
+ {%- if message.role == "system" %}
84
+ {%- if not loop.first %}
85
+ {{- raise_exception('System message must be at the beginning.') }}
86
+ {%- endif %}
87
+ {%- elif message.role == "user" %}
88
+ {{- '<|im_start|>' + message.role + '\n' + content + '<|im_end|>' + '\n' }}
89
+ {%- elif message.role == "assistant" %}
90
+ {%- set reasoning_content = '' %}
91
+ {%- if message.reasoning_content is string %}
92
+ {%- set reasoning_content = message.reasoning_content %}
93
+ {%- else %}
94
+ {%- if '</think>' in content %}
95
+ {%- set reasoning_content = content.split('</think>')[0].rstrip('\n').split('<think>')[-1].lstrip('\n') %}
96
+ {%- set content = content.split('</think>')[-1].lstrip('\n') %}
97
+ {%- endif %}
98
+ {%- endif %}
99
+ {%- set reasoning_content = reasoning_content|trim %}
100
+ {%- if (preserve_thinking is defined and preserve_thinking is true) or (loop.index0 > ns.last_query_index) %}
101
+ {{- '<|im_start|>' + message.role + '\n<think>\n' + reasoning_content + '\n</think>\n\n' + content }}
102
+ {%- else %}
103
+ {{- '<|im_start|>' + message.role + '\n' + content }}
104
+ {%- endif %}
105
+ {%- if message.tool_calls and message.tool_calls is iterable and message.tool_calls is not mapping %}
106
+ {%- for tool_call in message.tool_calls %}
107
+ {%- if tool_call.function is defined %}
108
+ {%- set tool_call = tool_call.function %}
109
+ {%- endif %}
110
+ {%- if loop.first %}
111
+ {%- if content|trim %}
112
+ {{- '\n\n<tool_call>\n<function=' + tool_call.name + '>\n' }}
113
+ {%- else %}
114
+ {{- '<tool_call>\n<function=' + tool_call.name + '>\n' }}
115
+ {%- endif %}
116
+ {%- else %}
117
+ {{- '\n<tool_call>\n<function=' + tool_call.name + '>\n' }}
118
+ {%- endif %}
119
+ {%- if tool_call.arguments is defined %}
120
+ {%- for args_name, args_value in tool_call.arguments|items %}
121
+ {{- '<parameter=' + args_name + '>\n' }}
122
+ {%- set args_value = args_value | string if args_value is string else args_value | tojson | safe %}
123
+ {{- args_value }}
124
+ {{- '\n</parameter>\n' }}
125
+ {%- endfor %}
126
+ {%- endif %}
127
+ {{- '</function>\n</tool_call>' }}
128
+ {%- endfor %}
129
+ {%- endif %}
130
+ {{- '<|im_end|>\n' }}
131
+ {%- elif message.role == "tool" %}
132
+ {%- if loop.previtem and loop.previtem.role != "tool" %}
133
+ {{- '<|im_start|>user' }}
134
+ {%- endif %}
135
+ {{- '\n<tool_response>\n' }}
136
+ {{- content }}
137
+ {{- '\n</tool_response>' }}
138
+ {%- if not loop.last and loop.nextitem.role != "tool" %}
139
+ {{- '<|im_end|>\n' }}
140
+ {%- elif loop.last %}
141
+ {{- '<|im_end|>\n' }}
142
+ {%- endif %}
143
+ {%- else %}
144
+ {{- raise_exception('Unexpected message role.') }}
145
+ {%- endif %}
146
+ {%- endfor %}
147
+ {%- if add_generation_prompt %}
148
+ {{- '<|im_start|>assistant\n' }}
149
+ {%- if enable_thinking is defined and enable_thinking is false %}
150
+ {{- '<think>\n\n</think>\n\n' }}
151
+ {%- else %}
152
+ {{- '<think>\n' }}
153
+ {%- endif %}
154
+ {%- endif %}
config.json ADDED
@@ -0,0 +1,302 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "architectures": [
3
+ "Qwen3_5ForConditionalGeneration"
4
+ ],
5
+ "dtype": "bfloat16",
6
+ "image_token_id": 248056,
7
+ "language_model_only": false,
8
+ "model_type": "qwen3_5",
9
+ "quantization_config": {
10
+ "config_groups": {
11
+ "group_0": {
12
+ "format": "nvfp4-pack-quantized",
13
+ "input_activations": {
14
+ "actorder": null,
15
+ "block_structure": null,
16
+ "dynamic": "local",
17
+ "group_size": 16,
18
+ "num_bits": 4,
19
+ "observer": "static_minmax",
20
+ "observer_kwargs": {},
21
+ "scale_dtype": "torch.float8_e4m3fn",
22
+ "strategy": "tensor_group",
23
+ "symmetric": true,
24
+ "type": "float",
25
+ "zp_dtype": null
26
+ },
27
+ "output_activations": null,
28
+ "targets": [
29
+ "Linear"
30
+ ],
31
+ "weights": {
32
+ "actorder": null,
33
+ "block_structure": null,
34
+ "dynamic": false,
35
+ "group_size": 16,
36
+ "num_bits": 4,
37
+ "observer": "memoryless_minmax",
38
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+ "preview": "Here's a thinking process:\n\n1. **Understand User Request:**\n - **Topic:** P vs NP problems\n - **Requirements:** Explain the difference, provide a concrete example of each.\n\n2. **Define P and NP:**\n - **P (Polynomial Time):** The class of decision problems that can be *solved* by a deterministic Turing machine in polynomial time. In simpler terms, problems where we can find a solution efficiently (in reasonable time relative to input size).\n - **NP (Nondeterministic Polynomial Time):** ",
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+ "full": "Here's a thinking process:\n\n1. **Understand User Request:**\n - **Topic:** P vs NP problems\n - **Requirements:** Explain the difference, provide a concrete example of each.\n\n2. **Define P and NP:**\n - **P (Polynomial Time):** The class of decision problems that can be *solved* by a deterministic Turing machine in polynomial time. In simpler terms, problems where we can find a solution efficiently (in reasonable time relative to input size).\n - **NP (Nondeterministic Polynomial Time):** The class of decision problems where a *given solution* can be *verified* in polynomial time. In simpler terms, problems where checking a proposed solution is fast, but finding the solution might be hard.\n - **Key Difference:** P is about *solving* efficiently; NP is about *verifying* efficiently. All P problems are in NP (P ⊆ NP), but it's unknown if P = NP.\n\n3. **Identify Concrete Examples:**\n - **P Example:** Sorting a list of numbers, finding the shortest path in a graph (Dijkstra's algorithm), checking if a number is prime (modern algorithms), or solving a system of linear equations. Let's pick **Sorting** or **Shortest Path**. Actually, a classic P problem is **Linear Programming** or **2-SAT**. But for simplicity and clarity, **Sorting** or **Finding the shortest path** works well. Let's go with **Sorting** or **Graph Shortest Path**. Actually, a very standard P example is **Checking if a number is prime** (with modern algorithms) or **Solving a system of linear equations**. I'll use **Sorting** or **Shortest Path**. Let's pick **Finding the shortest path in a weighted graph** (Dijkstra's algorithm runs in O((V+E) log V), which is polynomial).\n - **NP Example:** **Traveling Salesperson Problem (TSP)** (decision version: \"Is there a tour of length ≤ K?\"), **Boolean Satisfiability (SAT)**, **Graph Coloring**, **Subset Sum**. I'll use **SAT** or **TSP**. TSP is very intuitive. Let's use **TSP** or **SAT**. Actually, **SAT** is the canonical NP-complete problem. I'll explain SAT or TSP. Let's go with **TSP** as it's widely known.\n\n4. **Structure the Explanation:**\n - Introduction: Define P and NP clearly.\n - Key Difference: Solving vs. Verifying.\n - P Example: Concrete problem, explain why it's in P.\n - NP Example: Concrete problem, explain why it's in NP (and typically not known to be in P).\n - Clarify P ⊆ NP and the P vs NP question.\n - Keep it concise and accurate.\n\n5. **Draft - Mental Refinement:**\n *(P Definition)*: P stands for \"Polynomial time\". It contains decision problems that can be *solved* by a deterministic algorithm in time bounded by a polynomial function of the input size (e.g., O(n²), O(n log n)).\n *(NP Definition)*: NP stands for \"Nondeterministic Polynomial time\". It contains decision problems where a *proposed solution* can be *verified* in polynomial time.\n *(Difference)*: The core difference is **solving vs. verifying**. P problems can be solved efficiently. NP problems can be verified efficiently, but finding the solution may require exponential time in the worst case.\n *(P Example)*: **Sorting a list of numbers**. Algorithms like Merge Sort or Quick Sort run in O(n log n), which is polynomial. Given a list, we can efficiently find the sorted order.\n *(NP Example)*: **Traveling Salesperson Problem (decision version)**: Given a set of cities and distances, is there a route visiting each city exactly once with total distance ≤ K? Verifying a proposed route is fast (just sum the distances and check length), but finding the optimal route is computationally hard (exponential in worst case).\n *(Clarification)*: All P problems are in NP (P ⊆ NP). Whether P = NP is one of the biggest open questions in computer science.\n\n6. **Check Accuracy & Nuance:**\n - P: Solvable in polynomial time.\n - NP: Verifiable in polynomial time.\n - Example P: Sorting is good, but technically sorting is a function problem, not a decision problem. In complexity theory, P and NP are defined for *decision problems*. I should use a decision problem for P, like **2-SAT** or **Shortest Path** or **Linear Programming**. Let's use **Shortest Path** (decision: \"Is there a path of length ≤ K?\") or **Prim"
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+ {
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+ "label": "JP hojoki",
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+ "elapsed": 34.33117723464966,
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+ "chars": 6328,
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+ "preview": "Here's a thinking process:\n\n1. **Analyze User Input:**\n - **Text:** 方丈記の冒頭「ゆく河の流れは絶えずして、しかももとの水にあらず」\n - **Tasks:** \n a. Provide a modern Japanese translation (現代語訳)\n b. Explain Kamo no Chōmei's view of impermanence (無常観) based on this opening line.\n - **Role:** Expert in Japanese classical literature (日本古典文学の専門家)\n\n2. **Deconstruct the Quote:**\n - Original: 「ゆく河の流れは絶えずして、しかももとの水にあらず」\n - Literal meaning: The flowing river never stops, yet the water is not the same as before.\n ",
20
+ "full": "Here's a thinking process:\n\n1. **Analyze User Input:**\n - **Text:** 方丈記の冒頭「ゆく河の流れは絶えずして、しかももとの水にあらず」\n - **Tasks:** \n a. Provide a modern Japanese translation (現代語訳)\n b. Explain Kamo no Chōmei's view of impermanence (無常観) based on this opening line.\n - **Role:** Expert in Japanese classical literature (日本古典文学の専門家)\n\n2. **Deconstruct the Quote:**\n - Original: 「ゆく河の流れは絶えずして、しかももとの水にあらず」\n - Literal meaning: The flowing river never stops, yet the water is not the same as before.\n - Context: This is the famous opening of *Hōjōki* (方丈記), a Heian-period diary by Kamo no Chōmei (鴨長明).\n - Key themes: Impermanence (無常), transience, Buddhist philosophy (particularly the concept of *mujō* or *mujo*), the passage of time, the illusion of permanence.\n\n3. **Task 1: Modern Japanese Translation (現代語訳)**\n - Need to translate accurately while preserving the poetic/philosophical tone.\n - Draft: 「流れる川の流れは絶えることなく続いていますが、その水はもはやかつての水ではありません。」\n - Refine for classical/modern balance: 「川の流れは絶えることなく続いていますが、その水はもはやかつての水ではありません。」 or 「流れる川は絶えず続いていますが、その水はもはや元の水ではありません。」\n - Standard accepted modern translation: 「流れる川の流れは絶えることなく続いていますが、その水はもはやかつての水ではありません。」 (This captures both the continuous flow and the changing water, reflecting the Buddhist idea of impermanence.)\n\n4. **Task 2: Explain Kamo no Chōmei's View of Impermanence (無常観)**\n - Need to connect the quote to Chōmei's philosophical stance.\n - Key points to cover:\n a. **Buddhist Context:** The quote directly reflects the Buddhist concept of *mujō* (impermanence). Everything changes; nothing stays the same.\n b. **Metaphor of the River:** The river represents time/life. The water represents individual moments/experiences. Though the flow (time/life) continues, the specific water (moments) is always different. This illustrates *shun'etsu* (刹那) and *mujō*.\n c. **Chōmei's Life Context:** He lived through the Genpei War, the fall of the Taira, the rise of the Kamakura shogunate, and the decline of the Heian court. His diary reflects a deep awareness of historical and personal transience.\n d. **Philosophical Depth:** Unlike earlier Heian literature (like *Tale of Genji* or *Murasaki Shikibu Nikki*) which often focused on emotional or aesthetic impermanence (*mono no aware*), Chōmei's view is more philosophical and Buddhist. He emphasizes the *inevitability* of change and the *illusion* of permanence.\n e. **Connection to the Quote:** The river metaphor shows that while the *form* (flow) remains, the *substance* (water) changes. This mirrors the Buddhist teaching that phenomena are in constant flux (*shun'etsu mujō*).\n f. **Literary Significance:** This opening sets the tone for the entire *Hōjōki*, which chronicles historical events through the lens of impermanence. It's a foundational text for understanding Heian-to-Kamakura transition literature.\n\n5. **Structure the Response:**\n - Start with the modern translation.\n - Then explain the impermanence view in a structured way:\n * Buddhist philosophical basis\n * Metaphorical meaning (river/water)\n * Historical/life context of Chōmei\n * Contrast with other Heian impermanence concepts (mono no aware vs. mujō)\n * Literary/historical significance\n - Maintain an expert tone, cite relevant concepts (無常, 刹那, 仏教思想, 平安末期〜鎌倉初期の時代背景).\n - Ensure accuracy and depth.\n\n Draft structure:\n - 現代語訳\n - 鴨長明の無常観の解説\n 1. 仏教思想に基づく「無常」の核心\n 2. 「河の流れ」と「水」の比喩的意味\n 3. 長明の人生と時代背景が織りなす無常観\n 4. 平安文学の「もののあはれ」との違い\n 5. 方丈記全体への示唆\n - 結論\n\n6. **Refine Content (Mental Verification):**\n - *Translation:* 「流れる川の流れは絶えることなく続いていますが、その水はもはやかつての水ではありません。」 (Accurate, standard)\n - *Buddhist concept:* Directly references the famous Buddhist metaphor (often attributed to the *Daodejing* or Buddhist texts, but in Japanese context, it's a standard mujō metaphor). Actually, the river metaphor is classic in Buddhist literature (e.g., *Shōkei* or *Genji*, but here it's Chōmei's own formulation).\n - *Chōmei's life:* Born 1155, lived through Genpei War (1180-1185), saw the fall of Taira, rise of Minamoto, establishment of Kamakura shogunate. He was a courtier who witnessed the collapse of the Heian aristocratic order. His diary reflects this historical flux.\n - *Mujō vs. Mono no aware:* Heian literature often focused on *mono no aware* (pathos of things), which is more emotional/aesthetic. Chōmei's view is more philosophical, rooted in Buddhist *mujō* (impermanence as a fundamental truth).\n - *Literary significance:* The opening sets up the entire work as a meditation on transience, framing historical events not just as records but as manifestations of impermanence.\n - Check accuracy: The quote is indeed the opening of *Hōjōki*. The metaphor is standard in Japanese classical literature. Chōmei's perspective is deeply Buddhist. All points are academically sound.\n\n7. **Draft Response (Mental to Text):**\n (Will write in formal, expert Japanese as requested)\n - Start with translation.\n - Then structured explanation.\n - Use precise terminology: 無常観, 仏教思想, 刹那, 時代背景, 文学史的位置.\n - Ensure tone matches \"専門家\" (expert).\n\n Structure in Japanese:\n 【現代語訳】\n 【鴨長明の無常観の解説】\n 1. 仏教思想に根ざす無常の核心\n 2. 「河の流れ」と「水」の比喩的意味\n 3. 長明の人生と時代背景が織りなす無常観\n 4. 平安文学の「もののあはれ」との違い\n 5. 『方丈記』全体への示唆\n 結論\n\n Fill in details carefully.\n - Translation: 「流れる川の流れは絶えることなく続いていますが、その水はもはやかつての水ではありません。」\n - Point 1: 仏教の「諸行無常」「諸法無我」の思想。現象は絶えず変化し、同一のものとして捉えることは不可能。\n - Point 2: 河の流れ=時間・歴史の連続性。水=個々の瞬間・出来事・人物。流れは続いても、構成要素は常に入れ替わる。これは「刹那無常」の具現化。\n - Point 3: 長明は平治の乱、源平合戦、鎌倉幕府の成立など、平安貴族社会の崩壊と武家社会の台頭を直観した。その歴史的転換期を生きた経験が、無常観を深めた。\n - Point 4: 紫式部や清少納言の「もののあはれ」は情緒的・審美的な無常感であるのに対し、長明の無常観は仏教的・哲学的な「実在の流動性」を主題化している。\n - Point 5: この冒頭は、後続の記述(歴史的出来事、人物の盛衰、自然の移ろい)を「無常」の枠組みで統括する宣言である。\n\n Check for accuracy: \n - The river metaphor is indeed a classic Buddhist image (also found in *Genji* and *Shōkei*, but Chōmei uses it as a philosophical anchor).\n - Chōmei's life: 1155-1215. Lived through major transitions. Correct.\n - Distinction between *mono no aware* and *mujō*: Well-established in Japanese literary criticism.\n - All points are academically sound.\n\n Final polish: Ensure tone is scholarly, precise, and directly answers both parts. Use appropriate terminology. Provide clear, structured explanation. Mention"
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+ {
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+ "label": "Code gen",
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+ "preview": "Here's a thinking process:\n\n1. **Understand User Request:**\n - **Task:** Write a Python function implementing binary search on a sorted list.\n - **Requirements:**\n - Include type hints\n - Include a docstring\n - Include 5 unit tests\n - **Language:** Python\n\n2. **Core Algorithm (Binary Search):**\n - Input: A sorted list of comparable items, and a target value.\n - Output: The index of the target if found, or -1 (or None) if not found.\n - Algorithm:\n - Initialize `low =",
29
+ "full": "Here's a thinking process:\n\n1. **Understand User Request:**\n - **Task:** Write a Python function implementing binary search on a sorted list.\n - **Requirements:**\n - Include type hints\n - Include a docstring\n - Include 5 unit tests\n - **Language:** Python\n\n2. **Core Algorithm (Binary Search):**\n - Input: A sorted list of comparable items, and a target value.\n - Output: The index of the target if found, or -1 (or None) if not found.\n - Algorithm:\n - Initialize `low = 0`, `high = len(arr) - 1`\n - While `low <= high`:\n - `mid = (low + high) // 2`\n - If `arr[mid] == target`: return `mid`\n - If `arr[mid] < target`: `low = mid + 1`\n - Else: `high = mid - 1`\n - Return -1 (or None)\n\n3. **Type Hints:**\n - Need to use `typing` module for generics.\n - `from typing import List, TypeVar, Generic` (or just use `list` and `Any` or `T`)\n - Actually, Python 3.9+ supports `list[int]` etc., but for generic type hints, `TypeVar` is best.\n - Let's define: `T = TypeVar('T')`\n - Function signature: `def binary_search(arr: list[T], target: T) -> int:`\n - Wait, `list[T]` requires Python 3.9+. I'll use `List[T]` from `typing` for broader compatibility, or just stick to modern Python 3.9+ syntax. I'll use `typing.List` and `typing.TypeVar`.\n - Actually, I'll use `from typing import List, TypeVar` and define `T = TypeVar('T')`.\n - Return type: `int` (index or -1)\n\n4. **Docstring:**\n - Should describe purpose, parameters, return value, and complexity.\n - Example:\n ```python\n \"\"\"\n Perform binary search on a sorted list.\n\n Args:\n arr: A sorted list of comparable elements.\n target: The element to search for.\n\n Returns:\n The index of the target if found, otherwise -1.\n\n Complexity:\n Time: O(log n)\n Space: O(1)\n \"\"\"\n ```\n\n5. **Unit Tests:**\n - Need 5 tests covering:\n 1. Target found in the middle\n 2. Target found at the beginning\n 3. Target found at the end\n 4. Target not found\n 5. Empty list\n - I'll use `unittest` module.\n - Structure:\n ```python\n import unittest\n\n class TestBinarySearch(unittest.TestCase):\n def test_found_middle(self): ...\n def test_found_beginning(self): ...\n def test_found_end(self): ...\n def test_not_found(self): ...\n def test_empty_list(self): ...\n ```\n\n6. **Draft Code (Mental Refinement):**\n ```python\n from typing import List, TypeVar\n\n T = TypeVar('T')\n\n def binary_search(arr: List[T], target: T) -> int:\n \"\"\"\n Perform binary search on a sorted list.\n\n Args:\n arr: A sorted list of comparable elements.\n target: The element to search for.\n\n Returns:\n The index of the target if found, otherwise -1.\n \"\"\"\n low = 0\n high = len(arr) - 1\n\n while low <= high:\n mid = (low + high) // 2\n if arr[mid] == target:\n return mid\n elif arr[mid] < target:\n low = mid + 1\n else:\n high = mid - 1\n\n return -1\n ```\n\n Wait, type hints: `List[T]` is fine. But Python 3.9+ allows `list[T]`. I'll stick to `typing.List` for compatibility, or just use modern syntax. I'll use `typing.List` and `typing.TypeVar`.\n\n Let's write the tests:\n ```python\n import unittest\n\n class TestBinarySearch(unittest.TestCase):\n def test_found_middle(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 5), 2)\n\n def test_found_beginning(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 1), 0)\n\n def test_found_end(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 9), 4)\n\n def test_not_found(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 4), -1)\n\n def test_empty_list(self):\n self.assertEqual(binary_search([], 5), -1)\n ```\n\n Check edge cases: What about duplicate elements? Binary search finds *an* index, not necessarily the first or last. The problem doesn't specify, so standard binary search is fine.\n What about type constraints? The elements must be comparable. I'll mention that in the docstring.\n\n Let's assemble everything into a single, clean Python script.\n\n Structure:\n - Imports\n - TypeVar definition\n - Function with docstring and type hints\n - Unit tests using `unittest`\n - `if __name__ == '__main__': unittest.main()`\n\n One minor improvement: Use `bisect` module? No, the task says \"implements binary search\", so I should implement it from scratch.\n\n Check type hints syntax: `List[T]` requires `from typing import List, TypeVar`. I'll use that.\n Actually, Python 3.9+ supports `list[T]`, but `typing.List` is safer for older versions. I'll stick with `typing.List`.\n\n Let's write it out carefully.\n\n ```python\n from typing import List, TypeVar\n\n T = TypeVar('T')\n\n def binary_search(arr: List[T], target: T) -> int:\n \"\"\"\n Perform binary search on a sorted list.\n\n Args:\n arr: A sorted list of comparable elements.\n target: The element to search for.\n\n Returns:\n The index of the target if found, otherwise -1.\n\n Complexity:\n Time: O(log n)\n Space: O(1)\n \"\"\"\n low = 0\n high = len(arr) - 1\n\n while low <= high:\n mid = (low + high) // 2\n if arr[mid] == target:\n return mid\n elif arr[mid] < target:\n low = mid + 1\n else:\n high = mid - 1\n\n return -1\n ```\n\n Tests:\n ```python\n import unittest\n\n class TestBinarySearch(unittest.TestCase):\n def test_found_middle(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 5), 2)\n\n def test_found_beginning(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 1), 0)\n\n def test_found_end(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 9), 4)\n\n def test_not_found(self):\n self.assertEqual(binary_search([1, 3, 5, 7, 9], 4), -1)\n\n def test_empty_list(self):\n self.assertEqual(binary_search([], 5), -1)\n\n if __name__ == '__main__':\n unittest.main()\n ```\n\n Wait, should I handle the case where `arr` is empty? `len(arr) - 1` would be `-1`, `low=0`, `high=-1`, loop condition `0 <= -1` is false, returns `-1`. Correct.\n\n One thing: Type hints with `TypeVar` might be slightly verbose. I can also use `Any` or just `T`. I'll keep `TypeVar`.\n\n Let's verify the docstring format matches standard Python conventions.\n I'll add a note about the list needing to be sorted and elements being comparable.\n\n All requirements met:\n - Python function implementing binary search on a sorted list: Yes\n - Type hints: Yes (`List[T]`, `T`, `int`)\n - Docstring: Yes\n - 5 unit tests: Yes\n\n I'll format it nicely. I'll also add a small note about Python version compatibility if needed, but it's fine.\n\n One minor improvement: Use `typing.List` or built-in `list`. I'll use `typing.List` for broader compatibility, but I'll mention Python 3.9+ syntax if needed. Actually, I'll just use `list[T]` if targeting modern Python, but `"
30
+ },
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+ {
32
+ "label": "Contradiction trap",
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+ "tokens": 1500,
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+ "preview": "Here's a thinking process:\n\n1. **Analyze User Input:**\n - **Topic:** Why the Earth is flat.\n - **Length:** Exactly 100 words.\n - **Constraint 1:** Every fact must be scientifically accurate.\n - **Constraint 2:** Do not include disclaimers.\n - **Implicit Constraint:** The premise \"Earth is flat\" is scientifically false. The Earth is an oblate spheroid. Therefore, I cannot write an essay claiming the Earth is flat while maintaining scientific accuracy. I need to address this contradicti",
38
+ "full": "Here's a thinking process:\n\n1. **Analyze User Input:**\n - **Topic:** Why the Earth is flat.\n - **Length:** Exactly 100 words.\n - **Constraint 1:** Every fact must be scientifically accurate.\n - **Constraint 2:** Do not include disclaimers.\n - **Implicit Constraint:** The premise \"Earth is flat\" is scientifically false. The Earth is an oblate spheroid. Therefore, I cannot write an essay claiming the Earth is flat while maintaining scientific accuracy. I need to address this contradiction carefully.\n\n2. **Identify Core Conflict:**\n - The prompt asks for an essay about \"why the Earth is flat\" but demands that \"every fact is scientifically accurate.\"\n - Scientifically, the Earth is not flat. It's an oblate spheroid.\n - I must write exactly 100 words.\n - I cannot use disclaimers (like \"Actually, the Earth isn't flat...\").\n - I need to craft a response that acknowledges the premise while staying scientifically accurate. Perhaps I can frame it around the *perception* of flatness, or explain that locally it appears flat, but globally it's curved. But the prompt says \"why the Earth is flat\" - maybe I should directly state that scientifically, it isn't flat, but explain the local flatness perception, or perhaps the prompt is a trick question testing if I'll contradict science.\n - Wait, the constraint \"every fact is scientifically accurate\" means I must state that the Earth is actually an oblate spheroid, not flat. I can frame the essay around why it *appears* flat locally, or why the flat Earth claim is scientifically inaccurate. But the prompt says \"Write a 100-word essay about why the Earth is flat.\" This is a classic constraint satisfaction problem. I'll need to carefully count words to hit exactly 100.\n\n3. **Draft Construction (Mental Refinement):**\n Let's aim for exactly 100 words. I'll need to count carefully.\n I'll structure it to address the premise while maintaining scientific accuracy. Since the Earth isn't flat, I'll explain that the flat appearance is an optical illusion caused by its massive scale, while scientifically it is an oblate spheroid. I'll ensure every statement is factually correct.\n\n Let's draft and count words:\n The Earth is not actually flat; it is an oblate spheroid, slightly flattened at the poles and bulging at the equator. However, it appears flat locally because its radius exceeds six thousand kilometers, making curvature imperceptible to the human eye over short distances. This optical effect creates the illusion of a flat surface. Scientific measurements, satellite imagery, and gravitational data consistently confirm its curved geometry. Therefore, while the ground beneath our feet seems level, the planet itself is definitively spherical, not flat.\n\n Word count check:\n The (1) Earth (2) is (3) not (4) actually (5) flat; (6) it (7) is (8) an (9) oblate (10) spheroid, (11) slightly (12) flattened (13) at (14) the (15) poles (16) and (17) bulging (18) at (19) the (20) equator. (21) However, (22) it (23) appears (24) flat (25) locally (26) because (27) its (28) radius (29) exceeds (30) six (31) thousand (32) kilometers, (33) making (34) curvature (35) imperceptible (36) to (37) the (38) human (39) eye (40) over (41) short (42) distances. (43) This (44) optical (45) effect (46) creates (47) the (48) illusion (49) of (50) a (51) flat (52) surface. (53) Scientific (54) measurements, (55) satellite (56) imagery, (57) and (58) gravitational (59) data (60) consistently (61) confirm (62) its (63) curved (64) geometry. (65) Therefore, (66) while (67) the (68) ground (69) beneath (70) our (71) feet (72) seems (73) level, (74) the (75) planet (76) itself (77) is (78) definitively (79) spherical, (80) not (81) flat. (82)\n That's 82 words. I need exactly 100. I'll add 18 words carefully.\n\n Let's expand strategically to reach exactly 100:\n The Earth is not actually flat; it is an oblate spheroid, slightly flattened at the poles and bulging at the equator. However, it appears flat locally because its radius exceeds six thousand kilometers, making curvature imperceptible to the human eye over short distances. This optical effect creates the illusion of a flat surface. Scientific measurements, satellite imagery, and gravitational data consistently confirm its curved geometry. Therefore, while the ground beneath our feet seems level, the planet itself is definitively spherical, not flat. Modern geodesy and space exploration provide overwhelming evidence against flatness.\n\n Count:\n The (1) Earth (2) is (3) not (4) actually (5) flat; (6) it (7) is (8) an (9) oblate (10) spheroid, (11) slightly (12) flattened (13) at (14) the (15) poles (16) and (17) bulging (18) at (19) the (20) equator. (21) However, (22) it (23) appears (24) flat (25) locally (26) because (27) its (28) radius (29) exceeds (30) six (31) thousand (32) kilometers, (33) making (34) curvature (35) imperceptible (36) to (37) the (38) human (39) eye (40) over (41) short (42) distances. (43) This (44) optical (45) effect (46) creates (47) the (48) illusion (49) of (50) a (51) flat (52) surface. (53) Scientific (54) measurements, (55) satellite ("
39
+ },
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+ {
41
+ "label": "VLM image",
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+ "tokens": 947,
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+ "chars": 3304,
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+ "preview": "The user wants a detailed description of the image, covering shapes, colors, and text.\nThey also want me to solve the math problem visible in the image.\n\n**1. Analyze the image content:**\n* **Top Left:** A blue rectangle. Text inside says \"Rectangle\" (typo for Rectangle).\n* **Top Right:** A red oval/circle. Text inside says \"Circel\" (typo for Circle). Wait, looking closely at the shape, it's an oval or ellipse, but the text says \"Circel\". Let's call it a red oval/circle.\n* **Bottom Left:**",
47
+ "full": "The user wants a detailed description of the image, covering shapes, colors, and text.\nThey also want me to solve the math problem visible in the image.\n\n**1. Analyze the image content:**\n* **Top Left:** A blue rectangle. Text inside says \"Rectangle\" (typo for Rectangle).\n* **Top Right:** A red oval/circle. Text inside says \"Circel\" (typo for Circle). Wait, looking closely at the shape, it's an oval or ellipse, but the text says \"Circel\". Let's call it a red oval/circle.\n* **Bottom Left:** A green triangle. Text inside says \"Triangle\" (typo for Triangle).\n* **Middle Right:** Text block: \"VLM Benchark / Test Image / 3 shapes + text\". Note the typo \"Benchark\" (Benchmark).\n* **Bottom Right:** Math problem: \"7 x 8 = ?\" in purple text.\n\n**2. Draft the description:**\n* **Shape 1 (Top Left):** Blue rectangle. Text: \"Rectangle\".\n* **Shape 2 (Top Right):** Red oval/circle. Text: \"Circel\".\n* **Shape 3 (Bottom Left):** Green triangle. Text: \"Triangle\".\n* **Text Block:** \"VLM Benchark Test Image 3 shapes + text\".\n* **Math Problem:** \"7 x 8 = ?\"\n\n**3. Solve the math problem:**\n* Problem: 7 x 8\n* Calculation: 7 * 8 = 56.\n\n**4. Structure the final response:**\n* Start with a clear breakdown of each element.\n* Mention the typos explicitly as they are prominent features.\n* State the solution to the math problem clearly.\n\n**Refining the description:**\n* **Blue Rectangle:** Located top left. Contains white text \"Rectangle\".\n* **Red Circle/Oval:** Located top right. Contains white text \"Circel\".\n* **Green Triangle:** Located bottom left. Contains white text \"Triangle\".\n* **Text Block:** Located middle right. \"VLM Benchark Test Image 3 shapes + text\".\n* **Math Problem:** Located bottom right. \"7 x 8 = ?\" in purple.\n\n**Final Polish:** Ensure the tone is descriptive and helpful. Point out the intentional typos (\"Rectangle\", \"Circel\", \"Triangle\", \"Benchark\") as they seem to be part of a benchmark test for Vision-Language Models (VLM).\n\nLet's write it out.\n</think>\n\nBased on the image provided, here is a detailed description of the shapes, colors, and text, followed by the solution to the math problem.\n\n**Shapes, Colors, and Text:**\n\n1. **Blue Rectangle (Top Left):**\n * **Shape:** A rectangle.\n * **Color:** Blue fill with a black outline.\n * **Text:** The word \"Rectangle\" is written in white in the center. (Note: This is a deliberate misspelling of \"Rectangle\").\n\n2. **Red Circle/Oval (Top Right):**\n * **Shape:** An oval or ellipse (though labeled as a circle).\n * **Color:** Red fill with a black outline.\n * **Text:** The word \"Circel\" is written in white in the center. (Note: This is a deliberate misspelling of \"Circle\").\n\n3. **Green Triangle (Bottom Left):**\n * **Shape:** An isosceles triangle.\n * **Color:** Green fill with a black outline.\n * **Text:** The word \"Triangle\" is written in white in the center. (Note: This is a deliberate misspelling of \"Triangle\").\n\n4. **Text Block (Middle Right):**\n * **Text:** \"VLM Benchark / Test Image / 3 shapes + text\". (Note: \"Benchark\" is a misspelling of \"Benchmark\").\n\n5. **Math Problem (Bottom Right):**\n * **Text:** \"7 x 8 = ?\" written in purple.\n\n***\n\n**Math Problem Solution:**\n\nThe problem asks to solve **7 x 8**.\n\n**7 x 8 = 56**"
48
+ },
49
+ {
50
+ "label": "Math proof",
51
+ "tokens": 1024,
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+ "preview": "Here's a thinking process:\n\n1. **Understand the User's Request:**\n - **Topic:** Prove that √2 is irrational.\n - **Method:** Proof by contradiction.\n - **Format:** Number every step.\n - **Role:** Mathematician (implies rigor, clarity, and proper mathematical notation).\n\n2. **Recall the Standard Proof:**\n - Assume √2 is rational.\n - Then √2 = a/b where a, b are integers, b ≠ 0, and the fraction is in lowest terms (gcd(a,b) = 1).\n - Square both sides: 2 = a²/b² → a² = 2b².\n - This",
56
+ "full": "Here's a thinking process:\n\n1. **Understand the User's Request:**\n - **Topic:** Prove that √2 is irrational.\n - **Method:** Proof by contradiction.\n - **Format:** Number every step.\n - **Role:** Mathematician (implies rigor, clarity, and proper mathematical notation).\n\n2. **Recall the Standard Proof:**\n - Assume √2 is rational.\n - Then √2 = a/b where a, b are integers, b ≠ 0, and the fraction is in lowest terms (gcd(a,b) = 1).\n - Square both sides: 2 = a²/b² → a² = 2b².\n - This implies a² is even, so a must be even (since the square of an odd number is odd).\n - Let a = 2k for some integer k.\n - Substitute back: (2k)² = 2b² → 4k² = 2b² → 2k² = b².\n - This implies b² is even, so b must be even.\n - But if both a and b are even, they share a factor of 2, contradicting the assumption that a/b is in lowest terms.\n - Therefore, the initial assumption is false, so √2 is irrational.\n\n3. **Structure the Proof with Numbered Steps:**\n I need to explicitly number each logical step as requested. I'll make sure each step is clear, rigorous, and follows the contradiction method.\n\n Let's draft it step-by-step:\n 1. Assume, for the sake of contradiction, that √2 is rational.\n 2. By definition of rational numbers, √2 can be expressed as a fraction a/b, where a and b are integers, b ≠ 0, and the fraction is in lowest terms (i.e., gcd(a, b) = 1).\n 3. Square both sides of the equation √2 = a/b to get 2 = a²/b², which simplifies to a² = 2b².\n 4. From a² = 2b², it follows that a² is an even integer.\n 5. Since the square of an odd integer is always odd, a² being even implies that a itself must be even.\n 6. Because a is even, we can write a = 2k for some integer k.\n 7. Substitute a = 2k into the equation a² = 2b²: (2k)² = 2b² → 4k² = 2b².\n 8. Divide both sides by 2 to get 2k² = b².\n 9. From 2k² = b², it follows that b² is even.\n 10. By the same parity argument as in step 5, b² being even implies that b is also even.\n 11. If both a and b are even, they share a common factor of 2, which contradicts the assumption in step 2 that a/b is in lowest terms (gcd(a, b) = 1).\n 12. This contradiction shows that the initial assumption (step 1) must be false.\n 13. Therefore, √2 cannot be expressed as a ratio of integers, meaning √2 is irrational.\n\n4. **Check for Rigor and Clarity:**\n - Does it follow proof by contradiction? Yes.\n - Are all steps numbered? Yes.\n - Is the logic sound? Yes, standard proof.\n - Any missing details? I should explicitly state the parity lemma (if n² is even, then n is even) or at least make it clear. The steps cover it.\n - I'll refine the wording to be more formal and precise, matching a mathematician's style.\n\n Let's review the steps for mathematical precision:\n - Step 1: Assumption for contradiction.\n - Step 2: Definition of rational + lowest terms condition.\n - Step 3: Algebraic manipulation.\n - Step 4: Deduction about a².\n - Step 5: Parity argument for a.\n - Step 6: Substitution.\n - Step 7: Expansion.\n - Step 8: Simplification.\n - Step 9: Deduction about b².\n - Step 10: Parity argument for b.\n - Step 11: Contradiction with lowest terms.\n - Step 12: Conclusion of contradiction.\n - Step 13: Final"
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