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| { | |
| "slug": "bleu-1-score", | |
| "title": "手撕机器翻译 BLEU-1 评测分值 (BLEU-1 Score)", | |
| "difficulty": "Medium", | |
| "category": "ML", | |
| "tags": [ | |
| "自然语言处理", | |
| "BLEU", | |
| "文本评估" | |
| ], | |
| "description_md": "### 题目描述\n给定候选生成 Token ID 列表 $cand \\in \\mathbb{Z}^C$ 与参考 Token ID 列表 $ref \\in \\mathbb{Z}^R$，计算截断 1-gram 精度 $\\displaystyle p_1 = \\frac{\\sum_{w} \\min(c_{cand}(w), c_{ref}(w))}{C}$，并结合简短惩罚因子 $\\text{BP} = \\min(1, \\exp(1 - R/C))$，输出 $\\text{BLEU-1} = \\text{BP} \\times p_1$。\n\n### 函数签名\n```python\ndef bleu1_score(\n cand_tokens: List[int],\n ref_tokens: List[int],\n) -> float:\n```\n\n### 示例\n```python\n# 输入\ncand_tokens = [1, 2, 3, 4]\nref_tokens = [1, 2, 3, 4]\n\n# 输出 (float)\n1.0\n```\n\n### 参数规格与约束\n- **`cand_tokens`**：`List[int]`\n- **`ref_tokens`**：`List[int]`\n- **返回值**：`float`，输出规格 `float` (示例值: `1.0`)\n- **精度容差**：`atol=0.0001, rtol=0.0001`", | |
| "entry_point": "bleu1_score", | |
| "starter_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import Optional, List, Tuple\n\ndef bleu1_score(\n cand_tokens: List[int],\n ref_tokens: List[int],\n) -> float:\n \"\"\"\n 手撕机器翻译 BLEU-1 评测分值 (BLEU-1 Score)\n \"\"\"\n # 请在此编写代码\n pass\n", | |
| "reference_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import Optional, List, Tuple\n\ndef bleu1_score(cand_tokens: List[int], ref_tokens: List[int]) -> float:\n if len(cand_tokens) == 0:\n return 0.0\n from collections import Counter\n cand_counts = Counter(cand_tokens)\n ref_counts = Counter(ref_tokens)\n clipped_hits = sum(min(count, ref_counts.get(w, 0)) for w, count in cand_counts.items())\n p1 = clipped_hits / len(cand_tokens)\n bp = 1.0 if len(cand_tokens) >= len(ref_tokens) else math.exp(1.0 - len(ref_tokens) / len(cand_tokens))\n return float(bp * p1)\n", | |
| "forbidden_modules": [ | |
| "os", | |
| "sys", | |
| "subprocess", | |
| "shutil", | |
| "socket", | |
| "requests" | |
| ], | |
| "forbidden_calls": [], | |
| "time_limit": 3.0, | |
| "memory_limit_mb": 512, | |
| "atol": 0.0001, | |
| "rtol": 0.0001, | |
| "test_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\n\ncases = [\n ('完全匹配 BLEU-1=1.0', [1, 2, 3, 4], [1, 2, 3, 4]),\n ('过短惩罚 BLEU-1', [1, 2], [1, 2, 3, 4]),\n ('多维批次与参数泛化验证', [1, 2, 3, 4, 4], [1, 2, 3, 4, 4]),\n ('边界极值与稳定性验证', [2, 1], [4, 3, 2, 1]),\n]\nfor idx, (name, *args) in enumerate(cases, 1):\n t0 = time.time()\n try:\n exp = ref_obj(*args)\n act = user_obj(*args)\n match, err, max_diff = compare_outputs(act, exp, atol=atol, rtol=rtol)\n passed, msg = match, err\n except Exception as e:\n passed, msg = False, f\"Runtime Exception: {str(e)}\"\n act, exp, max_diff = None, None, None\n cases_results.append({\n \"case_id\": idx, \"case_name\": name, \"passed\": passed,\n \"time_ms\": round((time.time() - t0) * 1000, 2), \"message\": msg,\n \"user_output_summary\": summarize_obj(act) if act is not None else None,\n \"expected_summary\": summarize_obj(exp) if exp is not None else None,\n \"max_diff\": max_diff,\n })\n", | |
| "is_featured": false, | |
| "editorial_md": "#### 💡 核心算法原理与数学推导\n**手撕机器翻译 BLEU-1 评测分值 (BLEU-1 Score)**（`bleu1_score`）聚焦于 **ML** 中的关键计算逻辑：\n\n给定候选生成 Token ID 列表 $cand \\in \\mathbb{Z}^C$ 与参考 Token ID 列表 $ref \\in \\mathbb{Z}^R$，计算截断 1-gram 精度 $\\displaystyle p_1 = \\frac{\\sum_{w} \\min(c_{cand}(w), c_{ref}(w))}{C}$，并结合简短惩罚因子 $\\text{BP} = \\min(1, \\exp(1 - R/C))$，输出 $\\text{BLEU-1} = \\text{BP} \\times p_1$。\n\n在实现中，函数接收参数 `cand_tokens` (`List[int]`)、`ref_tokens` (`List[int]`)，目标是计算出类型与形状严格符合 `float` 契约的结果。\n\n#### 📐 输入输出张量变换与步骤拆解\n- **输入基准规格**：`cand_tokens` 规格为 `List` (长度 `4`)，`ref_tokens` 规格为 `List` (长度 `4`)。\n- **期望输出规格**：`float` (示例值: `1.0`)。\n\n**具体推导与计算步骤如下：**\n1. 条件分支判断 `if len(cand_tokens) == 0`：处理边界条件、掩码过滤或特殊退化情形。\n2. 计算中间量 `cand_counts`：通过表达式 `Counter(cand_tokens)` 完成张量或数值变换。\n3. 计算中间量 `ref_counts`：通过表达式 `Counter(ref_tokens)` 完成张量或数值变换。\n4. 计算中间量 `clipped_hits`：通过表达式 `sum(min(count, ref_counts.get(w, 0)) for w, count in cand_counts.items())` 完成张量或数值变换。\n5. 计算中间量 `p1`：通过表达式 `clipped_hits / len(cand_tokens)` 完成张量或数值变换。\n6. 计算中间量 `bp`：通过表达式 `1.0 if len(cand_tokens) >= len(ref_tokens) else math.exp(1.0 - len(ref_tokens) / len(cand_tokens))` 完成张量或数值变换。\n7. 返回最终结果：输出 `float(bp * p1)`，严格对齐函数签名要求的返回类型与维度。\n\n#### 📊 复杂度分析\n- **时间复杂度**：$O(1)$，仅涉及标量代数运算或闭式公式求值，执行耗时与模型规模参数数值大小无关。\n- **空间复杂度**：$O(1)$，仅使用常数级标量局部变量，无额外张量显存分配。\n\n#### ⚠️ 关键实现细节与易错点\n- **除零保护与数值平滑 (`eps`)**：在执行分母归一化、标准差缩放或对数运算时，必须按公式位置准确加上 `eps`（例如在平方根内 `sqrt(var + eps)` 还是分母外 `+ eps`），防止全零或常量输入触发 `NaN` / `Inf`。\n- **指数与对数域数值稳定性**：直接对大幅值 logits 计算 `exp` 易导致浮点数上溢（Overflow），对接近 0 的概率直接计算 `log` 易导致下溢；应优先使用 `F.log_softmax`、`F.logsigmoid` 或减去最大值的稳定化写法。\n- **纯向量化算子优先**：尽量使用 PyTorch 原生向量化张量算子替代低效的 Python 逐元素循环，以兼顾代码简洁性与执行性能。\n\n#### 💻 官方标准参考实现\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import Optional, List, Tuple\n\ndef bleu1_score(cand_tokens: List[int], ref_tokens: List[int]) -> float:\n if len(cand_tokens) == 0:\n return 0.0\n from collections import Counter\n cand_counts = Counter(cand_tokens)\n ref_counts = Counter(ref_tokens)\n clipped_hits = sum(min(count, ref_counts.get(w, 0)) for w, count in cand_counts.items())\n p1 = clipped_hits / len(cand_tokens)\n bp = 1.0 if len(cand_tokens) >= len(ref_tokens) else math.exp(1.0 - len(ref_tokens) / len(cand_tokens))\n return float(bp * p1)\n```", | |
| "difficulty_breakdown": { | |
| "concept": 3, | |
| "implementation": 3, | |
| "math_derivation": 3, | |
| "boundary_complexity": 3 | |
| }, | |
| "test_cases": [ | |
| { | |
| "name": "完全匹配 BLEU-1=1.0", | |
| "input_desc": "真实参数契约用例 (cand_tokens, ref_tokens)", | |
| "params": [ | |
| { | |
| "name": "cand_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2, 3, 4]" | |
| }, | |
| { | |
| "name": "ref_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2, 3, 4]" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "cand_tokens": "[1, 2, 3, 4]", | |
| "ref_tokens": "[1, 2, 3, 4]" | |
| } | |
| }, | |
| { | |
| "name": "过短惩罚 BLEU-1", | |
| "input_desc": "真实参数契约用例 (cand_tokens, ref_tokens)", | |
| "params": [ | |
| { | |
| "name": "cand_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2]" | |
| }, | |
| { | |
| "name": "ref_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2, 3, 4]" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "cand_tokens": "[1, 2]", | |
| "ref_tokens": "[1, 2, 3, 4]" | |
| } | |
| }, | |
| { | |
| "name": "多维批次与参数泛化验证", | |
| "input_desc": "真实参数契约用例 (cand_tokens, ref_tokens)", | |
| "params": [ | |
| { | |
| "name": "cand_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2, 3, 4, 4]" | |
| }, | |
| { | |
| "name": "ref_tokens", | |
| "type": "List[int]", | |
| "value": "[1, 2, 3, 4, 4]" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "cand_tokens": "[1, 2, 3, 4, 4]", | |
| "ref_tokens": "[1, 2, 3, 4, 4]" | |
| } | |
| } | |
| ] | |
| } |