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Running on Zero
| { | |
| "slug": "adam-optimizer-memory-bytes", | |
| "title": "手撕 Adam 优化器状态显存占用计算", | |
| "difficulty": "Easy", | |
| "category": "AIInfra", | |
| "tags": [ | |
| "优化器显存", | |
| "Adam", | |
| "分布式训练" | |
| ], | |
| "description_md": "### 题目描述\n标准混合精度训练下，优化器状态需存储 FP32 Master Weights (4B)、一阶动量 $m$ (4B)、二阶动量 $v$ (4B)，每参数共 12 字节。\n\n### 函数签名\n```python\ndef adam_memory_bytes(num_params: int) -> int:\n```\n\n### 示例\n```python\n# 输入\nnum_params = 7000000000\n\n# 输出 (int)\n84000000000\n```\n\n### 参数规格与约束\n- **`num_params`**：`int`\n- **返回值**：`int`，输出规格 `int` (示例值: `84000000000`)\n- **精度容差**：`atol=0.0001, rtol=0.0001`", | |
| "entry_point": "adam_memory_bytes", | |
| "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 adam_memory_bytes(num_params: int) -> int:\n \"\"\"\n 手撕 Adam 优化器状态显存占用计算\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 adam_memory_bytes(num_params: int) -> int:\n return num_params * 12\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 ('7B 模型 Adam 优化器显存', 7000000000),\n ('数值缩放与幅值扰动验证', 14000000000),\n ('多维批次与参数泛化验证', 28000000000),\n ('边界极值与稳定性验证', 56000000000),\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 Adam 优化器状态显存占用计算**（`adam_memory_bytes`）聚焦于 **AIInfra** 中的关键计算逻辑：\n\n标准混合精度训练下，优化器状态需存储 FP32 Master Weights (4B)、一阶动量 $m$ (4B)、二阶动量 $v$ (4B)，每参数共 12 字节。\n\n在实现中，函数接收参数 `num_params` (`int`)，目标是计算出类型与形状严格符合 `int` 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**：`num_params` 规格为 `int` (示例值: `7000000000`)。\n- **期望输出规格**：`int` (示例值: `84000000000`)。\n\n**具体推导与计算步骤如下：**\n1. 返回最终结果：输出 `num_params * 12`，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- **输入输出类型与形状契约**：请严格按照函数签名返回对应类型（`torch.Tensor`、`Tuple` 或标量数值），避免遗漏批次维度或改变张量的数据类型（`dtype`）。\n- **边界输入鲁棒性**：注意单样本（`Batch=1`）、单步序列（`Seq=1`）、零值输入或极端超参数下的计算行为，不要在代码中硬编码特定测试用例的维度常数。\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 adam_memory_bytes(num_params: int) -> int:\n return num_params * 12\n```", | |
| "difficulty_breakdown": { | |
| "concept": 1, | |
| "implementation": 1, | |
| "math_derivation": 2, | |
| "boundary_complexity": 1 | |
| }, | |
| "test_cases": [ | |
| { | |
| "name": "7B 模型 Adam 优化器显存", | |
| "input_desc": "真实参数契约用例 (num_params)", | |
| "params": [ | |
| { | |
| "name": "num_params", | |
| "type": "int", | |
| "value": "7000000000" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "num_params": "7000000000" | |
| } | |
| }, | |
| { | |
| "name": "数值缩放与幅值扰动验证", | |
| "input_desc": "真实参数契约用例 (num_params)", | |
| "params": [ | |
| { | |
| "name": "num_params", | |
| "type": "int", | |
| "value": "14000000000" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "num_params": "14000000000" | |
| } | |
| }, | |
| { | |
| "name": "多维批次与参数泛化验证", | |
| "input_desc": "真实参数契约用例 (num_params)", | |
| "params": [ | |
| { | |
| "name": "num_params", | |
| "type": "int", | |
| "value": "28000000000" | |
| } | |
| ], | |
| "raw_inputs": { | |
| "num_params": "28000000000" | |
| } | |
| } | |
| ] | |
| } |