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"slug": "arcface-additive-angular-margin",
"title": "手撕 ArcFace 加性角度间隔损失 (ArcFace Angular Margin)",
"difficulty": "Hard",
"category": "Loss",
"tags": [
"ArcFace",
"加性间隔",
"人脸识别"
],
"description_md": "### 题目描述\n在归一化权重和特征下，输入余弦值 $\\cos \\theta \\in [-1, 1]^{B \\times C}$ 及真实类别索引 $labels \\in [0, C-1]^B$。对目标类别施加角度间隔 $\\cos(\\theta + m) = \\cos\\theta \\cos m - \\sin\\theta \\sin m$（其中 $\\sin\\theta = \\sqrt{1 - \\cos^2\\theta}$），输出调整后的余弦值矩阵。\n\n### 函数签名\n```python\ndef arcface_margin(\n cosine: torch.Tensor,\n labels: torch.Tensor,\n m: float = 0.5,\n) -> torch.Tensor:\n```\n\n### 示例\n```python\n# 输入\ncosine = [[0.8, 0.2], [0.3, 0.9]]\nlabels = [0, 1]\nm = 0.5\n\n# 输出 (Tensor, shape=[2, 2], dtype=float32)\n[[0.4144, 0.2], [0.3, 0.5808]]\n```\n\n### 参数规格与约束\n- **`cosine`**：`torch.Tensor`，测试规格 `shape=[2, 2], dtype=float32`\n- **`labels`**：`torch.Tensor`，测试规格 `shape=[2], dtype=int64`\n- **`m`**：`float`（默认 `0.5`）\n- **返回值**：`torch.Tensor`，输出规格 `shape=[2, 2], dtype=float32`\n- **精度容差**：`atol=0.0001, rtol=0.0001`",
"entry_point": "arcface_margin",
"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 arcface_margin(\n cosine: torch.Tensor,\n labels: torch.Tensor,\n m: float = 0.5,\n) -> torch.Tensor:\n \"\"\"\n 手撕 ArcFace 加性角度间隔损失 (ArcFace Angular Margin)\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 arcface_margin(cosine: torch.Tensor, labels: torch.Tensor, m: float = 0.5) -> torch.Tensor:\n B = cosine.shape[0]\n cos_m = math.cos(m)\n sin_m = math.sin(m)\n sine = torch.sqrt(torch.clamp(1.0 - cosine ** 2, min=0.0))\n phi = cosine * cos_m - sine * sin_m\n out = cosine.clone()\n batch_idx = torch.arange(B, device=cosine.device)\n out[batch_idx, labels] = phi[batch_idx, labels]\n return out\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 ('目标类余弦加间隔', torch.tensor([[0.8, 0.2], [0.3, 0.9]], dtype=torch.float32), torch.tensor([0, 1]), 0.5),\n ('多批次扩展泛化验证', torch.tensor([[0.8, 0.2], [0.3, 0.9], [1.2, 0.3], [0.45, 1.35]], dtype=torch.float32), torch.tensor([0, 1, 0, 1]), 0.5),\n ('多维批次与参数泛化验证', torch.tensor([[1.2, 0.3], [0.45, 1.35]], dtype=torch.float32), torch.tensor([0, 1]), 0.75),\n ('边界极值与稳定性验证', torch.tensor([[0.4, 0.1], [0.15, 0.45]], dtype=torch.float32), torch.tensor([0, 1]), 0.25),\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 ArcFace 加性角度间隔损失 (ArcFace Angular Margin)**（`arcface_margin`）聚焦于 **Loss** 中的关键计算逻辑：\n\n在归一化权重和特征下，输入余弦值 $\\cos \\theta \\in [-1, 1]^{B \\times C}$ 及真实类别索引 $labels \\in [0, C-1]^B$。对目标类别施加角度间隔 $\\cos(\\theta + m) = \\cos\\theta \\cos m - \\sin\\theta \\sin m$（其中 $\\sin\\theta = \\sqrt{1 - \\cos^2\\theta}$），输出调整后的余弦值矩阵。\n\n在实现中，函数接收参数 `cosine` (`torch.Tensor`)、`labels` (`torch.Tensor`)、`m` (`float`)，目标是计算出类型与形状严格符合 `torch.Tensor` 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**：`cosine` 规格为 `torch.Tensor(shape=[2, 2], dtype=float32)`，`labels` 规格为 `torch.Tensor(shape=[2], dtype=int64)`，`m` 规格为 `float` (示例值: `0.5`)。\n- **期望输出规格**：`torch.Tensor(shape=[2, 2], dtype=float32)`。\n\n**具体推导与计算步骤如下：**\n1. 计算中间量 `B`：通过表达式 `cosine.shape[0]` 完成张量或数值变换。\n2. 计算中间量 `cos_m`：通过表达式 `math.cos(m)` 完成张量或数值变换。\n3. 计算中间量 `sin_m`：通过表达式 `math.sin(m)` 完成张量或数值变换。\n4. 计算中间量 `sine`：通过表达式 `torch.sqrt(torch.clamp(1.0 - cosine ** 2, min=0.0))` 完成张量或数值变换。\n5. 计算中间量 `phi`：通过表达式 `cosine * cos_m - sine * sin_m` 完成张量或数值变换。\n6. 计算中间量 `out`：通过表达式 `cosine.clone()` 完成张量或数值变换。\n7. 计算中间量 `batch_idx`：通过表达式 `torch.arange(B, device=cosine.device)` 完成张量或数值变换。\n8. 计算中间量 `out[batch_idx, labels]`：通过表达式 `phi[batch_idx, labels]` 完成张量或数值变换。\n9. 返回最终结果：输出 `out`，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**：$O(N)$（线性于输入张量总元素个数 $\\prod d_i$），所有运算均为向量化逐元素算子或沿指定维度的归约计算。\n- **空间复杂度**：$O(N)$，需要与输入或输出张量同规模的显存空间保存计算结果。\n\n#### ⚠️ 关键实现细节与易错点\n- **避免非预期原地修改 (In-place Mutation)**：评测器会复用输入张量比对参考实现与用户实现的输出；若需修改输入张量的部分切片或掩码位置，请先执行 `.clone()` 再修改，避免污染原始输入。\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 arcface_margin(cosine: torch.Tensor, labels: torch.Tensor, m: float = 0.5) -> torch.Tensor:\n B = cosine.shape[0]\n cos_m = math.cos(m)\n sin_m = math.sin(m)\n sine = torch.sqrt(torch.clamp(1.0 - cosine ** 2, min=0.0))\n phi = cosine * cos_m - sine * sin_m\n out = cosine.clone()\n batch_idx = torch.arange(B, device=cosine.device)\n out[batch_idx, labels] = phi[batch_idx, labels]\n return out\n```",
"difficulty_breakdown": {
"concept": 4,
"implementation": 4,
"math_derivation": 4,
"boundary_complexity": 4
},
"test_cases": [
{
"name": "目标类余弦加间隔",
"input_desc": "真实参数契约用例 (cosine, labels, m)",
"params": [
{
"name": "cosine",
"type": "torch.Tensor",
"value": "torch.tensor([[0.8, 0.2], [0.3, 0.9]], dtype=torch.float32)"
},
{
"name": "labels",
"type": "torch.Tensor",
"value": "torch.tensor([0, 1])"
},
{
"name": "m",
"type": "float",
"value": "0.5"
}
],
"raw_inputs": {
"cosine": "torch.tensor([[0.8, 0.2], [0.3, 0.9]], dtype=torch.float32)",
"labels": "torch.tensor([0, 1])",
"m": "0.5"
}
},
{
"name": "多批次扩展泛化验证",
"input_desc": "真实参数契约用例 (cosine, labels, m)",
"params": [
{
"name": "cosine",
"type": "torch.Tensor",
"value": "torch.tensor([[0.8, 0.2], [0.3, 0.9], [1.2, 0.3], [0.45, 1.35]], dtype=torch.float32)"
},
{
"name": "labels",
"type": "torch.Tensor",
"value": "torch.tensor([0, 1, 0, 1])"
},
{
"name": "m",
"type": "float",
"value": "0.5"
}
],
"raw_inputs": {
"cosine": "torch.tensor([[0.8, 0.2], [0.3, 0.9], [1.2, 0.3], [0.45, 1.35]], dtype=torch.float32)",
"labels": "torch.tensor([0, 1, 0, 1])",
"m": "0.5"
}
},
{
"name": "多维批次与参数泛化验证",
"input_desc": "真实参数契约用例 (cosine, labels, m)",
"params": [
{
"name": "cosine",
"type": "torch.Tensor",
"value": "torch.tensor([[1.2, 0.3], [0.45, 1.35]], dtype=torch.float32)"
},
{
"name": "labels",
"type": "torch.Tensor",
"value": "torch.tensor([0, 1])"
},
{
"name": "m",
"type": "float",
"value": "0.75"
}
],
"raw_inputs": {
"cosine": "torch.tensor([[1.2, 0.3], [0.45, 1.35]], dtype=torch.float32)",
"labels": "torch.tensor([0, 1])",
"m": "0.75"
}
}
]
} |