{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 损失函数\n",
"\n",
"[](https://openi.pcl.ac.cn/MindSpore/docs/src/branch/r1.9/tutorials/source_zh_cn/advanced/modules/loss.ipynb?card=2&image=MindSpore1.8.1) [](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/notebook/r1.9/tutorials/zh_cn/advanced/modules/mindspore_loss.ipynb) [](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/notebook/r1.9/tutorials/zh_cn/advanced/modules/mindspore_loss.py) [](https://gitee.com/mindspore/docs/blob/r1.9/tutorials/source_zh_cn/advanced/modules/loss.ipynb)\n",
"\n",
"损失函数，亦称目标函数，用于衡量预测值与真实值差异的程度。\n",
"\n",
"在深度学习中，模型训练就是通过不断迭代来缩小损失函数值的过程。因此，在模型训练过程中损失函数的选择非常重要，一个好的损失函数能有效提升模型的性能。\n",
"\n",
"`mindspore.nn`模块中提供了许多[通用损失函数](https://www.mindspore.cn/docs/zh-CN/r1.9/api_python/mindspore.nn.html#损失函数)，但这些通用损失函数无法满足所有需求，很多情况需要用户自定义所需的损失函数。因此，本教程介绍如何自定义损失函数。\n",
"\n",
"\n",
"\n",
"## 内置损失函数\n",
"\n",
"首先介绍`mindspore.nn`模块中内置的[损失函数](https://www.mindspore.cn/docs/zh-CN/r1.9/api_python/mindspore.nn.html#损失函数)。\n",
"\n",
"下例以`nn.L1Loss`为例，计算预测值和目标值之间的平均绝对误差：\n",
"\n",
"$$\\ell(x, y) = L = \\{l_1,\\dots,l_N\\}^\\top, \\quad \\text{with } l_n = \\left| x_n - y_n \\right|$$\n",
"\n",
"其中N为数据集中的`batch_size`值。\n",
"\n",
"$$\\ell(x, y) =\n",
" \\begin{cases}\n",
" \\operatorname{mean}(L), & \\text{if reduction} = \\text{'mean';}\\\\\n",
" \\operatorname{sum}(L), & \\text{if reduction} = \\text{'sum'.}\n",
" \\end{cases}$$\n",
"\n",
"`nn.L1Loss`中的参数`reduction`取值可为`mean`，`sum`，或`none`。若`reduction` 为`mean`或`sum`，则输出一个经过均值或求和后的标量Tensor（降维）；若`reduction`为`none`，则所输出Tensor的shape为广播后的shape。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T03:42:22.717822Z",
"start_time": "2021-12-29T03:42:20.636585Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"loss: 1.5\n",
"loss_sum: 9.0\n",
"loss_none:\n",
" [[1. 0. 2.]\n",
" [1. 2. 3.]]\n"
]
}
],
"source": [
"import numpy as np\n",
"import mindspore.nn as nn\n",
"import mindspore as ms\n",
"\n",
"# 输出loss均值\n",
"loss = nn.L1Loss()\n",
"# 输出loss和\n",
"loss_sum = nn.L1Loss(reduction='sum')\n",
"# 输出loss原值\n",
"loss_none = nn.L1Loss(reduction='none')\n",
"\n",
"input_data = ms.Tensor(np.array([[1, 2, 3], [2, 3, 4]]).astype(np.float32))\n",
"target_data = ms.Tensor(np.array([[0, 2, 5], [3, 1, 1]]).astype(np.float32))\n",
"\n",
"print(\"loss:\", loss(input_data, target_data))\n",
"print(\"loss_sum:\", loss_sum(input_data, target_data))\n",
"print(\"loss_none:\\n\", loss_none(input_data, target_data))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 自定义损失函数\n",
"\n",
"自定义损失函数的方法有两种：一是基于`nn.Cell`来定义损失函数；二是`nn.LossBase`来定义损失函数。`nn.LossBase`继承自`nn.Cell`，额外提供了`get_loss`方法，利用`reduction`参数对损失值求和或求均值，输出一个标量。\n",
"\n",
"下面将分别使用继承`Cell`和继承`LossBase`的方法，来定义平均绝对误差损失函数(Mean Absolute Error，MAE)，MAE算法的公式如下所示：\n",
"\n",
"$$ loss= \\frac{1}{m}\\sum_{i=1}^m\\lvert y_i-f(x_i) \\rvert$$\n",
"\n",
"上式中$f(x)$为预测值，$y$为样本真实值，$loss$为预测值与真实值之间距离的平均值。\n",
"\n",
"### 基于`nn.Cell`构造损失函数\n",
"\n",
"`nn.Cell`是MindSpore的基类，不但可用于构建网络，还可用于定义损失函数。使用`nn.Cell`定义损失函数的过程与定义一个普通的网络相似，差别在于，其执行逻辑部分要计算的是前向网络输出与真实值之间的误差。\n",
"\n",
"下面展示怎样基于`nn.Cell`自定义损失函数`MAELoss`："
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T03:42:22.729232Z",
"start_time": "2021-12-29T03:42:22.723517Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.03333334\n"
]
}
],
"source": [
"import mindspore.ops as ops\n",
"\n",
"class MAELoss(nn.Cell):\n",
" \"\"\"自定义损失函数MAELoss\"\"\"\n",
"\n",
" def __init__(self):\n",
" \"\"\"初始化\"\"\"\n",
" super(MAELoss, self).__init__()\n",
" self.abs = ops.Abs()\n",
" self.reduce_mean = ops.ReduceMean()\n",
"\n",
" def construct(self, base, target):\n",
" \"\"\"调用算子\"\"\"\n",
" x = self.abs(base - target)\n",
" return self.reduce_mean(x)\n",
"\n",
"loss = MAELoss()\n",
"\n",
"input_data = ms.Tensor(np.array([0.1, 0.2, 0.3]).astype(np.float32)) # 生成预测值\n",
"target_data = ms.Tensor(np.array([0.1, 0.2, 0.2]).astype(np.float32)) # 生成真实值\n",
"\n",
"output = loss(input_data, target_data)\n",
"print(output)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 基于`nn.LossBase`构造损失函数\n",
"\n",
"基于[nn.LossBase](https://www.mindspore.cn/docs/zh-CN/r1.9/api_python/nn/mindspore.nn.LossBase.html#mindspore.nn.LossBase)构造损失函数`MAELoss`与基于`nn.Cell`构造损失函数的过程类似，都要重写`__init__`方法和`construct`方法。\n",
"\n",
"`nn.LossBase`可使用方法`get_loss`将`reduction`应用于损失计算。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T03:42:22.766767Z",
"start_time": "2021-12-29T03:42:22.759510Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.03333334\n"
]
}
],
"source": [
"class MAELoss(nn.LossBase):\n",
" \"\"\"自定义损失函数MAELoss\"\"\"\n",
"\n",
" def __init__(self, reduction=\"mean\"):\n",
" \"\"\"初始化并求loss均值\"\"\"\n",
" super(MAELoss, self).__init__(reduction)\n",
" self.abs = ops.Abs() # 求绝对值算子\n",
"\n",
" def construct(self, base, target):\n",
" x = self.abs(base - target)\n",
" return self.get_loss(x) # 返回loss均值\n",
"\n",
"loss = MAELoss()\n",
"\n",
"input_data = ms.Tensor(np.array([0.1, 0.2, 0.3]).astype(np.float32)) # 生成预测值\n",
"target_data = ms.Tensor(np.array([0.1, 0.2, 0.2]).astype(np.float32)) # 生成真实值\n",
"\n",
"output = loss(input_data, target_data)\n",
"print(output)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 损失函数与模型训练\n",
"\n",
"损失函数`MAELoss`自定义完成后，可使用MindSpore的接口[Model](https://www.mindspore.cn/docs/zh-CN/r1.9/api_python/mindspore/mindspore.Model.html#mindspore.Model)中`train`接口进行模型训练，构造`Model`时需传入前向网络、损失函数和优化器，`Model`会在内部将它们关联起来，生成一个可用于训练的网络模型。\n",
"\n",
"在`Model`中，前向网络和损失函数通过[nn.WithLossCell](https://www.mindspore.cn/docs/zh-CN/r1.9/api_python/nn/mindspore.nn.WithLossCell.html#mindspore.nn.WithLossCell)关联起来，`nn.WithLossCell`支持两个输入，分别为`data`和`label`。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T03:42:23.488075Z",
"start_time": "2021-12-29T03:42:23.312491Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 1 step: 10, loss is 7.047606468200684\n",
"epoch: 2 step: 10, loss is 2.6299655437469482\n",
"epoch: 3 step: 10, loss is 3.130779266357422\n",
"epoch: 4 step: 10, loss is 2.1852657794952393\n",
"epoch: 5 step: 10, loss is 1.413834571838379\n"
]
}
],
"source": [
"import mindspore as ms\n",
"from mindspore import dataset as ds\n",
"from mindspore.common.initializer import Normal\n",
"from mindspore import LossMonitor\n",
"\n",
"def get_data(num, w=2.0, b=3.0):\n",
" \"\"\"生成数据及对应标签\"\"\"\n",
" for _ in range(num):\n",
" x = np.random.uniform(-10.0, 10.0)\n",
" noise = np.random.normal(0, 1)\n",
" y = x * w + b + noise\n",
" yield np.array([x]).astype(np.float32), np.array([y]).astype(np.float32)\n",
"\n",
"def create_dataset(num_data, batch_size=16):\n",
" \"\"\"加载数据集\"\"\"\n",
" dataset = ds.GeneratorDataset(list(get_data(num_data)), column_names=['data', 'label'])\n",
" dataset = dataset.batch(batch_size)\n",
" return dataset\n",
"\n",
"class LinearNet(nn.Cell):\n",
" \"\"\"定义线性回归网络\"\"\"\n",
" def __init__(self):\n",
" super(LinearNet, self).__init__()\n",
" self.fc = nn.Dense(1, 1, Normal(0.02), Normal(0.02))\n",
"\n",
" def construct(self, x):\n",
" return self.fc(x)\n",
"\n",
"ds_train = create_dataset(num_data=160)\n",
"net = LinearNet()\n",
"loss = MAELoss()\n",
"opt = nn.Momentum(net.trainable_params(), learning_rate=0.005, momentum=0.9)\n",
"\n",
"# 使用model接口将网络、损失函数和优化器关联起来\n",
"model = ms.Model(net, loss, opt)\n",
"model.train(epoch=5, train_dataset=ds_train, callbacks=[LossMonitor()])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 多标签损失函数与模型训练\n",
"\n",
"上述定义了一个简单的平均绝对误差损失函数`MAELoss`，但许多深度学习应用的数据集较复杂，如目标检测网络Faster R-CNN的数据中就包含多个标签，而非简单的一条数据对应一个标签，这时损失函数的定义和使用略有不同。\n",
"\n",
"本节介绍在多标签数据集场景下，如何定义多标签损失函数（Multi label loss function），并使用Model进行模型训练。\n",
"\n",
"### 多标签数据集\n",
"\n",
"下例通过`get_multilabel_data`函数拟合两组线性数据$y1$和$y2$，拟合的目标函数为：\n",
"\n",
"$$f(x)=2x+3$$\n",
"\n",
"最终数据集应随机分布于函数周边，这里按以下公式的方式生成，其中`noise`为服从标准正态分布的随机值。`get_multilabel_data`函数返回数据$x$、$y1$和$y2$：\n",
"\n",
"$$f(x)=2x+3+noise$$\n",
"\n",
"通过`create_multilabel_dataset`生成多标签数据集，并将`GeneratorDataset`中的`column_names`参数设置为['data', 'label1', 'label2']，最终返回的数据集格式为一条数据`data`对应两个标签`label1`和`label2`。"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from mindspore import dataset as ds\n",
"\n",
"def get_multilabel_data(num, w=2.0, b=3.0):\n",
" for _ in range(num):\n",
" x = np.random.uniform(-10.0, 10.0)\n",
" noise1 = np.random.normal(0, 1)\n",
" noise2 = np.random.normal(-1, 1)\n",
" y1 = x * w + b + noise1\n",
" y2 = x * w + b + noise2\n",
" yield np.array([x]).astype(np.float32), np.array([y1]).astype(np.float32), np.array([y2]).astype(np.float32)\n",
"\n",
"def create_multilabel_dataset(num_data, batch_size=16):\n",
" dataset = ds.GeneratorDataset(list(get_multilabel_data(num_data)), column_names=['data', 'label1', 'label2'])\n",
" dataset = dataset.batch(batch_size) # 每个batch有16个数据\n",
" return dataset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 多标签损失函数\n",
"\n",
"针对上一步创建的多标签数据集，定义多标签损失函数`MAELossForMultiLabel`。\n",
"\n",
"$$ loss1= \\frac{1}{m}\\sum_{i=1}^m\\lvert y1_i-f(x_i) \\rvert$$\n",
"\n",
"$$ loss2= \\frac{1}{m}\\sum_{i=1}^m\\lvert y2_i-f(x_i) \\rvert$$\n",
"\n",
"$$ loss = \\frac{(loss1 + loss2)}{2}$$\n",
"\n",
"上式中，$f(x)$ 为样例标签的预测值，$y1$ 和 $y2$ 为样例标签的真实值，$loss1$ 为预测值与真实值 $y1$ 之间距离的平均值，$loss2$ 为预测值与真实值 $y2$ 之间距离的平均值 ，$loss$ 为损失值 $loss1$ 与损失值 $loss2$ 平均值。\n",
"\n",
"在`MAELossForMultiLabel`中的`construct`方法的输入有三个，预测值`base`，真实值`target1`和`target2`，在`construct`中分别计算预测值与真实值`target1`、预测值与真实值`target2`之间的误差，将两误差取平均后作为最终的损失函数值。\n",
"\n",
"示例代码如下："
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"class MAELossForMultiLabel(nn.LossBase):\n",
" def __init__(self, reduction=\"mean\"):\n",
" super(MAELossForMultiLabel, self).__init__(reduction)\n",
" self.abs = ops.Abs()\n",
"\n",
" def construct(self, base, target1, target2):\n",
" x1 = self.abs(base - target1)\n",
" x2 = self.abs(base - target2)\n",
" return (self.get_loss(x1) + self.get_loss(x2)) / 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 多标签模型训练\n",
"\n",
"使用`Model`关联指定的前向网络、损失函数和优化器时，因`Model`内默认使用的`nn.WithLossCell`只接受两个输入：`data`和`label`，故不适用于多标签场景。\n",
"\n",
"在多标签场景下，若想使用`Model`进行模型训练，则需事先把前向网络与多标签损失函数关联起来，即自定义损失网络。\n",
"\n",
"- 定义损失网络\n",
"\n",
"下例展示了如何定义损失网络`CustomWithLossCell`，其中`__init__`方法的两个参数`backbone`和`loss_fn`分别表示前向网络和损失函数，`construct`方法的输入分别为样例输入`data`和样例真实标签`label1`、`label2`，将样例输入`data`传给前向网络`backbone`，将预测值和两标签值传给损失函数`loss_fn`。"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"class CustomWithLossCell(nn.Cell):\n",
" def __init__(self, backbone, loss_fn):\n",
" super(CustomWithLossCell, self).__init__(auto_prefix=False)\n",
" self._backbone = backbone\n",
" self._loss_fn = loss_fn\n",
"\n",
" def construct(self, data, label1, label2):\n",
" output = self._backbone(data)\n",
" return self._loss_fn(output, label1, label2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 定义网络模型并训练\n",
"\n",
"使用Model连接前向网络、多标签损失函数和优化器时，`Model`的网络`network`指定为自定义的损失网络`loss_net`，损失函数`loss_fn`不指定，优化器仍使用`Momentum`。\n",
"\n",
"在未指定`loss_fn`时，`Model`会默认`network`内部已实现损失函数的逻辑，不再在内部使用`nn.WithLossCell`关联前向网络和损失函数。"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T03:42:24.079033Z",
"start_time": "2021-12-29T03:42:23.851418Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 1 step: 10, loss is 7.504277229309082\n",
"epoch: 2 step: 10, loss is 3.1470584869384766\n",
"epoch: 3 step: 10, loss is 2.810225486755371\n",
"epoch: 4 step: 10, loss is 2.774254322052002\n",
"epoch: 5 step: 10, loss is 1.572474718093872\n"
]
}
],
"source": [
"ds_train = create_multilabel_dataset(num_data=160)\n",
"net = LinearNet()\n",
"\n",
"# 定义多标签损失函数\n",
"loss = MAELossForMultiLabel()\n",
"\n",
"# 定义损失网络，连接前向网络和多标签损失函数\n",
"loss_net = CustomWithLossCell(net, loss)\n",
"\n",
"# 定义优化器\n",
"opt = nn.Momentum(net.trainable_params(), learning_rate=0.005, momentum=0.9)\n",
"\n",
"# 定义Model，多标签场景下Model无需指定损失函数\n",
"model = ms.Model(network=loss_net, optimizer=opt)\n",
"\n",
"model.train(epoch=5, train_dataset=ds_train, callbacks=[LossMonitor()])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"本章节简单讲解了多标签数据集场景下，如何定义损失函数并使用Model进行模型训练。在很多其他场景中，也可采用此类方法进行模型训练。"
]
}
],
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"kernelspec": {
"display_name": "MindSpore1.9GPU",
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