From 230c0665c8f0ea5074264a2aeb121b3b8988f526 Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Mon, 13 Jan 2025 11:37:05 +0800 Subject: [PATCH 1/7] add simple sgd tutorial --- README.md | 2 +- api-examples/README.md | 13 +- api-examples/optimizer/README.md | 0 api-examples/optimizer/sgd.md | 112 ++++++++++++++++++ .../create_a_simple_nerual_network.md | 29 +++++ 5 files changed, 149 insertions(+), 7 deletions(-) create mode 100644 api-examples/optimizer/README.md create mode 100644 api-examples/optimizer/sgd.md create mode 100644 model-examples/create_a_simple_nerual_network.md diff --git a/README.md b/README.md index 160f956..b569470 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,5 @@ ### guide - [mindspore 安装指南](./installation/installation.md) -- mindspore API 案例 +- [mindspore API 案例](./api-examples/README.md) - [mindspore 模型案例](./model-examples/README.md) diff --git a/api-examples/README.md b/api-examples/README.md index 5aae743..2b15685 100644 --- a/api-examples/README.md +++ b/api-examples/README.md @@ -1,8 +1,9 @@ ### 目录: -| 类别 | 链接 | -|:--|:-- | -| ops | [operator](./operator) | -| nn | [nerual network](./nn) | -| tensor | [tensor](./tensor) | -| runtime | [runtime](./runtime) | +| 类别 | 链接 | +|:---|:-----------------------------------| +| ops | [operator](./operator) | +| nn | [nerual network](./nn) | +| optimizer | [optimizer](./optimizer/README.md) | +| tensor | [tensor](./tensor) | +| runtime | [runtime](./runtime) | diff --git a/api-examples/optimizer/README.md b/api-examples/optimizer/README.md new file mode 100644 index 0000000..e69de29 diff --git a/api-examples/optimizer/sgd.md b/api-examples/optimizer/sgd.md new file mode 100644 index 0000000..1348c1c --- /dev/null +++ b/api-examples/optimizer/sgd.md @@ -0,0 +1,112 @@ +# sgd 优化器 + +> 基于 MindSpore 2.4.0 版本 + +## guide + +- [从0开始创建一个sgd优化器](#从0开始创建一个sgd优化器) +- [加速]() + +## 从0开始创建一个sgd优化器 + +- 第一步：定义sgd优化过程 + + ```python + from mindspore import ops + + def sgd_update(weights, grads, lr): + for w, dw in weights, grads: + ops.assign(w, w - lr * dw) + ``` + +- 第二步：更新模型参数 + + > `Net` 模型定义请[参考](../../model-examples/create_a_simple_nerual_network.md) + + ```python + import mindspore + from mindspore import Tensor + import numpy as np + + net = Net() + net.trainable_params() + grad_fn = mindspore.value_and_grad(net, None, net.trainable_params(), has_aux=False) + + def train(): + total_step = 10 + x, y = Tensor(np.random.randn(1, 1, 16, 16)), Tensor(np.ones(1)) + + for current_step in range(total_step): + loss, grads = grad_fn(x, y) + sgd_update(net.trainable_params(), grads, 0.01) + print(f"loss: {loss:>7f} [{current_step + 1:>5d}/{total_step:>5d}]") + ``` + +- 当然我们也可以将 `sgd` 优化器定义为一个类对象 + + ```python + from mindspore import nn, ops + + class SGD(nn.Cell): + def __init__(self, weights, lr): + super(SGD, self).__init__() + self.weights = weights + self.lr = lr + + def construct(self, grads): + for w, dw in self.weights, grads: + ops.assign(w, w - self.lr * dw) + ``` + +## 加速 + +- 使用 JIT(Just-In-Time) 编译加速 + + ```diff + import mindspore + from mindspore import nn, ops + + class SGD(nn.Cell): + def __init__(self, weights, lr): + super(SGD, self).__init__() + self.weights = weights + self.lr = lr + + + @mindspore.jit + def construct(self, grads): + for w, dw in self.weights, grads: + ops.assign(w, w - self.lr * dw) + ``` + +- 使用 `mindspore.ops.HyperMap` 操作替换 `for` 循环 + + ```diff + import mindspore + from mindspore import nn, ops + + +sgd_update = ops.MultitypeFuncGraph("_sgd_update") + + + +@sgd_update.register("Tensor", "Tensor", "Tensor") + +def run_sgd_update(lr, grad, weight): + + """Apply sgd optimizer to the weight parameter using Tensor.""" + + success = True + + ops.depend(success, ops.assign(weight, weight - lr * grad)) + + return success + + class SGD(nn.Cell): + def __init__(self, weights, lr): + super(SGD, self).__init__() + self.weights = weights + self.lr = lr + + self.hyper_map = ops.HyperMap() + + @mindspore.jit + def construct(self, grads): + - for w, dw in self.weights, grads: + - ops.assign(w, w - self.lr * dw) + + return self.hyper_map( + + ops.partial(sgd_update, self.lr), + + self.weights, + + grads + + ) + ``` diff --git a/model-examples/create_a_simple_nerual_network.md b/model-examples/create_a_simple_nerual_network.md new file mode 100644 index 0000000..8a33bf8 --- /dev/null +++ b/model-examples/create_a_simple_nerual_network.md @@ -0,0 +1,29 @@ +# 创建一个简单的神经网络 + +```python +from mindspore import nn, Tensor +import numpy as np + +class Net(nn.Cell): + def __init__(self): + super(Net, self).__init__() + self.mlp = nn.SequentialCell([ + nn.Dense(16*16, 128), + nn.ReLU(), + nn.Dense(128, 128), + nn.ReLU(), + nn.Dense(128, 10), + ]) + self.loss_fn = nn.CrossEntropyLoss() + + def construct(self, x, y): + x = self.mlp(x) + loss = self.loss_fn(x, y) + return loss + +net = Net() +x, y = Tensor(np.random.randn(1, 1, 16, 16)), Tensor(np.ones(1)) + +print(net) +print(net(x, y)) +``` From fe7ebc5c64c67726203f30d8cbaf8a4726848278 Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Mon, 13 Jan 2025 11:41:30 +0800 Subject: [PATCH 2/7] 1 --- api-examples/optimizer/sgd.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/api-examples/optimizer/sgd.md b/api-examples/optimizer/sgd.md index 1348c1c..37b819a 100644 --- a/api-examples/optimizer/sgd.md +++ b/api-examples/optimizer/sgd.md @@ -62,7 +62,7 @@ - 使用 JIT(Just-In-Time) 编译加速 - ```diff + ```pycon import mindspore from mindspore import nn, ops From f59cd99cd99a53e4a70e6d7908aca04af47d99bc Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Mon, 13 Jan 2025 11:42:14 +0800 Subject: [PATCH 3/7] 1 --- api-examples/optimizer/sgd.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/api-examples/optimizer/sgd.md b/api-examples/optimizer/sgd.md index 37b819a..055264a 100644 --- a/api-examples/optimizer/sgd.md +++ b/api-examples/optimizer/sgd.md @@ -62,7 +62,7 @@ - 使用 JIT(Just-In-Time) 编译加速 - ```pycon + ```python import mindspore from mindspore import nn, ops From 2719dba822dc970600387bee6b30ed1eb48b5558 Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Mon, 13 Jan 2025 14:44:46 +0800 Subject: [PATCH 4/7] update --- api-examples/optimizer/README.md | 6 +++ .../{sgd.md => create_a_simple_sgd.md} | 53 ++++++++++--------- 2 files changed, 33 insertions(+), 26 deletions(-) rename api-examples/optimizer/{sgd.md => create_a_simple_sgd.md} (69%) diff --git a/api-examples/optimizer/README.md b/api-examples/optimizer/README.md index e69de29..94e07de 100644 --- a/api-examples/optimizer/README.md +++ b/api-examples/optimizer/README.md @@ -0,0 +1,6 @@ +# 优化器 + + +| 案例 | 说明 | MindSpore版本 | +|:---------------------------------------------|:----|:----------------| +| [从零开始写一个简单的sgd优化器](./create_a_simple_sgd.md) | 无 | MindSpore 2.4.0 | diff --git a/api-examples/optimizer/sgd.md b/api-examples/optimizer/create_a_simple_sgd.md similarity index 69% rename from api-examples/optimizer/sgd.md rename to api-examples/optimizer/create_a_simple_sgd.md index 055264a..ee25d14 100644 --- a/api-examples/optimizer/sgd.md +++ b/api-examples/optimizer/create_a_simple_sgd.md @@ -1,15 +1,17 @@ -# sgd 优化器 +# 从零开始写一个简单的sgd优化器 -> 基于 MindSpore 2.4.0 版本 +> 备注：以下示例使用的是 MindSpore 2.4.0 版本 -## guide +## 目录 -- [从0开始创建一个sgd优化器](#从0开始创建一个sgd优化器) -- [加速]() +- [从零开始创建一个sgd优化器](#section1) +- [加速](#section2) -## 从0开始创建一个sgd优化器 -- 第一步：定义sgd优化过程 + +## 从零开始创建一个`sgd`优化器 + +- 第一步：定义`sgd`优化过程 ```python from mindspore import ops @@ -58,9 +60,10 @@ ops.assign(w, w - self.lr * dw) ``` + ## 加速 -- 使用 JIT(Just-In-Time) 编译加速 +- 使用 `JIT(Just-In-Time)` 编译加速 ```python import mindspore @@ -72,7 +75,7 @@ self.weights = weights self.lr = lr - + @mindspore.jit + @mindspore.jit def construct(self, grads): for w, dw in self.weights, grads: ops.assign(w, w - self.lr * dw) @@ -80,33 +83,31 @@ - 使用 `mindspore.ops.HyperMap` 操作替换 `for` 循环 - ```diff + ```python import mindspore from mindspore import nn, ops - +sgd_update = ops.MultitypeFuncGraph("_sgd_update") - + - +@sgd_update.register("Tensor", "Tensor", "Tensor") - +def run_sgd_update(lr, grad, weight): - + """Apply sgd optimizer to the weight parameter using Tensor.""" - + success = True - + ops.depend(success, ops.assign(weight, weight - lr * grad)) - + return success + sgd_update = ops.MultitypeFuncGraph("_sgd_update") + + @sgd_update.register("Tensor", "Tensor", "Tensor") + def run_sgd_update(lr, grad, weight): + """Apply sgd optimizer to the weight parameter using Tensor.""" + success = True + ops.depend(success, ops.assign(weight, weight - lr * grad)) + return success class SGD(nn.Cell): def __init__(self, weights, lr): super(SGD, self).__init__() self.weights = weights self.lr = lr - + self.hyper_map = ops.HyperMap() + self.hyper_map = ops.HyperMap() @mindspore.jit def construct(self, grads): - - for w, dw in self.weights, grads: - - ops.assign(w, w - self.lr * dw) - + return self.hyper_map( - + ops.partial(sgd_update, self.lr), - + self.weights, - + grads - + ) + return self.hyper_map( + ops.partial(sgd_update, self.lr), + self.weights, + grads + ) ``` From b72bbda3867dc8938d96ee7a3a7f9d4e582945c1 Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Tue, 14 Jan 2025 16:55:24 +0800 Subject: [PATCH 5/7] add auto-grad with function --- api-examples/README.md | 15 +- api-examples/auto-grad/README.md | 5 + .../taking_gradients_with_mindspore_grad.md | 153 ++++++++++++++++++ 3 files changed, 166 insertions(+), 7 deletions(-) create mode 100644 api-examples/auto-grad/README.md create mode 100644 api-examples/auto-grad/taking_gradients_with_mindspore_grad.md diff --git a/api-examples/README.md b/api-examples/README.md index 2b15685..1c5e1cc 100644 --- a/api-examples/README.md +++ b/api-examples/README.md @@ -1,9 +1,10 @@ ### 目录: -| 类别 | 链接 | -|:---|:-----------------------------------| -| ops | [operator](./operator) | -| nn | [nerual network](./nn) | -| optimizer | [optimizer](./optimizer/README.md) | -| tensor | [tensor](./tensor) | -| runtime | [runtime](./runtime) | +| 类别 | 链接 | +|:----------|:---------------------------------------------------| +| ops | [operator](./operator) | +| nn | [nerual network](./nn) | +| optimizer | [optimizer](./optimizer/README.md) | +| auto-grad | [automatic differentiation](./auto-grad/README.md) | +| tensor | [tensor](./tensor) | +| runtime | [runtime](./runtime) | diff --git a/api-examples/auto-grad/README.md b/api-examples/auto-grad/README.md new file mode 100644 index 0000000..f458b0b --- /dev/null +++ b/api-examples/auto-grad/README.md @@ -0,0 +1,5 @@ +# 自动微分接口 + +| 案例 | 说明 | MindSpore版本 | +|:------------------------------------------------------------------|:----|:----------------| +| [使用mindspore对函数求导](./taking_gradients_with_mindspore_grad.md) | 无 | MindSpore 2.4.0 | diff --git a/api-examples/auto-grad/taking_gradients_with_mindspore_grad.md b/api-examples/auto-grad/taking_gradients_with_mindspore_grad.md new file mode 100644 index 0000000..3c80552 --- /dev/null +++ b/api-examples/auto-grad/taking_gradients_with_mindspore_grad.md @@ -0,0 +1,153 @@ +# 使用mindspore对函数求导 + +> 备注：以下示例使用的是 MindSpore 2.4.0 版本 + +## 目录 + +- [使用`mindspore.grad`对函数进行求导](#section1) +- [使用`mindspore.grad`计算线性逻辑回归的梯度](#section2) +- [使用`mindspore.value_and_grad`计算梯度与数值](#section3) + +
+ + +## 使用`mindspore.grad`对函数进行求导 + +`f(x) = x^3 - 2x + 1` 的导数可以计算为： + +$$ +\begin{aligned} +& f(x) = x^3 - 2x + 1 \\ +& f'(x) = 3x - 2 \\ +& f''(x) = 3 +\end{aligned} +$$ + +使用MindSpore可以简单的表示为： + +```python +from mindspore import grad, Tensor + +f = lambda x: x**3 - 2*x + 1 + +dfdx = grad(f) +d2fdx = grad(grad(f)) +``` + +当`x=1`时，对上述内容进行评估可以得到： + +$$ +\begin{aligned} +& f(1) = 0 \\ +& f'(1) = 1 \\ +& f''(1) = 3 +\end{aligned} +$$ + +使用MindSpore: + +```python +print(f(Tensor(1.0))) +print(dfdx(Tensor(1.0))) +print(d2fdx(Tensor(1.0))) +``` + + +## 使用`mindspore.grad`计算线性逻辑回归的梯度 + +首先，我们做如下定义： + +```python +from mindspore import ops, grad, Tensor, set_seed + +set_seed(0) + +inputs = ops.randn((4, 3)) +targets = Tensor([True, True, False, True]) + +W, b = ops.randn((3,)), ops.randn((1,)) + +def loss(inputs, targets, W, b): + preds = ops.sigmoid(ops.matmul(inputs, W) + b) + logit_loss = preds * targets + (1 - preds) * (1 - targets) + return -ops.log(logit_loss).sum() + +print(f"inputs: {inputs}") +print(f"targets: {targets}") +print(f"W: {W}") +print(f"b: {b}") +``` + +分别计算`W`和`b`等输入的梯度： + +```python +x_grad = grad(loss, grad_position=0)(inputs, targets, W, b) +print(f'x_grad: {x_grad}') + +y_grad = grad(loss, 1)(inputs, targets, W, b) +print(f'y_grad: {y_grad}') + +W_grad = grad(loss, 2)(inputs, targets, W, b) +print(f'W_grad: {W_grad}') + +b_grad = grad(loss, 3)(W, b) +print(f'b_grad: {b_grad}') +``` + +当然也可以一次性计算所需要的梯度： + +```python +(W_grad, b_grad) = grad(loss, (2, 3))(inputs, targets, W, b) +print(f'W_grad: {W_grad}') +print(f'b_grad: {b_grad}') +``` + +如果函数输出多个`loss`，计算的梯度是所有`loss`对输入的导数， + +```python +def multi_loss(inputs, targets, W, b): + loss1 = loss(inputs, targets, W, b) + loss2 = (W ** 2).sum() + return loss1, loss2 + +(W_grad, b_grad) = grad(multi_loss, (2, 3))(inputs, targets, W, b) +print(f'W_grad: {W_grad}, b_grad: {b_grad}') +``` + +如果只想计算`loss1`的梯度，可以尝试用`ops.stop_gradient`进行截断： + +```python +def multi_loss_2(inputs, targets, W, b): + loss1 = loss(inputs, targets, W, b) + loss2 = (W ** 2).sum() + return loss1, ops.stop_gradient(loss2) + +(W_grad, b_grad) = grad(multi_loss_2, (2, 3))(inputs, targets, W, b) +print(f'W_grad: {W_grad}, b_grad: {b_grad}') +``` + +或者，也可以通过设置`has_aux=True`排除除了第一个以外的输出对梯度的影响： + +```python +(W_grad, b_grad) = grad(multi_loss, (2, 3), has_aux=True)(inputs, targets, W, b) +print(f'W_grad: {W_grad}, b_grad: {b_grad}') +``` + +`mindspore.grad`接口的更多细节可以参考 [MindSpore Docs](https://www.mindspore.cn/docs/zh-CN/r2.4.0/api_python/mindspore/mindspore.grad.html) + + + +## 使用`mindspore.value_and_grad`计算梯度与数值 + +计算线性逻辑回归函数的梯度，并获取`loss`： + +```python +from mindspore import value_and_grad + +loss, (W_grad, b_grad) = value_and_grad(loss, (2, 3))(inputs, targets, W, b) + +print(f"loss: {loss}") +print(f'W_grad: {W_grad}, b_grad: {b_grad}') +``` + +`mindspore.value_and_grad`接口的更多细节可以参考 [MindSpore Docs](https://www.mindspore.cn/docs/zh-CN/r2.4.0/api_python/mindspore/mindspore.value_and_grad.html) From 443fffae69face6aebe9d01ca2cd7b88edff639d Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Tue, 14 Jan 2025 17:53:50 +0800 Subject: [PATCH 6/7] update auto-grad --- api-examples/auto-grad/README.md | 7 +- ...dients_of_function_with_mindspore_grad.md} | 8 +- ..._gradients_of_model_with_mindspore_grad.md | 75 +++++++++++++++++++ 3 files changed, 83 insertions(+), 7 deletions(-) rename api-examples/auto-grad/{taking_gradients_with_mindspore_grad.md => taking_gradients_of_function_with_mindspore_grad.md} (94%) create mode 100644 api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md diff --git a/api-examples/auto-grad/README.md b/api-examples/auto-grad/README.md index f458b0b..d06d666 100644 --- a/api-examples/auto-grad/README.md +++ b/api-examples/auto-grad/README.md @@ -1,5 +1,6 @@ # 自动微分接口 -| 案例 | 说明 | MindSpore版本 | -|:------------------------------------------------------------------|:----|:----------------| -| [使用mindspore对函数求导](./taking_gradients_with_mindspore_grad.md) | 无 | MindSpore 2.4.0 | +| 案例 | 说明 | MindSpore版本 | +|:--------------------------------------------------------------------------|:----|:----------------| +| [使用mindspore对函数求导](./taking_gradients_of_function_with_mindspore_grad.md) | 无 | MindSpore 2.4.0 | +| [使用mindspore对模型求导](./taking_gradients_of_model_with_mindspore_grad.md) | 无 | MindSpore 2.4.0 | diff --git a/api-examples/auto-grad/taking_gradients_with_mindspore_grad.md b/api-examples/auto-grad/taking_gradients_of_function_with_mindspore_grad.md similarity index 94% rename from api-examples/auto-grad/taking_gradients_with_mindspore_grad.md rename to api-examples/auto-grad/taking_gradients_of_function_with_mindspore_grad.md index 3c80552..fa88e59 100644 --- a/api-examples/auto-grad/taking_gradients_with_mindspore_grad.md +++ b/api-examples/auto-grad/taking_gradients_of_function_with_mindspore_grad.md @@ -6,7 +6,7 @@ - [使用`mindspore.grad`对函数进行求导](#section1) - [使用`mindspore.grad`计算线性逻辑回归的梯度](#section2) -- [使用`mindspore.value_and_grad`计算梯度与数值](#section3) +- [使用`mindspore.value_and_grad`计算梯度与损失](#section3)
@@ -34,7 +34,7 @@ dfdx = grad(f) d2fdx = grad(grad(f)) ``` -当`x=1`时，对上述内容进行评估可以得到： +当`x=1`时，对上述内容进行验证可以得到： $$ \begin{aligned} @@ -44,7 +44,7 @@ $$ \end{aligned} $$ -使用MindSpore: +在MindSpore中运行: ```python print(f(Tensor(1.0))) @@ -137,7 +137,7 @@ print(f'W_grad: {W_grad}, b_grad: {b_grad}') -## 使用`mindspore.value_and_grad`计算梯度与数值 +## 使用`mindspore.value_and_grad`计算梯度与损失 计算线性逻辑回归函数的梯度，并获取`loss`： diff --git a/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md b/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md new file mode 100644 index 0000000..536fb17 --- /dev/null +++ b/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md @@ -0,0 +1,75 @@ +# 使用mindspore对模型求导 + +> 备注：以下示例使用的是 MindSpore 2.4.0 版本 + +## 计算模型输出对权重的梯度 + +先定义一个简单的模型 + +```python +from mindspore import nn, Parameter +import numpy as np + +np.random.seed(0) + +class Net(nn.Cell): + def __init__(self): + super(Net, self).__init__() + self.w = Parameter(np.random.randn(4, 4)) + self.b = Parameter(np.random.randn(4,)) + + def construct(self, x, y): + pred = self.w @ x + self.b + loss = (pred - y) ** 2 + return loss.sum() + +net = Net() + +print(f"net: \n{net}") +print(f"parameters of net: \n{net.get_parameters()}") +``` + +使用`mindspore.grad`接口计算模型对权重的梯度 + +> 注意：这里不需要计算模型对输入的梯度，所以设置`grad_position=None` + +```python +from mindspore import grad, Tensor +import numpy as np + +x, y = Tensor(np.random.randn(2, 4)), Tensor([1.0]) + +grad_fn = grad(net, grad_position=None, weights=net.get_parameters()) + +grads = grad_fn(x, y) + +print(f"grads: \n{grads}") +``` + +当然我们也可以使用`mindspore.value_and_grad`接口计算模型对权重的梯度并获取`loss`的情况 + +```python +from mindspore import value_and_grad + +grad_fn = value_and_grad(net, grad_position=None, weights=net.get_parameters()) + +loss, grads = grad_fn(x, y) + +print(f"loss: {loss}") +print(f"grads: \n{grads}") +``` + +使用 `JIT(Just-In-Time)` 编译加速 + +```python +from mindspore import jit + +@jit +def loss_and_grads(): + return grad_fn(x, y) + +loss, grads = loss_and_grads(x, y) + +print(f"loss: {loss}") +print(f"grads: \n{grads}") +``` From 9bca803117e25e73d1207ecad81ae1442935df16 Mon Sep 17 00:00:00 2001 From: zhanghuiyao <1814619459@qq.com> Date: Tue, 14 Jan 2025 17:55:12 +0800 Subject: [PATCH 7/7] update --- .../auto-grad/taking_gradients_of_model_with_mindspore_grad.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md b/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md index 536fb17..cdeedca 100644 --- a/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md +++ b/api-examples/auto-grad/taking_gradients_of_model_with_mindspore_grad.md @@ -2,7 +2,7 @@ > 备注：以下示例使用的是 MindSpore 2.4.0 版本 -## 计算模型输出对权重的梯度 +## 计算模型对权重的梯度 先定义一个简单的模型