From b0303a72e4d59faf3ff7b43c14cc738a06fb52d7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 19:57:13 +0800
Subject: [PATCH 1/7] =?UTF-8?q?=E6=96=B0=E5=BB=BA=2017307110367?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 assignment-2/submission/17307110367/.keep | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assignment-2/submission/17307110367/.keep

diff --git a/assignment-2/submission/17307110367/.keep b/assignment-2/submission/17307110367/.keep
new file mode 100644
index 0000000..e69de29
-- 
Gitee


From 45ad7cb8df16a9b3cf6817929e5db0b34b40c19a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 19:58:02 +0800
Subject: [PATCH 2/7] =?UTF-8?q?=E6=96=B0=E5=BB=BA=20img?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 assignment-2/submission/17307110367/img/.keep | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assignment-2/submission/17307110367/img/.keep

diff --git a/assignment-2/submission/17307110367/img/.keep b/assignment-2/submission/17307110367/img/.keep
new file mode 100644
index 0000000..e69de29
-- 
Gitee


From ecdd2fb2ce9ff0a77ed03501f92b9f1ad57f14b8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 19:59:29 +0800
Subject: [PATCH 3/7] !1 [submission] assignment-2 of 17307110367

---
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 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 assignment-2/submission/17307110367/img/loss_value1.png

diff --git a/assignment-2/submission/17307110367/img/loss_value1.png b/assignment-2/submission/17307110367/img/loss_value1.png
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HcmV?d00001

-- 
Gitee


From dd3f886ed06629a0891e4c9dab86b3c0d75c9c59 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 23:36:48 +0800
Subject: [PATCH 4/7] !1 [submission] assignment-2 of 17307110367

---
 .../submission/17307110367/homework2.md       | 186 ++++++++++++++++++
 1 file changed, 186 insertions(+)
 create mode 100644 assignment-2/submission/17307110367/homework2.md

diff --git a/assignment-2/submission/17307110367/homework2.md b/assignment-2/submission/17307110367/homework2.md
new file mode 100644
index 0000000..cbd41bb
--- /dev/null
+++ b/assignment-2/submission/17307110367/homework2.md
@@ -0,0 +1,186 @@
+# 课程报告
+
+##   模型的训练与测试
+
+直接运行numpy_minist.py，设定batch_size =128, learning_rate = 0.1, epoch_number = 3得到如下的结果:
+
+| 轮次 | Accuracy |
+| ---- | -------- |
+| [0]  | 0.9474   |
+| [1]  | 0.9654   |
+| [2]  | 0.9704   |
+
+得到的损失函数的变化如下图所示：
+
+![avatar](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-2/submission/17307110367/img/loss_value1.png)
+
+**减小batch_size的值为 64**，保持其他的参数不变进行实验，得到结果如下：
+
+| 轮次 | Accuracy |
+| ---- | -------- |
+| [0]  | 0.9548   |
+| [1]  | 0.9682   |
+| [2]  | 0.9679   |
+
+可见当batch_size 减小时，模型准确率在每一轮中进步的幅度会变小。
+
+
+
+## mini_batch 的替换
+
+```
+def mini_batch(dataset, batch_size=128,seed=0):
+    np.random.seed(seed)
+    x_train = dataset.train_data
+    y_train = dataset.train_labels
+    m = y_train.shape[0]
+    def mini_batch(dataset, batch_size=128,seed=0):
+    np.random.seed(seed)
+    x_train = dataset.train_data
+    y_train = dataset.train_labels
+    m = y_train.shape[0]
+    # m为所有样本的数量
+    mini_batchs =[]
+    permutation = list(np.random.permutation(m))
+    # 打乱样本顺序
+    shuffle_X = x_train[permutation, :, :]
+    shuffle_Y = y_train[permutation]
+    num_mini_batch = int(m//batch_size)
+    # num_mini_batch为mini_batch的块数
+    for i in range(num_mini_batch):
+        mini_batch_x = shuffle_X[i*batch_size:(i+1)*batch_size, :, :]
+        mini_batch_y = shuffle_Y[i*batch_size:(i+1)*batch_size]
+        mini_batch = (mini_batch_x, mini_batch_y)
+        mini_batchs.append(mini_batch)
+    if m % batch_size != 0:
+        # 如果样本数不能被整除，取余下的部分
+        mini_batch_X = shuffle_X[num_mini_batch * batch_size:m, :, :]
+        mini_batch_Y = shuffle_Y[num_mini_batch * batch_size:m]
+        mini_batch = (mini_batch_X, mini_batch_Y)
+        mini_batchs.append(mini_batch)
+    return mini_batchs
+    mini_batchs =[]
+    permutation = list(np.random.permutation(m))
+    shuffle_X = x_train[permutation, :, :]
+    shuffle_Y = y_train[permutation]
+    num_mini_batch = int(m//batch_size)
+    for i in range(num_mini_batch):
+        mini_batch_x = shuffle_X[i*batch_size:(i+1)*batch_size, :, :]
+        mini_batch_y = shuffle_Y[i*batch_size:(i+1)*batch_size]
+        mini_batch = (mini_batch_x, mini_batch_y)
+        mini_batchs.append(mini_batch)
+    if m % batch_size != 0:
+        # 如果样本数不能被整除，取余下的部分
+        mini_batch_X = shuffle_X[num_mini_batch * batch_size:m, :, :]
+        mini_batch_Y = shuffle_Y[num_mini_batch * batch_size:m]
+        mini_batch = (mini_batch_X, mini_batch_Y)
+        mini_batchs.append(mini_batch)
+    return mini_batchs
+```
+
+整体思路是打乱样本的顺序，然后依次取出batch_size个样本的数据，作为一个mini_batch组。最后mini_batch函数返回所有的mini_batch组的集合
+
+用numpy实现mini_batch之后，运行numpy_minist.py， 设定batch_size =128, learning_rate = 0.1, epoch_number = 3， 得到的实验结果如下：
+
+| 轮次 | Accuracy |
+| ---- | -------- |
+| [0]  | 0.8780   |
+| [1]  | 0.8994   |
+| [2]  | 0.9099   |
+
+
+
+## 反向传播公式的推导
+
+**Matmul**
+
+Matmul的计算式为
+$$
+Y = X*W
+$$
+根据矩阵的求导法则，可以推出
+$$
+\frac{\partial Y}{\partial X} = W^{T}
+$$
+
+$$
+\frac{\partial Y}{\partial W} = X^{T}
+$$
+
+ 对应代码段如下：
+
+```
+grad_W = np.matmul(self.memory['x'].T, grad_y)
+grad_x = np.matmul(grad_y, self.memory['W'].T)
+```
+
+
+
+**Relu**
+
+Relu的计算公式为
+$$
+Y=\begin{cases}
+X&X\ge0\\\\
+0&\text{otherwise}
+\end{cases}
+$$
+所以有
+$$
+\frac{\partial Y}{\partial X}=\begin{cases}
+1&X>0\\\\
+0&\text{otherwise}
+\end{cases}
+$$
+对应代码块如下：
+
+```
+grad_x = np.where(self.memory['x'] > 0, grad_y, np.zeros_like(self.memory['x']))
+```
+
+意思是说若x大于0， grad_x的结果就是传入的grad_y。否则结果为0
+
+
+
+**Log**
+
+log的计算公式为
+$$
+Y=\ln(X+\epsilon)
+$$
+因此有
+$$
+\frac{\partial Y}{\partial X} = \frac1{X+\epsilon}
+$$
+对应的代码块如下：
+
+```
+grad_x = np.multiply(1./(self.memory['x'] + self.epsilon), grad_y)
+```
+
+
+
+**Softmax**
+
+Softmax的计算公式为
+$$
+Y=\frac{\exp\{X\}}{\sum_{k=1}^c\exp\{X\}}
+$$
+根据邱老师书第411~412页对该公式的导数的推导（在这里直接引用结果），有
+
+
+$$
+\frac{\partial Y}{\partial X} = diag(softmax(x))-softmax(x)softmax(x)^{T}
+$$
+对应的代码块如下
+
+```
+out = self.memory['out']
+grad_x = []
+for idx in range(out.shape[0]):
+	dout = np.diag(out[idx]) - np.outer(out[idx], out[idx])
+    grad = np.matmul(dout, grad_y[idx])
+    grad_x.append(grad)
+grad_x = np.array(grad_x)
+```
+
-- 
Gitee


From 2b54ae73fd17235e0e0a945986c9747dab266174 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 23:40:39 +0800
Subject: [PATCH 5/7] update assignment-2/submission/17307110367/homework2.md.

---
 assignment-2/submission/17307110367/homework2.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/assignment-2/submission/17307110367/homework2.md b/assignment-2/submission/17307110367/homework2.md
index cbd41bb..9b99779 100644
--- a/assignment-2/submission/17307110367/homework2.md
+++ b/assignment-2/submission/17307110367/homework2.md
@@ -12,7 +12,7 @@
 
 得到的损失函数的变化如下图所示：
 
-![avatar](https://gitee.com/zhang-yanlin17/prml-21-spring/blob/master/assignment-2/submission/17307110367/img/loss_value1.png)
+<img src="./img/loss_value1.png" alt="loss" style="zoom:50%;" />
 
 **减小batch_size的值为 64**，保持其他的参数不变进行实验，得到结果如下：
 
-- 
Gitee


From 2730466eb45790e1746dac5879173e8b3e9158eb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 23:41:30 +0800
Subject: [PATCH 6/7] !1 [submission] assignment-2 of 17307110367

---
 .../submission/17307110367/numpy_fnn.py       | 173 ++++++++++++++++++
 .../submission/17307110367/numpy_mnist.py     |  62 +++++++
 2 files changed, 235 insertions(+)
 create mode 100644 assignment-2/submission/17307110367/numpy_fnn.py
 create mode 100644 assignment-2/submission/17307110367/numpy_mnist.py

diff --git a/assignment-2/submission/17307110367/numpy_fnn.py b/assignment-2/submission/17307110367/numpy_fnn.py
new file mode 100644
index 0000000..ea2d68f
--- /dev/null
+++ b/assignment-2/submission/17307110367/numpy_fnn.py
@@ -0,0 +1,173 @@
+import numpy as np
+
+
+class NumpyOp:
+
+    def __init__(self):
+        self.memory = {}
+        self.epsilon = 1e-12
+
+
+class Matmul(NumpyOp):
+
+    def forward(self, x, W):
+        """
+        x: shape(N, d)
+        w: shape(d, d')
+        """
+        self.memory['x'] = x
+        self.memory['W'] = W
+        h = np.matmul(x, W)
+        return h
+
+    def backward(self, grad_y):
+        """
+        grad_y: shape(N, d')
+        """
+        grad_W = np.matmul(self.memory['x'].T, grad_y)
+        grad_x = np.matmul(grad_y, self.memory['W'].T)
+
+        return grad_x, grad_W
+
+
+class Relu(NumpyOp):
+
+    def forward(self, x):
+        self.memory['x'] = x
+        return np.where(x > 0, x, np.zeros_like(x))
+
+    def backward(self, grad_y):
+        """
+        grad_y: same shape as x
+        """
+
+        grad_x = np.where(self.memory['x'] > 0, grad_y, np.zeros_like(self.memory['x']))
+
+        return grad_x
+
+
+class Log(NumpyOp):
+
+    def forward(self, x):
+        """
+        x: shape(N, c)
+        """
+
+        out = np.log(x + self.epsilon)
+        self.memory['x'] = x
+
+        return out
+
+    def backward(self, grad_y):
+        """
+        grad_y: same shape as x
+        """
+
+        grad_x = np.multiply(1./(self.memory['x'] + self.epsilon), grad_y)
+
+        return grad_x
+
+
+class Softmax(NumpyOp):
+    """
+    softmax over last dimension
+    """
+
+    def forward(self, x):
+        """
+        x: shape(N, c)
+        """
+        out = []
+        for index in range(x.shape[0]):
+            temp = x[index]
+            temp = temp - max(temp)
+            temp = np.exp(temp)
+            out.append(temp/sum(temp))
+        out = np.array(out)
+        self.memory['out'] = out
+        return out
+
+    def backward(self, grad_y):
+        """
+        grad_y: same shape as x
+        """
+
+        out = self.memory['out']
+        grad_x = []
+        for idx in range(out.shape[0]):
+            dout = np.diag(out[idx]) - np.outer(out[idx], out[idx])
+            grad = np.matmul(dout, grad_y[idx])
+            grad_x.append(grad)
+        grad_x = np.array(grad_x)
+
+        return grad_x
+
+
+class NumpyLoss:
+
+    def __init__(self):
+        self.target = None
+
+    def get_loss(self, pred, target):
+        self.target = target
+        return (-pred * target).sum(axis=1).mean()
+
+    def backward(self):
+        return -self.target / self.target.shape[0]
+
+
+class NumpyModel:
+    def __init__(self):
+        self.W1 = np.random.normal(size=(28 * 28, 256))
+        self.W2 = np.random.normal(size=(256, 64))
+        self.W3 = np.random.normal(size=(64, 10))
+
+        # 以下算子会在 forward 和 backward 中使用
+        self.matmul_1 = Matmul()
+        self.relu_1 = Relu()
+        self.matmul_2 = Matmul()
+        self.relu_2 = Relu()
+        self.matmul_3 = Matmul()
+        self.softmax = Softmax()
+        self.log = Log()
+
+        # 以下变量需要在 backward 中更新。 softmax_grad, log_grad 等为算子反向传播的梯度（ loss 关于算子输入的偏导）
+        self.x1_grad, self.W1_grad = None, None
+        self.relu_1_grad = None
+        self.x2_grad, self.W2_grad = None, None
+        self.relu_2_grad = None
+        self.x3_grad, self.W3_grad = None, None
+        self.softmax_grad = None
+        self.log_grad = None
+
+    def forward(self, x):
+        x = x.reshape(-1, 28 * 28)
+
+        x = x.reshape(-1, 28 * 28)
+        x = self.relu_1.forward(self.matmul_1.forward(x, self.W1))
+        x = self.relu_2.forward(self.matmul_2.forward(x, self.W2))
+        x = self.matmul_3.forward(x, self.W3)
+        x = self.softmax.forward(x)
+        x = self.log.forward(x)
+        return x
+
+    def backward(self, y):
+        self.log_grad = self.log.backward(y)
+        grad_y = self.log_grad
+        self.softmax_grad = self.softmax.backward(grad_y)
+        grad_y = self.softmax_grad
+        self.x3_grad, self.W3_grad = self.matmul_3.backward(grad_y)
+        grad_y = self.x3_grad
+        self.relu_2_grad =self.relu_2.backward(grad_y)
+        grad_y = self.relu_2_grad
+        self.x2_grad, self.W2_grad =self.matmul_2.backward(grad_y)
+        grad_y = self.x2_grad
+        self.relu_1_grad = self.relu_1.backward(grad_y)
+        grad_y = self.relu_1_grad
+        self.x1_grad, self.W1_grad = self.matmul_1.backward(grad_y)
+        pass
+
+    def optimize(self, learning_rate):
+        self.W1 -= learning_rate * self.W1_grad
+        self.W2 -= learning_rate * self.W2_grad
+        self.W3 -= learning_rate * self.W3_grad
diff --git a/assignment-2/submission/17307110367/numpy_mnist.py b/assignment-2/submission/17307110367/numpy_mnist.py
new file mode 100644
index 0000000..daea871
--- /dev/null
+++ b/assignment-2/submission/17307110367/numpy_mnist.py
@@ -0,0 +1,62 @@
+import numpy as np
+from numpy_fnn import NumpyModel, NumpyLoss
+from utils import download_mnist, batch, get_torch_initialization, plot_curve, one_hot
+
+def mini_batch(dataset, batch_size=128,seed=0):
+    np.random.seed(seed)
+    x_train = dataset.train_data
+    y_train = dataset.train_labels
+    m = y_train.shape[0]
+    # m为所有样本的数量
+    mini_batchs =[]
+    permutation = list(np.random.permutation(m))
+    # 打乱样本顺序
+    shuffle_X = x_train[permutation, :, :]
+    shuffle_Y = y_train[permutation]
+    num_mini_batch = int(m//batch_size)
+    # num_mini_batch为mini_batch的块数
+    for i in range(num_mini_batch):
+        mini_batch_x = shuffle_X[i*batch_size:(i+1)*batch_size, :, :]
+        mini_batch_y = shuffle_Y[i*batch_size:(i+1)*batch_size]
+        mini_batch = (mini_batch_x, mini_batch_y)
+        mini_batchs.append(mini_batch)
+    if m % batch_size != 0:
+        # 如果样本数不能被整除，取余下的部分
+        mini_batch_X = shuffle_X[num_mini_batch * batch_size:m, :, :]
+        mini_batch_Y = shuffle_Y[num_mini_batch * batch_size:m]
+        mini_batch = (mini_batch_X, mini_batch_Y)
+        mini_batchs.append(mini_batch)
+    return mini_batchs
+
+def numpy_run():
+    train_dataset, test_dataset = download_mnist()
+    model = NumpyModel()
+    numpy_loss = NumpyLoss()
+    model.W1, model.W2, model.W3 = get_torch_initialization()
+
+    train_loss = []
+
+    epoch_number = 3
+    learning_rate = 0.1
+
+    for epoch in range(epoch_number):
+        for x, y in mini_batch(train_dataset):
+            y = one_hot(y)
+            y_pred = model.forward(x.numpy()/255)
+            #y_pred = model.forward(x.numpy())
+            loss = numpy_loss.get_loss(y_pred, y)
+
+            model.backward(numpy_loss.backward())
+            model.optimize(learning_rate)
+
+            train_loss.append(loss.item())
+
+        x, y = batch(test_dataset)[0]
+        accuracy = np.mean((model.forward(x).argmax(axis=1) == y))
+        print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy))
+
+    plot_curve(train_loss)
+
+
+if __name__ == "__main__":
+    numpy_run()
-- 
Gitee


From 336716df5e62e9f86cebb575bf83c697f77af6f2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=BC=A0=E8=89=B3=E7=90=B3?= <17307110367@fudan.edu.cn>
Date: Wed, 28 Apr 2021 23:42:37 +0800
Subject: [PATCH 7/7] rename  to assignment-2/submission/17307110367/README.md.

---
 assignment-2/submission/17307110367/{homework2.md => README.md} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename assignment-2/submission/17307110367/{homework2.md => README.md} (100%)

diff --git a/assignment-2/submission/17307110367/homework2.md b/assignment-2/submission/17307110367/README.md
similarity index 100%
rename from assignment-2/submission/17307110367/homework2.md
rename to assignment-2/submission/17307110367/README.md
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