From 4da40089f5a6df213612ae8f13b58ed49d848ed8 Mon Sep 17 00:00:00 2001
From: CGH0S7 <776459475@qq.com>
Date: Fri, 14 Nov 2025 10:46:33 +0800
Subject: [PATCH] proj5 finished

---
 .../__pycache__/backend.cpython-313.pyc       | Bin 0 -> 38445 bytes
 .../__pycache__/models.cpython-313.pyc        | Bin 0 -> 19602 bytes
 proj5/machinelearning/models.py               |  98 +++++++++++--
 proj5/machinelearning/solution_steps.md       | 138 ++++++++++++++++++
 4 files changed, 226 insertions(+), 10 deletions(-)
 create mode 100644 proj5/machinelearning/__pycache__/backend.cpython-313.pyc
 create mode 100644 proj5/machinelearning/__pycache__/models.cpython-313.pyc
 create mode 100644 proj5/machinelearning/solution_steps.md

diff --git a/proj5/machinelearning/__pycache__/backend.cpython-313.pyc b/proj5/machinelearning/__pycache__/backend.cpython-313.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..7f83934c53a76f8e78cfa8997c531d116343ae4c
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diff --git a/proj5/machinelearning/models.py b/proj5/machinelearning/models.py
index 08ab6c4..025806a 100644
--- a/proj5/machinelearning/models.py
+++ b/proj5/machinelearning/models.py
@@ -37,7 +37,7 @@ class PerceptronModel(Module):
         """
         super(PerceptronModel, self).__init__()
         
-        "*** YOUR CODE HERE ***"
+        self.w = Parameter(ones(1, dimensions))
         
 
     def get_weights(self):
@@ -56,7 +56,7 @@ class PerceptronModel(Module):
 
         The pytorch function `tensordot` may be helpful here.
         """
-        "*** YOUR CODE HERE ***"
+        return tensordot(self.w, x, dims=2)
         
 
     def get_prediction(self, x):
@@ -65,7 +65,8 @@ class PerceptronModel(Module):
 
         Returns: 1 or -1
         """
-        "*** YOUR CODE HERE ***"
+        score = self.run(x)
+        return 1 if score.item() >= 0 else -1
 
 
 
@@ -80,7 +81,17 @@ class PerceptronModel(Module):
         """        
         with no_grad():
             dataloader = DataLoader(dataset, batch_size=1, shuffle=True)
-            "*** YOUR CODE HERE ***"
+            while True:
+                converged = True
+                for batch in dataloader:
+                    x = batch['x']
+                    y = batch['label']
+                    prediction = self.get_prediction(x)
+                    if prediction != y.item():
+                        self.w.data += y.item() * x
+                        converged = False
+                if converged:
+                    break
 
 
 
@@ -94,6 +105,9 @@ class RegressionModel(Module):
         # Initialize your model parameters here
         "*** YOUR CODE HERE ***"
         super().__init__()
+        self.layer1 = Linear(1, 256)
+        self.layer2 = Linear(256, 256)
+        self.layer3 = Linear(256, 1)
 
 
 
@@ -107,6 +121,9 @@ class RegressionModel(Module):
             A node with shape (batch_size x 1) containing predicted y-values
         """
         "*** YOUR CODE HERE ***"
+        x = relu(self.layer1(x))
+        x = relu(self.layer2(x))
+        return self.layer3(x)
 
     
     def get_loss(self, x, y):
@@ -120,6 +137,7 @@ class RegressionModel(Module):
         Returns: a tensor of size 1 containing the loss
         """
         "*** YOUR CODE HERE ***"
+        return mse_loss(self.forward(x), y)
  
         
 
@@ -138,6 +156,27 @@ class RegressionModel(Module):
             
         """
         "*** YOUR CODE HERE ***"
+        batch_size = 40
+        dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+        optimizer = optim.Adam(self.parameters(), lr=0.001)
+        scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=250, gamma=0.1)
+        
+        for epoch in range(1000): # Train for 1000 epochs, should be enough
+            total_loss = 0
+            num_samples = 0
+            for batch in dataloader:
+                optimizer.zero_grad()
+                loss = self.get_loss(batch['x'], batch['label'])
+                loss.backward()
+                optimizer.step()
+                total_loss += loss.item() * len(batch['x'])
+                num_samples += len(batch['x'])
+            
+            scheduler.step()
+            
+            avg_loss = total_loss / num_samples
+            if avg_loss < 0.02:
+                break
 
             
 
@@ -167,6 +206,9 @@ class DigitClassificationModel(Module):
         input_size = 28 * 28
         output_size = 10
         "*** YOUR CODE HERE ***"
+        self.layer1 = Linear(input_size, 256)
+        self.layer2 = Linear(256, 128)
+        self.layer3 = Linear(128, output_size)
 
 
 
@@ -186,6 +228,9 @@ class DigitClassificationModel(Module):
                 (also called logits)
         """
         """ YOUR CODE HERE """
+        x = relu(self.layer1(x))
+        x = relu(self.layer2(x))
+        return self.layer3(x)
 
  
 
@@ -203,6 +248,7 @@ class DigitClassificationModel(Module):
         Returns: a loss tensor
         """
         """ YOUR CODE HERE """
+        return cross_entropy(self.run(x), y)
 
     
         
@@ -212,6 +258,16 @@ class DigitClassificationModel(Module):
         Trains the model.
         """
         """ YOUR CODE HERE """
+        batch_size = 100
+        dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+        optimizer = optim.Adam(self.parameters(), lr=0.001)
+
+        for epoch in range(5): # Train for 5 epochs
+            for batch in dataloader:
+                optimizer.zero_grad()
+                loss = self.get_loss(batch['x'], batch['label'])
+                loss.backward()
+                optimizer.step()
 
 
 
@@ -314,13 +370,18 @@ def Convolve(input: tensor, weight: tensor):
 
     This returns a subtensor who's first element is tensor[y,x] and has height 'height, and width 'width'
     """
-    input_tensor_dimensions = input.shape
-    weight_dimensions = weight.shape
-    Output_Tensor = tensor(())
-    "*** YOUR CODE HERE ***"
-
+    input_h, input_w = input.shape
+    weight_h, weight_w = weight.shape
+    output_h = input_h - weight_h + 1
+    output_w = input_w - weight_w + 1
     
-    "*** End Code ***"
+    Output_Tensor = torch.zeros((output_h, output_w))
+    
+    for y in range(output_h):
+        for x in range(output_w):
+            sub_tensor = input[y:y+weight_h, x:x+weight_w]
+            Output_Tensor[y, x] = tensordot(sub_tensor, weight, dims=2)
+            
     return Output_Tensor
 
 
@@ -345,6 +406,10 @@ class DigitConvolutionalModel(Module):
 
         self.convolution_weights = Parameter(ones((3, 3)))
         """ YOUR CODE HERE """
+        conv_output_size = 26 * 26
+        hidden_size = 100
+        self.layer1 = Linear(conv_output_size, hidden_size)
+        self.layer2 = Linear(hidden_size, output_size)
 
 
 
@@ -361,6 +426,8 @@ class DigitConvolutionalModel(Module):
         x = stack(list(map(lambda sample: Convolve(sample, self.convolution_weights), x)))
         x = x.flatten(start_dim=1)
         """ YOUR CODE HERE """
+        x = relu(self.layer1(x))
+        return self.layer2(x)
 
 
     def get_loss(self, x, y):
@@ -377,6 +444,7 @@ class DigitConvolutionalModel(Module):
         Returns: a loss tensor
         """
         """ YOUR CODE HERE """
+        return cross_entropy(self.forward(x), y)
 
      
         
@@ -386,6 +454,16 @@ class DigitConvolutionalModel(Module):
         Trains the model.
         """
         """ YOUR CODE HERE """
+        batch_size = 64
+        dataloader = DataLoader(dataset, batch_size=batch_size, shuffle=True)
+        optimizer = optim.Adam(self.parameters(), lr=0.001)
+
+        for epoch in range(3):
+            for batch in dataloader:
+                optimizer.zero_grad()
+                loss = self.get_loss(batch['x'], batch['label'])
+                loss.backward()
+                optimizer.step()
 
 
 
diff --git a/proj5/machinelearning/solution_steps.md b/proj5/machinelearning/solution_steps.md
new file mode 100644
index 0000000..927e413
--- /dev/null
+++ b/proj5/machinelearning/solution_steps.md
@@ -0,0 +1,138 @@
+# **CS188 Proj5 机器学习实验完成步骤详解**
+
+本文档详细记录了在CS188项目5（机器学习）中，完成Q1、Q2、Q3和Q5四个部分的核心代码实现步骤。所有代码修改均在 `models.py` 文件中进行。
+
+## **问题一 (Q1): 感知机 (Perceptron)**
+
+此部分的目标是实现一个二元分类感知机模型。
+
+1. **`__init__(self, dimensions)` - 初始化**
+    * 初始化模型的权重 `self.w`。根据要求，权重需要是一个PyTorch的 `Parameter` 对象，以便自动评分系统能够识别。
+    * 权重向量的维度被设置为 `(1, dimensions)`，并使用 `ones` 进行初始化。
+
+    ```python
+    from torch.nn import Parameter
+    from torch import ones
+
+    self.w = Parameter(ones(1, dimensions))
+    ```
+
+2. **`run(self, x)` - 计算得分**
+    * 此函数计算感知机对输入数据 `x` 的得分。
+    * 通过计算权重 `self.w` 和输入 `x` 的点积来实现。这里使用了 `tensordot` 函数。
+
+    ```python
+    from torch import tensordot
+
+    return tensordot(self.w, x, dims=2)
+    ```
+
+3. **`get_prediction(self, x)` - 获取预测**
+    * 根据 `run` 方法计算出的得分，判断数据点的类别。
+    * 如果得分大于或等于0，则预测为类别 `1`；否则预测为 `-1`。
+
+    ```python
+    score = self.run(x)
+    return 1 if score.item() >= 0 else -1
+    ```
+
+4. **`train(self, dataset)` - 训练模型**
+    * 此函数的目标是训练感知机直到收敛（即在整个数据集上不再有分类错误）。
+    * 使用一个 `while True` 循环，在每一轮迭代中遍历整个数据集。
+    * 对于每一个数据点，获取模型的预测。如果预测错误，则根据感知机学习规则更新权重：`self.w.data += y.item() * x`，其中 `y` 是真实标签，`x` 是输入特征。
+    * 设置一个标志位 `converged`。如果在一整轮的迭代中没有任何错误发生，则 `converged` 保持为 `True`，训练循环结束。
+
+## **问题二 (Q2): 非线性回归 (Non-linear Regression)**
+
+此部分要求构建一个神经网络来近似 `sin(x)` 函数。
+
+1. **`__init__(self)` - 初始化**
+    * 构建一个简单的两层全连接神经网络。
+    * 第一层 (`self.layer1`) 是一个 `Linear` 层，将1维输入映射到100维的隐藏层。
+    * 第二层 (`self.layer2`) 也是一个 `Linear` 层，将100维的隐藏层映射到1维的输出。
+
+    ```python
+    from torch.nn import Linear
+
+    self.layer1 = Linear(1, 100)
+    self.layer2 = Linear(100, 1)
+    ```
+
+2. **`forward(self, x)` - 前向传播**
+    * 定义数据在网络中的流动方式。
+    * 输入 `x` 首先通过第一层，然后应用 `relu` 激活函数，最后通过第二层得到最终输出。
+
+    ```python
+    from torch.nn.functional import relu
+
+    x = relu(self.layer1(x))
+    return self.layer2(x)
+    ```
+
+3. **`get_loss(self, x, y)` - 计算损失**
+    * 使用均方误差（Mean Squared Error）作为损失函数。
+    * 调用 `forward(x)` 得到预测值，然后使用 `mse_loss` 计算与真实值 `y` 之间的损失。
+
+    ```python
+    from torch.nn.functional import mse_loss
+
+    return mse_loss(self.forward(x), y)
+    ```
+
+4. **`train(self, dataset)` - 训练模型**
+    * 使用 `Adam` 优化器进行梯度下降。
+    * 设置合适的批处理大小（`batch_size`），例如50（因为Q2数据集大小为200，可以被50整除）。
+    * 训练循环进行固定次数的迭代（Epoch），例如500次。在每个Epoch中，遍历数据加载器（`DataLoader`）中的所有批次，执行标准的训练步骤：梯度清零、计算损失、反向传播、更新权重。
+    * 在每个Epoch结束后，计算整个数据集的平均损失。如果平均损失小于0.02，则提前终止训练。
+
+## **问题三 (Q3): 数字分类 (Digit Classification)**
+
+此部分要求构建一个模型来对MNIST手写数字数据集进行分类。
+
+1. **`__init__(self)` - 初始化**
+    * 构建一个具有两个隐藏层的多层感知机（MLP）。
+    * 输入层大小为 `784` (28x28像素)，输出层大小为 `10` (0-9共10个类别)。
+    * 网络结构：`Linear(784, 256)` -> `Linear(256, 128)` -> `Linear(128, 10)`。
+
+2. **`run(self, x)` - 前向传播**
+    * 数据流经两个隐藏层，每个隐藏层后都应用 `relu` 激活函数。
+    * 输出层不使用激活函数，直接返回 logits 分数。
+
+3. **`get_loss(self, x, y)` - 计算损失**
+    * 使用交叉熵损失函数 `cross_entropy`。
+    * 一个关键点是，PyTorch的 `cross_entropy` 函数可以直接接受 one-hot 编码的浮点型标签 `y`。因此，直接将模型的输出 `self.run(x)` 和标签 `y` 传入即可。
+    * （注：最初尝试使用 `y.argmax(dim=1)` 将 one-hot 标签转换为索引，但这会导致自动评分器中的梯度检查失败。直接传递 one-hot 标签解决了这个问题。）
+
+4. **`train(self, dataset)` - 训练模型**
+    * 同样使用 `Adam` 优化器和 `DataLoader`。批处理大小设置为100（可被训练集大小60000整除）。
+    * 根据实验指导，训练5个Epoch就足以达到要求的准确率。
+    * 因此，实现一个简单的循环，迭代5次，在其中执行标准的模型训练流程。
+    * （注：最初尝试使用 `dataset.get_validation_accuracy(self)` 进行早停，但遇到了 `TypeError`。简化为固定Epoch次数的训练后，成功通过了测试。）
+
+## **问题五 (Q5): 卷积神经网络 (Convolutional Neural Networks)**
+
+此部分要求从零开始实现一个卷积函数，并构建一个简单的卷积神经网络。
+
+1. **`Convolve(input: tensor, weight: tensor)` - 实现卷积函数**
+    * 此函数手动实现2D卷积操作，不使用PyTorch内置的卷积层。
+    * 首先，根据输入张量和权重张量的尺寸，计算输出张量的尺寸（无填充，步长为1）。
+    * 创建一个全为零的输出张量 `Output_Tensor`。
+    * 使用嵌套循环遍历输出张量的每一个位置 `(y, x)`。
+    * 在每个位置，从输入张量中提取一个与权重张量大小相同的子张量 `sub_tensor`。
+    * 使用 `tensordot` 计算 `sub_tensor` 和 `weight` 的点积（即元素乘积之和），并将结果存入 `Output_Tensor[y, x]`。
+    * 返回计算完成的 `Output_Tensor`。
+
+2. **`DigitConvolutionalModel` - 构建CNN模型**
+    * **`__init__(self)`**:
+        * 模型包含一个 `3x3` 的卷积核 `self.convolution_weights`。
+        * 卷积操作的输出是一个 `26x26` 的特征图，展平后大小为 `676`。
+        * 在卷积层之后，添加一个简单的全连接网络，例如 `Linear(676, 100)` -> `ReLU` -> `Linear(100, 10)`。
+    * **`forward(self, x)`**:
+        * 函数的前半部分已提供，它会将输入的 `(batch_size, 784)` 数据重塑为 `(batch_size, 28, 28)` 的图像，然后使用我们实现的 `Convolve` 函数对批次中的每个样本进行卷积，最后将结果展平。
+        * 我们需要做的，是将这个展平后的一维向量传入我们定义的两层全连接网络中，并返回最终的分类分数。
+    * **`get_loss(self, x, y)` 和 `train(self, dataset)`**:
+        * 这两个函数的实现与Q3中的 `DigitClassificationModel` 非常相似。
+        * `get_loss` 使用 `cross_entropy`。
+        * `train` 使用 `Adam` 优化器，训练一个较少的Epoch次数（例如3次），因为此问题的数据集较为简单，训练速度很快。
+
+---