From 407f8afaf39bdd723a5e84c156b44ea08af32df9 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 30 Mar 2021 00:50:18 +0800 Subject: [PATCH 01/28] feat: _get_k_nearest_neighbors --- .../submission/18307130003/tester_demo.py | 24 +++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 assignment-1/submission/18307130003/tester_demo.py diff --git a/assignment-1/submission/18307130003/tester_demo.py b/assignment-1/submission/18307130003/tester_demo.py new file mode 100644 index 0000000..6fe1511 --- /dev/null +++ b/assignment-1/submission/18307130003/tester_demo.py @@ -0,0 +1,24 @@ +import numpy as np + +from source import KNN + +train_data = np.array([ + [1, 2, 3, 4], + [4, 2, 3, 1], + [12, 12, 13, 14], + [14, 12, 13, 11], + [12, 14, 15, 16], +]) +train_label = np.array([0, 0, 1, 1, 1]) + +test_data = np.array([ + [3, 4, 4, 2], + [18, 14, 15, 16], +]) +test_label = np.array([0, 1]) + +model = KNN() +model.fit(train_data, train_label) +res = model.predict(test_data) + +print("acc =", np.mean(np.equal(res, test_label))) -- Gitee From a70a664d7058e896d9b6238a8f419379e30d1096 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 16:10:17 +0800 Subject: [PATCH 02/28] feat: _get_most_common_label chore: fix comments and modify parameter names --- assignment-1/submission/18307130003/source.py | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index 3676e4e..a672bc8 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -42,7 +42,12 @@ class KNN: :param `dataset`: which dataset to use ''' - def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: + if dataset == Dataset.TRAIN_SET: + data = self.train_data + else: + data = self.test_data + + def _distance(p1_i: int, p2_i: int, mode: int = 2) -> float: ''' Get the distance between two points. -- Gitee From b9afc8f62b4a449801741b69b8d7c8e413ec71f0 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 21:57:28 +0800 Subject: [PATCH 03/28] feat: fit, predict fix: change .size to .shape[0] --- assignment-1/submission/18307130003/source.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index a672bc8..aed1027 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -44,6 +44,8 @@ class KNN: if dataset == Dataset.TRAIN_SET: data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data else: data = self.test_data -- Gitee From dbc19c6f2aac30265aeb8677f32e71100a7fd053 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 1 Apr 2021 22:25:11 +0800 Subject: [PATCH 04/28] fix: fixed all issues to get the program worked --- assignment-1/submission/18307130003/source.py | 11 +++-------- 1 file changed, 3 insertions(+), 8 deletions(-) diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index aed1027..1c472cf 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -42,14 +42,7 @@ class KNN: :param `dataset`: which dataset to use ''' - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data - else: - data = self.test_data - - def _distance(p1_i: int, p2_i: int, mode: int = 2) -> float: + def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: ''' Get the distance between two points. @@ -156,6 +149,8 @@ class KNN: print(f'best k = {self.k}\n') + print("\n") + def predict(self, test_data: np.ndarray) -> np.ndarray: ''' Predict the label of a point using our model. -- Gitee From 58d5e433dc2e1f8c50ec095d9038e6ac416a2458 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 00:01:37 +0800 Subject: [PATCH 05/28] feat: done doc: done --- assignment-1/submission/18307130003/README.md | 502 ++++++------------ .../submission/18307130003/img/test.png | Bin 0 -> 25961 bytes .../submission/18307130003/img/train.png | Bin 0 -> 38778 bytes assignment-1/submission/18307130003/source.py | 2 +- 4 files changed, 155 insertions(+), 349 deletions(-) create mode 100644 assignment-1/submission/18307130003/img/test.png create mode 100644 assignment-1/submission/18307130003/img/train.png diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 2bd04be..9e5140a 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -1,179 +1,169 @@ # 实验报告 -## 目录 - -[TOC] - ## KNN 模型实现 -KNN 算法的主要思路是，根据当前点 `base_p` 最近的 `k` 个邻居 `p` 的标签，选择其中出现频率最高的标签，作为 `base_p` 标签的预测结果。 - -具体来说，我们使用函数 `_distance` 获取两点间的距离。 - ```python {.line-numbers} -def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: +class KNN: ''' - Get the distance between two points. - - :param `p1`: the first point - :param `p2`: the second point - :param `mode`: which exponent to use when calculating distance, \ - using `2` by default for Euclidean distance + k-Nearest Neighbors algorithm, which predicts the class of a data point + according to the most common class among its `k` nearest neighbors. ''' - assert p1.shape == p2.shape, ( - '_distance: dimensions not match for ' - f'{p1.shape} and {p2.shape}' - ) - return np.linalg.norm(p1 - p2, ord=mode) -``` + def __init__(self) -> None: + ''' + Initialize our KNN model. + ''' -这里我们使用了 `numpy` 库提供的 `np.linalg.norm` 方法来获取两点间的距离。特别地，当参数 `ord` 为 `2` 时，即采用 Euclidean 距离。我们这里使用 `2` 作为默认参数。 + self.k: int = 1 + self.train_data: np.ndarray = None + self.train_label: np.ndarray = None + self.dev_data: np.ndarray = None + self.dev_label: np.ndarray = None + self.test_data: np.ndarray = None -接下来，我们维护一个大小为 `k` 的最小堆，来得到最近的 `k` 个邻居。思想就是 top k 问题的经典算法。 + def _get_k_nearest_neighbors( + self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET + ) -> List[int]: + ''' + Get k nearest neighbors of a point from dataset. Each point (except the + base point) is denoted by its index in the dataset. -```python {.line-numbers} -def _get_k_nearest_neighbors( - self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET -) -> List[int]: - ''' - Get k nearest neighbors of a point from dataset. Each point (except the - base point) is denoted by its index in the dataset. + :param `base_p`: the base point + :param `dataset`: which dataset to use + ''' - :param `base_p`: the base point - :param `dataset`: which dataset to use - ''' + def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: + ''' + Get the distance between two points. - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data - else: - data = self.test_data - - # Use a min heap of size k to get the k nearest neighbors - heap: List[Tuple[float, np.ndarray]] = [] - for p_i in range(data.shape[0]): - dist: float = _distance(base_p, data[p_i]) - if (len(heap) < k): - heappush(heap, (-dist, p_i)) - else: - heappushpop(heap, (-dist, p_i)) + :param `p1`: the first point + :param `p2`: the second point + :param `mode`: which exponent to use when calculating distance, \ + using `2` by default for Euclidean distance + ''' - # Return the indices of the k points in the dataset - return [item[1] for item in heap] -``` + assert p1.shape == p2.shape, ( + '_distance: dimensions not match for ' + f'{p1.shape} and {p2.shape}' + ) + return np.linalg.norm(p1 - p2, ord=mode) -最后我们对这 `k` 个邻居的标签分别进行计数，选择其中出现次数最多的标签作为预测结果。 + if dataset == Dataset.TRAIN_SET: + data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data + else: + data = self.test_data + + # Use a min heap of size k to get the k nearest neighbors + heap: List[Tuple[float, np.ndarray]] = [] + for p_i in range(data.shape[0]): + dist: float = _distance(base_p, data[p_i]) + if (len(heap) < k): + heappush(heap, (-dist, p_i)) + else: + heappushpop(heap, (-dist, p_i)) + + # Return the indices of the k points in the dataset + return [item[1] for item in heap] + + def _get_most_common_label( + self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET + ) -> int: + ''' + Get the most common label in given labels. Each label is denoted by + its data point's index in the dataset. -```python {.line-numbers} -def _get_most_common_label( - self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET -) -> int: - ''' - Get the most common label in given labels. Each label is denoted by - its data point's index in the dataset. + :param `labels_i`: the indices of given labels + :param `dataset`: which dataset to use + ''' - :param `labels_i`: the indices of given labels - :param `dataset`: which dataset to use - ''' + if dataset == Dataset.TRAIN_SET: + all_labels = self.train_label + else: + all_labels = self.dev_label - if dataset == Dataset.TRAIN_SET: - all_labels = self.train_label - else: - all_labels = self.dev_label + labels: List[int] = [all_labels[i] for i in labels_i] + return max(set(labels), key=labels.count) - labels: List[int] = [all_labels[i] for i in labels_i] - return max(set(labels), key=labels.count) -``` + def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: + ''' + Train the model using a training set with labels. -训练模型时，我们先将数据集打乱，然后将其中的 75% 作为训练集 `train_data`，剩下 25% 作为验证集 `dev_data`，然后使用 KNN 算法进行训练。我们选择不同的 `k` 值，通过比较验证集 `dev_data` 的预测结果和其实际标签 `dev_label`，得到每个 `k` 值所对应的预测准确率 `accuracy`。最终，我们选择准确率最高的 `k` 值作为我们将在测试集 `test_data` 上使用的参数 `k`。 + :param `train_data`: training set + :param `train_label`: provided labels for data in training set + ''' -```python {.line-numbers} -def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: - ''' - Train the model using a training set with labels. + # Shuffle the dataset with labels + assert train_data.shape[0] == train_label.shape[0], ( + 'fit: data size not match for ' + f'{train_data.shape[0]} and {train_label.shape[0]}' + ) + shuffled_i = np.random.permutation(train_data.shape[0]) + shuffled_data: np.ndarray = train_data[shuffled_i] + shuffled_label: np.ndarray = train_label[shuffled_i] + + # Separate training set and development set (for validation) + train_ratio: float = 0.75 + train_size: int = floor(shuffled_data.shape[0] * train_ratio) + self.train_data = shuffled_data[:train_size] + self.train_label = shuffled_label[:train_size] + self.dev_data = shuffled_data[train_size:] + self.dev_label = shuffled_label[train_size:] + + print('=== Training ===') + + # Compare the predicted and expected results, calculate the accuracy + # for each parameter k, and find out the best k for prediction. + k_threshold: int = train_size if train_size < 20 else 20 + accuracy_table: List[float] = [0.0] + max_accuracy: float = 0.0 + + for k in range(1, k_threshold): + predicted_labels: List[int] = [] + for p in self.dev_data: + k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( + k, p, Dataset.TRAIN_SET + ) + predicted_label: int = self._get_most_common_label( + k_nearest_neighbors, Dataset.TRAIN_SET + ) + predicted_labels.append(predicted_label) + prediction: np.ndarray = np.array(predicted_labels) + + accuracy: float = np.mean(np.equal(prediction, self.dev_label)) + accuracy_table.append(accuracy) + print(f'k = {k}, train_acc = {accuracy * 100} %') + if accuracy > max_accuracy: + max_accuracy, self.k = accuracy, k + + print(f'best k = {self.k}\n') + + def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the label of a point using our model. - :param `train_data`: training set - :param `train_label`: provided labels for data in training set - ''' + :param `test_data`: testing set + ''' + + self.test_data = test_data - # Shuffle the dataset with labels - assert train_data.shape[0] == train_label.shape[0], ( - 'fit: data size not match for ' - f'{train_data.shape[0]} and {train_label.shape[0]}' - ) - shuffled_i = np.random.permutation(train_data.shape[0]) - shuffled_data: np.ndarray = train_data[shuffled_i] - shuffled_label: np.ndarray = train_label[shuffled_i] - - # Separate training set and development set (for validation) - train_ratio: float = 0.75 - train_size: int = floor(shuffled_data.shape[0] * train_ratio) - self.train_data = shuffled_data[:train_size] - self.train_label = shuffled_label[:train_size] - self.dev_data = shuffled_data[train_size:] - self.dev_label = shuffled_label[train_size:] - - print('=== Training ===') - - # Compare the predicted and expected results, calculate the accuracy - # for each parameter k, and find out the best k for prediction. - k_threshold: int = train_size if train_size < 20 else 20 - accuracy_table: List[float] = [0.0] - max_accuracy: float = 0.0 - - for k in range(1, k_threshold): predicted_labels: List[int] = [] - for p in self.dev_data: + for p in self.test_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - k, p, Dataset.TRAIN_SET + self.k, p, Dataset.TRAIN_SET ) predicted_label: int = self._get_most_common_label( k_nearest_neighbors, Dataset.TRAIN_SET ) predicted_labels.append(predicted_label) prediction: np.ndarray = np.array(predicted_labels) - - accuracy: float = np.mean(np.equal(prediction, self.dev_label)) - accuracy_table.append(accuracy) - print(f'k = {k}, train_acc = {accuracy * 100} %') - if accuracy > max_accuracy: - max_accuracy, self.k = accuracy, k - - print(f'best k = {self.k}\n') -``` - -对测试集进行预测时，我们就使用之前得到的最优的参数 `k` 进行预测，同样使用 KNN 算法。 - -```python {.line-numbers} -def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the label of a point using our model. - - :param `test_data`: testing set - ''' - - self.test_data = test_data - - print('=== Predicting ===') - - predicted_labels: List[int] = [] - for p in self.test_data: - k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - self.k, p, Dataset.TRAIN_SET - ) - predicted_label: int = self._get_most_common_label( - k_nearest_neighbors, Dataset.TRAIN_SET - ) - predicted_labels.append(predicted_label) - prediction: np.ndarray = np.array(predicted_labels) - return prediction + return prediction ``` -## 生成数据 +## 实验探究部分 -我们使用不同的参数生成数据集，并保存到文件 `data.npy`。这里由于时间有限，为了方便起见，我们直接在函数 `generate` 的 `parameters` 变量中对相应参数进行修改。 +生成数据集，并保存到文件： ```python {.line-numbers} def generate() -> None: @@ -190,7 +180,7 @@ def generate() -> None: def _generate_with_parameters(param: Parameter) -> np.ndarray: ''' - Generate a dataset using given parameters. + Generate a dataset using given parameters :param `param`: a tuple of `mean`, `cov`, `size` `mean`: the mean of the dataset @@ -248,34 +238,27 @@ def generate() -> None: )) ``` -为了直观起见，我们提供了函数 `display` 用于将当前使用的数据集可视化，并将图片保存到 `./img` 目录下。 +作图： ```python {.line-numbers} -def display(data: np.ndarray, label: np.ndarray, name: str) -> None: +def display(data, label, name): ''' - Visualize dataset with labels using `matplotlib.pyplot`. - - :param `data`: dataset - :param `label`: labels for data in the dataset - :param `name`: file name when saving to file + Visualize data and labels using `matplotlib.pyplot`. ''' - datasets_with_label: List[List[np.ndarray]] = [[], [], []] - for i in range(data.shape[0]): - datasets_with_label[label[i]].append(data[i]) - - for dataset_with_label in datasets_with_label: - dataset_with_label_: np.ndarray = np.array(dataset_with_label) - plt.scatter(dataset_with_label_[:, 0], dataset_with_label_[:, 1]) + datas = [[], [], []] + for i in range(len(data)): + datas[label[i]].append(data[i]) + for each in datas: + each = np.array(each) + plt.scatter(each[:, 0], each[:, 1]) plt.savefig(f'img/{name}') plt.show() ``` ## 运行代码 -在当前目录下，我们可以使用以下参数执行代码 `source.py`，具体功能参见注释。 - ```bash # 训练模型及预测 python ./source.py g @@ -284,40 +267,9 @@ python ./source.py g python ./source.py d ``` -### 输出样例 - -```text -=== Training === -k = 1, train_acc = 67.5 % -k = 2, train_acc = 67.75 % -k = 3, train_acc = 70.5 % -k = 4, train_acc = 72.5 % -k = 5, train_acc = 72.75 % -k = 6, train_acc = 73.25 % -k = 7, train_acc = 74.25 % -k = 8, train_acc = 74.0 % -k = 9, train_acc = 75.75 % -k = 10, train_acc = 75.5 % -k = 11, train_acc = 75.75 % -k = 12, train_acc = 75.5 % -k = 13, train_acc = 75.75 % -k = 14, train_acc = 75.5 % -k = 15, train_acc = 75.5 % -k = 16, train_acc = 74.5 % -k = 17, train_acc = 75.0 % -k = 18, train_acc = 75.0 % -k = 19, train_acc = 75.25 % -best k = 9 - -=== Predicting === -k = 9, predict_acc = 71.5 % -``` - -## 实验探究 +## 数据集 -### 1. 实验 1 - -#### 1.1 参数 +数据生成使用的参数： ```python {.line-numbers} mean = (1, 2) @@ -337,27 +289,21 @@ cov = [[10, 5], [5, 10]] size = 1000 ``` -其中： - -- `mean` 表示数据集的均值 -- `cov` 表示数据集的协方差 -- `size` 表示数据集的大小 +其中，`mean` 表示数据集的均值、`cov` 表示数据集的协方差、`size` 表示数据集的大小。 -下同。 +### 训练集 -#### 1.2 数据集 +![训练集](./img/train.png) -训练集： +在训练时，我们随机选取 80% 作为训练集、20% 作为验证集。 -![训练集](./img/train_1.png) +### 测试集 -测试集： +![测试集](./img/test.png) -![测试集](./img/test_1.png) +## 参数 -#### 1.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示： +训练时使用的参数 `k` 及相应的准确率： ```text k = 1, train_acc = 95.75 % @@ -381,146 +327,6 @@ k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % ``` -预测时使用的参数 `k` 及相应的准确率如下所示： - -```text -k = 3, predict_acc = 96.0 % -``` - -可见，对于此数据集，最优的参数 `k` 为 `3`，其对测试集的预测准确率为 96.0 %。 - -### 2. 实验 2 - -这次，我们调大数据集之间的距离，观察预测准确率的变化。 - -#### 2.1 参数 - -```python {.line-numbers} -mean = (-5, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (30, -10) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (20, 40) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -#### 2.2 数据集 - -训练集： - -![训练集](./img/train_2.png) - -测试集： - -![测试集](./img/test_2.png) - -#### 2.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示： - -```text -k = 1, train_acc = 100.0 % -k = 2, train_acc = 100.0 % -k = 3, train_acc = 100.0 % -k = 4, train_acc = 100.0 % -k = 5, train_acc = 100.0 % -k = 6, train_acc = 100.0 % -k = 7, train_acc = 100.0 % -k = 8, train_acc = 100.0 % -k = 9, train_acc = 100.0 % -k = 10, train_acc = 100.0 % -k = 11, train_acc = 100.0 % -k = 12, train_acc = 100.0 % -k = 13, train_acc = 100.0 % -k = 14, train_acc = 100.0 % -k = 15, train_acc = 100.0 % -k = 16, train_acc = 100.0 % -k = 17, train_acc = 100.0 % -k = 18, train_acc = 100.0 % -k = 19, train_acc = 100.0 % -``` - -预测时使用的参数 `k` 及相应的准确率如下所示： - -```text -k = 1, predict_acc = 100.0 % -``` - -可见，对于不同标签区分度较大（即彼此间距离较远）的数据集，所有 `k` 的预测准确率均为 100.0 %。这说明 KNN 算法对于较分散的数据有着很高的准确率。 - -### 3. 实验 3 - -我们再试试减小数据集间的距离，观察预测准确率的变化。 - -#### 3.1 参数 - -```python {.line-numbers} -mean = (1, 2) -cov = [[73, 0], [0, 22]] -size = 800 -``` - -```python {.line-numbers} -mean = (3, -2) -cov = [[21.2, 0], [0, 32.1]] -size = 200 -``` - -```python {.line-numbers} -mean = (-5, 4) -cov = [[10, 5], [5, 10]] -size = 1000 -``` - -#### 3.2 数据集 - -训练集： - -![训练集](./img/train_3.png) - -测试集： - -![测试集](./img/test_3.png) - -#### 3.3 预测准确率 - -训练时使用的参数 `k` 及相应的准确率如下所示： - -```text -k = 1, train_acc = 65.0 % -k = 2, train_acc = 65.75 % -k = 3, train_acc = 69.25 % -k = 4, train_acc = 68.25 % -k = 5, train_acc = 72.5 % -k = 6, train_acc = 71.5 % -k = 7, train_acc = 73.75 % -k = 8, train_acc = 75.0 % -k = 9, train_acc = 76.0 % -k = 10, train_acc = 75.75 % -k = 11, train_acc = 76.0 % -k = 12, train_acc = 74.5 % -k = 13, train_acc = 75.25 % -k = 14, train_acc = 75.0 % -k = 15, train_acc = 74.75 % -k = 16, train_acc = 75.5 % -k = 17, train_acc = 75.0 % -k = 18, train_acc = 75.0 % -k = 19, train_acc = 74.5 % -``` - -预测时使用的参数 `k` 及相应的准确率如下所示： - -```text -k = 9, predict_acc = 76.0 % -``` +可见，对于此数据集，最优的参数 `k` 为 `3`。 -此时，最优的参数 `k` 为 `9`，其对测试集的预测准确率为 76.0 %。可见，当数据集间的区分度较低时，较高的 `k` 值有着相对较高的准确率。这是可以理解的，因为提高可参考的邻居数量可以尽可能地减少噪声的影响。 +相应的准确率为 96%。 diff --git a/assignment-1/submission/18307130003/img/test.png b/assignment-1/submission/18307130003/img/test.png new file mode 100644 index 0000000000000000000000000000000000000000..77b898ff8a239b7338b029c2b7e1f76c0fd149f2 GIT binary patch literal 25961 zcmeFZWmJ_>+cmlY0i{EvLy+$7P`bNg)3xdDlrBL+T9EEeX$eW`?(S}c@7_M&dEYbM zGrsfl{5lLp2YcP?UU9{o^ID4tB?U=TBmyK52!tvvC8h!b!3KapFl(<7fS+)VFKq$; 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z&^cWk7zkmOhqp~04@9}7q5zfaqfoZtRY!P0fF|k|d3lNO`Q*pAc(knCeo?yBWMg72F59?m=aJ~ zw5rzm-3zdXtYUdJ-u<=sqDCBhT|&<-4_rempY`-f(9yC zBE1zwNfdT#H=N{|1_cIE%FXk@x^?XA?ARc&;r*?oW&%^ifg+R1a4|74*NR*g#E&I@ zpcet5btkTH@nK$G*{Ahkv%RkH*X7lKcUpaEJ;|B3h~v$u@_x)w**%v#W6v89|@_NPyjSFGc(JBN?uCIs4*E1UMBs*Kh21qwU$i)euylEGwt=2Z_uroM!5Evu zgDw+)tu*nbEc5hZ#_EU%?mDW2Bp?5CeDOQs$N&G~>&r?ai;DHQ_bT-$`1yGIp({O) GWc>rO%;R$a literal 0 HcmV?d00001 diff --git a/assignment-1/submission/18307130003/source.py b/assignment-1/submission/18307130003/source.py index 1c472cf..e6bc70f 100644 --- a/assignment-1/submission/18307130003/source.py +++ b/assignment-1/submission/18307130003/source.py @@ -149,7 +149,7 @@ class KNN: print(f'best k = {self.k}\n') - print("\n") + print(f'best k = {self.k}\n') def predict(self, test_data: np.ndarray) -> np.ndarray: ''' -- Gitee From 42cfc5f0654916e737de1971f9ca02a013a3bb27 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:04:01 +0800 Subject: [PATCH 06/28] doc: improve report --- assignment-1/submission/18307130003/README.md | 437 ++++++++++++------ .../submission/18307130003/img/test.png | Bin 25961 -> 0 bytes .../submission/18307130003/img/train.png | Bin 38778 -> 0 bytes .../submission/18307130003/tester_demo.py | 24 - 4 files changed, 292 insertions(+), 169 deletions(-) delete mode 100644 assignment-1/submission/18307130003/img/test.png delete mode 100644 assignment-1/submission/18307130003/img/train.png delete mode 100644 assignment-1/submission/18307130003/tester_demo.py diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 9e5140a..21cd813 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -1,169 +1,177 @@ # 实验报告 +## 目录 + +[TOC] + ## KNN 模型实现 +KNN 算法的主要思路是，根据当前点 `base_p` 最近的 `k` 个邻居 `p` 的标签，选择其中出现频率最高的标签，作为 `base_p` 标签的预测结果。 + +具体来说，我们使用函数 `_distance` 获取两点间的距离。 + ```python {.line-numbers} -class KNN: +def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: ''' - k-Nearest Neighbors algorithm, which predicts the class of a data point - according to the most common class among its `k` nearest neighbors. - ''' - - def __init__(self) -> None: - ''' - Initialize our KNN model. - ''' + Get the distance between two points. - self.k: int = 1 - self.train_data: np.ndarray = None - self.train_label: np.ndarray = None - self.dev_data: np.ndarray = None - self.dev_label: np.ndarray = None - self.test_data: np.ndarray = None + :param `p1`: the first point + :param `p2`: the second point + :param `mode`: which exponent to use when calculating distance, \ + using `2` by default for Euclidean distance + ''' - def _get_k_nearest_neighbors( - self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET - ) -> List[int]: - ''' - Get k nearest neighbors of a point from dataset. Each point (except the - base point) is denoted by its index in the dataset. + assert p1.shape == p2.shape, ( + '_distance: dimensions not match for ' + f'{p1.shape} and {p2.shape}' + ) + return np.linalg.norm(p1 - p2, ord=mode) +``` - :param `base_p`: the base point - :param `dataset`: which dataset to use - ''' +这里我们使用了 `numpy` 库提供的 `np.linalg.norm` 方法来获取两点间的距离。特别地，当参数 `ord` 为 `2` 时，即采用 Euclidean 距离。我们这里使用 `2` 作为默认参数。 - def _distance(p1: np.ndarray, p2: np.ndarray, mode: int = 2) -> float: - ''' - Get the distance between two points. +接下来，我们维护一个大小为 `k` 的最小堆，来得到最近的 `k` 个邻居。思想就是 top k 问题的经典算法。 - :param `p1`: the first point - :param `p2`: the second point - :param `mode`: which exponent to use when calculating distance, \ - using `2` by default for Euclidean distance - ''' +```python {.line-numbers} +def _get_k_nearest_neighbors( + self, k: int, base_p: np.ndarray, dataset: int = Dataset.TRAIN_SET +) -> List[int]: + ''' + Get k nearest neighbors of a point from dataset. Each point (except the + base point) is denoted by its index in the dataset. - assert p1.shape == p2.shape, ( - '_distance: dimensions not match for ' - f'{p1.shape} and {p2.shape}' - ) - return np.linalg.norm(p1 - p2, ord=mode) + :param `base_p`: the base point + :param `dataset`: which dataset to use + ''' - if dataset == Dataset.TRAIN_SET: - data = self.train_data - elif dataset == Dataset.DEV_SET: - data = self.dev_data + if dataset == Dataset.TRAIN_SET: + data = self.train_data + elif dataset == Dataset.DEV_SET: + data = self.dev_data + else: + data = self.test_data + + # Use a min heap of size k to get the k nearest neighbors + heap: List[Tuple[float, np.ndarray]] = [] + for p_i in range(data.shape[0]): + dist: float = _distance(base_p, data[p_i]) + if (len(heap) < k): + heappush(heap, (-dist, p_i)) else: - data = self.test_data - - # Use a min heap of size k to get the k nearest neighbors - heap: List[Tuple[float, np.ndarray]] = [] - for p_i in range(data.shape[0]): - dist: float = _distance(base_p, data[p_i]) - if (len(heap) < k): - heappush(heap, (-dist, p_i)) - else: - heappushpop(heap, (-dist, p_i)) - - # Return the indices of the k points in the dataset - return [item[1] for item in heap] - - def _get_most_common_label( - self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET - ) -> int: - ''' - Get the most common label in given labels. Each label is denoted by - its data point's index in the dataset. + heappushpop(heap, (-dist, p_i)) - :param `labels_i`: the indices of given labels - :param `dataset`: which dataset to use - ''' + # Return the indices of the k points in the dataset + return [item[1] for item in heap] +``` - if dataset == Dataset.TRAIN_SET: - all_labels = self.train_label - else: - all_labels = self.dev_label +最后我们对这 k 个邻居的标签分别进行计数，选择其中出现次数最多的标签作为预测结果。 - labels: List[int] = [all_labels[i] for i in labels_i] - return max(set(labels), key=labels.count) +```python {.line-numbers} +def _get_most_common_label( + self, labels_i: List[int], dataset: int = Dataset.TRAIN_SET +) -> int: + ''' + Get the most common label in given labels. Each label is denoted by + its data point's index in the dataset. - def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: - ''' - Train the model using a training set with labels. + :param `labels_i`: the indices of given labels + :param `dataset`: which dataset to use + ''' - :param `train_data`: training set - :param `train_label`: provided labels for data in training set - ''' + if dataset == Dataset.TRAIN_SET: + all_labels = self.train_label + else: + all_labels = self.dev_label - # Shuffle the dataset with labels - assert train_data.shape[0] == train_label.shape[0], ( - 'fit: data size not match for ' - f'{train_data.shape[0]} and {train_label.shape[0]}' - ) - shuffled_i = np.random.permutation(train_data.shape[0]) - shuffled_data: np.ndarray = train_data[shuffled_i] - shuffled_label: np.ndarray = train_label[shuffled_i] - - # Separate training set and development set (for validation) - train_ratio: float = 0.75 - train_size: int = floor(shuffled_data.shape[0] * train_ratio) - self.train_data = shuffled_data[:train_size] - self.train_label = shuffled_label[:train_size] - self.dev_data = shuffled_data[train_size:] - self.dev_label = shuffled_label[train_size:] - - print('=== Training ===') - - # Compare the predicted and expected results, calculate the accuracy - # for each parameter k, and find out the best k for prediction. - k_threshold: int = train_size if train_size < 20 else 20 - accuracy_table: List[float] = [0.0] - max_accuracy: float = 0.0 - - for k in range(1, k_threshold): - predicted_labels: List[int] = [] - for p in self.dev_data: - k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - k, p, Dataset.TRAIN_SET - ) - predicted_label: int = self._get_most_common_label( - k_nearest_neighbors, Dataset.TRAIN_SET - ) - predicted_labels.append(predicted_label) - prediction: np.ndarray = np.array(predicted_labels) - - accuracy: float = np.mean(np.equal(prediction, self.dev_label)) - accuracy_table.append(accuracy) - print(f'k = {k}, train_acc = {accuracy * 100} %') - if accuracy > max_accuracy: - max_accuracy, self.k = accuracy, k - - print(f'best k = {self.k}\n') - - def predict(self, test_data: np.ndarray) -> np.ndarray: - ''' - Predict the label of a point using our model. + labels: List[int] = [all_labels[i] for i in labels_i] + return max(set(labels), key=labels.count) +``` - :param `test_data`: testing set - ''' +训练模型时，我们先将数据集打乱，然后将其中的 75% 作为训练集 `train_data`，剩下 25% 作为验证集 `dev_data`，然后使用 KNN 算法进行训练。我们选择不同的 `k` 值，通过比较验证集 `dev_data` 的预测结果和其实际标签 `dev_label`，得到每个 `k` 值所对应的预测准确率 `accuracy`。最终，我们选择准确率最高的 `k` 值作为我们将在测试集 `test_data` 上使用的参数 `k`。 - self.test_data = test_data +```python {.line-numbers} +def fit(self, train_data: np.ndarray, train_label: np.ndarray) -> None: + ''' + Train the model using a training set with labels. + :param `train_data`: training set + :param `train_label`: provided labels for data in training set + ''' + + # Shuffle the dataset with labels + assert train_data.shape[0] == train_label.shape[0], ( + 'fit: data size not match for ' + f'{train_data.shape[0]} and {train_label.shape[0]}' + ) + shuffled_i = np.random.permutation(train_data.shape[0]) + shuffled_data: np.ndarray = train_data[shuffled_i] + shuffled_label: np.ndarray = train_label[shuffled_i] + + # Separate training set and development set (for validation) + train_ratio: float = 0.75 + train_size: int = floor(shuffled_data.shape[0] * train_ratio) + self.train_data = shuffled_data[:train_size] + self.train_label = shuffled_label[:train_size] + self.dev_data = shuffled_data[train_size:] + self.dev_label = shuffled_label[train_size:] + + print('=== Training ===') + + # Compare the predicted and expected results, calculate the accuracy + # for each parameter k, and find out the best k for prediction. + k_threshold: int = train_size if train_size < 20 else 20 + accuracy_table: List[float] = [0.0] + max_accuracy: float = 0.0 + + for k in range(1, k_threshold): predicted_labels: List[int] = [] - for p in self.test_data: + for p in self.dev_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( - self.k, p, Dataset.TRAIN_SET + k, p, Dataset.TRAIN_SET ) predicted_label: int = self._get_most_common_label( k_nearest_neighbors, Dataset.TRAIN_SET ) predicted_labels.append(predicted_label) prediction: np.ndarray = np.array(predicted_labels) - return prediction + + accuracy: float = np.mean(np.equal(prediction, self.dev_label)) + accuracy_table.append(accuracy) + print(f'k = {k}, train_acc = {accuracy * 100} %') + if accuracy > max_accuracy: + max_accuracy, self.k = accuracy, k + + print(f'best k = {self.k}\n') ``` -## 实验探究部分 +对测试集进行预测时，我们就使用之前得到的最优的参数 `k` 进行预测，同样使用 KNN 算法。 -生成数据集，并保存到文件： +```python {.line-numbers} +def predict(self, test_data: np.ndarray) -> np.ndarray: + ''' + Predict the label of a point using our model. + + :param `test_data`: testing set + ''' + + self.test_data = test_data + + predicted_labels: List[int] = [] + for p in self.test_data: + k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( + self.k, p, Dataset.TRAIN_SET + ) + predicted_label: int = self._get_most_common_label( + k_nearest_neighbors, Dataset.TRAIN_SET + ) + predicted_labels.append(predicted_label) + prediction: np.ndarray = np.array(predicted_labels) + return prediction +``` + +## 生成数据 + +我们使用不同的参数生成数据集，并保存到文件 `data.npy`。这里由于时间有限，为了方便起见，我们直接在函数 `generate` 的 `parameters` 变量中对相应参数进行修改。 ```python {.line-numbers} def generate() -> None: @@ -238,7 +246,7 @@ def generate() -> None: )) ``` -作图： +为了直观起见，我们提供了函数 `display` 用于将当前使用的数据集可视化，并将图片保存到 `./img` 目录下。 ```python {.line-numbers} def display(data, label, name): @@ -259,6 +267,8 @@ def display(data, label, name): ## 运行代码 +在当前目录下，我们可以使用以下参数执行代码 `source.py`，具体功能参见注释。 + ```bash # 训练模型及预测 python ./source.py g @@ -267,9 +277,11 @@ python ./source.py g python ./source.py d ``` -## 数据集 +## 实验探究 + +### 1. 实验 1 -数据生成使用的参数： +#### 1.1 参数 ```python {.line-numbers} mean = (1, 2) @@ -289,21 +301,27 @@ cov = [[10, 5], [5, 10]] size = 1000 ``` -其中，`mean` 表示数据集的均值、`cov` 表示数据集的协方差、`size` 表示数据集的大小。 +其中： -### 训练集 +- `mean` 表示数据集的均值 +- `cov` 表示数据集的协方差 +- `size` 表示数据集的大小 -![训练集](./img/train.png) +下同。 -在训练时，我们随机选取 80% 作为训练集、20% 作为验证集。 +#### 1.2 数据集 -### 测试集 +训练集： -![测试集](./img/test.png) +![训练集](./img/train_1.png) -## 参数 +测试集： -训练时使用的参数 `k` 及相应的准确率： +![测试集](./img/test_1.png) + +#### 1.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示： ```text k = 1, train_acc = 95.75 % @@ -325,8 +343,137 @@ k = 16, train_acc = 96.75 % k = 17, train_acc = 96.75 % k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % +best k = 3 + +acc = 0.96 +``` + +可见，对于此数据集，最优的参数 `k` 为 `3`，其对测试集的预测准确率为 96%。 + +### 2. 实验 2 + +这次，我们调大数据之间的距离，观察预测准确率的变化。 + +#### 2.1 参数 + +```python {.line-numbers} +mean = (-5, 2) +cov = [[73, 0], [0, 22]] +size = 800 +``` + +```python {.line-numbers} +mean = (30, -10) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (20, 40) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +#### 2.2 数据集 + +训练集： + +![训练集](./img/train_2.png) + +测试集： + +![测试集](./img/test_2.png) + +#### 2.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示： + +```text +k = 1, train_acc = 100.0 % +k = 2, train_acc = 100.0 % +k = 3, train_acc = 100.0 % +k = 4, train_acc = 100.0 % +k = 5, train_acc = 100.0 % +k = 6, train_acc = 100.0 % +k = 7, train_acc = 100.0 % +k = 8, train_acc = 100.0 % +k = 9, train_acc = 100.0 % +k = 10, train_acc = 100.0 % +k = 11, train_acc = 100.0 % +k = 12, train_acc = 100.0 % +k = 13, train_acc = 100.0 % +k = 14, train_acc = 100.0 % +k = 15, train_acc = 100.0 % +k = 16, train_acc = 100.0 % +k = 17, train_acc = 100.0 % +k = 18, train_acc = 100.0 % +k = 19, train_acc = 100.0 % +best k = 1 + +acc = 1.0 +``` + +可见，对于不同标签区分度较大（即彼此间距离较远）的数据集，所有 `k` 的预测准确率均为 100%。这说明 KNN 算法对于较分散的数据有着很高的准确率。 + +### 3. 实验 3 + +#### 3.1 参数 + +```python {.line-numbers} +mean = (1, 2) +cov = [[73, 0], [0, 22]] +size = 800 ``` -可见，对于此数据集，最优的参数 `k` 为 `3`。 +```python {.line-numbers} +mean = (3, -2) +cov = [[21.2, 0], [0, 32.1]] +size = 200 +``` + +```python {.line-numbers} +mean = (-5, 4) +cov = [[10, 5], [5, 10]] +size = 1000 +``` + +#### 3.2 数据集 + +训练集： + +![训练集](./img/train_3.png) + +测试集： + +![测试集](./img/test_3.png) + +#### 3.3 预测准确率 + +训练时使用的参数 `k` 及相应的准确率如下所示： + +```text +k = 1, train_acc = 65.0 % +k = 2, train_acc = 65.75 % +k = 3, train_acc = 69.25 % +k = 4, train_acc = 68.25 % +k = 5, train_acc = 72.5 % +k = 6, train_acc = 71.5 % +k = 7, train_acc = 73.75 % +k = 8, train_acc = 75.0 % +k = 9, train_acc = 76.0 % +k = 10, train_acc = 75.75 % +k = 11, train_acc = 76.0 % +k = 12, train_acc = 74.5 % +k = 13, train_acc = 75.25 % +k = 14, train_acc = 75.0 % +k = 15, train_acc = 74.75 % +k = 16, train_acc = 75.5 % +k = 17, train_acc = 75.0 % +k = 18, train_acc = 75.0 % +k = 19, train_acc = 74.5 % +best k = 9 + +acc = 0.76 +``` -相应的准确率为 96%。 +此时，最优的参数 `k` 为 `9`，其对测试集的预测准确率为 76%。可见，当数据集间的区分度较低时，较高的 `k` 值有着相对较高的准确率。这是可以理解的，因为这样可以尽可能地减少噪声的影响。 diff --git a/assignment-1/submission/18307130003/img/test.png 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a/assignment-1/submission/18307130003/tester_demo.py +++ /dev/null @@ -1,24 +0,0 @@ -import numpy as np - -from source import KNN - -train_data = np.array([ - [1, 2, 3, 4], - [4, 2, 3, 1], - [12, 12, 13, 14], - [14, 12, 13, 11], - [12, 14, 15, 16], -]) -train_label = np.array([0, 0, 1, 1, 1]) - -test_data = np.array([ - [3, 4, 4, 2], - [18, 14, 15, 16], -]) -test_label = np.array([0, 1]) - -model = KNN() -model.fit(train_data, train_label) -res = model.predict(test_data) - -print("acc =", np.mean(np.equal(res, test_label))) -- Gitee From f8231355368a06419640b5bd5fdc454ab1c54b08 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:09:56 +0800 Subject: [PATCH 07/28] doc: minor fix --- assignment-1/submission/18307130003/README.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 21cd813..511563b 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -64,7 +64,7 @@ def _get_k_nearest_neighbors( return [item[1] for item in heap] ``` -最后我们对这 k 个邻居的标签分别进行计数，选择其中出现次数最多的标签作为预测结果。 +最后我们对这 `k` 个邻居的标签分别进行计数，选择其中出现次数最多的标签作为预测结果。 ```python {.line-numbers} def _get_most_common_label( @@ -352,7 +352,7 @@ acc = 0.96 ### 2. 实验 2 -这次，我们调大数据之间的距离，观察预测准确率的变化。 +这次，我们调大数据集之间的距离，观察预测准确率的变化。 #### 2.1 参数 @@ -417,6 +417,8 @@ acc = 1.0 ### 3. 实验 3 +我们再试试减小数据集间的距离，观察预测准确率的变化。 + #### 3.1 参数 ```python {.line-numbers} -- Gitee From 5afc128d705757ddba9b996c88aac4c8185bf08c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 2 Apr 2021 01:50:03 +0800 Subject: [PATCH 08/28] style: type annotations --- assignment-1/submission/18307130003/README.md | 81 ++++++++++++++----- 1 file changed, 63 insertions(+), 18 deletions(-) diff --git a/assignment-1/submission/18307130003/README.md b/assignment-1/submission/18307130003/README.md index 511563b..2bd04be 100644 --- a/assignment-1/submission/18307130003/README.md +++ b/assignment-1/submission/18307130003/README.md @@ -156,6 +156,8 @@ def predict(self, test_data: np.ndarray) -> np.ndarray: self.test_data = test_data + print('=== Predicting ===') + predicted_labels: List[int] = [] for p in self.test_data: k_nearest_neighbors: List[int] = self._get_k_nearest_neighbors( @@ -188,7 +190,7 @@ def generate() -> None: def _generate_with_parameters(param: Parameter) -> np.ndarray: ''' - Generate a dataset using given parameters + Generate a dataset using given parameters. :param `param`: a tuple of `mean`, `cov`, `size` `mean`: the mean of the dataset @@ -249,18 +251,23 @@ def generate() -> None: 为了直观起见，我们提供了函数 `display` 用于将当前使用的数据集可视化，并将图片保存到 `./img` 目录下。 ```python {.line-numbers} -def display(data, label, name): +def display(data: np.ndarray, label: np.ndarray, name: str) -> None: ''' - Visualize data and labels using `matplotlib.pyplot`. + Visualize dataset with labels using `matplotlib.pyplot`. + + :param `data`: dataset + :param `label`: labels for data in the dataset + :param `name`: file name when saving to file ''' - datas = [[], [], []] - for i in range(len(data)): - datas[label[i]].append(data[i]) + datasets_with_label: List[List[np.ndarray]] = [[], [], []] + for i in range(data.shape[0]): + datasets_with_label[label[i]].append(data[i]) + + for dataset_with_label in datasets_with_label: + dataset_with_label_: np.ndarray = np.array(dataset_with_label) + plt.scatter(dataset_with_label_[:, 0], dataset_with_label_[:, 1]) - for each in datas: - each = np.array(each) - plt.scatter(each[:, 0], each[:, 1]) plt.savefig(f'img/{name}') plt.show() ``` @@ -277,6 +284,35 @@ python ./source.py g python ./source.py d ``` +### 输出样例 + +```text +=== Training === +k = 1, train_acc = 67.5 % +k = 2, train_acc = 67.75 % +k = 3, train_acc = 70.5 % +k = 4, train_acc = 72.5 % +k = 5, train_acc = 72.75 % +k = 6, train_acc = 73.25 % +k = 7, train_acc = 74.25 % +k = 8, train_acc = 74.0 % +k = 9, train_acc = 75.75 % +k = 10, train_acc = 75.5 % +k = 11, train_acc = 75.75 % +k = 12, train_acc = 75.5 % +k = 13, train_acc = 75.75 % +k = 14, train_acc = 75.5 % +k = 15, train_acc = 75.5 % +k = 16, train_acc = 74.5 % +k = 17, train_acc = 75.0 % +k = 18, train_acc = 75.0 % +k = 19, train_acc = 75.25 % +best k = 9 + +=== Predicting === +k = 9, predict_acc = 71.5 % +``` + ## 实验探究 ### 1. 实验 1 @@ -343,12 +379,15 @@ k = 16, train_acc = 96.75 % k = 17, train_acc = 96.75 % k = 18, train_acc = 96.75 % k = 19, train_acc = 97.0 % -best k = 3 +``` + +预测时使用的参数 `k` 及相应的准确率如下所示： -acc = 0.96 +```text +k = 3, predict_acc = 96.0 % ``` -可见，对于此数据集，最优的参数 `k` 为 `3`，其对测试集的预测准确率为 96%。 +可见，对于此数据集，最优的参数 `k` 为 `3`，其对测试集的预测准确率为 96.0 %。 ### 2. 实验 2 @@ -408,12 +447,15 @@ k = 16, train_acc = 100.0 % k = 17, train_acc = 100.0 % k = 18, train_acc = 100.0 % k = 19, train_acc = 100.0 % -best k = 1 +``` + +预测时使用的参数 `k` 及相应的准确率如下所示： -acc = 1.0 +```text +k = 1, predict_acc = 100.0 % ``` -可见，对于不同标签区分度较大（即彼此间距离较远）的数据集，所有 `k` 的预测准确率均为 100%。这说明 KNN 算法对于较分散的数据有着很高的准确率。 +可见，对于不同标签区分度较大（即彼此间距离较远）的数据集，所有 `k` 的预测准确率均为 100.0 %。这说明 KNN 算法对于较分散的数据有着很高的准确率。 ### 3. 实验 3 @@ -473,9 +515,12 @@ k = 16, train_acc = 75.5 % k = 17, train_acc = 75.0 % k = 18, train_acc = 75.0 % k = 19, train_acc = 74.5 % -best k = 9 +``` -acc = 0.76 +预测时使用的参数 `k` 及相应的准确率如下所示： + +```text +k = 9, predict_acc = 76.0 % ``` -此时，最优的参数 `k` 为 `9`，其对测试集的预测准确率为 76%。可见，当数据集间的区分度较低时，较高的 `k` 值有着相对较高的准确率。这是可以理解的，因为这样可以尽可能地减少噪声的影响。 +此时，最优的参数 `k` 为 `9`，其对测试集的预测准确率为 76.0 %。可见，当数据集间的区分度较低时，较高的 `k` 值有着相对较高的准确率。这是可以理解的，因为提高可参考的邻居数量可以尽可能地减少噪声的影响。 -- Gitee From 20cf11737ace757561b774cdfdcaaa39b4b57ca5 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 20 Apr 2021 18:08:34 +0800 Subject: [PATCH 09/28] chore: initialize --- assignment-2/submission/18307130003/README.md | 0 .../submission/18307130003/numpy_fnn.py | 153 +++++++++++++++ .../submission/18307130003/numpy_mnist.py | 36 ++++ .../submission/18307130003/tester_demo.py | 180 ++++++++++++++++++ .../submission/18307130003/torch_mnist.py | 64 +++++++ assignment-2/submission/18307130003/utils.py | 71 +++++++ 6 files changed, 504 insertions(+) create mode 100644 assignment-2/submission/18307130003/README.md create mode 100644 assignment-2/submission/18307130003/numpy_fnn.py create mode 100644 assignment-2/submission/18307130003/numpy_mnist.py create mode 100644 assignment-2/submission/18307130003/tester_demo.py create mode 100644 assignment-2/submission/18307130003/torch_mnist.py create mode 100644 assignment-2/submission/18307130003/utils.py diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md new file mode 100644 index 0000000..e69de29 diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py new file mode 100644 index 0000000..150ab17 --- /dev/null +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -0,0 +1,153 @@ +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') + """ + + #################### + # code 1 # + #################### + + 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 + """ + + #################### + # code 2 # + #################### + + 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 + """ + + #################### + # code 3 # + #################### + + return grad_x + + +class Softmax(NumpyOp): + """ + softmax over last dimension + """ + + def forward(self, x): + """ + x: shape(N, c) + """ + + #################### + # code 4 # + #################### + + return out + + def backward(self, grad_y): + """ + grad_y: same shape as x + """ + + #################### + # code 5 # + #################### + + return grad_x + + +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 + 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) + + #################### + # code 6 # + #################### + + return x + + def backward(self, y): + for size in y.shape: + y /= size + + #################### + # code 7 # + #################### + + 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/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py new file mode 100644 index 0000000..903d7a7 --- /dev/null +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -0,0 +1,36 @@ +import numpy as np +from numpy_fnn import NumpyModel +from utils import download_mnist, batch, mini_batch, get_torch_initialization, plot_curve, one_hot + + +def numpy_run(): + train_dataset, test_dataset = download_mnist() + + model = NumpyModel() + 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()) + loss = (-y_pred * y).sum(axis=1).mean() + model.backward(y) + 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() diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py new file mode 100644 index 0000000..563de6b --- /dev/null +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -0,0 +1,180 @@ +import numpy as np +import torch +from torch import matmul as torch_matmul, relu as torch_relu, softmax as torch_softmax, log as torch_log + +from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel +from torch_mnist import TorchModel +from utils import get_torch_initialization, one_hot + +err_epsilon = 1e-3 +err_p = 0.4 + + +def check_result(numpy_result, torch_result=None): + if isinstance(numpy_result, list) and torch_result is None: + flag = True + for (n, t) in numpy_result: + flag = flag and check_result(n, t) + return flag + T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() + direction = T / torch_result.numel() < err_p + return direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + + +def case_1(): + x = np.random.normal(size=[5, 6]) + W = np.random.normal(size=[6, 4]) + + numpy_matmul = Matmul() + numpy_out = numpy_matmul.forward(x, W) + numpy_x_grad, numpy_W_grad = numpy_matmul.backward(np.ones_like(numpy_out)) + + torch_x = torch.from_numpy(x).clone().requires_grad_() + torch_W = torch.from_numpy(W).clone().requires_grad_() + + torch_out = torch_matmul(torch_x, torch_W) + torch_out.sum().backward() + + return check_result([ + (numpy_out, torch_out), + (numpy_x_grad, torch_x.grad), + (numpy_W_grad, torch_W.grad) + ]) + + +def case_2(): + x = np.random.normal(size=[5, 6]) + + numpy_relu = Relu() + numpy_out = numpy_relu.forward(x) + numpy_x_grad = numpy_relu.backward(np.ones_like(numpy_out)) + + torch_x = torch.from_numpy(x).clone().requires_grad_() + + torch_out = torch_relu(torch_x) + torch_out.sum().backward() + + return check_result([ + (numpy_out, torch_out), + (numpy_x_grad, torch_x.grad), + ]) + + +def case_3(): + x = np.random.uniform(low=0.0, high=1.0, size=[3, 4]) + + numpy_log = Log() + numpy_out = numpy_log.forward(x) + numpy_x_grad = numpy_log.backward(np.ones_like(numpy_out)) + + torch_x = torch.from_numpy(x).clone().requires_grad_() + + torch_out = torch_log(torch_x) + torch_out.sum().backward() + + return check_result([ + (numpy_out, torch_out), + (numpy_x_grad, torch_x.grad), + ]) + + +def case_4(): + x = np.random.normal(size=[4, 5]) + + numpy_softmax = Softmax() + numpy_out = numpy_softmax.forward(x) + + torch_x = torch.from_numpy(x).clone().requires_grad_() + + torch_out = torch_softmax(torch_x, 1) + + return check_result(numpy_out, torch_out) + + +def case_5(): + x = np.random.normal(size=[20, 25]) + + numpy_softmax = Softmax() + numpy_out = numpy_softmax.forward(x) + numpy_x_grad = numpy_softmax.backward(np.ones_like(numpy_out)) + + torch_x = torch.from_numpy(x).clone().requires_grad_() + + torch_out = torch_softmax(torch_x, 1) + torch_out.sum().backward() + + return check_result([ + (numpy_out, torch_out), + (numpy_x_grad, torch_x.grad), + ]) + + +def test_model(): + try: + numpy_model = NumpyModel() + torch_model = TorchModel() + torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = get_torch_initialization(numpy=False) + numpy_model.W1 = torch_model.W1.detach().clone().numpy() + numpy_model.W2 = torch_model.W2.detach().clone().numpy() + numpy_model.W3 = torch_model.W3.detach().clone().numpy() + + x = torch.randn((10000, 28, 28)) + y = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 0] * 1000) + + y = one_hot(y, numpy=False) + x2 = x.numpy() + y_pred = torch_model.forward(x) + loss = (-y_pred * y).sum(dim=1).mean() + loss.backward() + + y_pred_numpy = numpy_model.forward(x2) + y2 = y.numpy() + loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() + + check_flag_1 = check_result(y_pred_numpy, y_pred) + print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) + except: + print("[Runtime Error in forward]") + print("+ {:12} {}/{}".format("forward", 0, 10)) + return 0 + + try: + + numpy_model.backward(y2) + + check_flag_2 = [ + check_result(numpy_model.log_grad, torch_model.log.grad), + check_result(numpy_model.softmax_grad, torch_model.softmax.grad), + check_result(numpy_model.W3_grad, torch_model.W3.grad), + check_result(numpy_model.W2_grad, torch_model.W2.grad), + check_result(numpy_model.W1_grad, torch_model.W1.grad) + ] + check_flag_2 = sum(check_flag_2) >= 4 + print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) + except: + print("[Runtime Error in backward]") + print("+ {:12} {}/{}".format("backward", 0, 20)) + check_flag_2 = False + + return 10 * check_flag_1 + 20 * check_flag_2 + + +if __name__ == "__main__": + testcases = [ + ["matmul", case_1, 5], + ["relu", case_2, 5], + ["log", case_3, 5], + ["softmax_1", case_4, 5], + ["softmax_2", case_5, 10], + ] + score = 0 + for case in testcases: + try: + res = case[2] if case[1]() else 0 + except: + print("[Runtime Error in {}]".format(case[0])) + res = 0 + score += res + print("+ {:12} {}/{}".format(case[0], res, case[2])) + score += test_model() + print("{:14} {}/60".format("FINAL SCORE", score)) diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py new file mode 100644 index 0000000..6a5649b --- /dev/null +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -0,0 +1,64 @@ +import torch +from utils import mini_batch, batch, download_mnist, get_torch_initialization, one_hot, plot_curve + + +class TorchModel: + + def __init__(self): + self.W1 = torch.randn((28 * 28, 256), requires_grad=True) + self.W2 = torch.randn((256, 64), requires_grad=True) + self.W3 = torch.randn((64, 10), requires_grad=True) + + def forward(self, x): + x = x.reshape(-1, 28 * 28) + x = torch.relu(torch.matmul(x, self.W1)) + x = torch.relu(torch.matmul(x, self.W2)) + x = torch.matmul(x, self.W3) + self.softmax = torch.softmax(x, 1) + self.log = torch.log(self.softmax) + self.softmax.retain_grad() # for test only + self.log.retain_grad() # for test only + return self.log + + def optimize(self, learning_rate): + with torch.no_grad(): + self.W1 -= learning_rate * self.W1.grad + self.W2 -= learning_rate * self.W2.grad + self.W3 -= learning_rate * self.W3.grad + + self.W1.grad = None + self.W2.grad = None + self.W3.grad = None + + +def torch_run(): + train_dataset, test_dataset = download_mnist() + + model = TorchModel() + model.W1.data, model.W2.data, model.W3.data = get_torch_initialization(numpy=False) + + train_loss = [] + + epoch_number = 3 + learning_rate = 0.1 + + for epoch in range(epoch_number): + for x, y in mini_batch(train_dataset, numpy=False): + y = one_hot(y, numpy=False) + + y_pred = model.forward(x) + loss = (-y_pred * y).sum(dim=1).mean() + loss.backward() + model.optimize(learning_rate) + + train_loss.append(loss.item()) + + x, y = batch(test_dataset, numpy=False)[0] + accuracy = model.forward(x).argmax(dim=1).eq(y).float().mean().item() + print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) + + plot_curve(train_loss) + + +if __name__ == "__main__": + torch_run() diff --git a/assignment-2/submission/18307130003/utils.py b/assignment-2/submission/18307130003/utils.py new file mode 100644 index 0000000..709220c --- /dev/null +++ b/assignment-2/submission/18307130003/utils.py @@ -0,0 +1,71 @@ +import torch +import numpy as np +from matplotlib import pyplot as plt + + +def plot_curve(data): + plt.plot(range(len(data)), data, color='blue') + plt.legend(['loss_value'], loc='upper right') + plt.xlabel('step') + plt.ylabel('value') + plt.show() + + +def download_mnist(): + from torchvision import datasets, transforms + + transform = transforms.Compose([ + transforms.ToTensor(), + transforms.Normalize(mean=(0.1307,), std=(0.3081,)) + ]) + + train_dataset = datasets.MNIST(root="./data/", transform=transform, train=True, download=True) + test_dataset = datasets.MNIST(root="./data/", transform=transform, train=False, download=True) + + return train_dataset, test_dataset + + +def one_hot(y, numpy=True): + if numpy: + y_ = np.zeros((y.shape[0], 10)) + y_[np.arange(y.shape[0], dtype=np.int32), y] = 1 + return y_ + else: + y_ = torch.zeros((y.shape[0], 10)) + y_[torch.arange(y.shape[0], dtype=torch.long), y] = 1 + return y_ + + +def batch(dataset, numpy=True): + data = [] + label = [] + for each in dataset: + data.append(each[0]) + label.append(each[1]) + data = torch.stack(data) + label = torch.LongTensor(label) + if numpy: + return [(data.numpy(), label.numpy())] + else: + return [(data, label)] + + +def mini_batch(dataset, batch_size=128, numpy=False): + return torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=True) + + +def get_torch_initialization(numpy=True): + fc1 = torch.nn.Linear(28 * 28, 256) + fc2 = torch.nn.Linear(256, 64) + fc3 = torch.nn.Linear(64, 10) + + if numpy: + W1 = fc1.weight.T.detach().clone().numpy() + W2 = fc2.weight.T.detach().clone().numpy() + W3 = fc3.weight.T.detach().clone().numpy() + else: + W1 = fc1.weight.T.detach().clone().data + W2 = fc2.weight.T.detach().clone().data + W3 = fc3.weight.T.detach().clone().data + + return W1, W2, W3 -- Gitee From 1c81868708fae8a169cc662a53c467fc1fb47595 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Tue, 20 Apr 2021 18:15:48 +0800 Subject: [PATCH 10/28] style: fix coding style --- .../submission/18307130003/numpy_fnn.py | 58 +++++++++--------- .../submission/18307130003/numpy_mnist.py | 16 ++--- .../submission/18307130003/tester_demo.py | 60 ++++++++++--------- .../submission/18307130003/torch_mnist.py | 28 +++++---- assignment-2/submission/18307130003/utils.py | 18 +++--- 5 files changed, 93 insertions(+), 87 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 150ab17..f50cb4c 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -2,14 +2,14 @@ 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) @@ -19,58 +19,58 @@ class Matmul(NumpyOp): self.memory['W'] = W h = np.matmul(x, W) return h - + def backward(self, grad_y): """ grad_y: shape(N, d') """ - + #################### # code 1 # #################### - + 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 """ - + #################### # code 2 # #################### - + 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 """ - + #################### # code 3 # #################### - + return grad_x @@ -78,27 +78,27 @@ class Softmax(NumpyOp): """ softmax over last dimension """ - + def forward(self, x): """ x: shape(N, c) """ - + #################### # code 4 # #################### - + return out - + def backward(self, grad_y): """ grad_y: same shape as x """ - + #################### # code 5 # #################### - + return grad_x @@ -108,7 +108,6 @@ class NumpyModel: 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() @@ -126,27 +125,26 @@ class NumpyModel: 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) - + #################### # code 6 # #################### - + return x - + def backward(self, y): for size in y.shape: y /= size - + #################### # code 7 # #################### - + pass - + def optimize(self, learning_rate): self.W1 -= learning_rate * self.W1_grad self.W2 -= learning_rate * self.W2_grad diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index 903d7a7..c92e1a7 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -5,30 +5,30 @@ from utils import download_mnist, batch, mini_batch, get_torch_initialization, p def numpy_run(): train_dataset, test_dataset = download_mnist() - + model = NumpyModel() 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()) loss = (-y_pred * y).sum(axis=1).mean() model.backward(y) 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) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 563de6b..39e137c 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -24,17 +24,17 @@ def check_result(numpy_result, torch_result=None): def case_1(): x = np.random.normal(size=[5, 6]) W = np.random.normal(size=[6, 4]) - + numpy_matmul = Matmul() numpy_out = numpy_matmul.forward(x, W) numpy_x_grad, numpy_W_grad = numpy_matmul.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() torch_W = torch.from_numpy(W).clone().requires_grad_() - + torch_out = torch_matmul(torch_x, torch_W) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -44,16 +44,16 @@ def case_1(): def case_2(): x = np.random.normal(size=[5, 6]) - + numpy_relu = Relu() numpy_out = numpy_relu.forward(x) numpy_x_grad = numpy_relu.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_relu(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -62,16 +62,16 @@ def case_2(): def case_3(): x = np.random.uniform(low=0.0, high=1.0, size=[3, 4]) - + numpy_log = Log() numpy_out = numpy_log.forward(x) numpy_x_grad = numpy_log.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_log(torch_x) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -80,29 +80,29 @@ def case_3(): def case_4(): x = np.random.normal(size=[4, 5]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) - + return check_result(numpy_out, torch_out) def case_5(): x = np.random.normal(size=[20, 25]) - + numpy_softmax = Softmax() numpy_out = numpy_softmax.forward(x) numpy_x_grad = numpy_softmax.backward(np.ones_like(numpy_out)) - + torch_x = torch.from_numpy(x).clone().requires_grad_() - + torch_out = torch_softmax(torch_x, 1) torch_out.sum().backward() - + return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), @@ -113,35 +113,37 @@ def test_model(): try: numpy_model = NumpyModel() torch_model = TorchModel() - torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = get_torch_initialization(numpy=False) + torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = ( + get_torch_initialization(numpy=False) + ) numpy_model.W1 = torch_model.W1.detach().clone().numpy() numpy_model.W2 = torch_model.W2.detach().clone().numpy() numpy_model.W3 = torch_model.W3.detach().clone().numpy() - + x = torch.randn((10000, 28, 28)) y = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 0] * 1000) - + y = one_hot(y, numpy=False) x2 = x.numpy() y_pred = torch_model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() - + y_pred_numpy = numpy_model.forward(x2) y2 = y.numpy() loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() - + check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) except: print("[Runtime Error in forward]") print("+ {:12} {}/{}".format("forward", 0, 10)) return 0 - + try: - + numpy_model.backward(y2) - + check_flag_2 = [ check_result(numpy_model.log_grad, torch_model.log.grad), check_result(numpy_model.softmax_grad, torch_model.softmax.grad), @@ -155,7 +157,7 @@ def test_model(): print("[Runtime Error in backward]") print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False - + return 10 * check_flag_1 + 20 * check_flag_2 diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py index 6a5649b..c1315f0 100644 --- a/assignment-2/submission/18307130003/torch_mnist.py +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -3,12 +3,12 @@ from utils import mini_batch, batch, download_mnist, get_torch_initialization, o class TorchModel: - + def __init__(self): self.W1 = torch.randn((28 * 28, 256), requires_grad=True) self.W2 = torch.randn((256, 64), requires_grad=True) self.W3 = torch.randn((64, 10), requires_grad=True) - + def forward(self, x): x = x.reshape(-1, 28 * 28) x = torch.relu(torch.matmul(x, self.W1)) @@ -19,13 +19,13 @@ class TorchModel: self.softmax.retain_grad() # for test only self.log.retain_grad() # for test only return self.log - + def optimize(self, learning_rate): with torch.no_grad(): self.W1 -= learning_rate * self.W1.grad self.W2 -= learning_rate * self.W2.grad self.W3 -= learning_rate * self.W3.grad - + self.W1.grad = None self.W2.grad = None self.W3.grad = None @@ -33,30 +33,32 @@ class TorchModel: def torch_run(): train_dataset, test_dataset = download_mnist() - + model = TorchModel() - model.W1.data, model.W2.data, model.W3.data = get_torch_initialization(numpy=False) - + model.W1.data, model.W2.data, model.W3.data = ( + get_torch_initialization(numpy=False) + ) + train_loss = [] - + epoch_number = 3 learning_rate = 0.1 - + for epoch in range(epoch_number): for x, y in mini_batch(train_dataset, numpy=False): y = one_hot(y, numpy=False) - + y_pred = model.forward(x) loss = (-y_pred * y).sum(dim=1).mean() loss.backward() model.optimize(learning_rate) - + train_loss.append(loss.item()) - + x, y = batch(test_dataset, numpy=False)[0] accuracy = model.forward(x).argmax(dim=1).eq(y).float().mean().item() print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) - + plot_curve(train_loss) diff --git a/assignment-2/submission/18307130003/utils.py b/assignment-2/submission/18307130003/utils.py index 709220c..f471049 100644 --- a/assignment-2/submission/18307130003/utils.py +++ b/assignment-2/submission/18307130003/utils.py @@ -13,15 +13,19 @@ def plot_curve(data): def download_mnist(): from torchvision import datasets, transforms - + transform = transforms.Compose([ transforms.ToTensor(), transforms.Normalize(mean=(0.1307,), std=(0.3081,)) ]) - - train_dataset = datasets.MNIST(root="./data/", transform=transform, train=True, download=True) - test_dataset = datasets.MNIST(root="./data/", transform=transform, train=False, download=True) - + + train_dataset = datasets.MNIST( + root="./data/", transform=transform, train=True, download=True + ) + test_dataset = datasets.MNIST( + root="./data/", transform=transform, train=False, download=True + ) + return train_dataset, test_dataset @@ -58,7 +62,7 @@ def get_torch_initialization(numpy=True): fc1 = torch.nn.Linear(28 * 28, 256) fc2 = torch.nn.Linear(256, 64) fc3 = torch.nn.Linear(64, 10) - + if numpy: W1 = fc1.weight.T.detach().clone().numpy() W2 = fc2.weight.T.detach().clone().numpy() @@ -67,5 +71,5 @@ def get_torch_initialization(numpy=True): W1 = fc1.weight.T.detach().clone().data W2 = fc2.weight.T.detach().clone().data W3 = fc3.weight.T.detach().clone().data - + return W1, W2, W3 -- Gitee From 14b8a71153a5c2356a9bb51194c3f964c7b13d31 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Wed, 21 Apr 2021 03:04:08 +0800 Subject: [PATCH 11/28] feat: implement Matmul, Relu, Log style: fix coding style --- .../submission/18307130003/numpy_fnn.py | 133 +++++++++++------- .../submission/18307130003/tester_demo.py | 4 +- 2 files changed, 86 insertions(+), 51 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index f50cb4c..f17c5f3 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -1,7 +1,11 @@ +from typing import Tuple import numpy as np class NumpyOp: + ''' + The base class for Numpy operations. + ''' def __init__(self): self.memory = {} @@ -9,97 +13,128 @@ class NumpyOp: class Matmul(NumpyOp): + ''' + Matrix multiplication unit.. + ''' + + def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + w: shape(d, d') + + Returns: + shape(N, d') + ''' - 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 + self.memory['w'] = w + return np.matmul(x, w) - def backward(self, grad_y): - """ - grad_y: shape(N, d') - """ + def backward(self, grad_y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: + ''' + Args: + grad_y: shape(N, d') - #################### - # code 1 # - #################### + Returns: + grad_x: shape(N, d) + grad_w: shape(d, d') + ''' - return grad_x, grad_W + x: np.ndarray = self.memory['x'] + w: np.ndarray = self.memory['w'] + grad_x: np.ndarray = np.matmul(grad_y, w.T) + grad_w: np.ndarray = np.matmul(x.T, grad_y) + return grad_x, grad_w class Relu(NumpyOp): + ''' + Rectified Linear Unit. + ''' + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + + Returns: + shape(N, d) + ''' - def forward(self, x): self.memory['x'] = x - return np.where(x > 0, x, np.zeros_like(x)) + return np.where(x > 0, x, 0) - def backward(self, grad_y): - """ - grad_y: same shape as x - """ + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) - #################### - # code 2 # - #################### + Returns: + shape(N, d) + ''' - return grad_x + x: np.ndarray = self.memory['x'] + grad_y[x < 0] = 0 + return grad_y class Log(NumpyOp): + ''' + Natural logarithm unit. + ''' - def forward(self, x): - """ - x: shape(N, c) - """ + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) - out = np.log(x + self.epsilon) - self.memory['x'] = x + Returns: + shape(N, d) + ''' - return out + self.memory['x'] = x + return np.log(x + self.epsilon) - def backward(self, grad_y): - """ - grad_y: same shape as x - """ + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) - #################### - # code 3 # - #################### + Returns: + shape(N, d) + ''' - return grad_x + x: np.ndarray = self.memory['x'] + return grad_y / x class Softmax(NumpyOp): - """ + ''' softmax over last dimension - """ + ''' def forward(self, x): - """ + ''' x: shape(N, c) - """ + ''' #################### # code 4 # #################### - return out + # return out def backward(self, grad_y): - """ + ''' grad_y: same shape as x - """ + ''' #################### # code 5 # #################### - return grad_x + # return grad_x class NumpyModel: diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 39e137c..c2c9bc5 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -173,8 +173,8 @@ if __name__ == "__main__": for case in testcases: try: res = case[2] if case[1]() else 0 - except: - print("[Runtime Error in {}]".format(case[0])) + except Exception as err: + print("[Runtime Error in {}, error: {}]".format(case[0], err)) res = 0 score += res print("+ {:12} {}/{}".format(case[0], res, case[2])) -- Gitee From a81128c79c2c566152b4816efd4267aa59ac2e75 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:08 +0800 Subject: [PATCH 12/28] feat: implement Softmax, NumpyModel --- .../submission/18307130003/numpy_fnn.py | 111 ++++++++++++------ 1 file changed, 72 insertions(+), 39 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index f17c5f3..dbb1d34 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -111,76 +111,109 @@ class Log(NumpyOp): class Softmax(NumpyOp): ''' - softmax over last dimension + Softmax over last dimension. ''' - def forward(self, x): - ''' - x: shape(N, c) + def forward(self, x: np.ndarray) -> np.ndarray: ''' + Args: + x: shape(N, d) - #################### - # code 4 # - #################### + Returns: + shape(N, d) + ''' - # return out + y: np.ndarray = np.exp(x) / np.exp(x).sum(axis=1)[:, None] + self.memory['y'] = y + return y - def backward(self, grad_y): - ''' - grad_y: same shape as x + def backward(self, grad_y: np.ndarray) -> np.ndarray: ''' + Args: + grad_y: shape(N, d) - #################### - # code 5 # - #################### + Returns: + shape(N, d) + ''' - # return grad_x + y: np.ndarray = self.memory['y'] + return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) class NumpyModel: + ''' + An FNN model implemented in NumPy. + ''' + 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)) + self.W1: np.ndarray = np.random.normal(size=(28 * 28, 256)) + self.W2: np.ndarray = np.random.normal(size=(256, 64)) + self.W3: np.ndarray = 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() + self.softmax_3 = Softmax() + self.log_3 = Log() # 以下变量需要在 backward 中更新 - 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) - #################### - # code 6 # - #################### + self.x1_grad: np.ndarray = None + self.W1_grad: np.ndarray = None + self.relu_1_grad: np.ndarray = None + + self.x2_grad: np.ndarray = None + self.W2_grad: np.ndarray = None + self.relu_2_grad: np.ndarray = None + + self.x3_grad: np.ndarray = None + self.W3_grad: np.ndarray = None + self.softmax_grad: np.ndarray = None + self.log_grad: np.ndarray = None + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + Returns: + shape(N, d) + ''' + + 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.softmax_3.forward(self.matmul_3.forward(x, self.W3)) + x = self.log_3.forward(x) return x - def backward(self, y): + def backward(self, y: np.ndarray) -> None: + ''' + Args: + y: shape(N, d) + ''' + for size in y.shape: + size: int y /= size - #################### - # code 7 # - #################### + self.log_grad = self.log_3.backward(y) + self.softmax_grad = self.softmax_3.backward(self.log_grad) + self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) + + self.relu_2_grad = self.relu_2.backward(self.x3_grad) + self.x2_grad, self.W2_grad = self.matmul_2.backward(self.relu_2_grad) - pass + self.relu_1_grad = self.relu_1.backward(self.x2_grad) + self.x1_grad, self.W1_grad = self.matmul_1.backward(self.relu_1_grad) - def optimize(self, learning_rate): + def optimize(self, learning_rate: float): self.W1 -= learning_rate * self.W1_grad self.W2 -= learning_rate * self.W2_grad self.W3 -= learning_rate * self.W3_grad -- Gitee From 6e1151dfcc6eab665b5a8504ca190e5e6762df17 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:26 +0800 Subject: [PATCH 13/28] feat: add more logs in tester --- .../submission/18307130003/tester_demo.py | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index c2c9bc5..c607208 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -18,7 +18,9 @@ def check_result(numpy_result, torch_result=None): return flag T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() direction = T / torch_result.numel() < err_p - return direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + result = direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + print(result) + return result def case_1(): @@ -135,13 +137,12 @@ def test_model(): check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) - except: - print("[Runtime Error in forward]") + except Exception as err: + print("[Runtime Error in forward, error: {}]".format(err)) print("+ {:12} {}/{}".format("forward", 0, 10)) return 0 try: - numpy_model.backward(y2) check_flag_2 = [ @@ -151,10 +152,10 @@ def test_model(): check_result(numpy_model.W2_grad, torch_model.W2.grad), check_result(numpy_model.W1_grad, torch_model.W1.grad) ] - check_flag_2 = sum(check_flag_2) >= 4 + check_flag_2 = sum(check_flag_2) / 5 print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) - except: - print("[Runtime Error in backward]") + except Exception as err: + print("[Runtime Error in backward, error: {}]".format(err)) print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False -- Gitee From 56125d6d12009eeb7c148c97d81a995a9396c291 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:29 +0800 Subject: [PATCH 14/28] fix: negative loss function issue --- .../submission/18307130003/numpy_fnn.py | 19 +------------------ .../submission/18307130003/tester_demo.py | 8 +++++--- 2 files changed, 6 insertions(+), 21 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index dbb1d34..ac9ee2f 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -150,8 +150,6 @@ class NumpyModel: self.W2: np.ndarray = np.random.normal(size=(256, 64)) self.W3: np.ndarray = 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() @@ -162,21 +160,6 @@ class NumpyModel: self.softmax_3 = Softmax() self.log_3 = Log() - # 以下变量需要在 backward 中更新 - - self.x1_grad: np.ndarray = None - self.W1_grad: np.ndarray = None - self.relu_1_grad: np.ndarray = None - - self.x2_grad: np.ndarray = None - self.W2_grad: np.ndarray = None - self.relu_2_grad: np.ndarray = None - - self.x3_grad: np.ndarray = None - self.W3_grad: np.ndarray = None - self.softmax_grad: np.ndarray = None - self.log_grad: np.ndarray = None - def forward(self, x: np.ndarray) -> np.ndarray: ''' Args: @@ -203,7 +186,7 @@ class NumpyModel: size: int y /= size - self.log_grad = self.log_3.backward(y) + self.log_grad = self.log_3.backward(-y) self.softmax_grad = self.softmax_3.backward(self.log_grad) self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index c607208..38530cd 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -18,7 +18,9 @@ def check_result(numpy_result, torch_result=None): return flag T = (torch_result * torch.from_numpy(numpy_result) < 0).sum().item() direction = T / torch_result.numel() < err_p - result = direction and ((torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon).item() + result = direction and ( + (torch.from_numpy(numpy_result) - torch_result).abs().mean() < err_epsilon + ).item() print(result) return result @@ -153,13 +155,13 @@ def test_model(): check_result(numpy_model.W1_grad, torch_model.W1.grad) ] check_flag_2 = sum(check_flag_2) / 5 - print("+ {:12} {}/{}".format("backward", 20 * check_flag_2, 20)) + print("+ {:12} {}/{}".format("backward", int(20 * check_flag_2), 20)) except Exception as err: print("[Runtime Error in backward, error: {}]".format(err)) print("+ {:12} {}/{}".format("backward", 0, 20)) check_flag_2 = False - return 10 * check_flag_1 + 20 * check_flag_2 + return int(10 * check_flag_1 + 20 * check_flag_2) if __name__ == "__main__": -- Gitee From 9f35413968e5c9df62185e18040384187778cd8f Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:33 +0800 Subject: [PATCH 15/28] fix: merge fixes from upstream --- .../submission/18307130003/numpy_fnn.py | 16 ++++++++++++ .../submission/18307130003/numpy_mnist.py | 24 +++++++++++++---- .../submission/18307130003/tester_demo.py | 26 ++++++++++++------- .../submission/18307130003/torch_mnist.py | 24 +++++++++++------ 4 files changed, 67 insertions(+), 23 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index ac9ee2f..46823b2 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -140,6 +140,22 @@ class Softmax(NumpyOp): return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) +class NumpyLoss: + ''' + Loss function. + ''' + + def __init__(self): + self.target: np.ndarray = None + + def get_loss(self, pred: np.ndarray, target: np.ndarray) -> float: + self.target = target + return (-pred * target).sum(axis=1).mean() + + def backward(self) -> np.ndarray: + return -self.target / self.target.shape[0] + + class NumpyModel: ''' An FNN model implemented in NumPy. diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index c92e1a7..630e38f 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,15 +1,28 @@ +from typing import List import numpy as np -from numpy_fnn import NumpyModel -from utils import download_mnist, batch, mini_batch, get_torch_initialization, plot_curve, one_hot +from numpy_fnn import NumpyModel, NumpyLoss +from utils import ( + download_mnist, + batch, + mini_batch, + get_torch_initialization, + plot_curve, + one_hot, +) def numpy_run(): + ''' + Train the FNN network on MNIST. + ''' + train_dataset, test_dataset = download_mnist() model = NumpyModel() + numpy_loss = NumpyLoss() model.W1, model.W2, model.W3 = get_torch_initialization() - train_loss = [] + train_loss: List[float] = [] epoch_number = 3 learning_rate = 0.1 @@ -19,8 +32,9 @@ def numpy_run(): y = one_hot(y) y_pred = model.forward(x.numpy()) - loss = (-y_pred * y).sum(axis=1).mean() - model.backward(y) + loss = numpy_loss.get_loss(y_pred, y) + + model.backward(numpy_loss.backward()) model.optimize(learning_rate) train_loss.append(loss.item()) diff --git a/assignment-2/submission/18307130003/tester_demo.py b/assignment-2/submission/18307130003/tester_demo.py index 38530cd..68874de 100644 --- a/assignment-2/submission/18307130003/tester_demo.py +++ b/assignment-2/submission/18307130003/tester_demo.py @@ -1,12 +1,17 @@ import numpy as np import torch -from torch import matmul as torch_matmul, relu as torch_relu, softmax as torch_softmax, log as torch_log - -from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel +from torch import ( + matmul as torch_matmul, + relu as torch_relu, + softmax as torch_softmax, + log as torch_log, +) + +from numpy_fnn import Matmul, Relu, Softmax, Log, NumpyModel, NumpyLoss from torch_mnist import TorchModel from utils import get_torch_initialization, one_hot -err_epsilon = 1e-3 +err_epsilon = 1e-6 err_p = 0.4 @@ -42,7 +47,7 @@ def case_1(): return check_result([ (numpy_out, torch_out), (numpy_x_grad, torch_x.grad), - (numpy_W_grad, torch_W.grad) + (numpy_W_grad, torch_W.grad), ]) @@ -115,6 +120,7 @@ def case_5(): def test_model(): try: + numpy_loss = NumpyLoss() numpy_model = NumpyModel() torch_model = TorchModel() torch_model.W1.data, torch_model.W2.data, torch_model.W3.data = ( @@ -134,8 +140,7 @@ def test_model(): loss.backward() y_pred_numpy = numpy_model.forward(x2) - y2 = y.numpy() - loss_numpy = (-y_pred_numpy * y2).sum(axis=1).mean() + numpy_loss.get_loss(y_pred_numpy, y.numpy()) check_flag_1 = check_result(y_pred_numpy, y_pred) print("+ {:12} {}/{}".format("forward", 10 * check_flag_1, 10)) @@ -145,11 +150,12 @@ def test_model(): return 0 try: - numpy_model.backward(y2) + numpy_model.backward(numpy_loss.backward()) check_flag_2 = [ - check_result(numpy_model.log_grad, torch_model.log.grad), - check_result(numpy_model.softmax_grad, torch_model.softmax.grad), + check_result(numpy_model.log_grad, torch_model.log_input.grad), + check_result(numpy_model.softmax_grad, + torch_model.softmax_input.grad), check_result(numpy_model.W3_grad, torch_model.W3.grad), check_result(numpy_model.W2_grad, torch_model.W2.grad), check_result(numpy_model.W1_grad, torch_model.W1.grad) diff --git a/assignment-2/submission/18307130003/torch_mnist.py b/assignment-2/submission/18307130003/torch_mnist.py index c1315f0..dec6c89 100644 --- a/assignment-2/submission/18307130003/torch_mnist.py +++ b/assignment-2/submission/18307130003/torch_mnist.py @@ -8,17 +8,26 @@ class TorchModel: self.W1 = torch.randn((28 * 28, 256), requires_grad=True) self.W2 = torch.randn((256, 64), requires_grad=True) self.W3 = torch.randn((64, 10), requires_grad=True) + self.softmax_input = None + self.log_input = None def forward(self, x): x = x.reshape(-1, 28 * 28) x = torch.relu(torch.matmul(x, self.W1)) x = torch.relu(torch.matmul(x, self.W2)) x = torch.matmul(x, self.W3) - self.softmax = torch.softmax(x, 1) - self.log = torch.log(self.softmax) - self.softmax.retain_grad() # for test only - self.log.retain_grad() # for test only - return self.log + + self.softmax_input = x + self.softmax_input.retain_grad() + + x = torch.softmax(x, 1) + + self.log_input = x + self.log_input.retain_grad() + + x = torch.log(x) + + return x def optimize(self, learning_rate): with torch.no_grad(): @@ -35,9 +44,8 @@ def torch_run(): train_dataset, test_dataset = download_mnist() model = TorchModel() - model.W1.data, model.W2.data, model.W3.data = ( - get_torch_initialization(numpy=False) - ) + model.W1.data, model.W2.data, model.W3.data = get_torch_initialization( + numpy=False) train_loss = [] -- Gitee From db8aba37b92361a5d49923475e04b4057a8f55a0 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 19:06:36 +0800 Subject: [PATCH 16/28] fix: minor fix for previous changes --- assignment-2/submission/18307130003/numpy_fnn.py | 6 +----- assignment-2/submission/18307130003/numpy_mnist.py | 8 +++++--- 2 files changed, 6 insertions(+), 8 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 46823b2..6db4b6c 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -198,11 +198,7 @@ class NumpyModel: y: shape(N, d) ''' - for size in y.shape: - size: int - y /= size - - self.log_grad = self.log_3.backward(-y) + self.log_grad = self.log_3.backward(y) self.softmax_grad = self.softmax_3.backward(self.log_grad) self.x3_grad, self.W3_grad = self.matmul_3.backward(self.softmax_grad) diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index 630e38f..c584c4c 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,5 +1,6 @@ from typing import List import numpy as np +from torch import Tensor from numpy_fnn import NumpyModel, NumpyLoss from utils import ( download_mnist, @@ -29,9 +30,10 @@ def numpy_run(): for epoch in range(epoch_number): for x, y in mini_batch(train_dataset): - y = one_hot(y) + x: np.ndarray = x.numpy() + y: np.ndarray = one_hot(y) - y_pred = model.forward(x.numpy()) + y_pred = model.forward(x) loss = numpy_loss.get_loss(y_pred, y) model.backward(numpy_loss.backward()) @@ -40,7 +42,7 @@ def numpy_run(): train_loss.append(loss.item()) x, y = batch(test_dataset)[0] - accuracy = np.mean((model.forward(x).argmax(axis=1) == y)) + accuracy: float = np.mean((model.forward(x).argmax(axis=1) == y)) print('[{}] Accuracy: {:.4f}'.format(epoch, accuracy)) plot_curve(train_loss) -- Gitee From acd1603d3d30a6b32f4a9730a8eed6772665bf2c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 22:47:24 +0800 Subject: [PATCH 17/28] feat: mini_batch in numpy --- .../submission/18307130003/numpy_mnist.py | 34 ++++++++++++++++--- 1 file changed, 30 insertions(+), 4 deletions(-) diff --git a/assignment-2/submission/18307130003/numpy_mnist.py b/assignment-2/submission/18307130003/numpy_mnist.py index c584c4c..101aac0 100644 --- a/assignment-2/submission/18307130003/numpy_mnist.py +++ b/assignment-2/submission/18307130003/numpy_mnist.py @@ -1,17 +1,43 @@ -from typing import List +from typing import Any, List, Tuple import numpy as np -from torch import Tensor from numpy_fnn import NumpyModel, NumpyLoss from utils import ( download_mnist, batch, - mini_batch, + # mini_batch, get_torch_initialization, plot_curve, one_hot, ) +def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: + ''' + Split the data and labels from the given dataset into batches. + + Args: + dataset: the given dataset + batch_size: the size of retrieved data + + Returns: + Batches of [data, labels] pair. + ''' + + data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) + labels: np.ndarray = np.array([pair[1] for pair in dataset]) + + # Shuffle the dataset + size: int = len(dataset) + indices: np.ndarray = np.arange(size) + np.random.shuffle(indices) + + batches: List[Tuple[np.ndarray, np.ndarray]] = [] + for i in range(0, size, batch_size): + chunk: np.ndarray = indices[i:i+batch_size] + batches.append((data[chunk], labels[chunk])) + return batches + + def numpy_run(): ''' Train the FNN network on MNIST. @@ -30,7 +56,7 @@ def numpy_run(): for epoch in range(epoch_number): for x, y in mini_batch(train_dataset): - x: np.ndarray = x.numpy() + x: np.ndarray y: np.ndarray = one_hot(y) y_pred = model.forward(x) -- Gitee From d3a0a5a592394ae2a2ef77b2e74d5233964db6f7 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Thu, 29 Apr 2021 23:02:30 +0800 Subject: [PATCH 18/28] chore: doc string minor fix --- assignment-2/submission/18307130003/numpy_fnn.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 6db4b6c..7849408 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -14,7 +14,7 @@ class NumpyOp: class Matmul(NumpyOp): ''' - Matrix multiplication unit.. + Matrix multiplication unit. ''' def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: -- Gitee From ebe438c05319ce7db8b323054a60c02c37fb7feb Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:25:44 +0800 Subject: [PATCH 19/28] doc: backward chap. 1 --- assignment-2/submission/18307130003/README.md | 232 ++++++++++++++++++ 1 file changed, 232 insertions(+) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index e69de29..062594f 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -0,0 +1,232 @@ +# 实验报告 + +本次作业完成了选题 1 的实验内容，利用 NumPy 实现了一个 FNN 模型，并在 MNIST 数据集上进行了训练。 + +## 目录 + +[TOC] + +## FNN 算子的反向传播 + +### 1. Matmul + +#### 1.1 公式推导 + +输入一个 $n\times d$ 的矩阵 $X$ 和一个 $d\times d'$ 的矩阵 $W$，算子 `Matmul` 的正向传播公式为： + +$$ +Y = X\times W \tag{1.1} +$$ + +输出一个 $n\times d'$ 的矩阵 $Y$。 + +对于梯度的反向传播，有 + +$$ +\nabla{z} = ( + \frac{\partial z}{\partial X}_{n\times d}, + \frac{\partial z}{\partial W}_{d\times d'} +) \tag{1.2} +$$ + +我们利用向量化（vectorization）进行对矩阵求导的求解： + +$$ +\begin{split} +\mathit{vec}(\frac{\partial z}{\partial X}_{n\times d}) +&= {(\frac{\partial Y}{\partial X})^T}_{nd\times nd'} + \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ +&= {({\frac + {\partial ({\mathit{vec}(X\times W)}_{nd'})} + {\partial ({\mathit{vec}(X)}_{nd})} + })^T}_{nd\times nd'} + \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ +&= {({\frac + {\partial ( + {\mathit{vec}(X)}_{nd} + \times {(I_n\otimes W)}_{nd\times nd'} + )} + {\partial ({\mathit{vec}(X)}_{nd})} + })^T}_{nd\times nd'} + \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ +&= {(I_n\otimes W)}_{nd\times nd'} + \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ +&= \mathit{vec}({(\frac{\partial z}{\partial Y}\times W^T)}_{n\times d}) +\end{split} \tag{1.3} +$$ + +这里 $\otimes$ 表示 Kronecker 积，下标表示矩阵或向量的维度。 + +因此有 + +$$ +\frac{\partial z}{\partial X}_{n\times d} += {(\frac{\partial z}{\partial Y}\times W^T)}_{n\times d} \tag{1.4} +$$ + +类似 $(1.3)$ 的推导，同理可得 + +$$ +\frac{\partial z}{\partial W}_{d\times d'} += {(X^T\times \frac{\partial z}{\partial Y})}_{d\times d'} \tag{1.5} +$$ + +#### 1.2 代码实现 + +```python {.line-numbers} +# numpy_fnn.py + +class Matmul(NumpyOp): + ''' + Matrix multiplication unit. + ''' + + def forward(self, x: np.ndarray, w: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + w: shape(d, d') + + Returns: + shape(N, d') + ''' + + self.memory['x'] = x + self.memory['w'] = w + return np.matmul(x, w) + + def backward(self, grad_y: np.ndarray) -> Tuple[np.ndarray, np.ndarray]: + ''' + Args: + grad_y: shape(N, d') + + Returns: + grad_x: shape(N, d) + grad_w: shape(d, d') + ''' + + x: np.ndarray = self.memory['x'] + w: np.ndarray = self.memory['w'] + grad_x: np.ndarray = np.matmul(grad_y, w.T) + grad_w: np.ndarray = np.matmul(x.T, grad_y) + return grad_x, grad_w +``` + +### 2. Relu + +#### 2.1 公式推导 + +#### 2.2 代码实现 + +```python {.line-numbers} +# numpy_fnn.py + +class Relu(NumpyOp): + ''' + Rectified Linear Unit. + ''' + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + + Returns: + shape(N, d) + ''' + + self.memory['x'] = x + return np.where(x > 0, x, 0) + + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) + + Returns: + shape(N, d) + ''' + + x: np.ndarray = self.memory['x'] + grad_y[x < 0] = 0 + return grad_y +``` + +### 3. Log + +#### 3.1 公式推导 + +#### 3.2 代码实现 + +```python {.line-numbers} +# numpy_fnn.py + +class Log(NumpyOp): + ''' + Natural logarithm unit. + ''' + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + + Returns: + shape(N, d) + ''' + + self.memory['x'] = x + return np.log(x + self.epsilon) + + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) + + Returns: + shape(N, d) + ''' + + x: np.ndarray = self.memory['x'] + return grad_y / x +``` + +### 4. Softmax + +#### 4.1 公式推导 + +#### 4.2 代码实现 + +```python {.line-numbers} +# numpy_fnn.py + +class Softmax(NumpyOp): + ''' + Softmax over last dimension. + ''' + + def forward(self, x: np.ndarray) -> np.ndarray: + ''' + Args: + x: shape(N, d) + + Returns: + shape(N, d) + ''' + + y: np.ndarray = np.exp(x) / np.exp(x).sum(axis=1)[:, None] + self.memory['y'] = y + return y + + def backward(self, grad_y: np.ndarray) -> np.ndarray: + ''' + Args: + grad_y: shape(N, d) + + Returns: + shape(N, d) + ''' + + y: np.ndarray = self.memory['y'] + return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) +``` -- Gitee From 4bbdf057724d0e28e0e98d4ee28cb49048301f2c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:28:08 +0800 Subject: [PATCH 20/28] doc: create TOC --- assignment-2/submission/18307130003/README.md | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 062594f..a9ac9b0 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -4,7 +4,21 @@ ## 目录 -[TOC] +- [实验报告](#实验报告) + - [目录](#目录) + - [FNN 算子的反向传播](#fnn-算子的反向传播) + - [1. Matmul](#1-matmul) + - [1.1 公式推导](#11-公式推导) + - [1.2 代码实现](#12-代码实现) + - [2. Relu](#2-relu) + - [2.1 公式推导](#21-公式推导) + - [2.2 代码实现](#22-代码实现) + - [3. Log](#3-log) + - [3.1 公式推导](#31-公式推导) + - [3.2 代码实现](#32-代码实现) + - [4. Softmax](#4-softmax) + - [4.1 公式推导](#41-公式推导) + - [4.2 代码实现](#42-代码实现) ## FNN 算子的反向传播 -- Gitee From 10fc1f13c57febd213f7fe3cbd6cd74c38e4dba7 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:42:00 +0800 Subject: [PATCH 21/28] doc: minor fix latex layout --- assignment-2/submission/18307130003/README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index a9ac9b0..8216661 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -48,22 +48,22 @@ $$ $$ \begin{split} \mathit{vec}(\frac{\partial z}{\partial X}_{n\times d}) -&= {(\frac{\partial Y}{\partial X})^T}_{nd\times nd'} +&= {(\frac{\partial Y}{\partial X})^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac {\partial ({\mathit{vec}(X\times W)}_{nd'})} {\partial ({\mathit{vec}(X)}_{nd})} - })^T}_{nd\times nd'} + })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac {\partial ( {\mathit{vec}(X)}_{nd} - \times {(I_n\otimes W)}_{nd\times nd'} + \times {(I_n\otimes W)}_{nd\times {nd'}} )} {\partial ({\mathit{vec}(X)}_{nd})} - })^T}_{nd\times nd'} + })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ -&= {(I_n\otimes W)}_{nd\times nd'} +&= {(I_n\otimes W)}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= \mathit{vec}({(\frac{\partial z}{\partial Y}\times W^T)}_{n\times d}) \end{split} \tag{1.3} -- Gitee From 7e6c72802d2b88e64d9ba1ce62112bad0a3bd5b0 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Fri, 30 Apr 2021 03:58:22 +0800 Subject: [PATCH 22/28] doc: add some details for chap. 1 --- assignment-2/submission/18307130003/README.md | 13 ++++++++++++- 1 file changed, 12 insertions(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 8216661..488bde9 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -69,7 +69,18 @@ $$ \end{split} \tag{1.3} $$ -这里 $\otimes$ 表示 Kronecker 积，下标表示矩阵或向量的维度。 +这里 $\mathit{vec}(X_{m\times n})$ 表示向量 + +$$ +\begin{split} +[&x_{11}, x_{12},\ &..., x_{1n}, \\ + &x_{21}, x_{22},\ &..., x_{2n}, \\ + &&... \\ + &x_{m1}, x_{m2},\ &..., x_{mn}] +\end{split} +$$ + +$\otimes$ 表示 Kronecker 积，下标表示矩阵或向量的维度。 因此有 -- Gitee From f0d3bb584f01326bdb0a11e43641e3e041ded07d Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 14:13:49 +0800 Subject: [PATCH 23/28] doc: backward chap. 2 --- assignment-2/submission/18307130003/README.md | 60 +++++++++++++++++-- .../submission/18307130003/numpy_fnn.py | 3 +- 2 files changed, 56 insertions(+), 7 deletions(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 488bde9..cbb037b 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -51,8 +51,8 @@ $$ &= {(\frac{\partial Y}{\partial X})^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac - {\partial ({\mathit{vec}(X\times W)}_{nd'})} - {\partial ({\mathit{vec}(X)}_{nd})} + {\partial {\mathit{vec}(X\times W)}_{nd'}} + {\partial {\mathit{vec}(X)}_{nd}} })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {({\frac @@ -60,7 +60,7 @@ $$ {\mathit{vec}(X)}_{nd} \times {(I_n\otimes W)}_{nd\times {nd'}} )} - {\partial ({\mathit{vec}(X)}_{nd})} + {\partial {\mathit{vec}(X)}_{nd}} })^T}_{nd\times {nd'}} \times {\mathit{vec}(\frac{\partial z}{\partial Y})}_{nd'} \\ &= {(I_n\otimes W)}_{nd\times {nd'}} @@ -141,6 +141,57 @@ class Matmul(NumpyOp): #### 2.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Relu` 的正向传播公式为： + +$$ +Y_{ij} = \left\{ + \begin{aligned} + &X_{ij}\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播，有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} \\ +&= \frac{\partial z}{\partial Y}_{n\times d} + \odot \frac{\partial Y}{\partial X}_{n\times d} +\end{split} \tag{2.2} +$$ + +这里 $\odot$ 表示 Hadamard 积，即逐元素（element-wise）乘积。 + +其中，对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$，由 $(2.1)$ 有 + +$$ +{Y'}_{ij} = \left\{ + \begin{aligned} + &1\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.3} +$$ + +因此，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$，令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$，由 $(2.2)$ 有 + +$$ +{Z'}_{ij} = \left\{ + \begin{aligned} + &{({Z_Y}')}_{ij}\quad &(X_{ij} > 0) \\ + &0\quad &(X_{ij} \le 0) + \end{aligned} +\right. +\tag{2.4} +$$ + #### 2.2 代码实现 ```python {.line-numbers} @@ -173,8 +224,7 @@ class Relu(NumpyOp): ''' x: np.ndarray = self.memory['x'] - grad_y[x < 0] = 0 - return grad_y + return np.where(x > 0, grad_y, 0) ``` ### 3. Log diff --git a/assignment-2/submission/18307130003/numpy_fnn.py b/assignment-2/submission/18307130003/numpy_fnn.py index 7849408..4331007 100644 --- a/assignment-2/submission/18307130003/numpy_fnn.py +++ b/assignment-2/submission/18307130003/numpy_fnn.py @@ -75,8 +75,7 @@ class Relu(NumpyOp): ''' x: np.ndarray = self.memory['x'] - grad_y[x < 0] = 0 - return grad_y + return np.where(x > 0, grad_y, 0) class Log(NumpyOp): -- Gitee From df2d0f47ed263b2284e4917d462f768d22463c7b Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 14:28:13 +0800 Subject: [PATCH 24/28] doc: backward chap. 3 --- assignment-2/submission/18307130003/README.md | 33 +++++++++++++++++++ 1 file changed, 33 insertions(+) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index cbb037b..8ba1cac 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -231,8 +231,41 @@ class Relu(NumpyOp): #### 3.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Log` 的正向传播公式为： + +$$ +Y_{ij} = \log{X_{ij}} \tag{3.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播，有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} \\ +&= \frac{\partial z}{\partial Y}_{n\times d} + \odot \frac{\partial Y}{\partial X}_{n\times d} +\end{split} \tag{3.2} +$$ + +其中，对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$，由 $(3.1)$ 有 + +$$ +{Y'}_{ij} = \frac{1}{X_{ij}} \tag{3.3} +$$ + +因此，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$，令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$，由 $(3.2)$ 有 + +$$ +{Z'}_{ij} = \frac{{({Z_Y}')}_{ij}}{X_{ij}} \tag{3.4} +$$ + #### 3.2 代码实现 +为了防止 $X_{ij} = 0$ 时出现 $\log{X_{ij}} = -\infty$ 导致溢出，这里我们给 $X_{ij}$ 附加了一个 $\epsilon = 10^{-12}$ 的修正。 + ```python {.line-numbers} # numpy_fnn.py -- Gitee From 5acf27b257d05a30519c1e9d33960db67a46fbeb Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 17:16:16 +0800 Subject: [PATCH 25/28] doc: backward chap. 4 --- assignment-2/submission/18307130003/README.md | 58 +++++++++++++++++++ 1 file changed, 58 insertions(+) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 8ba1cac..a83d87d 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -303,6 +303,64 @@ class Log(NumpyOp): #### 4.1 公式推导 +输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Softmax` 的正向传播公式为： + +$$ +Y_{ij} = \frac{e^{X_{ij}}}{\sum\limits_{k=1}^d e^{X_{ik}}} \tag{4.1} +$$ + +输出一个 $n\times d$ 的矩阵 $Y$。 + +对于梯度的反向传播，有 + +$$ +\begin{split} +\nabla{z} +&= \frac{\partial z}{\partial X}_{n\times d} +\end{split} \tag{4.2} +$$ + +其中，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$ 有 + +$$ +\begin{split} +{Z'}_{ij} +&= \frac{\partial z}{\partial X_{ij}} \\ +&= {(\frac{\partial z}{\partial Y_i})}_d + \cdot {(\frac{\partial Y_i}{\partial X_{ij}})}_d \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{\partial Y_{ij}}{\partial X_{ij}} + + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{\partial Y_{ik}}{\partial X_{ij}} \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{\partial}{\partial X_{ij}}( + \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + ) + + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{\partial}{\partial X_{ij}}( + \frac{e^{X_{ik}}}{\sum\limits_{t=1}^d e^{X_{it}}} + ) \\ +&= \frac{\partial z}{\partial Y_{ij}} + \cdot \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + \cdot (1 - \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}}) - + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}} + \cdot \frac{e^{X_{ij}}}{\sum\limits_{t=1}^d e^{X_{it}}} + \cdot \frac{e^{X_{ik}}}{\sum\limits_{t=1}^d e^{X_{it}}} \\ +&= \frac{\partial z}{\partial Y_{ij}}\cdot Y_{ij}\cdot (1 - Y_{ij}) - + \sum\limits_{k=1,\,k\ne j}^d + \frac{\partial z}{\partial Y_{ik}}\cdot Y_{ij}\cdot Y_{ik} \\ +&= Y_{ij}\cdot ( + \frac{\partial z}{\partial Y_{ij}} - + \sum\limits_{k=1}^d + \frac{\partial z}{\partial Y_{ik}}\cdot Y_{ik} + ) +\end{split} +\tag{4.3} +$$ + #### 4.2 代码实现 ```python {.line-numbers} -- Gitee From 26d7bd86c117110f42f62235cbefb1c7c58b5b0c Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 18:12:19 +0800 Subject: [PATCH 26/28] doc: report done --- assignment-2/submission/18307130003/README.md | 187 ++++++++++++++++++ .../18307130003/img/loss_value_1.png | Bin 0 -> 53631 bytes .../18307130003/img/loss_value_2.png | Bin 0 -> 44338 bytes .../18307130003/img/loss_value_3.png | Bin 0 -> 45915 bytes .../18307130003/img/loss_value_4.png | Bin 0 -> 37914 bytes .../submission/18307130003/numpy_mnist.py | 7 +- 6 files changed, 191 insertions(+), 3 deletions(-) create mode 100644 assignment-2/submission/18307130003/img/loss_value_1.png create mode 100644 assignment-2/submission/18307130003/img/loss_value_2.png create mode 100644 assignment-2/submission/18307130003/img/loss_value_3.png create mode 100644 assignment-2/submission/18307130003/img/loss_value_4.png diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index a83d87d..61860fc 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -19,6 +19,24 @@ - [4. Softmax](#4-softmax) - [4.1 公式推导](#41-公式推导) - [4.2 代码实现](#42-代码实现) + - [函数 `mini_batch` 实现](#函数-mini_batch-实现) + - [实验过程与结果](#实验过程与结果) + - [1. 实验 1](#1-实验-1) + - [1.1 参数](#11-参数) + - [1.2 预测准确率](#12-预测准确率) + - [1.3 损失函数值](#13-损失函数值) + - [2. 实验 2](#2-实验-2) + - [2.1 参数](#21-参数) + - [2.2 预测准确率](#22-预测准确率) + - [2.3 损失函数值](#23-损失函数值) + - [3. 实验 3](#3-实验-3) + - [3.1 参数](#31-参数) + - [3.2 预测准确率](#32-预测准确率) + - [3.3 损失函数值](#33-损失函数值) + - [4. 实验 4](#4-实验-4) + - [4.1 参数](#41-参数) + - [4.2 预测准确率](#42-预测准确率) + - [4.3 损失函数值](#43-损失函数值) ## FNN 算子的反向传播 @@ -396,3 +414,172 @@ class Softmax(NumpyOp): y: np.ndarray = self.memory['y'] return y * (grad_y - (grad_y * y).sum(axis=1)[:, None]) ``` + +## 函数 `mini_batch` 实现 + +我们使用 NumPy 重写了函数 `mini_batch`，用于之后的训练。 + +```python {.line-numbers} +# numpy_mnist.py + +def mini_batch(dataset: List[Tuple[Any, int]], batch_size=128) -> np.ndarray: + ''' + Split the data and labels from the given dataset into batches. + + Args: + dataset: the given dataset + batch_size: the size of retrieved data + + Returns: + Batches of [data, labels] pair. + ''' + + data: np.ndarray = np.array([np.array(pair[0]) for pair in dataset]) + labels: np.ndarray = np.array([pair[1] for pair in dataset]) + + # Shuffle the dataset + size: int = len(dataset) + indices: np.ndarray = np.arange(size) + np.random.shuffle(indices) + + batches: List[Tuple[np.ndarray, np.ndarray]] = [] + for i in range(0, size, batch_size): + chunk: np.ndarray = indices[i:i+batch_size] + batches.append((data[chunk], labels[chunk])) + return batches +``` + +## 实验过程与结果 + +执行以下命令开始训练。 + +```bash +python ./numpy_mnist.py +``` + +### 1. 实验 1 + +#### 1.1 参数 + +```python {.line-numbers} +epoch_number = 3 +batch_size = 128 +learning_rate = 0.1 +``` + +#### 1.2 预测准确率 + +```text +[0] Accuracy: 0.9485 +[1] Accuracy: 0.9647 +[2] Accuracy: 0.9715 +``` + +#### 1.3 损失函数值 + +![Loss value 1](./img/loss_value_1.png) + +### 2. 实验 2 + +这次，我们调大训练轮数（`epoch_number`），观察预测准确率的变化。 + +#### 2.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 128 +learning_rate = 0.1 +``` + +#### 2.2 预测准确率 + +```text +[0] Accuracy: 0.9496 +[1] Accuracy: 0.9600 +[2] Accuracy: 0.9675 +[3] Accuracy: 0.9761 +[4] Accuracy: 0.9755 +[5] Accuracy: 0.9775 +[6] Accuracy: 0.9791 +[7] Accuracy: 0.9795 +[8] Accuracy: 0.9781 +[9] Accuracy: 0.9810 +``` + +可见，训练轮数越多，预测准确率越高，但到达一定准确率后开始波动，不再明显上升。 + +#### 2.3 损失函数值 + +![Loss value 2](./img/loss_value_2.png) + +可见，训练轮数越多，损失函数值越低，波动越小。 + +### 3. 实验 3 + +这次，我们调大批处理时每批数据大小（`batch_size`），观察预测准确率的变化。 + +#### 3.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 256 +learning_rate = 0.1 +``` + +#### 3.2 预测准确率 + +```text +[0] Accuracy: 0.9253 +[1] Accuracy: 0.9477 +[2] Accuracy: 0.9522 +[3] Accuracy: 0.9651 +[4] Accuracy: 0.9680 +[5] Accuracy: 0.9731 +[6] Accuracy: 0.9755 +[7] Accuracy: 0.9766 +[8] Accuracy: 0.9766 +[9] Accuracy: 0.9790 +``` + +可见，每批数据的大小越大，训练速度越慢，但最终达到的准确率没有明显变化。 + +#### 3.3 损失函数值 + +![Loss value 3](./img/loss_value_3.png) + +可见，每批数据的大小越大，损失函数值整体的波动越小。 + +### 4. 实验 4 + +这次，我们提高学习率（`learnin_rate`），观察预测准确率的变化。 + +#### 4.1 参数 + +```python {.line-numbers} +epoch_number = 10 +batch_size = 256 +learning_rate = 0.5 +``` + +#### 4.2 预测准确率 + +```text +[0] Accuracy: 0.9505 +[1] Accuracy: 0.9675 +[2] Accuracy: 0.9706 +[3] Accuracy: 0.9471 +[4] Accuracy: 0.9737 +[5] Accuracy: 0.8980 +[6] Accuracy: 0.9757 +[7] Accuracy: 0.9573 +[8] Accuracy: 0.9770 +[9] Accuracy: 0.9792 +``` + +可见，学习率越高，训练速度越快，但训练时的波动也可能较大。 + +#### 4.3 损失函数值 + +![Loss value 4](./img/loss_value_4.png) + +可见，学习率越高，损失函数值下降越快，但整体的波动也可能较大。 diff --git a/assignment-2/submission/18307130003/img/loss_value_1.png b/assignment-2/submission/18307130003/img/loss_value_1.png new file mode 100644 index 0000000000000000000000000000000000000000..ac76f374937aadf8ea57663647c3fbf8c8efc8fc GIT binary patch literal 53631 zcmeEucT`l_m+mDfDnYw#K@kKML9&8?fCQxtB_fEDB`6@0l_HZehsbMpH?aBq>=v;T|wx?Sh~exoaJ z^p4DhJ0IrHsaq#;Y}>I%ka?TVmPbZ4`(LPwx;4G3rvy(6ITAwpgcQX^GTPm*&-%`Z 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in mini_batch(train_dataset): + for x, y in mini_batch(train_dataset, batch_size=batch_size): x: np.ndarray y: np.ndarray = one_hot(y) -- Gitee From db3bb81caff2ded95be3ad897fc90bf6d47d5516 Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 19:27:04 +0800 Subject: [PATCH 27/28] doc: fix tex layout for gitee --- assignment-2/submission/18307130003/README.md | 115 ++++++++++++------ .../18307130003/img/equation_1.1.svg | 2 + .../18307130003/img/equation_1.2.svg | 2 + .../18307130003/img/equation_1.3.1.svg | 2 + .../18307130003/img/equation_1.3.svg | 2 + .../18307130003/img/equation_1.4.svg | 2 + .../18307130003/img/equation_1.5.svg | 2 + .../18307130003/img/equation_2.1.svg | 2 + .../18307130003/img/equation_2.2.svg | 2 + .../18307130003/img/equation_2.3.svg | 2 + .../18307130003/img/equation_2.4.svg | 2 + .../18307130003/img/equation_3.1.svg | 2 + .../18307130003/img/equation_3.2.svg | 2 + .../18307130003/img/equation_3.3.svg | 2 + .../18307130003/img/equation_3.4.svg | 2 + .../18307130003/img/equation_4.1.svg | 2 + .../18307130003/img/equation_4.2.svg | 2 + .../18307130003/img/equation_4.3.svg | 2 + 18 files changed, 110 insertions(+), 39 deletions(-) create mode 100644 assignment-2/submission/18307130003/img/equation_1.1.svg create mode 100644 assignment-2/submission/18307130003/img/equation_1.2.svg create mode 100644 assignment-2/submission/18307130003/img/equation_1.3.1.svg create mode 100644 assignment-2/submission/18307130003/img/equation_1.3.svg create mode 100644 assignment-2/submission/18307130003/img/equation_1.4.svg create mode 100644 assignment-2/submission/18307130003/img/equation_1.5.svg create mode 100644 assignment-2/submission/18307130003/img/equation_2.1.svg create mode 100644 assignment-2/submission/18307130003/img/equation_2.2.svg create mode 100644 assignment-2/submission/18307130003/img/equation_2.3.svg create mode 100644 assignment-2/submission/18307130003/img/equation_2.4.svg create mode 100644 assignment-2/submission/18307130003/img/equation_3.1.svg create mode 100644 assignment-2/submission/18307130003/img/equation_3.2.svg create mode 100644 assignment-2/submission/18307130003/img/equation_3.3.svg create mode 100644 assignment-2/submission/18307130003/img/equation_3.4.svg create mode 100644 assignment-2/submission/18307130003/img/equation_4.1.svg create mode 100644 assignment-2/submission/18307130003/img/equation_4.2.svg create mode 100644 assignment-2/submission/18307130003/img/equation_4.3.svg diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 61860fc..6361105 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -1,3 +1,5 @@ + + # 实验报告 本次作业完成了选题 1 的实验内容，利用 NumPy 实现了一个 FNN 模型，并在 MNIST 数据集上进行了训练。 @@ -46,24 +48,28 @@ 输入一个 $n\times d$ 的矩阵 $X$ 和一个 $d\times d'$ 的矩阵 $W$，算子 `Matmul` 的正向传播公式为： -$$ + + +Equation 1.1 输出一个 $n\times d'$ 的矩阵 $Y$。 对于梯度的反向传播，有 -$$ + + +Equation 1.2 我们利用向量化（vectorization）进行对矩阵求导的求解： -$$ + + +Equation 1.3 这里 $\mathit{vec}(X_{m\times n})$ 表示向量 -$$ + + +Equation 1.3.1 $\otimes$ 表示 Kronecker 积，下标表示矩阵或向量的维度。 因此有 -$$ + + +Equation 1.4 类似 $(1.3)$ 的推导，同理可得 -$$ + + +Equation 1.5 #### 1.2 代码实现 @@ -161,7 +176,7 @@ class Matmul(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Relu` 的正向传播公式为： -$$ + + +Equation 2.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播，有 -$$ + + +Equation 2.2 这里 $\odot$ 表示 Hadamard 积，即逐元素（element-wise）乘积。 -其中，对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$，由 $(2.1)$ 有 +其中，对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$，由 $(2.1)$ 有 -$$ + -因此，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$，令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$，由 $(2.2)$ 有 +Equation 2.3 -$$ +因此，对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$，令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$，由 $(2.2)$ 有 + + + +Equation 2.4 #### 2.2 代码实现 @@ -251,34 +274,42 @@ class Relu(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Log` 的正向传播公式为： -$$ + + +Equation 3.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播，有 -$$ + -其中，对于 $\frac{\partial Y}{\partial X}_{n\times d}$ 中的每个元素 ${Y'}_{ij}$，由 $(3.1)$ 有 +Equation 3.2 -$$ +其中，对于 $\frac{\partial Y}{\partial X}\_{n\times d}$ 中的每个元素 ${Y'}\_{ij}$，由 $(3.1)$ 有 + + + +Equation 3.3 -因此，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$，令 ${Z_Y}' = \frac{\partial z}{\partial Y}_{n\times d}$，由 $(3.2)$ 有 +因此，对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$，令 ${Z\_Y}' = \frac{\partial z}{\partial Y}\_{n\times d}$，由 $(3.2)$ 有 -$$ + + +Equation 3.4 #### 3.2 代码实现 @@ -323,24 +354,28 @@ class Log(NumpyOp): 输入一个 $n\times d$ 的矩阵 $X$，对于 $X$ 中的每个元素 $X_{ij}$，算子 `Softmax` 的正向传播公式为： -$$ + + +Equation 4.1 输出一个 $n\times d$ 的矩阵 $Y$。 对于梯度的反向传播，有 -$$ + -其中，对于 $\frac{\partial z}{\partial X}_{n\times d}$ 中的每个元素 ${Z'}_{ij}$ 有 +Equation 4.2 -$$ +其中，对于 $\frac{\partial z}{\partial X}\_{n\times d}$ 中的每个元素 ${Z'}\_{ij}$ 有 + + + +Equation 4.3 #### 4.2 代码实现 diff --git a/assignment-2/submission/18307130003/img/equation_1.1.svg b/assignment-2/submission/18307130003/img/equation_1.1.svg new file mode 100644 index 0000000..048e56f --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_1.1.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_1.2.svg b/assignment-2/submission/18307130003/img/equation_1.2.svg new file mode 100644 index 0000000..33892d4 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_1.2.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_1.3.1.svg b/assignment-2/submission/18307130003/img/equation_1.3.1.svg new file mode 100644 index 0000000..005032e --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_1.3.1.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git 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/dev/null +++ b/assignment-2/submission/18307130003/img/equation_2.4.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_3.1.svg b/assignment-2/submission/18307130003/img/equation_3.1.svg new file mode 100644 index 0000000..391e193 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_3.1.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_3.2.svg b/assignment-2/submission/18307130003/img/equation_3.2.svg new file mode 100644 index 0000000..3d623c2 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_3.2.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_3.3.svg b/assignment-2/submission/18307130003/img/equation_3.3.svg new file mode 100644 index 0000000..6f5a883 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_3.3.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_3.4.svg b/assignment-2/submission/18307130003/img/equation_3.4.svg new file mode 100644 index 0000000..27682ed --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_3.4.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_4.1.svg b/assignment-2/submission/18307130003/img/equation_4.1.svg new file mode 100644 index 0000000..a4a9041 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_4.1.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_4.2.svg b/assignment-2/submission/18307130003/img/equation_4.2.svg new file mode 100644 index 0000000..2256e00 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_4.2.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/assignment-2/submission/18307130003/img/equation_4.3.svg b/assignment-2/submission/18307130003/img/equation_4.3.svg new file mode 100644 index 0000000..2136ae5 --- /dev/null +++ b/assignment-2/submission/18307130003/img/equation_4.3.svg @@ -0,0 +1,2 @@ + + \ No newline at end of file -- Gitee From 3acf06c7a23e2e518c2d296544c64adeb0c795de Mon Sep 17 00:00:00 2001 From: Hakula Chen Date: Sun, 2 May 2021 19:29:11 +0800 Subject: [PATCH 28/28] doc: fix typo --- assignment-2/submission/18307130003/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/assignment-2/submission/18307130003/README.md b/assignment-2/submission/18307130003/README.md index 6361105..13d2047 100644 --- a/assignment-2/submission/18307130003/README.md +++ b/assignment-2/submission/18307130003/README.md @@ -588,7 +588,7 @@ learning_rate = 0.1 ### 4. 实验 4 -这次，我们提高学习率（`learnin_rate`），观察预测准确率的变化。 +这次，我们提高学习率（`learning_rate`），观察预测准确率的变化。 #### 4.1 参数 -- Gitee

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