编写代码，用python语言实现深度神经网络识别mnist手写数字集，需要3层隐藏层，并通过struct读取数据集，不使用TensorFlow或PyTorch框架

非常感谢您的提问。以下是实现您所描述的任务的代码：

import struct
import numpy as np

# 读取MNIST数据集
def load_mnist_data(path):
    with open(path, 'rb') as file:
        # 读取文件头部信息，魔数和数据集/标签数目
        magic, num = struct.unpack(">II", file.read(8))

        # 读取每个数据集/标签的行列数
        rows, cols = struct.unpack(">II", file.read(8))

        # 读取所有数据集/标签
        data = np.fromfile(file, dtype=np.dtype('uint8').newbyteorder('>'))
        data = np.reshape(data, (num, rows * cols))

        # 归一化数据集
        data = data / 255

        return data

# 设计神经网络的参数
input_size = 784
hidden_size_1 = 256
hidden_size_2 = 128
hidden_size_3 = 64
output_size = 10

# 初始化权重矩阵和偏置向量
W1 = np.random.randn(input_size, hidden_size_1) * 0.01
b1 = np.zeros((1, hidden_size_1))

W2 = np.random.randn(hidden_size_1, hidden_size_2) * 0.01
b2 = np.zeros((1, hidden_size_2))

W3 = np.random.randn(hidden_size_2, hidden_size_3) * 0.01
b3 = np.zeros((1, hidden_size_3))

W4 = np.random.randn(hidden_size_3, output_size) * 0.01
b4 = np.zeros((1, output_size))

# 定义激活函数（这里使用ReLU）
def relu(Z):
    return np.maximum(0, Z)

# 定义softmax函数
def softmax(Z):
    exp_Z = np.exp(Z)
    return exp_Z / np.sum(exp_Z, axis=1, keepdims=True)

# 前向传播算法
def forward(X):
    Z1 = np.dot(X, W1) + b1
    A1 = relu(Z1)

    Z2 = np.dot(A1, W2) + b2
    A2 = relu(Z2)

    Z3 = np.dot(A2, W3) + b3
    A3 = relu(Z3)

    Z4 = np.dot(A3, W4) + b4
    A4 = softmax(Z4)

    cache = [Z1, A1, Z2, A2, Z3, A3, Z4, A4]

    return A4, cache

# 反向传播算法
def backward(X, Y, cache):
    Z1, A1, Z2, A2, Z3, A3, Z4, A4 = cache

    dZ4 = A4 - Y
    dW4 = np.dot(A3.T, dZ4)
    db4 = np.sum(dZ4, axis=0, keepdims=True)

    dA3 = np.dot(dZ4, W4.T)
    dZ3 = np.multiply(dA3, np.int64(A3 > 0))
    dW3 = np.dot(A2.T, dZ3)
    db3 = np.sum(dZ3, axis=0, keepdims=True)

    dA2 = np.dot(dZ3, W3.T)
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    dW2 = np.dot(A1.T, dZ2)
    db2 = np.sum(dZ2, axis=0, keepdims=True)

    dA1 = np.dot(dZ2, W2.T)
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    dW1 = np.dot(X.T, dZ1)
    db1 = np.sum(dZ1, axis=0, keepdims=True)

    return dW1, db1, dW2, db2, dW3, db3, dW4, db4

# 定义训练函数
def train(X, Y, learning_rate, epochs, batch_size):
    num_samples, _ = X.shape
    num_batches = num_samples // batch_size
    loss_list = []

    for epoch in range(epochs):
        epoch_loss = 0

        for batch_index in range(num_batches):
            # 从数据集中随机选取一个batch
            batch_start = batch_index * batch_size
            batch_end = (batch_index + 1) * batch_size
            X_batch = X[batch_start:batch_end]
            Y_batch = Y[batch_start:batch_end]

            # 前向传播
            Y_pred, cache = forward(X_batch)

            # 计算损失函数
            loss = -np.mean(Y_batch * np.log(Y_pred))
            epoch_loss += loss

            # 反向传播
            dW1, db1, dW2, db2, dW3, db3, dW4, db4 = backward(X_batch, Y_batch, cache)

            # 更新权重和偏置
            W1 -= learning_rate * dW1
            b1 -= learning_rate * db1

            W2 -= learning_rate * dW2
            b2 -= learning_rate * db2

            W3 -= learning_rate * dW3
            b3 -= learning_rate * db3

            W4 -= learning_rate * dW4
            b4 -= learning_rate * db4

        epoch_loss /= num_batches
        loss_list.append(epoch_loss)

        print("Epoch %d: loss = %.4f" % (epoch, epoch_loss))

    return loss_list

# 主函数
if __name__ == '__main__':
    # 读取MNIST数据集
    X_train = load_mnist_data("train-images-idx3-ubyte")
    Y_train = load_mnist_data("train-labels-idx1-ubyte")
    X_test = load_mnist_data("t10k-images-idx3-ubyte")
    Y_test = load_mnist_data("t10k-labels-idx1-ubyte")

    # 将标签转为one-hot向量形式
    Y_train_one_hot = np.zeros((Y_train.shape[0], output_size))
    Y_train_one_hot[np.arange(Y_train.shape[0]), Y_train.astype(int)] = 1

    Y_test_one_hot = np.zeros((Y_test.shape[0], output_size))
    Y_test_one_hot[np.arange(Y_test.shape[0]), Y_test.astype(int)] = 1

    # 训练神经网络
    loss_list = train(X_train, Y_train_one_hot, learning_rate=0.1, epochs=10, batch_size=100)

    # 测试神经网络
    Y_pred, _ = forward(X_test)
    accuracy = np.mean(np.argmax(Y_test_one_hot, axis=1) == np.argmax(Y_pred, axis=1))
    print("Accuracy on test set: %.4f" % accuracy)

该代码实现了一个基本的三层神经网络，可以用于识别MNIST手写数字集。其中，第一层和第二层使用ReLU激活函数，第三层使用softmax激活函数。训练过程中使用了随机梯度下降算法，且每个batch的数据集大小为100。最后，我们将MNIST测试集输入到该神经网络中，并计算其准确率，以测试该神经网络的性能。

请注意，该代码实现的是基本的三层神经网络模型，因此准确率可能并不高。对于该模型，我们希望通过调整超参数或修改网络结构等手段进一步优化其性能。