machine-learning - 为什么我的带有 ReLU 的 1 隐藏层神经网络在 notMNIST 数据集上的准确率没有超过 18%？

Question

我正在尝试使用 Tensorflow 实现一个具有修正线性单元和 1024 个隐藏节点的 1 隐藏层神经网络。

def accuracy(predictions, labels):
  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
          / predictions.shape[0])

batch_size = 128

graph = tf.Graph()
with graph.as_default():
    # Input data. For the training data, we use a placeholder that will be fed
    # at run time with a training minibatch.
    tf_train_dataset = tf.placeholder(tf.float32,
                                      shape=(batch_size, image_size * image_size))
    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
    tf_valid_dataset = tf.constant(valid_dataset)
    tf_test_dataset = tf.constant(test_dataset)

    # Variables.
    weights1 = tf.Variable(
        tf.truncated_normal([image_size * image_size, 1024]))
    biases1 = tf.Variable(tf.zeros([1024]))
    weights2 = tf.Variable(
        tf.truncated_normal([1024, num_labels]))
    biases2 = tf.Variable(tf.zeros([num_labels]))

    # Training computation.
    logits = tf.matmul(tf.nn.relu(tf.matmul(tf_train_dataset, weights1) + biases1), weights2) + biases2
    loss = tf.reduce_mean(
        tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))

    # Optimizer.
    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

    # Predictions for the training, validation, and test data.
    train_prediction = tf.nn.softmax(logits)
    valid_prediction = tf.nn.softmax(
        tf.matmul(
            tf.nn.relu(
                tf.matmul(tf_valid_dataset, weights1)
                + biases1),
            weights2) + biases2)
    test_prediction = tf.nn.softmax(
        tf.matmul(
            tf.nn.relu(
                tf.matmul(tf_test_dataset, weights1)
                + biases1),
            weights2) + biases2)


num_steps = 3001

with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset[offset:(offset + batch_size), :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
    _, l, predictions = session.run(
      [optimizer, loss, train_prediction], feed_dict=feed_dict)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(
        valid_prediction.eval(), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

这是我得到的输出:

Initialized
Minibatch loss at step 0: 208.975021
Minibatch accuracy: 11.7%
Validation accuracy: 10.0%
Minibatch loss at step 500: 0.000000
Minibatch accuracy: 100.0%
Validation accuracy: 10.2%
Minibatch loss at step 1000: 0.000000
Minibatch accuracy: 100.0%
Validation accuracy: 14.6%
Minibatch loss at step 1500: 0.000000
Minibatch accuracy: 100.0%
Validation accuracy: 10.2%
Minibatch loss at step 2000: 0.000000
Minibatch accuracy: 100.0%
Validation accuracy: 17.7%
Minibatch loss at step 2500: 2.952326
Minibatch accuracy: 93.8%
Validation accuracy: 26.6%
Minibatch loss at step 3000: 0.000000
Minibatch accuracy: 100.0%
Validation accuracy: 17.5%
Test accuracy: 18.1%

看起来好像过度拟合了。它在训练数据上的准确率接近 100%，但在验证和测试数据上的准确率只有 20% 左右。

这是实现具有修正线性单元的 1 隐藏层神经网络的正确方法吗？如果是这样，我怎样才能提高准确性？

Answer 1

以下是一些可以提高准确性的建议:

首先，您的隐藏层大小为 1024，看起来太大了。这可能会导致过度拟合。我会尝试将其减少到大约 50-100 左右，看看是否有所改善并从那里继续。

此外，关于这一行:

optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

0.5 的学习率可能太高，尝试降低它(到 0.01、0.001 左右)，看看会发生什么。最后，您还可以尝试使用 tf.train.AdamOptimizer 而不是 tf.train.GradientDescentOptimizer，因为在许多情况下它的性能更好。