Visualization of MLP weights on MNIST

Sometimes looking at the learned coefficients of a neural network can provide insight into the learning behavior. For example if weights look unstructured, maybe some were not used at all, or if very large coefficients exist, maybe regularization was too low or the learning rate too high.

This example shows how to plot some of the first layer weights in a MLPClassifier trained on the MNIST dataset.

The input data consists of 28x28 pixel handwritten digits, leading to 784 features in the dataset. Therefore the first layer weight matrix have the shape (784, hidden_layer_sizes[0]). We can therefore visualize a single column of the weight matrix as a 28x28 pixel image.

To make the example run faster, we use very few hidden units, and train only for a very short time. Training longer would result in weights with a much smoother spatial appearance.

Traceback (most recent call last):
  File "/usr/lib/python3/dist-packages/sphinx_gallery/gen_rst.py", line 440, in _memory_usage
    out = func()
  File "/usr/lib/python3/dist-packages/sphinx_gallery/gen_rst.py", line 425, in __call__
    exec(self.code, self.globals)
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/examples/neural_networks/plot_mnist_filters.py", line 30, in <module>
    X, y = fetch_openml('mnist_784', version=1, return_X_y=True)
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 639, in fetch_openml
    data_info = _get_data_info_by_name(name, version, data_home)
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 377, in _get_data_info_by_name
    json_data = _get_json_content_from_openml_api(url, None, False,
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 159, in _get_json_content_from_openml_api
    return _load_json()
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 59, in wrapper
    return f()
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 155, in _load_json
    with closing(_open_openml_url(url, data_home)) as response:
  File "/build/scikit-learn-WWYjTV/scikit-learn-0.22.2.post1+dfsg/.pybuild/cpython3_3.8/build/sklearn/datasets/_openml.py", line 104, in _open_openml_url
    with closing(urlopen(req)) as fsrc:
  File "/usr/lib/python3.8/urllib/request.py", line 222, in urlopen
    return opener.open(url, data, timeout)
  File "/usr/lib/python3.8/urllib/request.py", line 525, in open
    response = self._open(req, data)
  File "/usr/lib/python3.8/urllib/request.py", line 542, in _open
    result = self._call_chain(self.handle_open, protocol, protocol +
  File "/usr/lib/python3.8/urllib/request.py", line 502, in _call_chain
    result = func(*args)
  File "/usr/lib/python3.8/urllib/request.py", line 1393, in https_open
    return self.do_open(http.client.HTTPSConnection, req,
  File "/usr/lib/python3.8/urllib/request.py", line 1353, in do_open
    raise URLError(err)
urllib.error.URLError: <urlopen error [Errno -2] Name or service not known>
import matplotlib.pyplot as plt
from sklearn.datasets import fetch_openml
from sklearn.neural_network import MLPClassifier

print(__doc__)

# Load data from https://www.openml.org/d/554
X, y = fetch_openml('mnist_784', version=1, return_X_y=True)
X = X / 255.

# rescale the data, use the traditional train/test split
X_train, X_test = X[:60000], X[60000:]
y_train, y_test = y[:60000], y[60000:]

mlp = MLPClassifier(hidden_layer_sizes=(50,), max_iter=10, alpha=1e-4,
                    solver='sgd', verbose=10, random_state=1,
                    learning_rate_init=.1)

mlp.fit(X_train, y_train)
print("Training set score: %f" % mlp.score(X_train, y_train))
print("Test set score: %f" % mlp.score(X_test, y_test))

fig, axes = plt.subplots(4, 4)
# use global min / max to ensure all weights are shown on the same scale
vmin, vmax = mlp.coefs_[0].min(), mlp.coefs_[0].max()
for coef, ax in zip(mlp.coefs_[0].T, axes.ravel()):
    ax.matshow(coef.reshape(28, 28), cmap=plt.cm.gray, vmin=.5 * vmin,
               vmax=.5 * vmax)
    ax.set_xticks(())
    ax.set_yticks(())

plt.show()

Total running time of the script: ( 0 minutes 0.005 seconds)

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