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). 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. The example will throw a warning because it doesn’t converge, in this case this is what we want because of CI’s time constraints.
Iteration 1, loss = 0.32009978 Iteration 2, loss = 0.15347534 Iteration 3, loss = 0.11544755 Iteration 4, loss = 0.09279764 Iteration 5, loss = 0.07889367 Iteration 6, loss = 0.07170497 Iteration 7, loss = 0.06282111 Iteration 8, loss = 0.05530788 Iteration 9, loss = 0.04960484 Iteration 10, loss = 0.04645355 Training set score: 0.986800 Test set score: 0.970000
import warnings import matplotlib.pyplot as plt from sklearn.datasets import fetch_openml from sklearn.exceptions import ConvergenceWarning 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) # this example won't converge because of CI's time constraints, so we catch the # warning and are ignore it here with warnings.catch_warnings(): warnings.filterwarnings("ignore", category=ConvergenceWarning, module="sklearn") 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_.min(), mlp.coefs_.max() for coef, ax in zip(mlp.coefs_.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: ( 1 minutes 1.885 seconds)