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 has 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 resource usage constraints on our Continuous Integration infrastructure that is used to build this documentation on a regular basis.
Iteration 1, loss = 0.44139186 Iteration 2, loss = 0.19174891 Iteration 3, loss = 0.13983521 Iteration 4, loss = 0.11378556 Iteration 5, loss = 0.09443967 Iteration 6, loss = 0.07846529 Iteration 7, loss = 0.06506307 Iteration 8, loss = 0.05534985 Training set score: 0.986429 Test set score: 0.953061
import warnings import matplotlib.pyplot as plt from sklearn.datasets import fetch_openml from sklearn.exceptions import ConvergenceWarning from sklearn.neural_network import MLPClassifier from sklearn.model_selection import train_test_split # Load data from https://www.openml.org/d/554 X, y = fetch_openml("mnist_784", version=1, return_X_y=True, as_frame=False) X = X / 255.0 # Split data into train partition and test partition X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0, test_size=0.7) mlp = MLPClassifier( hidden_layer_sizes=(40,), max_iter=8, alpha=1e-4, solver="sgd", verbose=10, random_state=1, learning_rate_init=0.2, ) # this example won't converge because of resource usage constraints on # our Continuous Integration infrastructure, so we catch the warning and # 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=0.5 * vmin, vmax=0.5 * vmax) ax.set_xticks(()) ax.set_yticks(()) plt.show()
Total running time of the script: ( 0 minutes 19.738 seconds)