Visualization of MLP weights on MNISTΒΆ

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.



Iteration 1, loss = 0.32212731
Iteration 2, loss = 0.15738787
Iteration 3, loss = 0.11647274
Iteration 4, loss = 0.09631113
Iteration 5, loss = 0.08074513
Iteration 6, loss = 0.07163224
Iteration 7, loss = 0.06351392
Iteration 8, loss = 0.05694146
Iteration 9, loss = 0.05213487
Iteration 10, loss = 0.04708320
Training set score: 0.985733
Test set score: 0.971000


import matplotlib.pyplot as plt
from sklearn.datasets import fetch_mldata
from sklearn.neural_network import MLPClassifier

mnist = fetch_mldata("MNIST original")
# rescale the data, use the traditional train/test split
X, y = / 255.,
X_train, X_test = X[:60000], X[60000:]
y_train, y_test = y[:60000], y[60000:]

# mlp = MLPClassifier(hidden_layer_sizes=(100, 100), max_iter=400, alpha=1e-4,
#                     solver='sgd', verbose=10, tol=1e-4, random_state=1)
mlp = MLPClassifier(hidden_layer_sizes=(50,), max_iter=10, alpha=1e-4,
                    solver='sgd', verbose=10, tol=1e-4, random_state=1,
                    learning_rate_init=.1), 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),, vmin=.5 * vmin,
               vmax=.5 * vmax)

Total running time of the script: ( 0 minutes 14.366 seconds)

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