Research map / Learning theory and algorithms / Prediction and decision losses
Empirical Studies on the Properties of Linear Regions in Deep Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add batch normalization | Fully connected ReLU DNN · MNIST test | test accuracy (%): 97.8 -> 97.9; 98.0 -> 98.3 | No clear effect |
| Add dropout | Fully connected ReLU DNN · MNIST test | test accuracy (%): 97.8 -> 97.5; 98.0 -> 98.2 | No clear effect |
| Add batch normalization | Fully connected ReLU DNN · MNIST manifold regions | distortion: 26.35 -> 14.90; 23.81 -> 07.61 | Mixed |
| Add dropout | Fully connected ReLU DNN · MNIST decision regions | inradius | Hurt |
| Add batch normalization | Fully connected ReLU DNN · linear-region hyperplane directions | orthogonality | Helped |
| Add dropout | Fully connected ReLU DNN · linear-region hyperplane directions | directional consistency | Helped |
| Add dropout | Fully connected ReLU DNN · MNIST manifold region | average number of classification regions: 1.116 -> 1.012; 8.766 -> 1.048 | Helped |
| Add batch normalization | CNN · CIFAR-10 manifold region | average number of classification regions: 7.811 -> 9.984 | Hurt |
| Add dropout | CNN · CIFAR-10 manifold region | average number of classification regions: 7.811 -> 2.901 | Helped |
| Train with a larger learning rate (1e-3) rather than 1e-4 | Fully connected ReLU DNN · MNIST manifold region | average number of classification regions: Vanilla: 8.766 -> 1.116; BN: 2.622 -> 1.083; Dropout: 1.048 -> 1.012 | Mixed |
| Use BN | Fully connected ReLU DNN · surrounding linear regions | gradient-direction cosine similarity | Hurt |
| Add dropout | CNN · CIFAR-10 manifold region | distortion: 27.08 -> 25.25 | Helped |
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