Research map / Optimization / Implicit bias and generalization
Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the trained wide network with its first-order Taylor expansion at initialization | Wide neural networks · MNIST subset, CIFAR-10, and other experiments described | training-dynamics agreement | Helped |
| Use the empirical tangent kernel at initialization instead of the infinite-width analytic kernel | Linearized network · Finite-width networks | training-dynamics agreement | Helped |
| Increase network width | Fully connected, convolutional, and wide residual networks · Varying depth and dataset size | RMSE between network and linearization | Helped |
| Increase dataset size without a corresponding increase in model size | Wide neural networks and their linearizations · Varying dataset size | RMSE between network and linearization | Hurt |
| Train only the readout layer rather than all network parameters | Infinite-width neural network · Squared loss | agreement with NNGP posterior predictive distribution | Helped |
| Train all parameters instead of only the readout layer | Infinite-width neural network · Squared loss | agreement with NNGP posterior predictive distribution | Hurt |
| Use cross-entropy loss with softmax and continue training into late times | Original and linearized networks · MNIST and binary CIFAR classification | logit agreement | Hurt |
| Use standard rather than NTK parameterization | Wide neural networks · MNIST and CIFAR experiments | model performance | No clear effect |
| Train a wide residual network and its linearization with SGD and momentum | Wide ResNet · CIFAR-10 | training-dynamics agreement | Helped |
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