Guided by our observations, we then present examples of overparameterized linear classifiers and neural networks trained by gradient descent (GD) where uniform convergence provably cannot ``explain generalization'' -- even if we take into account the implicit bias of GD {\em to the fullest extent...
Guided by our observations, we then present examples of overparameterized linear classifiers and neural networks trained by gradient descent (GD) where uniform convergence provably cannot "explain generalization" - even if we take into account the implicit bias of GD to the fullest extent possible. ...
1. Introduction Deep learning has achieved many recent advances in pre- dictive modeling in various tasks, but the community has nonetheless become alarmed by the unintuitive generaliza- tion behaviors of neural networks, such as the capacity in memor...
Placing more power in the first few modes makes learning faster. When the labels have nonzero noise σ2 > 0 (Fig. 2d, e), generalization error is non-monotonic with a peak, a feature that has been named “double-descent”3,37. By decomposing Eg into the bias and the variance ...
The readout was optimised using batch gradient descent with Adam. The learning rate was set to 0.001 and the readout was trained for 1000 iterations. The loss was weighted for each class to account for the imbalance of classes in the training set. This procedure was repe...
can be found in Supplementary TablesS1, S2. For each empirical spectral tuning curve, the best fit parameters of the model are iteratively estimated using a standard gradient descent algorithm under the least squares estimation method. We consider a set ofNobservations of the activities of third ...
In practice, a CNN learnsthe values of these filters on its own during the training process. (although we still need to specify parameters such as numbers of filters, filter size, architecture of the network etc. before the training process). The more number of filters we have, the more...
Although those approaches predict future traffic flow with high accuracy, they are based on deep learning and involve stacked nonlinear operations, which are unexplainable and impede their deployment in cities. To understand black box systems, in recent years, great achievements have been made in conv...