Frequentist statistics says that there exists some true underlying parameters for a model. While Bayesian statistics says that there are different beliefs about parameters for a model.
In backpropgation, we essentially throw data at a neural network, backpropagate the gradients error, and hope that the network learns the true underlying parameters.
Is training a neural network model with backpropagation, a frequentist approach?
Backpropagation uses a regularizer $\lambda$ to penalize magnitudes of the weights to prevent overfitting. This is a frequentist approach to applying the Occam's Razor principle.
In the Bayesian formulation, this is expressed equivalently as putting a prior distribution on the weights. Your regularizer term $\lambda$ would now be expressed in terms of the prior hyperparameters.
Both approaches work and equivalent in an algorithmic sense. The Bayesian formulation might require a few additional math steps to see how $\lambda$ depends on the prior.
The frequentist approach would use cross-validation to determine $\lambda$ directly. Bayesian's may use cross-validation to fix a prior. Or they may not.
