The remarkable capability of over-parameterised neural networks to generalise effectively has been explained by invoking a "simplicity bias": neural networks prevent overfitting by initially learning simple classifiers before progressing to

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries - a broad subclass of continuous symmetries present in the model architecture or loss function - interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a "Noether flow") of the parameters θ along the degenerate direction to a unique initialization-independent fixed point θ

However, such a global learning rate schedule does not take into account the structural characteristics of neural networks (NNs).

An elephant foot bone found by archaeologists digging in southern Spain may be evidence that a troop of war elephants stomped through ancient Europe. It would be the first concrete proof of the legendary Carthaginian General Hannibal's troop of battle elephants, according to academics. Drawings of Hannibal's war against the Romans had long suggested that the beasts were used in fighting, but no hard evidence backed up the theories. Now the creatures' skeletal remains appear to have been found in an Iron Age dig near Cordoba. Beyond ivory, the discovery of elephant remains in European archaeological contexts is exceptionally rare, says the team of scientists in a paper published in Journal of Archaeological Science: Reports.

They do not study how the population loss decreases during the first stage.

Many applications seek to recover low-rank approximations of noisy tensor data.

This work investigates how these complexities necessarily arise for feature learning in the presence of computational-statistical gaps.