Archetypal landscapes for deep neural networks.

Area of Science:

• Machine Learning
• Deep Learning
• Optimization Theory

Background:

• Deep neural networks (DNNs) demonstrate remarkable predictive power, yet the underlying reasons for their successful training on high-dimensional, non-convex loss functions remain unclear.
• Understanding why standard optimization algorithms like stochastic gradient descent avoid poor local minima is crucial for advancing DNNs.

Purpose of the Study:

• To elucidate the optimizability of deep neural networks by analyzing their loss-function landscapes (LFLs).
• To characterize the properties of local minima and transition states within DNN LFLs and their connectivity.

Main Methods:

• Analysis of the loss-function landscape (LFL) of deep neural networks (DNNs).
• Characterization of local minima and transition states, and their connectivity.
• Examination of DNNs in both shallow/data-abundant and deep/low-data regimes.

Main Results:

• In the shallow network or data-abundant limit, the LFL is 'funneled,' facilitating optimization.
• In the deep network or low-data limit, numerous similar-valued minima exist, separated by low energy barriers.
• This landscape organization differs from hierarchical landscapes observed in structural glass formers.

Conclusions:

• The specific organization of DNN loss landscapes explains the success of common minimization procedures.
• DNNs can be effectively optimized because their landscapes allow navigation to low-lying solutions, even with simple algorithms.
• The findings provide insights into the inherent optimizability of deep learning models.