The Unreasonable Effectiveness of Deep Learning in Artificial Intelligence

Division of Biological Sciences, University of California San Diego, La Jolla, California 92093 USA Abstract: Deep learning networks have been trained to recognize speech, caption photographs and translate text between languages at high levels of performance. Although applications of deep learning networks to real world problems have become ubiquitous, our understanding of why they are so effective is lacking. These empirical results should not be possible according to sample complexity in statistics and non-convex optimization theory. However, paradoxes in the training and effectiveness of deep learning networks are being investigated and insights are being found in the geometry of high-dimensional spaces. A mathematical theory of deep learning would illuminate how they function, allow us to assess the strengths and weaknesses of different network architectures and lead to major improvements. Deep learning has provided natural ways for humans to communicate with digital devices and is foundational for building artificial general intelligence. Deep learning was inspired by the architecture of the cerebral cortex and insights into autonomy and general intelligence may be found in other brain regions that are essential for planning and survival, but major breakthroughs will be needed to achieve these goals. This book was written as a satire on Victorian society, but it has endured because of its exploration of how dimensionality can change our intuitions about space. Flatland was a two-dimensional world inhabited by geometrical creatures. The mathematics of two dimensions was fully understood by these creatures, with circles being more perfect than triangles. In it a gentleman square has a dream about a sphere and wakes up to the possibility that his universe might be much larger than he or anyone in flatland could imagine.