The Distinctive Dynamics of Biological Networks and Foams Resemble Deep Learning

A variety of biological and soft matter systems display surprisingly similar `glassy' dynamics, including super-diffusive relaxation and non-Gaussian fluctuations.  In the case of ripening wet foams, these have been shown to be due to the geometry of the high-dimensional configuration space path formed as the foam undergoes biased relaxation on a high-dimensional energy landscape¹.  The dynamics of the actin cortex of living animal cells display very similar features, despite the cortex presumably evolving on a very different energy landscape.  Emerging research considers a new class of active matter, called tunable matter, consisting of coupled individual agents evolving according to simple rules and local information to effectively perform gradient descent of a generic global cost function.  In this view, both the cortex and ripening foams are examples of tunable matter.  Surprisingly, computational studies reveal that the observed glassy dynamics are a feature of a variety of tunable matter and deep learning systems.  A toy model of gradient descent with uncorrelated heavy-tailed transverse noise appears to reproduce the observed glassy dynamics, suggesting that it is a common feature of gradient descent paths on many high-dimensional landscapes occurring in a variety of contexts.