Discovering Model Manifolds of Emergent Function from High-Dimensional Data

Natural systems of many interacting constituents often organize to produce low dimensional emergent behaviors. For example, hundreds of thousands of neurons in the brain coordinate to represent the three-dimensional world around us. Similar emergent behaviors arise in the tens of thousands of genes that coordinate to produce the cellular processes that maintain life. What is the bottleneck for understanding how such emergent behaviors arise from these complex systems? This challenging problem is no longer limited by data: recent technological advances now allow us to measure the expression of every gene at the resolution of single cells, and the simultaneous activity of a million neurons, giving us the opportunity to model emergence at an unprecedented scale. What is missing are methods for taking such high dimensional data and mapping them to a small number of relevant emergent variables in a principled and quantitative way.

In this talk, I will discuss novel methods I am pioneering that combine differential geometry with deep neural networks to quantitatively model emergent behaviors using high-dimensional, high-throughput data from genomics and neuroscience. I will discuss fundamental problems of model identifiability (degeneracy in model parameters that fit the data), interpretability (mapping emergent variables back to gene and neuron circuits), and predictive power, and how geometry-aware deep learning models ameliorate these problems to enable new discoveries. Finally, I will describe some of the discoveries that we have made using this method including new pathways for cancers to develop (thereby providing new potential targets for drug therapies) and how mice update the representations of the mazes that they run through.