Abstract
Recent developments in GPU-accelerated computing, as well as the advent of artificialintelligence and the rise of deep artificial neural networks (ANNs), have created a
wealth of opportunity to explore purely data-driven computational modeling techniques
on datasets and dynamical systems previously deemed overly complex or
outright infeasible to model. One such example of a domain in which these questions
are now being brought to light is in the field of computational neuroscience, where
both single neuron and neuronal network dynamical responses prove difficult and
arduous to model in many cases.
This thesis work is dedicated to the development of computationally feasible,
purely data-driven machine learning methods for inferring, learning, and modeling
both single-neuron and many-neuron dynamics at multiple time-scales through novel
employment of ANNs.
The first portion of this dissertation focuses on the development of purely datadriven
recurrent neural network (RNN) models of hippocampal CA1 pyramidal neuron
dynamics in response to constant-amplitude applied external input. These CA1
pyramidal neurons exhibit highly nonlinear dynamics, with multiple bifurcations in
behavioral response dependent on the magnitude of the externally applied input to
the system. This approach involves the use of deep LSTM networks in conjunction
with a novel translation trick borrowed from natural language processing (NLP) applications
in language translation problems. We demonstrate that the network is capable
of learning a complete representation of the dynamics, including multiple bifurcations
in behavior. Additionally, we demonstrate that predictive accuracy of the devised
LSTM network increases as the length of timeseries on which it is trained does as
well.
The second portion of this work focuses on the development of a generative
machine learning method to infer firing rate dynamics of a neuronal population in an
unsupervised autoencoding framework. This is centered around the idea that stochastic
neuronal populations are better described using powerful rate-based dynamical
models under the assumption that their firing activity can be described as a manyiv
body nonhomogeneous Poisson point process. We use a sequential adaptation of a
popular generative machine learning algorithm, the Variational Autoencoder (VAE) to
infer firing rates that maximize the likelihood of the original data in an unsupervised
manner, and demonstrate that this architecture is capable of discovering coherent
dynamical representations of smoothed firing rates directly from binned spiking data.