Mathematical analysis and empirical tests clarify the relationships between predictive coding and backpropagation in deep neural networks (see Rosenbaum, 2022).

PhD students, Cody Baker and Vicky Zhu developed a mathematical approach for studying nonlinear stimulus representations in cortical circuits with balanced excitation and inhibition (see Baker, Zhu, and Rosenbaum, PLoS Comp. Bio., 2020).

PhD student, Ryan Pyle, modeled cortical and basal ganglia contributions to motor learning by combining reinforcement and unsupervised learning rules for recurrent neural nets (see Pyle and Rosenbaum, Neural Computation, 2019).

Undergraduate student, David Connelly, studied synaptic scaling laws that arise from axonal growth dynamics.

Stochastic analysis, spiking network simulations, and a collaboration with experimental neuroscientists showed how spatial connectivity structure shapes correlated variability in neural circuits (see Rosenbaum et al., Nature Neuroscience, 2017).

Stochastic analysis and a collaboration with experimental neuroscientists revealed novel mechanisms of correlated variability in recurrent spiking neural networks with balanced excitation and inhibition (see Baker, et al., PRE, 2019).

PhD student, Ryan Pyle, used Fokker-Planck approaches to explain pattern-forming instabilities that improve the computational power of recurrent spiking neural networks (see Pyle and Rosenbaum, PRL, 2017).

PhD student, Christopher Ebsch, showed how excitatory-inhibitory balance determines neural circuits' responses to natural and optogenetic stimuli (see Ebsch and Rosenbaum, PLoS Comp. Bio., 2018).

Undergraduate student, Gabrielle Thivierge, used integro-differential equations to model visual hallucinations evoked by pattern forming dynamics in visual cortex.