A complex-valued firing-rate model that approximates the dynamics of spiking networks.

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

A study of animal action segmentation algorithms across supervised, unsupervised, and semi-supervised learning paradigms.

Action segmentation of behavioral videos is the process of labeling each frame as belonging to one or more discrete classes, and is a crucial component of many studies that investigate animal behavior. A wide range of algorithms exist to automatically parse discrete animal behavior, encompassing supervised, unsupervised, and semi-supervised learning paradigms. These algorithms - which include tree-based models, deep neural networks, and graphical models - differ widely in their structure and assumptions on the data. Using four datasets spanning multiple species - fly, mouse, and human - we systematically study how the outputs of these various algorithms align with manually annotated behaviors of interest. Along the way, we introduce a semi-supervised action segmentation model that bridges the gap between supervised deep neural networks and unsupervised graphical models. We find that fully supervised temporal convolutional networks with the addition of temporal information in the observations perform the best on our supervised metrics across all datasets.

The spatial and temporal structure of neural activity across the fly brain.

What are the spatial and temporal scales of brainwide neuronal activity? We used swept, confocally-aligned planar excitation (SCAPE) microscopy to image all cells in a large volume of the brain of adult Drosophila with high spatiotemporal resolution while flies engaged in a variety of spontaneous behaviors. This revealed neural representations of behavior on multiple spatial and temporal scales. The activity of most neurons correlated (or anticorrelated) with running and flailing over timescales that ranged from seconds to a minute. Grooming elicited a weaker global response. Significant residual activity not directly correlated with behavior was high dimensional and reflected the activity of small clusters of spatially organized neurons that may correspond to genetically defined cell types. These clusters participate in the global dynamics, indicating that neural activity reflects a combination of local and broadly distributed components. This suggests that microcircuits with highly specified functions are provided with knowledge of the larger context in which they operate.

Odor Perception on the Two Sides of the Brain: Consistency Despite Randomness.

Neurons in piriform cortex receive input from a random collection of glomeruli, resulting in odor representations that lack the stereotypic organization of the olfactory bulb. We have performed in vivo optical imaging and mathematical modeling to demonstrate that correlations are retained in the transformation from bulb to piriform cortex, a feature essential for generalization across odors. Random connectivity also implies that the piriform representation of a given odor will differ among different individuals and across brain hemispheres in a single individual. We show that these different representations can nevertheless support consistent agreement about odor quality across a range of odors. Our model also demonstrates that, whereas odor discrimination and categorization require far fewer neurons than reside in piriform cortex, consistent generalization may require the full complement of piriform neurons.

Inhibitory stabilization of the cortical network underlies visual surround suppression.

In what regime does the cortical circuit operate? Our intracellular studies of surround suppression in cat primary visual cortex (V1) provide strong evidence on this question. Although suppression has been thought to arise from an increase in lateral inhibition, we find that the inhibition that cells receive is reduced, not increased, by a surround stimulus. Instead, suppression is mediated by a withdrawal of excitation. Thalamic recordings and previous work show that these effects cannot be explained by a withdrawal of thalamic input. We find in theoretical work that this behavior can only arise if V1 operates as an inhibition-stabilized network (ISN), in which excitatory recurrence alone is strong enough to destabilize visual responses but feedback inhibition maintains stability. We confirm two strong tests of this scenario experimentally and show through simulation that observed cell-to-cell variability in surround effects, from facilitation to suppression, can arise naturally from variability in the ISN.