arXiv subjects

Gabriel Koch Ocker

Publications and source records attributed to Gabriel Koch Ocker.

11 recordsLinked to original sources

arXiv2026

Coherent dynamics in soft-threshold integrate-and-fire networks

We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of the population dynamics, we characterize spatial, temporal, and spatiotemporal patterns of macroscopic activity. In the mean-field theory, synaptic delays give rise to uniform oscillations across the population through a subcritical Hopf bifurcation of the stationary uniform equilibrium. With local excitation and long-range inhibition the network undergoes a Turing bifurcation, resulting in a localized area of sustained activity, or stationary bump. When the coupling has both delays, local inhibition, and long range excitation, the network undergoes a Turing-Hopf bifurcation leading to spatiotemporal dynamics, such as standing and traveling waves. When multiple instabilities are excited, we observe other complex spatiotemporal dynamics. We confirm all these predictions of the mean-field theory in simulations of the underlying stochastic model.

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arXiv2025

The Impact of Structural Changes on Learning Capacity in the Fly Olfactory Neural Circuit

The Drosophila mushroom body (MB) is known to be involved in olfactory learning and memory; the synaptic plasticity of the Kenyon cell (KC) to mushroom body output neuron (MBON) synapses plays a key role in the learning process. Previous research has focused on projection neuron (PN) to Kenyon cell (KC) connectivity within the MB; we examine how perturbations to the mushroom body circuit structure and changes in connectivity, specifically within the KC to mushroom body output neuron (MBON) neural circuit, affect the MBONs' ability to distinguish between odor classes. We constructed a neural network that incorporates the connectivity between PNs, KCs, and MBONs. To train our model, we generated ten artificial input classes, which represent the projection neuron activity in response to different odors. We collected data on the number of KC-to-MBON connections, MBON error rates, and KC-to-MBON synaptic weights, among other metrics. We observed that MBONs with very few presynaptic KCs consistently performed worse than others in the odor classification task. The developmental types of KCs also played a significant role in each MBON's output. We performed random and targeted KC ablation and observed that ablating developmentally mature KCs had a greater negative impact on MBONs' learning capacity than ablating immature KCs. Random and targeted pruning of KC-MBON synaptic connections yielded results largely consistent with the ablation experiments. To further explore the various types of KCs, we also performed rewiring experiments in the PN to KC circuit. Our study furthers our understanding of olfactory neuroplasticity and provides important clues to understanding learning and memory in general. Understanding how the olfactory circuits process and learn can also have potential applications in artificial intelligence and treatments for neurodegenerative diseases.

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arXiv2025

Field-theoretic approach to compartmental neuronal networks: impact of dendritic calcium spike-dependent bursting

Neurons are spatially extended cells; different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially compartmentalized, with different sources targeting different locations on the cell. Classic mean-field theories for neural population activity, however, rely on point-neuron models with at most one type of spike. Here, we develop a statistical field-theoretic approach to understanding collective activity in networks of compartmental neurons, including those generating multiple types of spikes. We use this to examine simple models of networks with thick-tufted layer 5 pyramidal cells, which generate calcium spikes in their apical dendrite when dendritic depolarization coincides with a back-propagating somatic spike. In the weakly-coupled regime, we uncover an exact mean-field limit for these networks that maps them to a marked point process. We use this mean-field limit to compare the impact of compartmentalized recurrent excitatory and inhibitory connectivity on the equilibrium phase diagram. This exposes regions of metastability between various activity states, including activity with silent vs active dendrites, with and without inhibitory activity, and oscillations.

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arXiv2025

Diverse mean-field dynamics of clustered, inhibition-stabilized Hawkes networks via combinatorial threshold-linear networks

Networks of interconnected neurons display diverse patterns of collective activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the re-activation of learned patterns. Previous studies of clustered networks have focused on metastabilty between fixed points, leaving open the question of whether clustered spiking networks can display more rich dynamics--and if so, whether these can be predicted from their connectivity. Here, we show that in the limits of large population size and fast inhibition, the combinatorial threshold linear network (CTLN) model is a mean-field theory for inhibition-stabilized nonlinear Hawkes networks with clustered connectivity. The CTLN has a large body of ``graph rules'' relating network structure to dynamics. By applying these, we can predict the dynamic attractors of our clustered spiking networks from the structure of between-cluster connectivity. This allows us to construct networks displaying a diverse array of nonlinear cluster dynamics, including metastable periodic orbits and chaotic attractors. Relaxing the assumption that inhibition is fast, we see that the CTLN model is still able to predict the activity of clustered spiking networks with reasonable inhibitory timescales. For slow enough inhibition, we observe bifurcations between CTLN-like dynamics and global excitatory/inhibitory oscillations.

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arXiv2024

Metastability in networks of nonlinear stochastic integrate-and-fire neurons

Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant bombardment of information. How these collective patterns of activity depend on single-neuron properties is often unclear. Single-neuron recordings have shown that individual neurons' responses to inputs are nonlinear, which prevents a straightforward extrapolation from single neuron features to emergent collective states. Here, we use a field-theoretic formulation of a stochastic leaky integrate-and-fire model to study the impact of single-neuron nonlinearities on macroscopic network activity. In this model, a neuron integrates spiking output from other neurons in its membrane voltage and emits spikes stochastically with an intensity depending on the membrane voltage, after which the voltage resets. We show that the interplay between nonlinear spike intensity functions and membrane potential resets can i) give rise to metastable active firing rate states in recurrent networks, and ii) can enhance or suppress mean firing rates and membrane potentials in the same or paradoxically opposite directions.

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arXiv2023

Dynamics of stochastic integrate-and-fire networks

The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual neurons, while biological neurons are highly complex cells. Integrate-and-fire neuron models balance biophysical detail and analytical tractability. Here, we develop a statistical field theory for networks of integrate-and-fire neurons with stochastic spike emission. This reveals an exact mapping to a self-consistent renewal process and a new mean field theory for the activity in these networks. The mean field theory has a rate-dependent leak, approximating the spike-driven resets of the membrane voltage. This gives rise to bistability between quiescent and active states in homogenous and excitatory-inhibitory pulse-coupled networks. The field-theoretic framework also exposes fluctuation corrections to the mean field theory. We find that due to the spike reset, fluctuations suppress activity. We then examine the roles of spike resets and recurrent inhibition in stabilizing network activity. We calculate the phase diagram for inhibitory stabilization and find that an inhibition-stabilized regime occurs in wide regions of parameter space, consistent with experimental reports of inhibitory stabilization in diverse brain regions. Fluctuations narrow the region of inhibitory stabilization, consistent with their role in suppressing activity through spike resets.

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arXiv2021

Tensor decomposition of higher-order correlations by nonlinear Hebbian plasticity

Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. These nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher-order input correlations. The particular input correlation decomposed and the form of the decomposition depend on the location of nonlinearities in the plasticity rule. For simple, biologically motivated parameters, the neuron learns eigenvectors of higher-order input correlation tensors. We prove that tensor eigenvectors are attractors and determine their basins of attraction. We calculate the volume of those basins, showing that the dominant eigenvector has the largest basin of attraction. We then study arbitrary learning rules and find that any learning rule that admits a finite Taylor expansion into the neural input and output also has stable equilibria at generalized eigenvectors of higher-order input correlation tensors. Nonlinearities in synaptic plasticity thus allow a neuron to encode higher-order input correlations in a simple fashion.

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arXiv2020

Linking structure and activity in nonlinear spiking networks

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of {\it structure-driven activity} has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities---including those of different cell types---combine with connectivity to shape population activity and function.

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arXiv2017

From the statistics of connectivity to the statistics of spike times in neuronal networks

An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending on the spatial scales of recurrent and feedforward connectivity. We close by showing how these ideas, together with plasticity rules, can help to close the loop between network structure and activity statistics.

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arXiv2016

Training and spontaneous reinforcement of neuronal assemblies by spike timing

The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations where analytic insight is lacking. A simple account for how fast spike time correlations affect both micro- and macroscopic network structure remains lacking. We develop a low-dimensional mean field theory showing how STDP gives rise to strongly coupled assemblies of neurons with shared stimulus preferences, with the connectivity actively reinforced by spike train correlations during spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has often been associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where temporal correlations and STDP form and actively maintain learned structure in cortical networks.

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arXiv2014

Self-organization of microcircuits in networks of neurons with plastic synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory that describes the evolution of network structure by combining fast spiking covariance with a fast-slow theory for synaptic weight dynamics. Through a finite-size expansion of network dynamics, we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on the frequency of weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP, these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

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