arXiv subjects

Brent Doiron

Publications and source records attributed to Brent Doiron.

13 recordsLinked to original sources

arXiv2026

Dynamic Mean Field Theories for Nonlinear Noise in Recurrent Neuronal Networks

Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that replaces nonlinear functions of Ornstein-Uhlenbeck (OU) noise with a Gaussian-equivalent process matched in mean and covariance, and combine this with a lognormal moment closure for expansive nonlinearities to derive a closed dynamical mean-field theory for recurrent neuronal networks. The resulting theory captures order-one transients, fixed points, and noise-induced shifts of bifurcation structure, and outperforms standard linearization-based approximations in the strong-fluctuation regime. More broadly, the approach applies whenever dynamics depend smoothly on OU processes via nonlinear transformations, offering a tractable route to noise-dependent phase diagrams in computational neuroscience models.

q-bio.NC↗

arXiv2025

Causal Spike Timing Dependent Plasticity Prevents Assembly Fusion in Recurrent Networks

The organization of neurons into functionally related assemblies is a fundamental feature of cortical networks, yet our understanding of how these assemblies maintain distinct identities while sharing members remains limited. Here we analyze how spike-timing-dependent plasticity (STDP) shapes the formation and stability of overlapping neuronal assemblies in recurrently coupled networks of spiking neuron models. Using numerical simulations and an associated mean-field theory, we demonstrate that the temporal structure of the STDP rule, specifically its degree of causality, critically determines whether assemblies that share neurons maintain segregation or merge together after training is completed. We find that causal STDP rules, where potentiation/depression occurs strictly when presynaptic spikes precede/proceed postsynaptic spikes, allow assemblies to remain distinct even with substantial overlap in membership. This stability arises because causal STDP effectively cancels the symmetric correlations introduced by common inputs from shared neurons. In contrast, acausal STDP rules lead to assembly fusion when overlap exceeds a critical threshold, due to unchecked growth of common input correlations. Our results provide theoretical insight into how spike-timing-dependent learning rules can support distributed representation where individual neurons participate in multiple assemblies while maintaining functional specificity.

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arXiv2023

A Step Towards Uncovering The Structure of Multistable Neural Networks

We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function. This nonlinearity partitions the phase space into regions with different, yet linear dynamics. In each region either a stable equilibrium state exists, or network activity flows to outside of the region. The stable states are identified by their semipositivity constraints on the synaptic weight matrix. The restrictions can be separated by their effects on the signs or the strengths of the connections. Exact results on network topology, sign stability, weight matrix factorization, pattern completion and pattern coupling are derived and proven. Our work may lay the foundation for multistability in more complex recurrent neural networks.

cs.NE↗

arXiv2021

Large-scale neural recordings call for new insights to link brain and behavior

Neuroscientists today can measure activity from more neurons than ever before, and are facing the challenge of connecting these brain-wide neural recordings to computation and behavior. Here, we first describe emerging tools and technologies being used to probe large-scale brain activity and new approaches to characterize behavior in the context of such measurements. We next highlight insights obtained from large-scale neural recordings in diverse model systems, and argue that some of these pose a challenge to traditional theoretical frameworks. Finally, we elaborate on existing modelling frameworks to interpret these data, and argue that interpreting brain-wide neural recordings calls for new theoretical approaches that may depend on the desired level of understanding at stake. These advances in both neural recordings and theory development will pave the way for critical advances in our understanding of the brain.

q-bio.NC↗

arXiv2019

Correlation transfer by layer 5 cortical neurons under recreated synaptic inputs in vitro

Correlated electrical activity in neurons is a prominent characteristic of cortical microcircuits. Despite a growing amount of evidence concerning both spike-count and subthreshold membrane potential pairwise correlations, little is known about how different types of cortical neurons convert correlated inputs into correlated outputs. We studied pyramidal neurons and two classes of GABAergic interneurons of layer 5 in neocortical brain slices obtained from rats of both sexes, and we stimulated them with biophysically realistic correlated inputs, generated using dynamic clamp. We found that the physiological differences between cell types manifested unique features in their capacity to transfer correlated inputs. We used linear response theory and computational modeling to gain clear insights into how cellular properties determine both the gain and timescale of correlation transfer, thus tying single-cell features with network interactions. Our results provide further ground for the functionally distinct roles played by various types of neuronal cells in the cortical microcircuit.

q-bio.NC↗

arXiv2019

Decision Dynamics in Groups with Interacting Members

Group decisions involve the combination of evidence accumulation by individual members and direct member-to-member interactions. We consider a simplified framework of two deciders, each undergoing a two alternative forced choice task, with the choices of early deciding members biasing members who have yet to choose. We model decision dynamics as a drift-diffusion process and present analysis of the associated Fokker-Planck equation for the group. We show that the probability of coordinated group decisions (both members make the same decision) is maximized by setting the decision threshold of one member to a lower value than its neighbor's. This result is akin to a speed-accuracy tradeoff, where the penalty of lowering the decision threshold is choice inaccuracy while the benefit is that earlier decisions have a higher probability of influencing the other member. We numerically extend these results to large group decisions, where it is shown that by choosing the appropriate parameters, a small but vocal component of the population can have a large amount of influence on the total system.

physics.soc-ph↗

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.

q-bio.NC↗

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.

q-bio.NC↗

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.

q-bio.NC↗

arXiv2013

Balanced networks of spiking neurons with spatially dependent recurrent connections

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the spatial separation between neurons. In the continuum limit we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. For finite size networks we investigate the pattern forming dynamics arising when balanced conditions are not satisfied. The spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.

q-bio.NC↗

arXiv2013

Optimizing working memory with heterogeneity of recurrent cortical excitation

A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural activity, linking network architecture and parametric working memory. Cortical neurons receive noisy input fluctuations which causes persistent activity to diffusively wander about the network, degrading memory over time. We explore how cortical architecture that supports parametric working memory affects the diffusion of persistent neural activity. Studying both a spiking network and a simplified potential well model, we show that spatially heterogeneous excitatory coupling stabilizes a discrete number of persistent states, reducing the diffusion of persistent activity over the network. However, heterogeneous coupling also coarse-grains the stimulus representation space, limiting the capacity of parametric working memory. The storage errors due to coarse-graining and diffusion tradeoff so that information transfer between the initial and recalled stimulus is optimized at a fixed network heterogeneity. For sufficiently long delay times, the optimal number of attractors is less than the number of possible stimuli, suggesting that memory networks can under-represent stimulus space to optimize performance. Our results clearly demonstrate the effects of network architecture and stochastic fluctuations on parametric memory storage.

q-bio.NC↗

arXiv2008

Stimulus-dependent correlations and population codes

The magnitude of correlations between stimulus-driven responses of pairs of neurons can itself be stimulus-dependent. We examine how this dependence impacts the information carried by neural populations about the stimuli that drive them. Stimulus-dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances. We use Fisher information to quantify these effects and show that, although stimulus dependent correlations often carry little information directly, their modulatory effects on the overall information can be large. In particular, if the stimulus-dependence is such that correlations increase with stimulus-induced firing rates, this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus. However, in the presence of additional strong spatial decay of correlations, such stimulus-dependence may have a negative impact. Opposite relationships hold when correlations decrease with firing rates.

q-bio.NC↗

arXiv2007

Universal properties of correlation transfer in integrate-and-fire neurons

One of the fundamental characteristics of a nonlinear system is how it transfers correlations in its inputs to correlations in its outputs. This is particularly important in the nervous system, where correlations between spiking neurons are prominent. Using linear response and asymptotic methods for pairs of unconnected integrate-and-fire (IF) neurons receiving white noise inputs, we show that this correlation transfer depends on the output spike firing rate in a strong, stereotyped manner, and is, surprisingly, almost independent of the interspike variance. For cells receiving heterogeneous inputs, we further show that correlation increases with the geometric mean spiking rate in the same stereotyped manner, greatly extending the generality of this relationship. We present an immediate consequence of this relationship for population coding via tuning curves.

q-bio.NC↗