Title: Predictive coding in balanced neural networks with noise, chaos and delays
Biological neural networks face a formidable task: performing reliable computations in the face of intrinsic stochasticity in individual neurons, imprecisely specified synaptic connectivity, and nonnegligible delays in synaptic transmission. A common approach to combatting such biological heterogeneity involves averaging over large redundant networks of N neurons resulting in coding errors that decrease classically as the square root of N. Recent work demonstrated a novel mechanism whereby recurrent spiking networks could efficiently encode dynamic stimuli achieving a superclassical scaling in which coding errors decrease as 1/N. This specific mechanism involved two key ideas: predictive coding, and a tight balance, or cancellation between strong feedforward inputs and strong recurrent feedback. However, the theoretical principles governing the efficacy of balanced predictive coding and its robustness to noise, synaptic weight heterogeneity and communication delays remain poorly understood. To discover such principles, we introduce an analytically tractable model of balanced predictive coding, in which the degree of balance and the degree of weight disorder can be dissociated unlike in previous balanced network models, and we develop a mean-field theory of coding accuracy. Overall, our work provides and solves a general theoretical framework for dissecting the differential contributions neural noise, synaptic disorder, chaos, synaptic delays, and balance to the fidelity of predictive neural codes, reveals the fundamental role that balance plays in achieving superclassical scaling, and unifies previously disparate models in theoretical neuroscience. more »« less
The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.
Barranca, Victor J.; Bhuiyan, Asha; Sundgren, Max; Xing, Fangzhou(
, Frontiers in Neuroscience)
The notion that a neuron transmits the same set of neurotransmitters at all of its post-synaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decision-making tasks, and it plays a key role in the current understanding of the structure-function relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this single-population network model in the context of two competing pools of neurons to demonstrate that effective decision-making dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical two-population balanced neuronal network, we argue that the one-population network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the two-population network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.
Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.
Winding, Michael; Pedigo, Benjamin D.; Barnes, Christopher L.; Patsolic, Heather G.; Park, Youngser; Kazimiers, Tom; Fushiki, Akira; Andrade, Ingrid V.; Khandelwal, Avinash; Valdes-Aleman, Javier; et al(
, Science)
INTRODUCTION A brainwide, synaptic-resolution connectivity map—a connectome—is essential for understanding how the brain generates behavior. However because of technological constraints imaging entire brains with electron microscopy (EM) and reconstructing circuits from such datasets has been challenging. To date, complete connectomes have been mapped for only three organisms, each with several hundred brain neurons: the nematode C. elegans , the larva of the sea squirt Ciona intestinalis , and of the marine annelid Platynereis dumerilii . Synapse-resolution circuit diagrams of larger brains, such as insects, fish, and mammals, have been approached by considering select subregions in isolation. However, neural computations span spatially dispersed but interconnected brain regions, and understanding any one computation requires the complete brain connectome with all its inputs and outputs. RATIONALE We therefore generated a connectome of an entire brain of a small insect, the larva of the fruit fly, Drosophila melanogaster. This animal displays a rich behavioral repertoire, including learning, value computation, and action selection, and shares homologous brain structures with adult Drosophila and larger insects. Powerful genetic tools are available for selective manipulation or recording of individual neuron types. In this tractable model system, hypotheses about the functional roles of specific neurons and circuit motifs revealed by the connectome can therefore be readily tested. RESULTS The complete synaptic-resolution connectome of the Drosophila larval brain comprises 3016 neurons and 548,000 synapses. We performed a detailed analysis of the brain circuit architecture, including connection and neuron types, network hubs, and circuit motifs. Most of the brain’s in-out hubs (73%) were postsynaptic to the learning center or presynaptic to the dopaminergic neurons that drive learning. We used graph spectral embedding to hierarchically cluster neurons based on synaptic connectivity into 93 neuron types, which were internally consistent based on other features, such as morphology and function. We developed an algorithm to track brainwide signal propagation across polysynaptic pathways and analyzed feedforward (from sensory to output) and feedback pathways, multisensory integration, and cross-hemisphere interactions. We found extensive multisensory integration throughout the brain and multiple interconnected pathways of varying depths from sensory neurons to output neurons forming a distributed processing network. The brain had a highly recurrent architecture, with 41% of neurons receiving long-range recurrent input. However, recurrence was not evenly distributed and was especially high in areas implicated in learning and action selection. Dopaminergic neurons that drive learning are amongst the most recurrent neurons in the brain. Many contralateral neurons, which projected across brain hemispheres, were in-out hubs and synapsed onto each other, facilitating extensive interhemispheric communication. We also analyzed interactions between the brain and nerve cord. We found that descending neurons targeted a small fraction of premotor elements that could play important roles in switching between locomotor states. A subset of descending neurons targeted low-order post-sensory interneurons likely modulating sensory processing. CONCLUSION The complete brain connectome of the Drosophila larva will be a lasting reference study, providing a basis for a multitude of theoretical and experimental studies of brain function. The approach and computational tools generated in this study will facilitate the analysis of future connectomes. Although the details of brain organization differ across the animal kingdom, many circuit architectures are conserved. As more brain connectomes of other organisms are mapped in the future, comparisons between them will reveal both common and therefore potentially optimal circuit architectures, as well as the idiosyncratic ones that underlie behavioral differences between organisms. Some of the architectural features observed in the Drosophila larval brain, including multilayer shortcuts and prominent nested recurrent loops, are found in state-of-the-art artificial neural networks, where they can compensate for a lack of network depth and support arbitrary, task-dependent computations. Such features could therefore increase the brain’s computational capacity, overcoming physiological constraints on the number of neurons. Future analysis of similarities and differences between brains and artificial neural networks may help in understanding brain computational principles and perhaps inspire new machine learning architectures. The connectome of the Drosophila larval brain. The morphologies of all brain neurons, reconstructed from a synapse-resolution EM volume, and the synaptic connectivity matrix of an entire brain. This connectivity information was used to hierarchically cluster all brains into 93 cell types, which were internally consistent based on morphology and known function.
Synchronization in the gamma band (25–150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.
Kadmon, J., Timcheck, J., and Ganguli, S. Predictive coding in balanced neural networks with noise, chaos and delays. Retrieved from https://par.nsf.gov/biblio/10291301. Advances in neural information processing systems 33.
Kadmon, J., Timcheck, J., & Ganguli, S. Predictive coding in balanced neural networks with noise, chaos and delays. Advances in neural information processing systems, 33 (). Retrieved from https://par.nsf.gov/biblio/10291301.
Kadmon, J., Timcheck, J., and Ganguli, S.
"Predictive coding in balanced neural networks with noise, chaos and delays". Advances in neural information processing systems 33 (). Country unknown/Code not available. https://par.nsf.gov/biblio/10291301.
@article{osti_10291301,
place = {Country unknown/Code not available},
title = {Predictive coding in balanced neural networks with noise, chaos and delays},
url = {https://par.nsf.gov/biblio/10291301},
abstractNote = {Biological neural networks face a formidable task: performing reliable computations in the face of intrinsic stochasticity in individual neurons, imprecisely specified synaptic connectivity, and nonnegligible delays in synaptic transmission. A common approach to combatting such biological heterogeneity involves averaging over large redundant networks of N neurons resulting in coding errors that decrease classically as the square root of N. Recent work demonstrated a novel mechanism whereby recurrent spiking networks could efficiently encode dynamic stimuli achieving a superclassical scaling in which coding errors decrease as 1/N. This specific mechanism involved two key ideas: predictive coding, and a tight balance, or cancellation between strong feedforward inputs and strong recurrent feedback. However, the theoretical principles governing the efficacy of balanced predictive coding and its robustness to noise, synaptic weight heterogeneity and communication delays remain poorly understood. To discover such principles, we introduce an analytically tractable model of balanced predictive coding, in which the degree of balance and the degree of weight disorder can be dissociated unlike in previous balanced network models, and we develop a mean-field theory of coding accuracy. Overall, our work provides and solves a general theoretical framework for dissecting the differential contributions neural noise, synaptic disorder, chaos, synaptic delays, and balance to the fidelity of predictive neural codes, reveals the fundamental role that balance plays in achieving superclassical scaling, and unifies previously disparate models in theoretical neuroscience.},
journal = {Advances in neural information processing systems},
volume = {33},
author = {Kadmon, J. and Timcheck, J. and Ganguli, S},
editor = {null}
}
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