Title: Input correlations impede suppression of chaos and learning in balanced firing-rate networks
Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks. 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.
Xia, Ji; Marks, Tyler D.; Goard, Michael J.; Wessel, Ralf(
, Journal of Neurophysiology)
null
(Ed.)
Both experimenter-controlled stimuli and stimulus-independent variables impact cortical neural activity. A major hurdle to understanding neural representation is distinguishing between qualitatively different causes of the fluctuating population activity. We applied an unsupervised low-rank tensor decomposition analysis to the recorded population activity in the visual cortex of awake mice in response to repeated presentations of naturalistic visual stimuli. We found that neurons covaried largely independently of individual neuron stimulus response reliability and thus encoded both stimulus-driven and stimulus-independent variables. Importantly, a neuron’s response reliability and the neuronal coactivation patterns substantially reorganized for different external visual inputs. Analysis of recurrent balanced neural network models revealed that both the stimulus specificity and the mixed encoding of qualitatively different variables can arise from clustered external inputs. These results establish that coactive neurons with diverse response reliability mediate a mixed representation of stimulus-driven and stimulus-independent variables in the visual cortex. NEW & NOTEWORTHY V1 neurons covary largely independently of individual neuron’s response reliability. A single neuron’s response reliability imposes only a weak constraint on its encoding capabilities. Visual stimulus instructs a neuron’s reliability and coactivation pattern. Network models revealed using clustered external inputs.
Liu, Benjamin; Seay, Michael J.; Buonomano, Dean V.(
, The Journal of Neuroscience)
Cortical computations emerge from the dynamics of neurons embedded in complex cortical circuits. Within these circuits, neuronal ensembles, which represent subnetworks with shared functional connectivity, emerge in an experience-dependent manner. Here we induced ensembles inex vivocortical circuits from mice of either sex by differentially activating subpopulations through chronic optogenetic stimulation. We observed a decrease in voltage correlation, and importantly a synaptic decoupling between the stimulated and nonstimulated populations. We also observed a decrease in firing rate during Up-states in the stimulated population. These ensemble-specific changes were accompanied by decreases in intrinsic excitability in the stimulated population, and a decrease in connectivity between stimulated and nonstimulated pyramidal neurons. By incorporating the empirically observed changes in intrinsic excitability and connectivity into a spiking neural network model, we were able to demonstrate that changes in both intrinsic excitability and connectivity accounted for the decreased firing rate, but only changes in connectivity accounted for the observed decorrelation. Our findings help ascertain the mechanisms underlying the ability of chronic patterned stimulation to create ensembles within cortical circuits and, importantly, show that while Up-states are a global network-wide phenomenon, functionally distinct ensembles can preserve their identity during Up-states through differential firing rates and correlations.
SIGNIFICANCE STATEMENTThe connectivity and activity patterns of local cortical circuits are shaped by experience. This experience-dependent reorganization of cortical circuits is driven by complex interactions between different local learning rules, external input, and reciprocal feedback between many distinct brain areas. Here we used anex vivoapproach to demonstrate how simple forms of chronic external stimulation can shape local cortical circuits in terms of their correlated activity and functional connectivity. The absence of feedback between different brain areas and full control of external input allowed for a tractable system to study the underlying mechanisms and development of a computational model. Results show that differential stimulation of subpopulations of neurons significantly reshapes cortical circuits and forms subnetworks referred to as neuronal ensembles.
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.
Kadmon, J.; Timcheck, J.; Ganguli, S(
, Advances in neural information processing systems)
null
(Ed.)
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.
Engelken, Rainer, Ingrosso, Alessandro, Khajeh, Ramin, Goedeke, Sven, and Abbott, L. F. Input correlations impede suppression of chaos and learning in balanced firing-rate networks. Retrieved from https://par.nsf.gov/biblio/10432378. PLOS Computational Biology 18.12 Web. doi:10.1371/journal.pcbi.1010590.
Engelken, Rainer, Ingrosso, Alessandro, Khajeh, Ramin, Goedeke, Sven, and Abbott, L. F.
"Input correlations impede suppression of chaos and learning in balanced firing-rate networks". PLOS Computational Biology 18 (12). Country unknown/Code not available. https://doi.org/10.1371/journal.pcbi.1010590.https://par.nsf.gov/biblio/10432378.
@article{osti_10432378,
place = {Country unknown/Code not available},
title = {Input correlations impede suppression of chaos and learning in balanced firing-rate networks},
url = {https://par.nsf.gov/biblio/10432378},
DOI = {10.1371/journal.pcbi.1010590},
abstractNote = {Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks.},
journal = {PLOS Computational Biology},
volume = {18},
number = {12},
author = {Engelken, Rainer and Ingrosso, Alessandro and Khajeh, Ramin and Goedeke, Sven and Abbott, L. F.},
editor = {Aljadeff, Johnatan}
}
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