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Sompolinsky, H.

Publications and source records attributed to Sompolinsky, H..

3 recordsLinked to original sources
bioRxiv2018

Coherent chaos in a recurrent neural network with structured connectivity

We present a simple model for coherent, spatially correlated chaos in a recurrent neural network. Networks of randomly connected neurons exhibit chaotic fluctuations and have been studied as a model for capturing the temporal variability of cortical activity. The dynamics generated by such networks, however, are spatially uncorrelated and do not generate coherent fluctuations, which are commonly observed across spatial scales of the neocortex. In our model we introduce a structured component of connectivity, in addition to random connections, which effectively embeds a feedforward structure via unidirectional coupling between a pair of orthogonal modes. Local fluctuations driven by the random connectivity are summed by an output mode and drive coherent activity along an input mode. The orthogonality between input and output mode preserves chaotic fluctuations even as coherence develops. In the regime of weak structured connectivity we apply a perturbative approach to solve the dynamic mean-field equations, showing that in this regime coherent fluctuations are driven passively by the chaos of local residual fluctuations. Strikingly, the chaotic dynamics are not subdued even by very strong structured connectivity if we add a row balance constraint on the random connectivity. In this regime the system displays longer time-scales and switching-like activity reminiscent of \"Up-Down\" states observed in cortical circuits. The level of coherence grows with increasing strength of structured connectivity until the dynamics are almost entirely constrained to a single spatial mode. We describe how in this regime the model achieves intermittent self-tuned criticality in which the coherent component of the dynamics self-adjusts to yield periods of slow chaos. Furthermore, we show how the dynamics depend qualitatively on the particular realization of the connectivity matrix: a complex leading eigenvalue can yield coherent oscillatory chaos while a real leading eigenvalue can yield chaos with broken symmetry. We examine the effects of network-size scaling and show that these results are not finite-size effects. Finally, we show that in the regime of weak structured connectivity, coherent chaos emerges also for a generalized structured connectivity with multiple input-output modes.\n\nAuthor SummaryNeural activity observed in the neocortex is temporally variable, displaying irregular temporal fluctuations at every accessible level of measurement. Furthermore, these temporal fluctuations are often found to be spatially correlated whether at the scale of local measurements such as membrane potentials and spikes, or global measurements such as EEG and fMRI. A thriving field of study has developed models of recurrent networks which intrinsically generate irregular temporal variability, the paradigmatic example being networks of randomly connected rate neurons which exhibit chaotic dynamics. These models have been examined analytically and numerically in great detail, yet until now the intrinsic variability generated by these networks have been spatially uncorrelated, yielding no large-scale coherent fluctuations. Here we present a simple model of a recurrent network of firing-rate neurons that intrinsically generates spatially correlated activity yielding coherent fluctuations across the entire network. The model incorporates random connections and adds a structured component of connectivity that sums network activity over a spatial \"output\" mode and projects it back to the network along an orthogonal \"input\" mode. We show that this form of structured connectivity is a general mechanism for producing coherent chaos.

neuroscience↗
bioRxiv2018

Brainwide organization of neuronal activity and convergent sensorimotor transformations in larval zebrafish

Simultaneous recordings of large populations of neurons in behaving animals allow detailed observation of high-dimensional, complex brain activity. However, experimental design and analysis approaches have not sufficiently evolved to fully realize the potential of these methods. We recorded whole-brain neuronal activity for larval zebrafish presented with a battery of visual stimuli while recording fictive motor output. These data were used to develop analysis methods including regression techniques that leverage trial-to-trial variations and unsupervised clustering techniques that organize neurons into functional groups. We used these methods to obtain brain-wide maps of concerted activity, which revealed both known and heretofore uncharacterized brain nuclei. We also identified neurons tuned to each stimulus type and motor output, and revealed nuclei in the anterior hindbrain that respond to multiple stimuli that elicit the same behavior. However, these convergent sensorimotor representations were only weakly correlated to instantaneous motor behavior, suggesting that they inform, but do not directly generate, behavioral output. These findings motivate a novel model of sensorimotor transformation spanning distinct behavioral contexts, within which these hindbrain convergence neurons likely constitute a key step.

neuroscience↗
bioRxiv2017

Optimal Sensory Coding By Populations Of ON And OFF Neurons

In many sensory systems the neural signal is coded by the coordinated response of heterogeneous populations of neurons. What computational benefit does this diversity confer on information processing? We derive an efficient coding framework assuming that neurons have evolved to communicate signals optimally given natural stimulus statistics and metabolic constraints. Incorporating nonlinearities and realistic noise, we study optimal population coding of the same sensory variable using two measures: maximizing the mutual information between stimuli and responses, and minimizing the error incurred by the optimal linear decoder of responses. Our theory is applied to a commonly observed splitting of sensory neurons into ON and OFF that signal stimulus increases or decreases, and to populations of monotonically increasing responses of the same type, ON. Depending on the optimality measure, we make different predictions about how to optimally split a population into ON and OFF, and how to allocate the firing thresholds of individual neurons given realistic stimulus distributions and noise, which accord with certain biases observed experimentally.

neuroscience↗