Linear and nonlinear systems analysis of the visual system: Why does it seem so linear?

Shapley, Robert

doi:10.1016/j.visres.2008.09.026

Cited by 45 publications

(45 citation statements)

References 83 publications

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“…Perhaps the greatest success of linear models is in the retina, where it has been used primarily to describe the spike responses of retinal ganglion cells (RGCs) [10], [11], [16]. For a given RGC, estimating the components of the linear model typically involves measuring its spiking response to a noise stimulus, and then computing the average stimulus that preceded its spikes: the spike-triggered average (STA).…”

Section: Resultsmentioning

confidence: 99%

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Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

2013

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The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation.

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Section: Resultsmentioning

confidence: 99%

“…While such descriptions can often provide good predictions of the neuronal response [9]–[11], they necessarily leave out the nonlinear elements of neuronal processing that likely play a major role in building the sensory percept.…”

Section: Introductionmentioning

confidence: 99%

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

2013

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“…Thus, application of an appropriately structured model reveals significant nonlinear processing in LGN neurons, which – outside of the context of luminance and contrast adaptation – have been generally thought of as well-described by linear models (Carandini et al, 2005; Shapley, 2009). Strong nonlinear elements, including separately tuned spatiotemporal elements of excitation and suppression, have a significant impact on the LGN response in both artificial and natural stimulus contexts.…”

Section: Discussionmentioning

confidence: 99%

Temporal Precision in the Visual Pathway through the Interplay of Excitation and Stimulus-Driven Suppression

Butts¹,

Weng²,

Jin³

et al. 2011

J. Neurosci.

116

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Visual neurons can respond with extremely precise temporal patterning to visual stimuli that change on much slower time scales. Here, we investigate how the precise timing of cat thalamic spike trains – which can have timing as precise as one millisecond – is related to the stimulus, in the context of both artificial noise and natural visual stimuli. Using a nonlinear modeling framework applied to extracellular data, we demonstrate that the precise timing of thalamic spike trains can be explained by the interplay between an excitatory and a delayed suppressive input that resembles inhibition, such that neuronal responses only occur in brief windows where excitation exceeds suppression. The resulting description of thalamic computation resembles earlier models of contrast adaptation, suggesting a more general role for mechanisms of contrast adaptation in visual processing. Thus, we describe a more complex computation underlying thalamic responses to artificial and natural stimuli, which has implications for understanding how visual information is represented in the early stages of visual processing.

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“…Despite the complexity of retinal circuitry, many aspects of the responses of ganglion cells to visual stimuli can be predicted with a straightforward Linear-Nonlinear (LN) cascade model (Shapley, 2009). In this model, a linear receptive field filters the stimulus, and a nonlinear function shapes the output by implementing the spike threshold and response saturation (Baccus and Meister, 2002; Chichilnisky, 2001; Kim and Rieke, 2001).…”

Section: Introductionmentioning

confidence: 99%

Divisive suppression explains high-precision firing and contrast adaptation in retinal ganglion cells

Cui

Wang

Park

et al. 2016

eLife

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Visual processing depends on specific computations implemented by complex neural circuits. Here, we present a circuit-inspired model of retinal ganglion cell computation, targeted to explain their temporal dynamics and adaptation to contrast. To localize the sources of such processing, we used recordings at the levels of synaptic input and spiking output in the in vitro mouse retina. We found that an ON-Alpha ganglion cell's excitatory synaptic inputs were described by a divisive interaction between excitation and delayed suppression, which explained nonlinear processing that was already present in ganglion cell inputs. Ganglion cell output was further shaped by spike generation mechanisms. The full model accurately predicted spike responses with unprecedented millisecond precision, and accurately described contrast adaptation of the spike train. These results demonstrate how circuit and cell-intrinsic mechanisms interact for ganglion cell function and, more generally, illustrate the power of circuit-inspired modeling of sensory processing.DOI: http://dx.doi.org/10.7554/eLife.19460.001

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Linear and nonlinear systems analysis of the visual system: Why does it seem so linear?

Cited by 45 publications

References 83 publications

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

Temporal Precision in the Visual Pathway through the Interplay of Excitation and Stimulus-Driven Suppression

Divisive suppression explains high-precision firing and contrast adaptation in retinal ganglion cells

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