Learning Quadratic Receptive Fields from Neural Responses to Natural Stimuli

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

doi:10.1162/neco_a_00463

Cited by 33 publications

(46 citation statements)

References 84 publications

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“…The STC eigenvectors are obtained by an eigendecomposition of the STC matrix C [10, 76], which is equivalent to solving an optimization problem: where U denotes a matrix whose columns are the orthonormal eigenvectors of C . In order to regularize these eigenvectors, we wish to add penalty terms to (10), which precludes a closed form solution to the problem.…”

Section: Methodsmentioning

confidence: 99%

Inferring hidden structure in multilayered neural circuits

et al. 2018

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A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we attempt to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit, using cascaded linear-nonlinear (LN-LN) models. We combine non-smooth regularization with proximal consensus algorithms to overcome difficulties in fitting such models that arise from the high dimensionality of their parameter space. We apply this framework to retinal ganglion cell processing, learning LN-LN models of retinal circuitry consisting of thousands of parameters, using 40 minutes of responses to white noise. Our models demonstrate a 53% improvement in predicting ganglion cell spikes over classical linear-nonlinear (LN) models. Internal nonlinear subunits of the model match properties of retinal bipolar cells in both receptive field structure and number. Subunits have consistently high thresholds, supressing all but a small fraction of inputs, leading to sparse activity patterns in which only one subunit drives ganglion cell spiking at any time. From the model’s parameters, we predict that the removal of visual redundancies through stimulus decorrelation across space, a central tenet of efficient coding theory, originates primarily from bipolar cell synapses. Furthermore, the composite nonlinear computation performed by retinal circuitry corresponds to a boolean OR function applied to bipolar cell feature detectors. Our methods are statistically and computationally efficient, enabling us to rapidly learn hierarchical non-linear models as well as efficiently compute widely used descriptive statistics such as the spike triggered average (STA) and covariance (STC) for high dimensional stimuli. This general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data.

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Section: Methodsmentioning

confidence: 99%

Inferring hidden structure in multilayered neural circuits

et al. 2018

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“…We emphasize that computing the naive spike-triggered average (STA) estimates gives a systematic change in filter shape with the stimulus skew, as shown in Fig. 3C, but this is simply an artifact of the STA estimation on non-spherically-symmetric stimuli [38], [45], [46], and is not indicative of any adaptation process.…”

Section: Resultsmentioning

confidence: 94%

“…Instead, we used maximally informative dimensions (MID) [37]. MID provides unbiased filter estimates that are consistent with the maximum likelihood inference [38]. Moreover, MID extracts the stimulus subspace that is informative about the spike without the need to assume the functional form of the nonlinearity, which is usually required for tractable maximum likelihood estimation of linear filters.…”

Section: Methodsmentioning

confidence: 99%

Adaptation to Changes in Higher-Order Stimulus Statistics in the Salamander Retina

et al. 2014

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Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.

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“…The STC eigenvectors are obtained by an eigendecomposition of the STC matrix C [10,74], which is equivalent to solving an optimization problem:…”

Section: Regularized Stc Analysismentioning

confidence: 99%

Inferring hidden structure in multilayered neural circuits

Maheswaranathan

Baccus

Ganguli

2017

Preprint

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A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we develop a computational framework to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit. We combine non-smooth regularization with proximal consensus algorithms to overcome difficulties in fitting such models that arise from the high dimensionality of their parameter space. Our methods are statistically and computationally efficient, enabling us to rapidly learn hierarchical non-linear models as well as efficiently compute widely used descriptive statistics such as the spike triggered average (STA) and covariance (STC) for high dimensional stimuli. For example, with our regularization framework, we can learn the STA and STC using 5 and 10 minutes of data, respectively, at a level of accuracy that otherwise requires 40 minutes of data without regularization. We apply our framework to retinal ganglion cell processing, learning cascaded linear-nonlinear (LN-LN) models of retinal circuitry, consisting of thousands of parameters, using 40 minutes of responses to white noise. Our models demonstrate a 53% improvement in predicting ganglion cell spikes over classical linear-nonlinear (LN) models. Internal nonlinear subunits of the model match properties of retinal bipolar cells in both receptive field structure and number. Subunits had consistently high thresholds, leading to sparse activity patterns in which only one subunit drives ganglion cell spiking at any time. From the model's parameters, we predict that the removal of visual redundancies through stimulus decorrelation across space, a central tenet of efficient coding theory, originates primarily from bipolar cell synapses. Furthermore, the composite nonlinear computation performed by retinal circuitry corresponds to a boolean OR function applied to bipolar cell feature detectors. Our general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data. Author SummaryComputation in neural circuits arises from the cascaded processing of inputs through multiple cell layers. Each of these cell layers performs operations such as filtering and thresholding in order to shape a circuit's output. It remains a challenge to describe both the computations and the mechanisms that mediate them given limited data recorded from a neural circuit. A standard approach to describing circuit computation involves building quantitative encoding models that predict the circuit response given its input, but these often fail to map in an interpretable way onto mechanisms within the circuit. In this work, we build two layer linear-nonlinear cascade models (LN-LN) in order to describe how the retinal output is shaped by nonlinear mechanisms in the inner retina. We find that these LN-LN models, fit to ganglion cell recordings alone, identify filters and nonlinearities that are readily mapp...

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Learning Quadratic Receptive Fields from Neural Responses to Natural Stimuli

Cited by 33 publications

References 84 publications

Inferring hidden structure in multilayered neural circuits

Inferring hidden structure in multilayered neural circuits

Adaptation to Changes in Higher-Order Stimulus Statistics in the Salamander Retina

Inferring hidden structure in multilayered neural circuits

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