Neural Quadratic Discriminant Analysis: Nonlinear Decoding with V1-Like Computation

Pagan, Marino; Simoncelli, Eero P.; Rust, Nicole C.

doi:10.1162/neco_a_00890

Cited by 23 publications

(26 citation statements)

References 55 publications

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“…One question of interest is the degree to which the target match versus distractor classification can be made with a linear decision boundary (or equivalently a linear decoder) applied to the IT neural data, as opposed to requiring a nonlinear decoding scheme. In a previous study, we assessed the format of IT target match information in the context of the classic DMS task design [ 11 , 19 ] and found that while a large component was linear, a considerable nonlinear (quadratic) component existed as well.…”

Section: Resultsmentioning

confidence: 99%

Inferotemporal cortex multiplexes behaviorally-relevant target match signals and visual representations in a manner that minimizes their interference

Roth

Rust

2018

PLoS ONE

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Finding a sought visual target object requires combining visual information about a scene with a remembered representation of the target to create a “target match” signal that indicates when a target is in view. Target match signals have been reported to exist within high-level visual brain areas including inferotemporal cortex (IT), where they are mixed with representations of image and object identity. However, these signals are not well understood, particularly in the context of the real-world challenge that the objects we search for typically appear at different positions, sizes, and within different background contexts. To investigate these signals, we recorded neural responses in IT as two rhesus monkeys performed a delayed-match-to-sample object search task in which target objects could appear at a variety of identity-preserving transformations. Consistent with the existence of behaviorally-relevant target match signals in IT, we found that IT contained a linearly separable target match representation that reflected behavioral confusions on trials in which the monkeys made errors. Additionally, target match signals were highly distributed across the IT population, and while a small fraction of units reflected target match signals as target match suppression, most units reflected target match signals as target match enhancement. Finally, we found that the potentially detrimental impact of target match signals on visual representations was mitigated by target match modulation that was approximately (albeit imperfectly) multiplicative. Together, these results support the existence of a robust, behaviorally-relevant target match representation in IT that is configured to minimally interfere with IT visual representations.

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Section: Resultsmentioning

confidence: 99%

Inferotemporal cortex multiplexes behaviorally-relevant target match signals and visual representations in a manner that minimizes their interference

Roth

Rust

2018

PLoS ONE

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“…We next consider the performance of the network after a quadratic nonlinearity g i (x) = x 2 for all neurons i [35]. In this case, both the Fisher information and mutual information are analytically intractable.…”

Section: Quadratic Nonlinearitymentioning

confidence: 99%

“…This simple architecture allowed us to analytically assess coding ability using both Fisher information [1,48,49,51], and Shannon mutual information. We evaluated the coding fidelity of both the linear representation and the nonlinear representation after a quadratic nonlinearity as a function of the distribution of synaptic weights that shape the shared variability within the representations [35]. We find that the linear stage representation's coding fidelity improves with diverse synaptic weighting, even if the Black curves denote mean responses to different stimuli.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous synaptic weighting improves neural coding in the presence of common noise

Sachdeva

Livezey

DeWeese

2019

Preprint

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Simultaneous recordings from the cortex have revealed that neural activity is highly variable, and that some variability is shared across neurons in a population. Further experimental work has demonstrated that the shared component of a neuronal population's variability is typically comparable to or larger than its private component. Meanwhile, an abundance of theoretical work has assessed the impact shared variability has upon a population code. For example, shared input noise is understood to have a detrimental impact on a neural population's coding fidelity. However, other contributions to variability, such as common noise, can also play a role in shaping correlated variability. We present a network of linear-nonlinear neurons in which we introduce a common noise input to model, for instance, variability resulting from upstream action potentials that are irrelevant for the task at hand. We show that by applying a heterogeneous set of synaptic weights to the neural inputs carrying the common noise, the network can improve its coding ability as measured by both Fisher information and Shannon mutual information, even in cases where this results in amplification of the common noise. With a broad and heterogeneous distribution of synaptic weights, a population of neurons can remove the harmful effects imposed by afferents that are uninformative about a stimulus. We demonstrate that some nonlinear networks benefit from weight diversification up to a certain population size, above which the drawbacks from amplified noise dominate over the benefits of diversification. We further characterize these benefits in terms of the relative strength of shared and private variability sources. Finally, we studied the asymptotic behavior of the mutual information and Fisher information analytically in our various networks as a function of population size. We find some surprising qualitative changes in the asymptotic behavior as we make seemingly minor changes in the synaptic weight distributions.

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“…can be described more compactly) than the stimuli themselves. These considerations have motivated perception and neuroscience researchers to develop methods for dimensionality reduction that characterize the statistical properties of proximal stimuli, that describe the responses of neurons to those stimuli, and that specify how those responses could be decoded [3,11,12,24,28,37,43,49,45,44,50,40,31,39]. However, many of these methods are task-independent; that is, they do not explicitly consider the sensory, perceptual, or behavioral tasks for which the encoded information will be used.…”

Section: Introductionmentioning

confidence: 99%

Linking Normative Models of Natural Tasks to Descriptive Models of Neural Response

Jaini

Burge

2017

Preprint

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Understanding how nervous systems exploit task relevant properties of sensory stimuli to perform natural tasks is fundamental to the study of perceptual systems. However, there are few formal methods for determining which stimulus properties are most useful for a given task. As a consequence, it is difficult to develop principled models for how to compute task-relevant latent variables from natural signals, and it is difficult to evaluate descriptive models fit to neural response. Accuracy Maxmization Analysis (AMA) is a recently developed Bayesian method for finding the optimal task-specific filters (receptive fields). Here, we introduce AMA-Gauss, a new faster form of AMA that incorporates the assumption that the class-conditional filter responses are Gaussian distributed. Next, we use AMA-Gauss to show that its assumptions are justified for two fundamental visual tasks: retinal speed estimation and binocular disparity estimation. Then, we show that AMAGauss has striking formal similarities to popular quadratic models of neural response: the energy model and the Generalized Quadratic Model (GQM). Together, these developments deepen our understanding of why the energy model of neural response have proven useful, improve our ability to evaluate results from subunit model fits to neural data, and should help accelerate psychophysics and neuroscience research with natural stimuli.

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Neural Quadratic Discriminant Analysis: Nonlinear Decoding with V1-Like Computation

Cited by 23 publications

References 55 publications

Inferotemporal cortex multiplexes behaviorally-relevant target match signals and visual representations in a manner that minimizes their interference

Inferotemporal cortex multiplexes behaviorally-relevant target match signals and visual representations in a manner that minimizes their interference

Heterogeneous synaptic weighting improves neural coding in the presence of common noise

Linking Normative Models of Natural Tasks to Descriptive Models of Neural Response

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