Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

Williamson, Richard; Cowley, Benjamin R.; Litwin-Kumar, Ashok; Doiron, Brent; Kohn, Adam; Ma, Smith; Yu, Byron M.

doi:10.1371/journal.pcbi.1005141

Cited by 99 publications

(162 citation statements)

References 60 publications

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“…corresponding to the first five modes calculated using factor analysis (33,68). B) Changes in average covariance associated with contrast, adaptation and attention in V4 or task switching in V1 between each unit's raw (left) or residual (first eigenmode removed) responses and all other simultaneously recorded units.…”

Section: Figure 4 -Contrast Adaptation and Attention Affect Populatimentioning

confidence: 99%

“…We showed recently that measuring how trial-to-trial response variability is shared across a neuronal population and how that covariability depends on sensory or cognitive processes provides strong constraints on a model of visual cortex. We and others have shown that covariability of firing rates in visual cortex is typically low rank (2)(3)(4)(29)(30)(31)(32)(33)(34)(35). This means that shared variability is well-described as a low-dimensional process that affects neurons with different weights rather than higher order interactions between neurons or subpopulations.…”

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Low rank mechanisms underlying flexible visual representations

Ruff

Xue

Kramer

et al. 2019

Preprint

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Neuronal population responses to sensory stimuli are remarkably flexible. The responses of neurons in visual cortex depend on stimulus properties (e.g. contrast), processes that affect all stages of visual processing (e.g. adaptation), and cognitive processes (e.g attention or task switching). The effects of all of these processes on trial-averaged responses of individual neurons are well-described by divisive normalization, in which responses are scaled by the total stimulus drive. Normalization describes how a staggering variety of sensory, cognitive, and motor processes affect individual neurons (1), but whether different normalization processes could be mediated by the same mechanism remains poorly understood. We and others recently showed that attention has low rank effects on the covariability of populations of neurons in visual area V4 (2-4), which strongly constrains mechanistic models mechanism (2). We hypothesized that measuring changes in population covariability associated with other normalization processes could clarify whether they might share a mechanism. Our experimental design included measurements in multiple visual areas using four normalization processes. We found that contrast, adaptation, attention, and task switching affect the responses of populations of neurons in primate visual cortex in a similarly low rank way. These results suggest that a given circuit uses a common mechanism to perform many forms of normalization and likely reflect a general principle that applies to a wide range of brain areas and sensory, cognitive, or motor processes. IntroductionUnderstanding the biological basis of a neural computation can clarify the cognitive processes by which our brains convert information about the sensory world into action. Divisive normalization, in which the responses of individual neurons are divisively scaled by the mean drive to the population, is a simple computation that explains a wide variety of sensory, cognitive, and motor processes. In the visual system, normalization accounts for the modulation involving changes to the visual stimulus (e.g. stimulus contrast or surround suppression; (1,(5)(6)(7)(8)(9)(10)(11)(12), modulation originating from the earliest stages of visual processing in the retina (e.g. adaptation; (1,(13)(14)(15)(16), and modulation originating from cognitive processes internal to the nervous system (e.g. attention, task switching, learning, task difficulty, or multisensory integration (17-28).The existence of normalization in multiple species, brain areas, and functional processes led to the appealing hypothesis that these processes share a common underlying mechanism (1). However, the normalization equation is not a mechanistic model, and the divisive scaling of trialaveraged responses is consistent with many models.

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Section: Figure 4 -Contrast Adaptation and Attention Affect Populatimentioning

confidence: 99%

mentioning

confidence: 95%

Low rank mechanisms underlying flexible visual representations

Ruff

Xue

Kramer

et al. 2019

Preprint

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“…Even though information is highly distributed across neurons in a population, most variability is captured by a low-dimensional subspace, leading to suggestions that we might only need to consider the information encoded in this subspace (Williamson et al, 2016). As we have shown, this argument does not consider that information does not only depend on variability, but also on how the signal aligns with this variability (Fig.…”

Section: Discussionmentioning

confidence: 95%

“…Previous work has observed that most neural population activity fluctuations are constrained to a low-dimensional linear subspace that is embedded in the high-dimensional space of neural activity (Engel & Steinmetz, 2019;Semedo, Zandvakili, Machens, Yu, & Kohn, 2019;Williamson et al, 2016). This might suggest that focusing on such a low-dimensional subspace is sufficient to understand brain function (Williamson et al, 2016).…”

Section: Information Is Not Well-aligned With Principal Noise Dimensionsmentioning

confidence: 99%

Scaling of information in large neural populations reveals signatures of information-limiting correlations

Kafashan

Jaffe

Chettih

et al. 2020

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How is information distributed across large neuronal populations within a given brain area? One possibility is that information is distributed roughly evenly across neurons, so that total information scales linearly with the number of recorded neurons. Alternatively, the neural code might be highly redundant, meaning that total information saturates. Here we investigated how information about the direction of a moving visual stimulus is distributed across hundreds of simultaneously recorded neurons in mouse primary visual cortex (V1). We found that information scales sublinearly, due to the presence of correlated noise in these populations. Using recent theoretical advances, we compartmentalized noise correlations into informationlimiting and nonlimiting components, and then extrapolated to predict how information grows when neural populations are even larger. We predict that tens of thousands of neurons are required to encode 95% of the information about visual stimulus direction, a number much smaller than the number of neurons in V1. Overall, these findings suggest that the brain uses a widely distributed, but nonetheless redundant code that supports recovering most information from smaller subpopulations. Figure 1. Information scaling in large neural populations, and the impact of noise correlations on information.a. The information that a population of neurons can encode about some stimulus value is always a non-decreasing function of the population size. Information might on average increase with every added neuron (unbounded scaling; red) if the information is evenly distributed across all neurons. In contrast, information can rapidly saturate if information is redundant, and thus it is not strictly limited by population size, but by other factors. In general, it has only been possible to record from a very small subset of neurons of a particular area (grey shaded), from which it is hard to tell the difference between the two scenarios if the sampled population size is too small. b. The encoded information is modulated by noise correlations. This is illustrated using two neurons with different tunings to the stimulus value (top). The amount of information to discriminate between two stimulus values ( " /red and # /blue) depends on the difference in mean population activity (crosses) between stimuli, and the noise correlations (shaded ellipsoids) for either stimulus (bottom, showing joint neural activity of both neurons). The information is largest when the noise is smallest in the direction of the mean population activity difference (black arrow), which leads to the largest separation across the optimal discrimination boundary (grey line). In this example, positive correlations boost information (middle), whereas negative correlations lower it (right), when compared to uncorrelated neurons (left). In general, the impact of noise correlations depends on how they interact with the population's tuning curves.

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“…The dynamics of single neurons within a given brain circuit are not independent, but highly correlated. Moreover, neural activity is often dominated by only a very low number of distinct correlation patterns [Churchland et al, 2012, Mante et al, 2013, Kaufman et al, 2014, Cunningham and Yu, 2014, Gao and Ganguli, 2015, Williamson et al, 2016, Pang et al, 2016, Mazzucato et al, 2016, Michaels et al, 2016, Elsayed and Cunningham, 2017, Gallego et al, 2017, Williams et al, 2018, Rus, 2018, Semedo et al, 2019. This implies that there exists a low-dimensional manifold in the high-dimensional population activity space, which most of the variance of the neural activity is confined to.…”

Section: Introductionmentioning

confidence: 99%

Neural manifold under plasticity in a goal driven learning behaviour

Feulner

Clopath

2020

Preprint

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Neural activity is often low dimensional and dominated by only a few prominent neural covariation patterns. It has been hypothesised that these covariation patterns could form the building blocks used for fast and flexible motor control. Supporting this idea, recent experiments have shown that monkeys can learn to adapt their neural activity in motor cortex on a timescale of minutes, given that the change lies within the original low-dimensional subspace, also called neural manifold. However, the neural mechanism underlying this within-manifold adaptation remains unknown. Here, we show in a computational model that modification of recurrent weights, driven by a learned feedback signal, can account for the observed behavioural difference between within-and outside-manifold learning. Our findings give a new perspective, showing that recurrent weight changes do not necessarily lead to change in the neural manifold. On the contrary, successful learning is naturally constrained to a common subspace.

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Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

Cited by 99 publications

References 60 publications

Low rank mechanisms underlying flexible visual representations

Low rank mechanisms underlying flexible visual representations

Scaling of information in large neural populations reveals signatures of information-limiting correlations

Neural manifold under plasticity in a goal driven learning behaviour

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