How Do Efficient Coding Strategies Depend on Origins of Noise in Neural Circuits?
Our sensory systems encode information about the external environment and transmit this information to higher brain areas with remarkable fidelity , despite a number of sources of noise that corrupt the incoming signal ., Noise—variability in neural responses that masks the relevant signal—can arise from the external inputs to the nervous system ( e . g . , in stochastic arrival of photons at the retina , which follow Poisson statistics ) and from properties intrinsic to the nervous system , such as variability in channel gating , vesicle release , and neurotransmitter diffusion ( reviewed in 1 ) ., This noise places fundamental limits on the accuracy with which information can be encoded by a cell or population 2–5 ., An equally important consideration , however , is that noise dictates which processing strategies adopted by the nervous system will be most effective in transmitting signal relative to noise ., Efficient coding theory has been an important principle in the study of neuroscience for over half a century , and a number of studies have found that neural circuits can encode and transmit as much useful information as possible given physical and physiological constraints 6–13 ., Foundational work by Laughlin successfully predicted the function by which an interneuron in the blowfly eye transformed its inputs 7 ., This and other early work prompted a myriad of studies that considered how neurons could make the most efficient use of their output range in a variety of systems and stimulus conditions 14–19 ., Efficient coding theory has played an important role in how we interpret biological systems ., However , one cannot know how efficiently a neuron or population is encoding its inputs without understanding the sources of noise present in the system ., Several previous studies have recognized noise as an important factor in determining optimal computations 8 , 11 , 12 , 20 , 21 ., These and related studies of efficient coding often make strong assumptions about the location of noise in the system in question , and these assumptions are typically not based on direct measurements of the underlying noise sources ., For example , noise is often assumed to arise at the output stage and follow Poisson statistics ., Yet experimental evidence has shown that spike generation itself is near-deterministic , implying that most noise observed in a neuron’s responses is inherited from earlier processing stages 22–24 ., Indeed , several different sources of noise may contribute to response variability , and the relative contributions of these noise sources can change under different environmental and stimulus conditions 25–27 ., Importantly , the results of efficient coding analyses depend on the assumptions made about the locations of noise in the system in question , but there has been to date no systematic study of the implications that different noise sources have for efficient coding strategies ., In particular , identifying failures of efficient coding theory—i . e . , neural computations that do not optimally transform inputs—necessitates a broad understanding of how different sources of noise alter efficient coding predictions ., Here , we consider how the optimal encoding strategies of neurons depend on the location of noise in a neural circuit ., We focus on the coding strategies of single neurons or pairs of neurons in feedforward circuits as simple cases with physiologically relevant applications ., Indeed , early sensory systems often encode stimuli in a small number of parallel channels , including in vision 28–30 , audition 31 , chemosensation 32 , thermosensation 33 , and somatosensation 34 ., We build a model that incorporates several different sources of noise , relaxing many of the assumptions of previously studied models , including the shape of the function by which a neuron transforms its inputs to outputs ., We determine the varied , and often competing , effects that different noise sources have on efficient coding strategies and how these strategies depend on the location , magnitude , and correlations of noise across neurons ., Much of the efficient coding literature is impacted by these results ., For example , Laughlin’s predictions assume that downstream noise is identical for all responses; when this is not true , a different processing strategy will be optimal ., Other recent work , considering such questions as when it is advantageous to have diverse encoding properties in a population and when sparse firing is beneficial , bears reinterpretation in light of these results 21 , 35 ., Our work demonstrates that understanding the sources of noise in a neural circuit is critical to interpreting circuit function ., The model is schematized in Fig 1 , and is detailed below ., We constructed this model with retinal circuitry in mind , though the model could be reinterpreted to represent other primarily feedforward early sensory systems , or even small segments of cortical circuitry ., We begin with a simple feature of neural circuits that captures a ubiquitous encoding transformation: a nonlinear conversion of inputs to outputs ., Nonlinear processing arises from several biological processes , such as dendritic integration , vesicle release at the synapse , and spike generation 36 , 37 ., Such nonlinearities appear in most neural coding models ( such as the commonly used linear-nonlinear-poisson ( LNP ) models or generalized linear models 38–40 ) ., Although there are likely several sites with some level of nonlinear processing in the retinal circuitry , there is a single dominant nonlinearity at most light levels which can be localized to the output synapse of the bipolar cells 41 ., Our goal is to determine the shape of the nonlinearity in this model that most faithfully encodes a distribution of inputs—i . e . , the optimal encoding strategy ., Indeed , in the retina , the shape of this nonlinearity has been shown to adapt under different stimulus conditions , suggesting that this adaptation might serve to improve encoding of visual stimuli as environmental conditions ( and hence noise ) change 18 , 42 ., The pathway receives an input signal or stimulus s , which is drawn from the standard normal distribution ., Generally , an individual value of s can represent any deviation from the mean stimulus value , and the full distribution of s represents the set of inputs that might be encountered over some time window in which the circuit is able to adapt ., In the context of the retinal circuitry , s can be understood as the contrast of a small region , or pixel , of the visual stimulus ., The contrast in this pixel might be positive or negative relative to the ambient illumination level ., The full distribution of s would then represent the distribution of contrasts encountered by this bipolar cell as the eye explores a particular scene ., ( We use Gaussian distributions here for simplicity in analytical computations , though similar results are obtained in simulations with skewed stimulus distributions , similar to the distributions of pixel contrast of natural scenes 43 . ), We assume the distribution of s is fixed in time ., If properties of the signal distribution varied randomly in time ( for example , if the variance of possible signals the circuit receives fluctuates between integration times ) , over long times the circuit would see an effectively broader distribution due to this extra variability ., Conversely , if the particular visual scene being viewed or other environmental conditions change suddenly , the input distribution as a whole ( for example , the range of contrasts , corresponding to the width of the input distribution ) also changes suddenly ., Therefore we expect the shape of the optimal nonlinearity to adapt to this new set of signal and noise distributions ., We do not model the adaptation process itself; our results for the optimal nonlinearity correspond to the end result of the adaptation process in this interpretation ., We incorporate three independent sources of noise , located before , during , and after the nonlinear processing stage ( Fig 1A and 1B ) ., The input stimulus is first corrupted by upstream noise η ., This noise source represents various forms of sensory noise that corrupt signals entering the circuit ., This might include noise in the incoming stimulus itself or noise in photoreceptors ., The strength of this noise source is governed by its variance , σ up 2 ., The signal plus noise ( Fig 1B , purple ) is then passed through a nonlinearity f ( ⋅ ) , which sets the mean of a scaled Poisson process with a quantal size κ ., The magnitude of κ determines the contribution of this noise source , with large values of κ corresponding to high noise ., This noise source captures quantal variations in response , such as synaptic vesicle release , which can be a significant source of noise at the bipolar cell to ganglion cell synapse 26 ., Finally , the scaled Poisson response is corrupted by downstream noise ζ ( with variance σ down 2 ) to obtain the output response ( Fig 1B , green ) ., This source of noise captures any variability introduced after the nonlinearity , such as noise in a postsynaptic target ., In the retina , this downstream noise captures noise intrinsic to a retinal ganglion cell , and the final output of the model is the current recorded in a ganglion cell ., If the sources of upstream and downstream noise are independent ( e . g . , photoreceptor noise and retinal ganglion cell channel noise , respectively ) , then the two kinds of noise will be uncorrelated in a feedforward circuit like we model here ., Lateral input from other channels , which we do not consider , could potentially introduce dependence between upstream and downstream noise ., Feedback connections operating on timescales within a single-integration window could also potentially introduce correlations between additive upstream and downstream noises ., However , while such connections could be important in cortical circuits , they are not significant in the sensory circuits that inspired this model , so we assume independent upstream and downstream noise in this work ., For further biological interpretation of the model , see Discussion ., We begin by studying a model of a single pathway ., We then consider how two pathways operating in parallel ought to divide the stimulus space to most efficiently code inputs ., These models are constructed of two parallel pathways of the single pathway motif ( Fig 1C ) , with the addition that noise may be correlated across both pathways ., The study of two parallel channels is motivated by the fact that a particular area of visual space is typically encoded by paired ON and OFF channels with otherwise similar functional properties , but similar parallel processing occurs throughout early sensory systems and in some cortical areas 29 , 31 , 32 ., We will return to further discussion of parallel pathways in the second half of the Results ., We begin with the case of a single pathway ., For simplicity , we start with cases in which one of the three noise sources dominates over the others ., Considering cases in which a single noise source dominates isolates the distinct effects of each noise source on the optimal nonlinearity ., We then show that these same effects govern how the three noise sources compete in setting the optimal nonlinearity when they are all of comparable magnitude ., Information in many sensory systems is encoded in parallel pathways ., In vision , for example , inputs are encoded by both ON cells and OFF cells ., In audition , an incoming stimulus is encoded in many parallel channels , each encoding a particular frequency band ., Allowing for multiple parallel channels raises fundamental questions about how these resources should be allocated: should multiple channels have the same or different response polarities ?, Should an input be encoded in multiple channels redundantly , or should different channels specialize in encoding a particular range of inputs ?, To understand these tradeoffs , we solved our model for the optimal nonlinearities for a pair of parallel pathways , the simplest case in which these questions can be investigated ., Indeed , in many cases , a small number of sensory neurons are responsible for carrying the relevant signal 46–49 ., Our circuit model for multiple pathways comprises parallel copies of the single pathway model ( Fig 1C ) , with the additional detail that both upstream and downstream noise may be correlated across pathways ., We show below that the sign and strength of these correlations can strongly affect optimal encoding strategies ., To focus on the effects of noise on optimal encoding strategies , we added complexity to the noise structure , while making significant simplifications in the stimulus structure ., In particular , we assume that both channels receive the same stimulus ., Correlated but non-identical stimuli in the two channels would likely affect optimal encoding strategies , but we did not explore this possibility and leave it as a direction for future inquiry ., We discuss the parallel pathway results in the following order: first , we discuss the possible pairs of nonlinearities , which are richer than the single-pathway case ., We then discuss the functional effects that each of the parameters , or in some cases combinations of parameters , has on the shapes of the nonlinearities , with a focus on which parameter regimes favor highly overlapping versus minimally overlapping encoding of inputs ( hereafter referred to as “overlapping” and “non-overlapping” ) ., Finally , we discuss factors that determine whether a circuit should encode inputs with channels of opposite polarity versus channels of the same polarity ., Noise in neural circuits arises from a variety of sources , both internal and external to the nervous system ( reviewed in 1 ) ., Noise is present in sensory inputs , such as fluctuations in photon arrival rate at the retina , which follow Poisson statistics , or variability in odorant molecule arrival at olfactory receptors due to random diffusion and the turbulent nature of odor plumes ., Noise also arises within the nervous system due to several biophysical processes , such as sensory transduction cascades , channel opening , synaptic vesicle release , and neurotransmitter diffusion ., Past work has focused on two complementary , but distinct aspects of neural coding:, 1 ) how noise limits coding fidelity , and, 2 ) how circuits should efficiently encode inputs in the presence of such noise ., Much of the work to date has focused on the first aspect , investigating how noise places fundamental limits on information transfer and coding fidelity for fixed neural coding strategies ( e . g . , tuning curves ) 2–5 ., Examples include studying how noise correlations lead to ambiguous separation of neural responses 2 and which correlation structures maximally inhibit coding performance 5 ., The second perspective dates back to the pioneering work of 6 and 7 ., These early works primarily considered how efficient codes are affected by constraints on neural responses , such as limited dynamic range ., Recent studies have built upon these foundational studies , investigating further questions such as how circuit architecture shapes optimal neural codes 20 , 21 , 35 , 56–58 ., However , this body of work has not systematically studied how efficient coding strategies depend on assumptions made about the nature of noise in a circuit ., Previous work has shown that the amount of noise in a circuit can qualitatively change optimal coding strategies 8 , 59 ., We also find that noise strength can be an important factor in determining efficient coding strategies ., A 5- to 10-fold decrease in the signal-to-noise ratio produces dramatic qualitative changes in the optimal nonlinearities ( Fig 2 ) , and those changes depend on noise location ., The SNR values used in our study correspond to a range of SNR values commonly observed in responses of neurons in early sensory systems 60 , 61 , suggesting that this result could be observed in biological circuits ., Our analysis goes beyond considerations of noise strength to reveal how efficient coding strategies change depending on where noise arises in a circuit , showing that different noise sources often having competing effects ., Other work in the context of decision making has similarly shown that the location of noise can impact the optimal architecture of a network , thus demonstrating that noise location in a circuit is important not only for signal transmission but also for computation 62 ., Knowledge of both noise strength and where noise arises is therefore crucial for determining whether a neural circuit is encoding efficiently or not ., Notably , even when the SNR of the circuit outputs is the same , the optimal nonlinearity can be very different depending on the location of the dominant noise source ., The locations of different noise sources have perhaps been most clearly elucidated in the retina ., Several studies have investigated noise within the photoreceptors , and in some cases have even implicated certain elements within the transduction cascade 61 , 63 , 64 ., Additional noise arises at the photoreceptor to bipolar cell synapse , where stochastic fluctuations in vesicle release obscure the signal 45 , 65–67 ., It has also been suggested that noise downstream of this synapse contributes a significant amount of the total noise observed in the ganglion cells , with some studies pointing to the bipolar cell to ganglion cell synapse specifically 26 , 67 ., Several pieces of evidence show that the relative contributions of different noise sources can change under different conditions as a circuit adapts ., For example , in starlight or similar conditions , external noise due to variability in photon arrival dominates noise in rod photoreceptors and the downstream retinal circuitry 61 , 68–70 ., As light levels increase , noise in the circuits reading out the photoreceptor signals—particularly at the synapse between cone bipolar cells and ganglion cells—can play a more prominent role 26 , 67 ., Moreover , even in cases where the magnitude of a given noise source remains unchanged , adaptation can engage different nonlinearities throughout the circuit , shifting the location of the dominant nonlinearity and thereby effectively changing the location of the noise sources relative to the circuit nonlinearity ., The fact that noise strength and nonlinearity location in neural circuits is subject to change under different conditions underscores the importance of understanding how these circuit features shape optimal encoding strategies ., In the retina , it has been observed that the nonlinearity at the cone bipolar to ganglion cell synapse can change dramatically depending on ambient illumination ., Under daylight viewing conditions , this synapse exhibits strong rectification ., Yet under dimmer viewing conditions , this synapse is nearly linear 42 ., The functional role of this change is unclear , though the fact that noise sources are known to change under different levels of illumination points to a possible answer ., If the dominant source of noise shifts from external sources to sources within downstream circuitry with increasing light level , as suggested by the evidence in 42 , our results indicate that the circuit indeed ought to operate more nonlinearly at higher light levels ., Furthermore , it is known that the strength of correlations not only varies between different types of retinal ganglion cells 71 , but these correlations may be stimulus dependent 72 , 73 ., Based on our results for paired nonlinearities , we predict that types of neurons that receive highly correlated input will have nonlinearities with small overlap , while cells that receive uncorrelated input will have highly overlapping nonlinearities ., Fully understanding this adaptation , and adaptations in other systems , will require further elucidation of the noise sources in the circuit ., Understanding how different aspects of circuit architecture shape efficient coding strategies has been a recent area of interest 20 , 21 , 35 , 56–58 ., However , a systematic study of the effects of noise was not the goal of these works , and so the properties of the noise in these studies has been limited , bound by specific assumptions on noise strength and location , and the allowed shapes of nonlinearities ., As a result , while there is some overlap in the conclusions of these studies , the differences in assumptions about the noise and nonlinearities also lead to some apparent disagreement ., Fortunately , we can investigate many similar questions within our model , and thereby complement the results of these previous studies and enrich our understanding of the role of circuit architecture and function ., We briefly discuss the connections that other published studies have to the work presented here , focusing on studies with questions that can be most directly investigated as special cases of our model ., Early work by Laughlin suggested a simple solution for how a single neuron can maximize the amount of information transmitted: a neuron should utilize all response levels with equal frequency , thereby maximizing the response entropy 7 ., Laughlin found that an interneuron in the compound eye of the blowfly transforms its inputs according to this principle ., More recent work investigated nonlinearities in salamander and macaque retinal ganglion cells , predicting that optimal nonlinearities should be steep with moderate thresholds 35 ., Experimental measurements of nonlinearities in ganglion cells were found to be near-optimal based on these predictions ., Although both of these studies ( along with many others ) predict that neurons are efficiently encoding their inputs , assumptions about noise are not well-constrained by experiment ., ( In one case , the model assumes very low noise of equal magnitude for all output levels , while in the other all noise is at the level of the nonlinearity output . ), As our work shows , one can arrive at different—even opposite—conclusions depending on where noise is assumed to enter the circuit ., Without experimentally determining the sources of noise in each circuit , it is impossible to determine whether that circuit is performing optimally ., Going beyond single neurons or pathways , several recent studies have investigated the benefits of using multiple channels to encode stimuli and assigning different roles to each of those channels depending on circuit inputs ., For example , Gjorgjieva and colleagues investigated when it is beneficial to encode inputs with multiple neurons of the same polarity versus encoding inputs with neurons of different polarity 56 ., They conclude that ON-ON and ON-OFF circuits generally produce the same amount of mutual information , with ON-OFF circuits doing so more efficiently per spike ., Our results provide a broader context in which we can interpret their findings , showing that when additive downstream noise ( which was not included in their model ) is anti-correlated , encoding with same polarity neurons can become a more favorable solution ., Another recent study investigated under what conditions it is beneficial for multiple neurons of the same polarity to have the same threshold and when it is beneficial to split thresholds 21 ., In particular , 21 find that nonlinearities split when the strength of upstream noise is weak ., Our results are consistent with this finding and again broaden our understanding of why this splitting occurs: by incorporating correlations , we show that it is not simply the amount of noise that determines splitting , but the combination of noise strength and noise correlations ., This identifies additional possibilities for testing these efficient coding predictions , by looking not just for cells that receive noisy input with similar magnitudes , but by looking for types of cells that receive correlated versus uncorrelated input and determining the degree of overlap of their nonlinearities ., We find that even in relatively simple circuit models , assumptions about the location and strength of multiple noise sources in neural circuits strongly impact conclusions about optimal encoding ., In particular , different relative strengths of noise upstream , downstream , or associated with nonlinear processing of signals yield different optimal coding strategies , even if the overall signal-to-noise ratio is the same ., Furthermore , correlations between noise sources across multiple channels alter the degree to which optimal channels encode overlapping portions of the signal distribution , as well as the overall polarity of the channels ., On the other hand , different combinations of noise sources can also yield very similar nonlinearities ., Consequently , measurements of noise at various locations in neural circuits are necessary to verify or refute ideas about efficient coding and to more broadly understand the strategies by which neurons mitigate the effects of unwanted variability in neural computations ., Our model is schematized in Fig 1 ., Biophysical interpretation is discussed in detail in the Results and Discussion ., We model the input to the circuit as a signal or stimulus s that comes from a distribution of possible inputs within a short integration time window , and hence is a random variable in our model ., Before this input can be encoded by the circuit , it is corrupted by noise η , which we also take to be a random variable ., The circuit then encodes total signal s + η by nonlinearly transforming it , f ( s + η ) ., This transformed signal sets the mean of a variable circuit response ., That is , the circuit does not respond deterministically , but stochastically ., We do not take this stochastic response to be spiking , due to the fact that spike generation has been shown to be repeatable , attributing variability in spiking to other sources 22–24 ., Instead , inspired by quantal neurotransmitter release , which results in post-synaptic potentials of integer multiples of a fixed minimum size , we model the stochastic response as a scaled Poisson distribution: responses come in integer multiples of a minimum non-zero response size κ , with an overall mean response f ( s + η ) , conditioned on the total input , s + η ., This stochastic response is then corrupted by downstream noise ζ , which we also take to be a random variable ., The total response r of a single-path circuit is thus, r = κ m + ζ , ( 2 ), where m is a Poisson-distributed random variable with mean κ − 1 f ( s + η ) , such that the mean of κm is f ( s + η ) ., Our circuit model thus has three sources of intrinsic variability: the additive noise sources ( η and ζ ) and the stochastic scaled-Poisson response ., We assume the statistics of the signal and noise are held fixed over a time window long enough that the circuit can adapt its nonlinearity to the full distribution of signal and noise ., That is , in a small integration time window Δt , the channel receives a draw from the signal and noise distributions to produce a response ., Thus , we model the signal s and noises η , ζ , and the scaled Poisson responses as random variables rather than stochastic processes ., In this work , we assume the distribution of possible inputs to be Gaussian with fixed variance σ s 2; without loss of generality we can take the mean to be zero ( i . e . , the signal represents variations relative to a mean background ) ., We assume the upstream and downstream noise to be Gaussian with mean 0 and variances σ up 2 and σ down 2 , respectively ., The assumption of Gaussian distributions for the input and noise is not a restriction of the model , but a choice we make to simplify our analyses and because we expect physiologically relevant noise sources to share many of the properties of a Gaussian distribution ., Even in cases where the input distribution is not Gaussian , pre-processing of inputs can remove heavy tails and lead to more Gaussian-like input distributions ., It has been shown that stimulus filtering in the retina indeed has this effect 74 ., An additional scenario to consider is the possibility that the signal properties , such as the variances , could themselves be random ., We might then wonder how this would impact the predicted nonlinearities ., As a “trial” of our model is a single draw from the stimulus and noise distributions , there is no well-defined variance on a single trial ., A changing variance on every trial would be equivalent to starting with a broader noise distribution of fixed variance ., We can thus interpret the stimulus distribution we use in the study to be the effective distribution after trial-by-trial variations in variance have already been taken into account ., The results for a signal of constant variance can thus be adapted , qualitatively , to the case of random trial-by-trial variance by increasing the stimulus variance in order to mimic the impact that trial-by-trial changes in variance have on the shape of the nonlinearity ., In order to understand how noise properties and location impact efficient coding strategies , we seek the nonlinearity that best encoded the input distribution for a variety of noise conditions ., We primarily consider the mean squared error ( MSE ) of a linear estimator of the stimulus , as outlined below , as our criterion of optimality ., This is not the only possible optimality criterion , so to check the effects that other criteria might have , we also consider maximizing the mutual information ( MI ) between stimulus and response ., MI provides a measure of coding fidelity that is free from assumptions about how information is read out from responses ., However , MI is difficult to evaluate analytically for all but the simplest models ., Indeed , for our model , deriving exact analytic equations for the optimal nonlinearities using MI is intractable ., We turn to simulations in this case ., We determine the nonlinearities obtained by minimizing the MSE using two complementary methods ., First , we take variational derivatives of the MSE with respect to the nonlinearities themselves to derive a set of exact equations for the optimal nonlinearities , free from any assumptions about their shape or functional form , as described below ., The only constraints we apply are that the nonlinearity must be non-negative and saturate at a value of 1 ., ( The choice of saturation level is arbitrary and does not affect the results . ), Applying such constraints are non-trivial—in most variational problems constraints enforce an equality , but in our method we are enforcing an inequality , discussed in the next section ., Using this analytic approach , we minimize the assumptions we make about the nonlinearities and obtain insights into the behavior of the model that are otherwise inaccessible ., Second , we parametrize the nonlinearities as sigmoidal or piecewise linear curves with two parameters that control the slope and offset ., We simulate the model , sweeping over the slope and offset parameters ( Fig 8A ) until we find the parameter set that minimizes the MSE of the linear readout ., This parametric approach makes strong assumptions about the form of the nonlinearity but also has distinct advantages ., Simulations allow us to test to what extent our conclusions about the shape ( i . e . , slope and offset ) of the optimal nonlinearity depend on its specific functional form ., For example , we find from our analytical calculations that optimal nonlinearities are roughly piecewise linear ( Fig 8C ) , but one might expect biophysical constraints to restrict neurons to having smooth nonlinearities ., For this reason , we also test sigmoidal shaped nonlinearities , a smooth approximation of the piecewise linear solutions that emerge from the nonparametric analytical approach , and use simulations to find the optimal parameters ., We find the results with sigmoidal nonlinearities qualitatively very similar to the analytical solution ( Fig 8C ) .,
Neural circuits reliably encode and transmit signals despite the presence of noise at multiple stages of processing ., The efficient coding hypothesis , a guiding principle in computational neuroscience , suggests that a neuron or population of neurons allocates its limited range of responses as efficiently as possible to best encode inputs while mitigating the effects of noise ., Previous work on this question relies on specific assumptions about where noise enters a circuit , limiting the generality of the resulting conclusions ., Here we systematically investigate how noise introduced at different stages of neural processing impacts optimal coding strategies ., Using simulations and a flexible analytical approach , we show how these strategies depend on the strength of each noise source , revealing under what conditions the different noise sources have competing or complementary effects ., We draw two primary conclusions: ( 1 ) differences in encoding strategies between sensory systems—or even adaptational changes in encoding properties within a given system—may be produced by changes in the structure or location of neural noise , and ( 2 ) characterization of both circuit nonlinearities as well as noise are necessary to evaluate whether a circuit is performing efficiently .
For decades the efficient coding hypothesis has been a guiding principle in determining how neural systems can most efficiently represent their inputs ., However , conclusions about whether neural circuits are performing optimally depend on assumptions about the noise sources encountered by neural signals as they are transmitted ., Here , we provide a coherent picture of how optimal encoding strategies depend on noise strength , type , location , and correlations ., Our results reveal that nonlinearities that are efficient if noise enters the circuit in one location may be inefficient if noise actually enters in a different location ., This offers new explanations for why different sensory circuits , or even a given circuit under different environmental conditions , might have different encoding properties .
medicine and health sciences, statistical noise, engineering and technology, nervous system, signal processing, ocular anatomy, electrophysiology, neuroscience, mathematics, statistics (mathematics), computational neuroscience, coding mechanisms, gaussian noise, computer and information sciences, animal cells, neural pathways, source coding, cellular neuroscience, retina, neuroanatomy, anatomy, cell biology, synapses, signal to noise ratio, neurons, physiology, information theory, biology and life sciences, cellular types, physical sciences, computational biology, ocular system, neurophysiology