The geometry of correlated variability leads to highly suboptimal discriminative sensory coding

The brain represents the world through the activity of neural populations; however, whether the computational goal of sensory coding is to support discrimination of sensory stimuli or to generate an internal model of the sensory world is unclear. Correlated variability across a neural population (noise correlations) is commonly observed experimentally, and many studies demonstrate that correlated variability improves discriminative sensory coding compared to a null model with no correlations. However, such results do not address whether correlated variability is optimal for discriminative sensory coding. If the computational goal of sensory coding is discriminative, than correlated variability should be optimized to support that goal. We assessed optimality of noise correlations for discriminative sensory coding in diverse datasets by developing two novel null models, each with a biological interpretation. Across datasets, we found that correlated variability in neural populations leads to highly suboptimal discriminative sensory coding according to both null models. Furthermore, biological constraints prevent many subsets of the neural populations from achieving optimality, and subselecting based on biological criteria leaves red discriminative coding performance suboptimal. Finally, we show that optimal subpopulations are exponentially small as the population size grows. Together, these results demonstrate that the geometry of correlated variability leads to highly suboptimal discriminative sensory coding.NEW & NOTEWORTHY The brain represents the world through the activity of neural populations that exhibit correlated variability. We assessed optimality of correlated variability for discriminative sensory coding in diverse datasets by developing two novel null models. Across datasets, correlated variability in neural populations leads to highly suboptimal discriminative sensory coding according to both null models. Biological constraints prevent the neural populations from achieving optimality. Together, these results demonstrate that the geometry of correlated variability leads to highly suboptimal discriminative sensory coding.

Efficient Decoding of Large-Scale Neural Population Responses With Gaussian-Process Multiclass Regression

Neural decoding methods provide a powerful tool for quantifying the information content of neural population codes and the limits imposed by correlations in neural activity. However, standard decoding methods are prone to overfitting and scale poorly to high-dimensional settings. Here, we introduce a novel decoding method to overcome these limitations. Our approach, the gaussian process multiclass decoder (GPMD), is well suited to decoding a continuous low-dimensional variable from high-dimensional population activity and provides a platform for assessing the importance of correlations in neural population codes. The GPMD is a multinomial logistic regression model with a gaussian process prior over the decoding weights. The prior includes hyperparameters that govern the smoothness of each neuron's decoding weights, allowing automatic pruning of uninformative neurons during inference. We provide a variational inference method for fitting the GPMD to data, which scales to hundreds or thousands of neurons and performs well even in data sets with more neurons than trials. We apply the GPMD to recordings from primary visual cortex in three species: monkey, ferret, and mouse. Our decoder achieves state-of-the-art accuracy on all three data sets and substantially outperforms independent Bayesian decoding, showing that knowledge of the correlation structure is essential for optimal decoding in all three species.

Transformations of sensory information in the brain suggest changing criteria for optimality

Neurons throughout the brain modulate their firing rate lawfully in response to sensory input. Theories of neural computation posit that these modulations reflect the outcome of a constrained optimization in which neurons aim to robustly and efficiently represent sensory information. Our understanding of how this optimization varies across different areas in the brain, however, is still in its infancy. Here, we show that neural sensory responses transform along the dorsal stream of the visual system in a manner consistent with a transition from optimizing for information preservation towards optimizing for perceptual discrimination. Focusing on the representation of binocular disparities-the slight differences in the retinal images of the two eyes-we re-analyze measurements characterizing neuronal tuning curves in brain areas V1, V2, and MT (middle temporal) in the macaque monkey. We compare these to measurements of the statistics of binocular disparity typically encountered during natural behaviors using a Fisher Information framework. The differences in tuning curve characteristics across areas are consistent with a shift in optimization goals: V1 and V2 population-level responses are more consistent with maximizing the information encoded about naturally occurring binocular disparities, while MT responses shift towards maximizing the ability to support disparity discrimination. We find that a change towards tuning curves preferring larger disparities is a key driver of this shift. These results provide new insight into previously-identified differences between disparity-selective areas of cortex and suggest these differences play an important role in supporting visually-guided behavior. Our findings emphasize the need to consider not just information preservation and neural resources, but also relevance to behavior, when assessing the optimality of neural codes.

Mutual information measure of visual perception based on noisy spiking neural networks

Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

Expansion and contraction of resource allocation in sensory bottlenecks

Topographic sensory representations often do not scale proportionally to the size of their input regions, with some expanded and others contracted. In vision, the foveal representation is magnified cortically, as are the fingertips in touch. What principles drive this allocation, and how should receptor density, for example, the high innervation of the fovea or the fingertips, and stimulus statistics, for example, the higher contact frequencies on the fingertips, contribute? Building on work in efficient coding, we address this problem using linear models that optimally decorrelate the sensory signals. We introduce a sensory bottleneck to impose constraints on resource allocation and derive the optimal neural allocation. We find that bottleneck width is a crucial factor in resource allocation, inducing either expansion or contraction. Both receptor density and stimulus statistics affect allocation and jointly determine convergence for wider bottlenecks. Furthermore, we show a close match between the predicted and empirical cortical allocations in a well-studied model system, the star-nosed mole. Overall, our results suggest that the strength of cortical magnification depends on resource limits.

Information thermodynamics of encoding and encoders

Non-isolated systems have diverse coupling relations with the external environment. These relations generate complex thermodynamics and information transmission between the system and its environment. The framework depicted in the current research attempts to glance at the critical role of the internal orders inside the non-isolated system in shaping the information thermodynamics coupling. We characterize the coupling as a generalized encoding process, where the system acts as an information thermodynamics encoder to encode the external information based on thermodynamics. We formalize the encoding process in the context of the nonequilibrium second law of thermodynamics, revealing an intrinsic difference in information thermodynamics characteristics between information thermodynamics encoders with and without internal correlations. During the information encoding process of an external source Y, specific sub-systems in an encoder X with internal correlations can exceed the information thermodynamics bound on ( X , Y ) and encode more information than system X works as a whole. We computationally verify this theoretical finding in an Ising model with a random external field and a neural data set of the human brain during visual perception and recognition. Our analysis demonstrates that the stronger internal correlation inside these systems implies a higher possibility for specific sub-systems to encode more information than the global one. These findings may suggest a new perspective in studying information thermodynamics in diverse physical and biological systems.

Neural tuning and representational geometry

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behaviour. The classic approach is to investigate how individual neurons encode stimuli and how their tuning determines the fidelity of the neural representation. Tuning analyses often use the Fisher information to characterize the sensitivity of neural responses to small changes of the stimulus. In recent decades, measurements of large populations of neurons have motivated a complementary approach, which focuses on the information available to linear decoders. The decodable information is captured by the geometry of the representational patterns in the multivariate response space. Here we review neural tuning and representational geometry with the goal of clarifying the relationship between them. The tuning induces the geometry, but different sets of tuned neurons can induce the same geometry. The geometry determines the Fisher information, the mutual information and the behavioural performance of an ideal observer in a range of psychophysical tasks. We argue that future studies can benefit from considering both tuning and geometry to understand neural codes and reveal the connections between stimuli, brain activity and behaviour.

Statistical Analysis of Decoding Performances of Diverse Populations of Neurons

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.

Efficient sensory coding of multidimensional stimuli

According to the efficient coding hypothesis, sensory systems are adapted to maximize their ability to encode information about the environment. Sensory neurons play a key role in encoding by selectively modulating their firing rate for a subset of all possible stimuli. This pattern of modulation is often summarized via a tuning curve. The optimally efficient distribution of tuning curves has been calculated in variety of ways for one-dimensional (1-D) stimuli. However, many sensory neurons encode multiple stimulus dimensions simultaneously. It remains unclear how applicable existing models of 1-D tuning curves are for neurons tuned across multiple dimensions. We describe a mathematical generalization that builds on prior work in 1-D to predict optimally efficient multidimensional tuning curves. Our results have implications for interpreting observed properties of neuronal populations. For example, our results suggest that not all tuning curve attributes (such as gain and bandwidth) are equally useful for evaluating the encoding efficiency of a population.

Our brains are tasked with processing a wide range of sensory inputs from the world around us. Natural sensory inputs are often complex and composed of multiple distinctive features (for example, an object may be characterized by its size, shape, color, and weight). Many neurons in the brain play a role in encoding multiple features, or dimensions, of sensory stimuli. Here, we employ the computational technique of population modeling to examine how groups of neurons in the brain can optimally encode multiple dimensions of sensory stimuli. This work provides predictions for theory-driven experiments that can leverage emerging high-throughput neural recording tools to characterize the properties of neuronal populations in response to complex natural stimuli.

Heterogeneous Synaptic Weighting Improves Neural Coding in the Presence of Common Noise

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 that shared variability has on 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 to 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.

Moth olfactory receptor neurons adjust their encoding efficiency to temporal statistics of pheromone fluctuations

The efficient coding hypothesis predicts that sensory neurons adjust their coding resources to optimally represent the stimulus statistics of their environment. To test this prediction in the moth olfactory system, we have developed a stimulation protocol that mimics the natural temporal structure within a turbulent pheromone plume. We report that responses of antennal olfactory receptor neurons to pheromone encounters follow the temporal fluctuations in such a way that the most frequent stimulus timescales are encoded with maximum accuracy. We also observe that the average coding precision of the neurons adjusted to the stimulus-timescale statistics at a given distance from the pheromone source is higher than if the same encoding model is applied at a shorter, non-matching, distance. Finally, the coding accuracy profile and the stimulus-timescale distribution are related in the manner predicted by the information theory for the many-to-one convergence scenario of the moth peripheral sensory system.

Coordinate invariance as a fundamental constraint on the form of stimulus-specific information measures

The value of Shannon's mutual information is commonly used to describe the total amount of information that the neural code transfers between the ensemble of stimuli and the ensemble of neural responses. In addition, it is often desirable to know which features of the stimulus or response are most informative. The literature offers several different decompositions of the mutual information into its stimulus or response-specific components, such as the specific surprise or the uncertainty reduction, but the number of mutually distinct measures is in fact infinite. We resolve this ambiguity by requiring the specific information measures to be invariant under invertible coordinate transformations of the stimulus and the response ensembles. We prove that the Kullback-Leibler divergence is then the only suitable measure of the specific information. On a more general level, we discuss the necessity and the fundamental aspects of the coordinate invariance as a selection principle. We believe that our results will encourage further research into invariant statistical methods for the analysis of neural coding.

Mutual Information and Information Gating in Synfire Chains

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains—SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Information-Theoretic Bounds and Approximations in Neural Population Coding

While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribution based on these approximation formulas is a convex optimization problem that allows efficient numerical solutions. Numerical simulation results confirmed that our asymptotic formulas were highly accurate for approximating mutual information for large neural populations. In special cases, the approximation formulas are exactly equal to the true mutual information. We also discuss techniques of variable transformation and dimensionality reduction to facilitate computation of the approximations.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

Representation of Multidimensional Stimuli: Quantifying the Most Informative Stimulus Dimension from Neural Responses

A common way to assess the function of sensory neurons is to measure the number of spikes produced by individual neurons while systematically varying a given dimension of the stimulus. Such measured tuning curves can then be used to quantify the accuracy of the neural representation of the stimulus dimension under study, which can in turn be related to behavioral performance. However, tuning curves often change shape when other dimensions of the stimulus are varied, reflecting the simultaneous sensitivity of neurons to multiple stimulus features. Here we illustrate how one-dimensional information analyses are misleading in this context, and propose a framework derived from Fisher information that allows the quantification of information carried by neurons in multidimensional stimulus spaces. We use this method to probe the representation of sound localization in auditory neurons of chinchillas and guinea pigs of both sexes, and show how heterogeneous tuning properties contribute to a representation of sound source position that is robust to changes in sound level.SIGNIFICANCE STATEMENT Sensory neurons' responses are typically modulated simultaneously by numerous stimulus properties, which can result in an overestimation of neural acuity with existing one-dimensional neural information transmission measures. To overcome this limitation, we develop new, compact expressions of Fisher information-derived measures that bound the robust encoding of separate stimulus dimensions in the context of multidimensional stimuli. We apply this method to the problem of the representation of sound source location in the face of changes in sound source level by neurons of the auditory midbrain.

Matched Behavioral and Neural Adaptations for Low Sound Level Echolocation in a Gleaning Bat, Antrozous pallidus

In active sensing, animals make motor adjustments to match sensory inputs to specialized neural circuitry. Here, we describe an active sensing system for sound level processing. The pallid bat uses downward frequency-modulated (FM) sweeps as echolocation calls for general orientation and obstacle avoidance. The bat's auditory cortex contains a region selective for these FM sweeps (FM sweep-selective region, FMSR). We show that the vast majority of FMSR neurons are sensitive and strongly selective for relatively low levels (30-60 dB SPL). Behavioral testing shows that when a flying bat approaches a target, it reduces output call levels to keep echo levels between ∼30 and 55 dB SPL. Thus, the pallid bat behaviorally matches echo levels to an optimized neural representation of sound levels. FMSR neurons are more selective for sound levels of FM sweeps than tones, suggesting that across-frequency integration enhances level tuning. Level-dependent timing of high-frequency sideband inhibition in the receptive field shapes increased level selectivity for FM sweeps. Together with previous studies, these data indicate that the same receptive field properties shape multiple filters (sweep direction, rate, and level) for FM sweeps, a sound common in multiple vocalizations, including human speech. The matched behavioral and neural adaptations for low-intensity echolocation in the pallid bat will facilitate foraging with reduced probability of acoustic detection by prey.

Efficient Neural Codes That Minimize Lp Reconstruction Error

The efficient coding hypothesis assumes that biological sensory systems use neural codes that are optimized to best possibly represent the stimuli that occur in their environment. Most common models use information-theoretic measures, whereas alternative formulations propose incorporating downstream decoding performance. Here we provide a systematic evaluation of different optimality criteria using a parametric formulation of the efficient coding problem based on the [Formula: see text] reconstruction error of the maximum likelihood decoder. This parametric family includes both the information maximization criterion and squared decoding error as special cases. We analytically derived the optimal tuning curve of a single neuron encoding a one-dimensional stimulus with an arbitrary input distribution. We show how the result can be generalized to a class of neural populations by introducing the concept of a meta-tuning curve. The predictions of our framework are tested against previously measured characteristics of some early visual systems found in biology. We find solutions that correspond to low values of [Formula: see text], suggesting that across different animal models, neural representations in the early visual pathways optimize similar criteria about natural stimuli that are relatively close to the information maximization criterion.

Coding accuracy on the psychophysical scale

Sensory neurons are often reported to adjust their coding accuracy to the stimulus statistics. The observed match is not always perfect and the maximal accuracy does not align with the most frequent stimuli. As an alternative to a physiological explanation we show that the match critically depends on the chosen stimulus measurement scale. More generally, we argue that if we measure the stimulus intensity on the scale which is proportional to the perception intensity, an improved adjustment in the coding accuracy is revealed. The unique feature of stimulus units based on the psychophysical scale is that the coding accuracy can be meaningfully compared for different stimuli intensities, unlike in the standard case of a metric scale.

Mutual Information, Fisher Information, and Efficient Coding

Fisher information is generally believed to represent a lower bound on mutual information (Brunel & Nadal, 1998), a result that is frequently used in the assessment of neural coding efficiency. However, we demonstrate that the relation between these two quantities is more nuanced than previously thought. For example, we find that in the small noise regime, Fisher information actually provides an upper bound on mutual information. Generally our results show that it is more appropriate to consider Fisher information as an approximation rather than a bound on mutual information. We analytically derive the correspondence between the two quantities and the conditions under which the approximation is good. Our results have implications for neural coding theories and the link between neural population coding and psychophysically measurable behavior. Specifically, they allow us to formulate the efficient coding problem of maximizing mutual information between a stimulus variable and the response of a neural population in terms of Fisher information. We derive a signature of efficient coding expressed as the correspondence between the population Fisher information and the distribution of the stimulus variable. The signature is more general than previously proposed solutions that rely on specific assumptions about the neural tuning characteristics. We demonstrate that it can explain measured tuning characteristics of cortical neural populations that do not agree with previous models of efficient coding.

Performance breakdown in optimal stimulus decoding

OBJECTIVE

One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest.

APPROACH

In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited.

MAIN RESULTS

We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision.

SIGNIFICANCE

We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.

Coding accuracy is not fully determined by the neuronal model

It is automatically assumed that the accuracy with which a stimulus can be decoded is entirely determined by the properties of the neuronal system. We challenge this perspective by showing that the identification of pure tone intensities in an auditory nerve fiber depends on both the stochastic response model and the arbitrarily chosen stimulus units. We expose an apparently paradoxical situation in which it is impossible to decide whether loud or quiet tones are encoded more precisely. Our conclusion reaches beyond the topic of auditory neuroscience, however, as we show that the choice of stimulus scale is an integral part of the neural coding problem and not just a matter of convenience.

The influence of population size, noise strength and behavioral task on best-encoded stimulus for neurons with unimodal or monotonic tuning curves

Tuning curves and receptive fields are widely used to describe the selectivity of sensory neurons, but the relationship between firing rates and information is not always intuitive. Neither high firing rates nor high tuning curve gradients necessarily mean that stimuli at that part of the tuning curve are well represented by a neuron. Recent research has shown that trial-to-trial variability (noise) and population size can strongly affect which stimuli are most precisely represented by a neuron in the context of a population code (the best-encoded stimulus), and that different measures of information can give conflicting indications. Specifically, the Fisher information is greatest where the tuning curve gradient is greatest, such as on the flanks of peaked tuning curves, but the stimulus-specific information (SSI) is greatest at the tuning curve peak for small populations with high trial-to-trial variability. Previous research in this area has focussed upon unimodal (peaked) tuning curves, and in this article we extend these analyses to monotonic tuning curves. In addition, we examine how stimulus spacing in forced choice tasks affects the best-encoded stimulus. Our results show that, regardless of the tuning curve, Fisher information correctly predicts the best-encoded stimulus for large populations and where the stimuli are closely spaced in forced choice tasks. In smaller populations with high variability, or in forced choice tasks with widely-spaced choices, the best-encoded stimulus falls at the peak of unimodal tuning curves, but is more variable for monotonic tuning curves. Task, population size and variability all need to be considered when assessing which stimuli a neuron represents, but the best-encoded stimulus can be estimated on a case-by case basis using commonly available computing facilities.

Decoding stimulus duration from neural responses in the auditory midbrain

Neurons with responses selective for the duration of an auditory stimulus are called duration-tuned neurons (DTNs). Temporal specificity in their spiking suggests that one function of DTNs is to encode stimulus duration; however, the efficacy of duration encoding by DTNs has yet to be investigated. Herein, we characterize the information content of individual cells and a population of DTNs from the mammalian inferior colliculus (IC) by measuring the stimulus-specific information (SSI) and estimated Fisher information (FI) of spike count responses. We found that SSI was typically greatest for those stimulus durations that evoked maximum spike counts, defined as best duration (BD) stimuli, and that FI was maximal for stimulus durations off BD where sensitivity to a change in duration was greatest. Using population data, we demonstrate that a maximum likelihood estimator (MLE) can accurately decode stimulus duration from evoked spike counts. We also simulated a two-alternative forced choice task by having MLE models decide whether two durations were the same or different. With this task we measured the just-noticeable difference threshold for stimulus duration and calculated the corresponding Weber fractions across the stimulus domain. Altogether, these results demonstrate that the spiking responses of DTNs from the mammalian IC contain sufficient information for the CNS to encode, decode, and discriminate behaviorally relevant auditory signal durations.

Detecting and quantifying topography in neural maps

Topographic maps are an often-encountered feature in the brains of many species, yet there are no standard, objective procedures for quantifying topography. Topographic maps are typically identified and described subjectively, but in cases where the scale of the map is close to the resolution limit of the measurement technique, identifying the presence of a topographic map can be a challenging subjective task. In such cases, an objective topography detection test would be advantageous. To address these issues, we assessed seven measures (Pearson distance correlation, Spearman distance correlation, Zrehen's measure, topographic product, topological correlation, path length and wiring length) by quantifying topography in three classes of cortical map model: linear, orientation-like, and clusters. We found that all but one of these measures were effective at detecting statistically significant topography even in weakly-ordered maps, based on simulated noisy measurements of neuronal selectivity and sparse sampling of the maps. We demonstrate the practical applicability of these measures by using them to examine the arrangement of spatial cue selectivity in pallid bat A1. This analysis shows that significantly topographic arrangements of interaural intensity difference and azimuth selectivity exist at the scale of individual binaural clusters.

The role of thalamic population synchrony in the emergence of cortical feature selectivity

In a wide range of studies, the emergence of orientation selectivity in primary visual cortex has been attributed to a complex interaction between feed-forward thalamic input and inhibitory mechanisms at the level of cortex. Although it is well known that layer 4 cortical neurons are highly sensitive to the timing of thalamic inputs, the role of the stimulus-driven timing of thalamic inputs in cortical orientation selectivity is not well understood. Here we show that the synchronization of thalamic firing contributes directly to the orientation tuned responses of primary visual cortex in a way that optimizes the stimulus information per cortical spike. From the recorded responses of geniculate X-cells in the anesthetized cat, we synthesized thalamic sub-populations that would likely serve as the synaptic input to a common layer 4 cortical neuron based on anatomical constraints. We used this synchronized input as the driving input to an integrate-and-fire model of cortical responses and demonstrated that the tuning properties match closely to those measured in primary visual cortex. By modulating the overall level of synchronization at the preferred orientation, we show that efficiency of information transmission in the cortex is maximized for levels of synchronization which match those reported in thalamic recordings in response to naturalistic stimuli, a property which is relatively invariant to the orientation tuning width. These findings indicate evidence for a more prominent role of the feed-forward thalamic input in cortical feature selectivity based on thalamic synchronization.

While the visual system is selective for a wide range of different inputs, orientation selectivity has been considered the preeminent property of the mammalian visual cortex. Existing models of this selectivity rely on varying relative importance of feedforward thalamic input and intracortical influence. Recently, we have shown that pairwise timing relationships between single thalamic neurons can be predictive of a high degree of orientation selectivity. Here we have constructed a computational model that predicts cortical orientation tuning from thalamic populations. We show that this arrangement, relying on precise timing differences between thalamic responses, accurately predicts tuning properties as well as demonstrates that certain timing relationships are optimal for transmitting information about the stimulus to cortex.

Adaptive stimulus optimization for sensory systems neuroscience

In this paper, we review several lines of recent work aimed at developing practical methods for adaptive on-line stimulus generation for sensory neurophysiology. We consider various experimental paradigms where on-line stimulus optimization is utilized, including the classical optimal stimulus paradigm where the goal of experiments is to identify a stimulus which maximizes neural responses, the iso-response paradigm which finds sets of stimuli giving rise to constant responses, and the system identification paradigm where the experimental goal is to estimate and possibly compare sensory processing models. We discuss various theoretical and practical aspects of adaptive firing rate optimization, including optimization with stimulus space constraints, firing rate adaptation, and possible network constraints on the optimal stimulus. We consider the problem of system identification, and show how accurate estimation of non-linear models can be highly dependent on the stimulus set used to probe the network. We suggest that optimizing stimuli for accurate model estimation may make it possible to successfully identify non-linear models which are otherwise intractable, and summarize several recent studies of this type. Finally, we present a two-stage stimulus design procedure which combines the dual goals of model estimation and model comparison and may be especially useful for system identification experiments where the appropriate model is unknown beforehand. We propose that fast, on-line stimulus optimization enabled by increasing computer power can make it practical to move sensory neuroscience away from a descriptive paradigm and toward a new paradigm of real-time model estimation and comparison.