Optimal Neuronal Tuning for Finite Stimulus Spaces

Stability of cross-sensory input to primary somatosensory cortex across experience

Merging information from across sensory modalities is key to forming robust, disambiguated percepts of the world, yet how the brain achieves this feat remains unclear. Recent observations of cross-modal influences in primary sensory cortical areas have suggested that multisensory integration may occur in the earliest stages of cortical processing, but the role of these responses is still poorly understood. We address these questions by testing several hypotheses about the possible functions served by auditory influences on the barrel field of mouse primary somatosensory cortex (S1) using in vivo 2-photon calcium imaging. We observed sound-evoked spiking activity in a small fraction of cells overall, and moreover that this sparse activity was insufficient to encode auditory stimulus identity; few cells responded preferentially to one sound or another, and a linear classifier trained to decode auditory stimuli from population activity performed barely above chance. Moreover S1 did not encode information about specific audio-tactile feature conjunctions that we tested. Our ability to decode auditory audio-tactile stimuli from neural activity remained unchanged after both passive experience and reinforcement. Collectively, these results suggest that while a primary sensory cortex is highly plastic with regard to its own modality, the influence of other modalities are remarkably stable and play a largely stimulus-non-specific role.

Plasticity of Response Properties of Mouse Visual Cortex Neurons Induced by Optogenetic Tetanization In Vivo

Heterosynaptic plasticity, along with Hebbian homosynaptic plasticity, is an important mechanism ensuring the stable operation of learning neuronal networks. However, whether heterosynaptic plasticity occurs in the whole brain in vivo, and what role(s) in brain function in vivo it could play, remains unclear. Here, we used an optogenetics approach to apply a model of intracellular tetanization, which was established and employed to study heterosynaptic plasticity in brain slices, to study the plasticity of response properties of neurons in the mouse visual cortex in vivo. We show that optogenetically evoked high-frequency bursts of action potentials (optogenetic tetanization) in the principal neurons of the visual cortex induce long-term changes in the responses to visual stimuli. Optogenetic tetanization had distinct effects on responses to different stimuli, as follows: responses to optimal and orthogonal orientations decreased, responses to null direction did not change, and responses to oblique orientations increased. As a result, direction selectivity of the neurons decreased and orientation tuning became broader. Since optogenetic tetanization was a postsynaptic protocol, applied in the absence of sensory stimulation, and, thus, without association of presynaptic activity with bursts of action potentials, the observed changes were mediated by mechanisms of heterosynaptic plasticity. We conclude that heterosynaptic plasticity can be induced in vivo and propose that it may play important homeostatic roles in operation of neural networks by helping to prevent runaway dynamics of responses to visual stimuli and to keep the tuning of neuronal responses within the range optimized for the encoding of multiple features in population activity.

State transitions in the statistically stable place cell population correspond to rate of perceptual change

The hippocampus occupies a central role in mammalian navigation and memory. Yet an understanding of the rules that govern the statistics and granularity of the spatial code, as well as its interactions with perceptual stimuli, is lacking. We analyzed CA1 place cell activity recorded while rats foraged in different large-scale environments. We found that place cell activity was subject to an unexpected but precise homeostasis—the distribution of activity in the population as a whole being constant at all locations within and between environments. Using a virtual reconstruction of the largest environment, we showed that the rate of transition through this statistically stable population matches the rate of change in the animals’ visual scene. Thus, place fields near boundaries were small but numerous, while in the environment’s interior, they were larger but more dispersed. These results indicate that hippocampal spatial activity is governed by a small number of simple laws and, in particular, suggest the presence of an information-theoretic bound imposed by perception on the fidelity of the spatial memory system.

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Neural activity in rodent CA1 place cell populations is homeostatically balanced

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Hippocampal place field size and frequency are governed by proximity to boundaries

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Transition rate through place cell population matches rate of change in visual scene

Nonlinear mixed selectivity supports reliable neural computation

Neuronal activity in the brain is variable, yet both perception and behavior are generally reliable. How does the brain achieve this? Here, we show that the conjunctive coding of multiple stimulus features, commonly known as nonlinear mixed selectivity, may be used by the brain to support reliable information transmission using unreliable neurons. Nonlinearly mixed feature representations have been observed throughout primary sensory, decision-making, and motor brain areas. In these areas, different features are almost always nonlinearly mixed to some degree, rather than represented separately or with only additive (linear) mixing, which we refer to as pure selectivity. Mixed selectivity has been previously shown to support flexible linear decoding for complex behavioral tasks. Here, we show that it has another important benefit: in many cases, it makes orders of magnitude fewer decoding errors than pure selectivity even when both forms of selectivity use the same number of spikes. This benefit holds for sensory, motor, and more abstract, cognitive representations. Further, we show experimental evidence that mixed selectivity exists in the brain even when it does not enable behaviorally useful linear decoding. This suggests that nonlinear mixed selectivity may be a general coding scheme exploited by the brain for reliable and efficient neural computation.

Neurons in the brain are unreliable, while both perception and behavior are generally reliable. In this work, we study how the neural population response to sensory, motor, and cognitive features can produce this reliability. Across the brain, single neurons have been shown to respond to particular conjunctions of multiple features, termed nonlinear mixed selectivity. In this work, we show that populations of these mixed selective neurons lead to many fewer decoding errors than populations without mixed selectivity, even when both neural codes are given the same number of spikes. We show that the reliability benefits from mixed selectivity are quite general, holding under different assumptions about metabolic costs and neural noise as well as for both categorical and sensory errors. Further, previous theoretical work has shown that mixed selectivity enables the learning of complex behaviors with simple decoders. Through the analysis of neural data, we show that the brain implements mixed selectivity even when it would not serve this purpose. Thus, we argue that the brain also implements mixed selectivity to exploit its general benefits for reliable and efficient neural computation.

Adaptive Tuning Curve Widths Improve Sample Efficient Learning

Natural brains perform miraculously well in learning new tasks from a small number of samples, whereas sample efficient learning is still a major open problem in the field of machine learning. Here, we raise the question, how the neural coding scheme affects sample efficiency, and make first progress on this question by proposing and analyzing a learning algorithm that uses a simple reinforce-type plasticity mechanism and does not require any gradients to learn low dimensional mappings. It harnesses three bio-plausible mechanisms, namely, population codes with bell shaped tuning curves, continous attractor mechanisms and probabilistic synapses, to achieve sample efficient learning. We show both theoretically and by simulations that population codes with broadly tuned neurons lead to high sample efficiency, whereas codes with sharply tuned neurons account for high final precision. Moreover, a dynamic adaptation of the tuning width during learning gives rise to both, high sample efficiency and high final precision. We prove a sample efficiency guarantee for our algorithm that lies within a logarithmic factor from the information theoretical optimum. Our simulations show that for low dimensional mappings, our learning algorithm achieves comparable sample efficiency to multi-layer perceptrons trained by gradient descent, although it does not use any gradients. Furthermore, it achieves competitive sample efficiency in low dimensional reinforcement learning tasks. From a machine learning perspective, these findings may inspire novel approaches to improve sample efficiency. From a neuroscience perspective, these findings suggest sample efficiency as a yet unstudied functional role of adaptive tuning curve width.

How are response properties in the middle temporal area related to inference on visual motion patterns?

Neurons in the primate middle temporal area (MT) respond to moving stimuli, with strong tuning for motion speed and direction. These responses have been characterized in detail, but the functional significance of these details (e.g. shapes and widths of speed tuning curves) is unclear, because they cannot be selectively manipulated. To estimate their functional significance, we used a detailed model of MT population responses as input to convolutional networks that performed sophisticated motion processing tasks (visual odometry and gesture recognition). We manipulated the distributions of speed and direction tuning widths, and studied the effects on task performance. We also studied performance with random linear mixtures of the responses, and with responses that had the same representational dissimilarity as the model populations, but were otherwise randomized. The width of speed and direction tuning both affected task performance, despite the networks having been optimized individually for each tuning variation, but the specific effects were different in each task. Random linear mixing improved performance of the odometry task, but not the gesture recognition task. Randomizing the responses while maintaining representational dissimilarity resulted in poor odometry performance. In summary, despite full optimization of the deep networks in each case, each manipulation of the representation affected performance of sophisticated visual tasks. Representation properties such as tuning width and representational similarity have been studied extensively from other perspectives, but this work provides new insight into their possible roles in sophisticated visual inference.

Optimal dynamic coding by mixed-dimensionality neurons in the head-direction system of bats

Ethologically relevant stimuli are often multidimensional. In many brain systems, neurons with “pure” tuning to one stimulus dimension are found along with “conjunctive” neurons that encode several dimensions, forming an apparently redundant representation. Here we show using theoretical analysis that a mixed-dimensionality code can efficiently represent a stimulus in different behavioral regimes: encoding by conjunctive cells is more robust when the stimulus changes quickly, whereas on long timescales pure cells represent the stimulus more efficiently with fewer neurons. We tested our predictions experimentally in the bat head-direction system and found that many head-direction cells switched their tuning dynamically from pure to conjunctive representation as a function of angular velocity—confirming our theoretical prediction. More broadly, our results suggest that optimal dimensionality depends on population size and on the time available for decoding—which might explain why mixed-dimensionality representations are common in sensory, motor, and higher cognitive systems across species.

Multidimensional stimuli are often represented by neurons encoding only a single dimension and those encoding multiple dimensions. Here, the authors present theoretical and experimental analyses to show that mixed representations are optimal to efficiently encode such stimuli under different behavioral modes.

Serotonin Selectively Increases Detectability of Motion Stimuli in the Electrosensory System

Serotonergic innervation of sensory areas is found ubiquitously across the central nervous system of vertebrates. Here, we used a system's level approach to investigate the role of serotonin on processing motion stimuli in the electrosensory system of the weakly electric fish Apteronotus albifrons. We found that exogenous serotonin application increased the firing activity of pyramidal neural responses to both looming and receding motion. Separating spikes belonging to bursts from those that were isolated revealed that this effect was primarily due to increased burst firing. Moreover, when investigating whether firing activity during stimulation could be discriminated from baseline (i.e., in the absence of stimulation), we found that serotonin increased stimulus discriminability only for some stimuli. This is because increased burst firing was most prominent for these. Further, the effects of serotonin were highly heterogeneous, with some neurons displaying large while others instead displaying minimal changes in responsiveness following serotonin application. Further analysis revealed that serotonin application had the greatest effect on neurons with low baseline firing rates and little to no effect on neurons with high baseline firing rates. Finally, the effects of serotonin on sensory neuron responses were largely independent of object velocity. Our results therefore reveal a novel function for the serotonergic system in selectively enhancing discriminability for motion stimuli.

An Energy Model of Place Cell Network in Three Dimensional Space

Place cells are important elements in the spatial representation system of the brain. A considerable amount of experimental data and classical models are achieved in this area. However, an important question has not been addressed, which is how the three dimensional space is represented by the place cells. This question is preliminarily surveyed by energy coding method in this research. Energy coding method argues that neural information can be expressed by neural energy and it is convenient to model and compute for neural systems due to the global and linearly addable properties of neural energy. Nevertheless, the models of functional neural networks based on energy coding method have not been established. In this work, we construct a place cell network model to represent three dimensional space on an energy level. Then we define the place field and place field center and test the locating performance in three dimensional space. The results imply that the model successfully simulates the basic properties of place cells. The individual place cell obtains unique spatial selectivity. The place fields in three dimensional space vary in size and energy consumption. Furthermore, the locating error is limited to a certain level and the simulated place field agrees to the experimental results. In conclusion, this is an effective model to represent three dimensional space by energy method. The research verifies the energy efficiency principle of the brain during the neural coding for three dimensional spatial information. It is the first step to complete the three dimensional spatial representing system of the brain, and helps us further understand how the energy efficiency principle directs the locating, navigating, and path planning function of the brain.

Physiological evidence of sensory integration in the electrosensory lateral line lobe of Gnathonemus petersii

Mormyrid fish rely on reafferent input for active electrolocation. Their electrosensory input consists of phase and amplitude information. These are encoded by differently tuned receptor cells within the Mormyromasts, A- and B-cells, respectively, which are distributed over the animal’s body. These convey their information to two topographically ordered medullary zones in the electrosensory lateral line lobe (ELL). The so-called medial zone receives only amplitude information, while the dorsolateral zone receives amplitude and phase information. Using both sources of information, Mormyrid fish can disambiguate electrical impedances. Where and how this disambiguation takes place is presently unclear. We here investigate phase-sensitivity downstream from the electroreceptors. We provide first evidence of phase-sensitivity in the medial zone of ELL. In this zone I-cells consistently decreased their rate to positive phase-shifts (6 of 20 cells) and increased their rate to negative shifts (11/20), while E-cells of the medial zone (3/9) responded oppositely to I-cells. In the dorsolateral zone the responses of E- and I-cells were opposite to those found in the medial zone. Tracer injections revealed interzonal projections that interconnect the dorsolateral and medial zones in a somatotopic manner. In summary, we show that phase information is processed differently in the dorsolateral and the medial zones. This is the first evidence for a mechanism that enhances the contrast between two parallel sensory channels in Mormyrid fish. This could be beneficial for impedance discrimination that ultimately must rely on a subtractive merging of these two sensory streams.

3-D Maps and Compasses in the Brain

The world has a complex, three-dimensional (3-D) spatial structure, but until recently the neural representation of space was studied primarily in planar horizontal environments. Here we review the emerging literature on allocentric spatial representations in 3-D and discuss the relations between 3-D spatial perception and the underlying neural codes. We suggest that the statistics of movements through space determine the topology and the dimensionality of the neural representation, across species and different behavioral modes. We argue that hippocampal place-cell maps are metric in all three dimensions, and might be composed of 2-D and 3-D fragments that are stitched together into a global 3-D metric representation via the 3-D head-direction cells. Finally, we propose that the hippocampal formation might implement a neural analogue of a Kalman filter, a standard engineering algorithm used for 3-D navigation.

Rate, not selectivity, determines neuronal population coding accuracy in auditory cortex

The notion that neurons with higher selectivity carry more information about external sensory inputs is widely accepted in neuroscience. High-selectivity neurons respond to a narrow range of sensory inputs, and thus would be considered highly informative by rejecting a large proportion of possible inputs. In auditory cortex, neuronal responses are less selective immediately after the onset of a sound and then become highly selective in the following sustained response epoch. These 2 temporal response epochs have thus been interpreted to encode first the presence and then the content of a sound input. Contrary to predictions from that prevailing theory, however, we found that the neural population conveys similar information about sound input across the 2 epochs in spite of the neuronal selectivity differences. The amount of information encoded turns out to be almost completely dependent upon the total number of population spikes in the read-out window for this system. Moreover, inhomogeneous Poisson spiking behavior is sufficient to account for this property. These results imply a novel principle of sensory encoding that is potentially shared widely among multiple sensory systems.

Sensor Array Design for Complex Sensing Tasks

Chemical detection in complex environments presents numerous challenges for successful implementation. Arrays of sensors are often implemented for complex chemical sensing tasks, but systematic understanding of how individual sensor response characteristics contribute overall detection system performance remains elusive, with generalized strategies for design and optimization of these arrays rarely reported and even less commonly adopted by practitioners. This review focuses on the literature of nonspecific sensor array design and optimization strategies as well as related work that may inform future efforts in complex sensing with arrays.

Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

Lattices abound in nature-from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution, and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in three dimensions, a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.

Efficient sensory encoding and Bayesian inference with heterogeneous neural populations

The efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment. We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons, each characterized by a tuning curve. We parameterize the population with two continuous functions that control the density and amplitude of the tuning curves, assuming that the tuning widths vary inversely with the cell density. This parameterization allows us to solve, in closed form, for the information-maximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables. For the optimal population, the cell density is proportional to the prior, such that more cells with narrower tuning are allocated to encode higher-probability stimuli and that each cell transmits an equal portion of the stimulus probability mass. We also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. We examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder, the Bayesian population vector, that closely approximates a Bayesian least-squares estimator that has explicit access to the prior. Finally, we generalize these results to sigmoidal tuning curves, correlated neural variability, and a broader class of objective functions. These results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental, physiological, and perceptual data.

A spiking neural network model of self-organized pattern recognition in the early mammalian olfactory system

Olfactory sensory information passes through several processing stages before an odor percept emerges. The question how the olfactory system learns to create odor representations linking those different levels and how it learns to connect and discriminate between them is largely unresolved. We present a large-scale network model with single and multi-compartmental Hodgkin-Huxley type model neurons representing olfactory receptor neurons (ORNs) in the epithelium, periglomerular cells, mitral/tufted cells and granule cells in the olfactory bulb (OB), and three types of cortical cells in the piriform cortex (PC). Odor patterns are calculated based on affinities between ORNs and odor stimuli derived from physico-chemical descriptors of behaviorally relevant real-world odorants. The properties of ORNs were tuned to show saturated response curves with increasing concentration as seen in experiments. On the level of the OB we explored the possibility of using a fuzzy concentration interval code, which was implemented through dendro-dendritic inhibition leading to winner-take-all like dynamics between mitral/tufted cells belonging to the same glomerulus. The connectivity from mitral/tufted cells to PC neurons was self-organized from a mutual information measure and by using a competitive Hebbian-Bayesian learning algorithm based on the response patterns of mitral/tufted cells to different odors yielding a distributed feed-forward projection to the PC. The PC was implemented as a modular attractor network with a recurrent connectivity that was likewise organized through Hebbian-Bayesian learning. We demonstrate the functionality of the model in a one-sniff-learning and recognition task on a set of 50 odorants. Furthermore, we study its robustness against noise on the receptor level and its ability to perform concentration invariant odor recognition. Moreover, we investigate the pattern completion capabilities of the system and rivalry dynamics for odor mixtures.

Multiscale codes in the nervous system: the problem of noise correlations and the ambiguity of periodic scales

Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number N of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as 0.8. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with N is unaffected.

Sensory flow shaped by active sensing: sensorimotor strategies in electric fish

Goal-directed behavior in most cases is composed of a sequential order of elementary motor patterns shaped by sensorimotor contingencies. The sensory information acquired thus is structured in both space and time. Here we review the role of motion during the generation of sensory flow focusing on how animals actively shape information by behavioral strategies. We use the well-studied examples of vision in insects and echolocation in bats to describe commonalities of sensory-related behavioral strategies across sensory systems, and evaluate what is currently known about comparable active sensing strategies in electroreception of electric fish. In this sensory system the sensors are dispersed across the animal's body and the carrier source emitting energy used for sensing, the electric organ, is moved while the animal moves. Thus ego-motions strongly influence sensory dynamics. We present, for the first time, data of electric flow during natural probing behavior in Gnathonemus petersii (Mormyridae), which provide evidence for this influence. These data reveal a complex interdependency between the physical input to the receptors and the animal's movements, posture and objects in its environment. Although research on spatiotemporal dynamics in electrolocation is still in its infancy, the emerging field of dynamical sensory systems analysis in electric fish is a promising approach to the study of the link between movement and acquisition of sensory information.

Representation of three-dimensional space in the hippocampus of flying bats

Many animals, on air, water, or land, navigate in three-dimensional (3D) environments, yet it remains unclear how brain circuits encode the animal's 3D position. We recorded single neurons in freely flying bats, using a wireless neural-telemetry system, and studied how hippocampal place cells encode 3D volumetric space during flight. Individual place cells were active in confined 3D volumes, and in >90% of the neurons, all three axes were encoded with similar resolution. The 3D place fields from different neurons spanned different locations and collectively represented uniformly the available space in the room. Theta rhythmicity was absent in the firing patterns of 3D place cells. These results suggest that the bat hippocampus represents 3D volumetric space by a uniform and nearly isotropic rate code.

Resolution of nested neuronal representations can be exponential in the number of neurons

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation.

Optimal population codes for space: grid cells outperform place cells

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

Insights from a simple expression for linear fisher information in a recurrently connected population of spiking neurons

A simple expression for a lower bound of Fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise-perturbed steady state. We call this lower bound linear Fisher information, as it corresponds to the Fisher information that can be recovered by a locally optimal linear estimator. Unlike recent similar calculations, the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network. Here, this expression is used to (1) compute the optimal (i.e., information-maximizing) firing rate of a neuron, (2) demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea, (3) show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss, and (4) show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network.

Reassessing optimal neural population codes with neurometric functions

Cortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool--Fisher information--can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and a reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information.

Quality time: representation of a multidimensional sensory domain through temporal coding

Receptive fields of sensory neurons in the brain are usually restricted to a portion of the entire stimulus domain. At all levels of the gustatory neuraxis, however, there are many cells that are broadly tuned, i.e., they respond well to each of the basic taste qualities (sweet, sour, salty, and bitter). Although it might seem that this broad tuning precludes a major role for these cells in representing taste space, here we show the opposite--namely, that the tastant-specific temporal aspects (firing rate envelope and spike timing) of their responses enable each cell to represent the entire stimulus domain. Specifically, we recorded the response patterns of cells in the nucleus of the solitary tract (NTS) to representatives of four basic taste qualities and their binary mixtures. We analyzed the temporal aspects of these responses, and used their similarities and differences to construct the taste space represented by each neuron. We found that for the more broadly tuned neurons in the NTS, the taste space is a systematic representation of the entire taste domain. That is, the taste space of these broadly tuned neurons is three dimensional, with basic taste qualities widely separated and binary mixtures placed close to their components. Further, the way that taste quality is represented by the firing rate envelope is consistent across the population of cells. Thus, the temporal characteristics of responses in the population of NTS neurons, especially those that are more broadly tuned, produce a comprehensive and logical representation of the taste world.

Computational role of large receptive fields in the primary somatosensory cortex

Computational studies are challenging the intuitive view that neurons with broad tuning curves are necessarily less discriminative than neurons with sharp tuning curves. In the context of somatosensory processing, broad tuning curves are equivalent to large receptive fields. To clarify the computational role of large receptive fields for cortical processing of somatosensory information, we recorded ensembles of single neurons from the infragranular forelimb/forepaw region of the rat primary somatosensory cortex while tactile stimuli were separately delivered to different locations on the forelimbs/forepaws under light anesthesia. We specifically adopted the perspective of individual columns/segregates receiving inputs from multiple body location. Using single-trial analyses of many single-neuron responses, we obtained two main results. 1) The responses of even small populations of neurons recorded from within the same estimated column/segregate can be used to discriminate between stimuli delivered to different surround locations in the excitatory receptive fields. 2) The temporal precision of surround responses is sufficiently high for spike timing to add information over spike count in the discrimination between surround locations. This surround spike-timing code (i) is particularly informative when spike count is ambiguous, e.g., in the discrimination between close locations or when receptive fields are large, (ii) becomes progressively more informative as the number of neurons increases, (iii) is a first-spike code, and (iv) is not limited by the assumption that the time of stimulus onset is known. These results suggest that even though large receptive fields result in a loss of spatial selectivity of single neurons, they can provide as a counterpart a sophisticated temporal code based on latency differences in large populations of neurons without necessarily sacrificing basic information about stimulus location.