A Simple Model of Optimal Population Coding for Sensory Systems

A fundamental task of a sensory system is to infer information about the environment. It has long been suggested that an important goal of the first stage of this process is to encode the raw sensory signal efficiently by reducing its redundancy in the neural representation. Some redundancy, however, would be expected because it can provide robustness to noise inherent in the system. Encoding the raw sensory signal itself is also problematic, because it contains distortion and noise. The optimal solution would be constrained further by limited biological resources. Here, we analyze a simple theoretical model that incorporates these key aspects of sensory coding, and apply it to conditions in the retina. The model specifies the optimal way to incorporate redundancy in a population of noisy neurons, while also optimally compensating for sensory distortion and noise. Importantly, it allows an arbitrary input-to-output cell ratio between sensory units (photoreceptors) and encoding units (retinal ganglion cells), providing predictions of retinal codes at different eccentricities. Compared to earlier models based on redundancy reduction, the proposed model conveys more information about the original signal. Interestingly, redundancy reduction can be near-optimal when the number of encoding units is limited, such as in the peripheral retina. We show that there exist multiple, equally-optimal solutions whose receptive field structure and organization vary significantly. Among these, the one which maximizes the spatial locality of the computation, but not the sparsity of either synaptic weights or neural responses, is consistent with known basic properties of retinal receptive fields. The model further predicts that receptive field structure changes less with light adaptation at higher input-to-output cell ratios, such as in the periphery.     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Role of statistical symmetries in sensory coding: an optimal scale invariant code for vision

The visual system is the most studied sensory pathway, which is partly because visual stimuli have rather intuitive properties. There are reasons to think that the underlying principle ruling coding, however, is the same for vision and any other type of sensory signal, namely the code has to satisfy some notion of optimality--understood as minimum redundancy or as maximum transmitted information. Given the huge variability of natural stimuli, it would seem that attaining an optimal code is almost impossible; however, regularities and symmetries in the stimuli can be used to simplify the task: symmetries allow predicting one part of a stimulus from another, that is, they imply a structured type of redundancy. Optimal coding can only be achieved once the intrinsic symmetries of natural scenes are understood and used to the best performance of the neural encoder. In this paper, we review the concepts of optimal coding and discuss the known redundancies and symmetries that visual scenes have. We discuss in depth the only approach which implements the three of them known so far: translational invariance, scale invariance and multiscaling. Not surprisingly, the resulting code possesses features observed in real visual systems in mammals.     

Smelling on the fly: sensory cues and strategies for olfactory navigation in Drosophila

Navigating toward (or away from) a remote odor source is a challenging problem that requires integrating olfactory information with visual and mechanosensory cues. Drosophila melanogaster is a useful organism for studying the neural mechanisms of these navigation behaviors. There are a wealth of genetic tools in this organism, as well as a history of inventive behavioral experiments. There is also a large and growing literature in Drosophila on the neural coding of olfactory, visual, and mechanosensory stimuli. Here we review recent progress in understanding how these stimulus modalities are encoded in the Drosophila nervous system. We also discuss what strategies a fly might use to navigate in a natural olfactory landscape while making use of all these sources of sensory information. We emphasize that Drosophila are likely to switch between multiple strategies for olfactory navigation, depending on the availability of various sensory cues. Finally, we highlight future research directions that will be important in understanding the neural circuits that underlie these behaviors.     

The systems analysis approach to mechanosensory coding

An important problem in neuroscience is to obtain quantitative knowledge of how information is represented, or encoded, in the signals that nerve cells process and transmit. Sensory receptors have provided important models for the study of neural coding because their inputs can often be relatively easily controlled and measured, while the resultant activity is recorded. A variety of engineering concepts have been successfully applied to physiological sciences, particularly those related to control of dynamic systems. Linear systems analysis was one of the earliest methods used to probe sensory coding, and measurements such as step responses and frequency responses have become standard tools for describing sensory functions. Modern systems analysis has evolved to provide accurate and efficient linear identification of encoding in sensory receptors that use either graded potentials or action potentials. It has also led to nonlinear systems analysis, the creation of parametric nonlinear models, and measures of information coding by sensory neurons. These methods promise to provide important new knowledge about sensory systems in the future, especially when complemented with parallel biophysical and molecular studies of sensory neurons. Mechanoreceptors provided some of the earliest preparations for the investigation of neural coding, and both the linear and nonlinear properties of wide variety of vertebrate and invertebrate mechanoreceptors continue to be explored. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Dynamical coding of sensory information with competitive networks.

Based on experiments with the locust olfactory system, we demonstrate that model sensory neural networks with lateral inhibition can generate stimulus specific identity-temporal patterns in the form of stimulus-dependent switching among small and dynamically changing neural ensembles (each ensemble being a group of synchronized projection neurons). Networks produce this switching mode of dynamical activity when lateral inhibitory connections are strongly non-symmetric. Such coding uses 'winner-less competitive' (WLC) dynamics. In contrast to the well known winner-take-all competitive (WTA) networks and Hopfield nets, winner-less competition represents sensory information dynamically. Such dynamics are reproducible, robust against intrinsic noise and sensitive to changes in the sensory input. We demonstrate the validity of sensory coding with WLC networks using two different formulations of the dynamics, namely the average and spiking dynamics of projection neurons (PN).     

Information and discriminability as measures of reliability of sensory coding

Response variability is a fundamental issue in neural coding because it limits all information processing. The reliability of neuronal coding is quantified by various approaches in different studies. In most cases it is largely unclear to what extent the conclusions depend on the applied reliability measure, making a comparison across studies almost impossible. We demonstrate that different reliability measures can lead to very different conclusions even if applied to the same set of data: in particular, we applied information theoretical measures (Shannon information capacity and Kullback-Leibler divergence) as well as a discrimination measure derived from signal-detection theory to the responses of blowfly photoreceptors which represent a well established model system for sensory information processing. We stimulated the photoreceptors with white noise modulated light intensity fluctuations of different contrasts. Surprisingly, the signal-detection approach leads to a safe discrimination of the photoreceptor response even when the response signal-to-noise ratio (SNR) is well below unity whereas Shannon information capacity and also Kullback-Leibler divergence indicate a very low performance. Applying different measures, can, therefore, lead to very different interpretations concerning the system's coding performance. As a consequence of the lower sensitivity compared to the signal-detection approach, the information theoretical measures overestimate internal noise sources and underestimate the importance of photon shot noise. We stress that none of the used measures and, most likely no other measure alone, allows for an unbiased estimation of a neuron's coding properties. Therefore the applied measure needs to be selected with respect to the scientific question and the analyzed neuron's functional context.     

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.     

Optimal Prediction of Moving Sound Source Direction in the Owl

Capturing nature’s statistical structure in behavioral responses is at the core of the ability to function adaptively in the environment. Bayesian statistical inference describes how sensory and prior information can be combined optimally to guide behavior. An outstanding open question of how neural coding supports Bayesian inference includes how sensory cues are optimally integrated over time. Here we address what neural response properties allow a neural system to perform Bayesian prediction, i.e., predicting where a source will be in the near future given sensory information and prior assumptions. The work here shows that the population vector decoder will perform Bayesian prediction when the receptive fields of the neurons encode the target dynamics with shifting receptive fields. We test the model using the system that underlies sound localization in barn owls. Neurons in the owl’s midbrain show shifting receptive fields for moving sources that are consistent with the predictions of the model. We predict that neural populations can be specialized to represent the statistics of dynamic stimuli to allow for a vector read-out of Bayes-optimal predictions.     

A computational system for simulating and analyzing arrays of biological and artificial chemical sensors

We have designed an approach for modeling olfactory pathways by which one can explore how the properties of individual receptors affect the information coding capacity of an entire system. The effect of receptor tuning breadth on system performance was explored explicitly. We presented model sensory arrays with sets of stimuli randomly and uniformly distributed in an "olfactory space". Arrays of uniformly sized model receptors responding to 25-35% of the stimuli gave the best performance as measured by the ability to capture the most information about the stimulus set. Arrays of variably sized model receptors that were both more broadly and more narrowly tuned than this optimum could, however, perform better than uniform arrays. This method and the results obtained using it suggest a framework for considering the growing body of evidence on the functional properties of individual olfactory receptor and relay neurons from a systems coding perspective.     

Involving Motor Capabilities in the Formation of Sensory Space Representations

A goal of sensory coding is to capture features of sensory input that are behaviorally relevant. Therefore, a generic principle of sensory coding should take into account the motor capabilities of an agent. Up to now, unsupervised learning of sensory representations with respect to generic coding principles has been limited to passively received sensory input. Here we propose an algorithm that reorganizes an agent''s representation of sensory space by maximizing the predictability of sensory state transitions given a motor action. We applied the algorithm to the sensory spaces of a number of simple, simulated agents with different motor parameters, moving in two-dimensional mazes. We find that the optimization algorithm generates compact, isotropic representations of space, comparable to hippocampal place fields. As expected, the size and spatial distribution of these place fields-like representations adapt to the motor parameters of the agent as well as to its environment. The representations prove to be well suited as a basis for path planning and navigation. They not only possess a high degree of state-transition predictability, but also are temporally stable. We conclude that the coding principle of predictability is a promising candidate for understanding place field formation as the result of sensorimotor reorganization.     

Information maximization for exploring neural coding in hippocampus and lateral septum

A central problem in neural coding is to understand what are the features of the stimulus that are encoded by the neural activity. Assuming that neuronal coding is optimized for information transmission, we can use mutual information maximization for extracting the relevant features encoded in certain activity patterns. We show that this algorithm can be successfully applied to the study of different encoding strategies for location and direction of movement in hippocampal and lateral septal cells. Using this approach, we find that in lateral septum, a significant amount of information about location can be encoded in patterns that are not place-fields.     

Beyond Motor Scheme: A Supramodal Distributed Representation in the Action-Observation Network

The representation of actions within the action-observation network is thought to rely on a distributed functional organization. Furthermore, recent findings indicate that the action-observation network encodes not merely the observed motor act, but rather a representation that is independent from a specific sensory modality or sensory experience. In the present study, we wished to determine to what extent this distributed and ‘more abstract’ representation of action is truly supramodal, i.e. shares a common coding across sensory modalities. To this aim, a pattern recognition approach was employed to analyze neural responses in sighted and congenitally blind subjects during visual and/or auditory presentation of hand-made actions. Multivoxel pattern analyses-based classifiers discriminated action from non-action stimuli across sensory conditions (visual and auditory) and experimental groups (blind and sighted). Moreover, these classifiers labeled as ‘action’ the pattern of neural responses evoked during actual motor execution. Interestingly, discriminative information for the action/non action classification was located in a bilateral, but left-prevalent, network that strongly overlaps with brain regions known to form the action-observation network and the human mirror system. The ability to identify action features with a multivoxel pattern analyses-based classifier in both sighted and blind individuals and independently from the sensory modality conveying the stimuli clearly supports the hypothesis of a supramodal, distributed functional representation of actions, mainly within the action-observation network.     

Encoding odorant identity by spiking packets of rate-invariant neurons in awake mice

Background

How do neural networks encode sensory information? Following sensory stimulation, neural coding is commonly assumed to be based on neurons changing their firing rate. In contrast, both theoretical works and experiments in several sensory systems showed that neurons could encode information as coordinated cell assemblies by adjusting their spike timing and without changing their firing rate. Nevertheless, in the olfactory system, there is little experimental evidence supporting such model.

Methodology/Principal Findings

To study these issues, we implanted tetrodes in the olfactory bulb of awake mice to record the odorant-evoked activity of mitral/tufted (M/T) cells. We showed that following odorant presentation, most M/T neurons do not significantly change their firing rate over a breathing cycle but rather respond to odorant stimulation by redistributing their firing activity within respiratory cycles. In addition, we showed that sensory information can be encoded by cell assemblies composed of such neurons, thus supporting the idea that coordinated populations of globally rate-invariant neurons could be efficiently used to convey information about the odorant identity. We showed that different coding schemes can convey high amount of odorant information for specific read-out time window. Finally we showed that the optimal readout time window corresponds to the duration of gamma oscillations cycles.

Conclusion

We propose that odorant can be encoded by population of cells that exhibit fine temporal tuning of spiking activity while displaying weak or no firing rate change. These cell assemblies may transfer sensory information in spiking packets sequence using the gamma oscillations as a clock. This would allow the system to reach a tradeoff between rapid and accurate odorant discrimination.     

From sensors to spikes: evolving receptive fields to enhance sensorimotor information in a robot-arm

In biological systems, instead of actual encoders at different joints, proprioception signals are acquired through distributed receptive fields. In robotics, a single and accurate sensor output per link (encoder) is commonly used to track the position and the velocity. Interfacing bio-inspired control systems with spiking neural networks emulating the cerebellum with conventional robots is not a straight forward task. Therefore, it is necessary to adapt this one-dimensional measure (encoder output) into a multidimensional space (inputs for a spiking neural network) to connect, for instance, the spiking cerebellar architecture; i.e. a translation from an analog space into a distributed population coding in terms of spikes. This paper analyzes how evolved receptive fields (optimized towards information transmission) can efficiently generate a sensorimotor representation that facilitates its discrimination from other "sensorimotor states". This can be seen as an abstraction of the Cuneate Nucleus (CN) functionality in a robot-arm scenario. We model the CN as a spiking neuron population coding in time according to the response of mechanoreceptors during a multi-joint movement in a robot joint space. An encoding scheme that takes into account the relative spiking time of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons is proposed. Due to the enormous number of possible encodings, we have applied an evolutionary algorithm to evolve the sensory receptive field representation from random to optimized encoding. Following the nature-inspired analogy, evolved configurations have shown to outperform simple hand-tuned configurations and other homogenized configurations based on the solution provided by the optimization engine (evolutionary algorithm). We have used artificial evolutionary engines as the optimization tool to circumvent nonlinearity responses in receptive fields.     

Neural coding and contextual influences in the whisker system

A fundamental problem in neuroscience, to which Prof. Segundo has made seminal contributions, is to understand how action potentials represent events in the external world. The aim of this paper is to review the issue of neural coding in the context of the rodent whiskers, an increasingly popular model system. Key issues we consider are: the role of spike timing; mechanisms of spike timing; decoding and context-dependence. Significant insight has come from the development of rigorous, information theoretic frameworks for tackling these questions, in conjunction with suitably designed experiments. We review both the theory and experimental studies. In contrast to the classical view that neurons are noisy and unreliable, it is becoming clear that many neurons in the subcortical whisker pathway are remarkably reliable and, by virtue of spike timing with millisecond-precision, have high bandwidth for conveying sensory information. In this way, even small (~200 neuron) subcortical modules are able to support the sensory processing underlying sophisticated whisker-dependent behaviours. Future work on neural coding in cortex will need to consider new findings that responses are highly dependent on context, including behavioural and internal states. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Understanding auditory spectro-temporal receptive fields and their changes with input statistics by efficient coding principles

Spectro-temporal receptive fields (STRFs) have been widely used as linear approximations to the signal transform from sound spectrograms to neural responses along the auditory pathway. Their dependence on statistical attributes of the stimuli, such as sound intensity, is usually explained by nonlinear mechanisms and models. Here, we apply an efficient coding principle which has been successfully used to understand receptive fields in early stages of visual processing, in order to provide a computational understanding of the STRFs. According to this principle, STRFs result from an optimal tradeoff between maximizing the sensory information the brain receives, and minimizing the cost of the neural activities required to represent and transmit this information. Both terms depend on the statistical properties of the sensory inputs and the noise that corrupts them. The STRFs should therefore depend on the input power spectrum and the signal-to-noise ratio, which is assumed to increase with input intensity. We analytically derive the optimal STRFs when signal and noise are approximated as Gaussians. Under the constraint that they should be spectro-temporally local, the STRFs are predicted to adapt from being band-pass to low-pass filters as the input intensity reduces, or the input correlation becomes longer range in sound frequency or time. These predictions qualitatively match physiological observations. Our prediction as to how the STRFs should be determined by the input power spectrum could readily be tested, since this spectrum depends on the stimulus ensemble. The potentials and limitations of the efficient coding principle are discussed.     

Encoding of Time-varying Stimuli in Populations of Cultured Neurons

We wondered whether random populations of dissociated cultured cortical neurons, despite of their lack of structure and/or regional specialization, are capable of modulating their neural activity as the effect of a time-varying stimulation – a simulated ‘sensory’ afference. More specifically, we used localized low-frequency, non-periodic trains of stimuli to simulate sensory afferences, and asked how much information about the original trains of stimuli could be extracted from the neural activity recorded at the different sites. Furthermore, motivated by the results of studies performed both in vivo and in vitro on different preparations, which suggested that isolated spikes and bursts may play different roles in coding time-varying signals, we explored the amount of such ‘sensory’ information that could be associated to these different firing modes. Finally, we asked whether and how such ‘sensory’ information is transferred from the sites of stimulation (i.e., the ‘sensory’ areas), to the other regions of the neural populations. To do this we applied stimulus reconstruction techniques and information theoretic concepts that are typically used to investigate neural coding in sensory systems. Our main results are that (1) slow variations of the rate of stimulation are coded into isolated spikes and in the time of occurrence of bursts (but not in the bursts’ temporal structure); (2) increasing the rate of stimulation has the effect of increasing the proportion of isolated spikes in the average evoked response and their importance in coding for the stimuli; and, (3) the ability to recover the time course of the pattern of stimulation is strongly related to the degree of functional connectivity between stimulation and recording sites. These observations parallel similar findings in intact nervous systems regarding the complementary roles of bursts and tonic spikes in encoding sensory information. Our results also have interesting implications in the field of neuro-robotic interfaces. In fact, the ability of populations of neurons to code information is a prerequisite for obtaining hybrid systems, in which neuronal populations are used to control external devices.     

Sensory adaptation

Adaptation occurs in a variety of forms in all sensory systems, motivating the question: what is its purpose? A productive approach has been to hypothesize that adaptation helps neural systems to efficiently encode stimuli whose statistics vary in time. To encode efficiently, a neural system must change its coding strategy, or computation, as the distribution of stimuli changes. Information theoretic methods allow this efficient coding hypothesis to be tested quantitatively. Empirically, adaptive processes occur over a wide range of timescales. On short timescales, underlying mechanisms include the contribution of intrinsic nonlinearities. Over longer timescales, adaptation is often power-law-like, implying the coexistence of multiple timescales in a single adaptive process. Models demonstrate that this can result from mechanisms within a single neuron.     

Information transmission in cercal giant interneurons is unaffected by axonal conduction noise

What are the fundamental constraints on the precision and accuracy with which nervous systems can process information? One constraint must reflect the intrinsic “noisiness” of the mechanisms that transmit information between nerve cells. Most neurons transmit information through the probabilistic generation and propagation of spikes along axons, and recent modeling studies suggest that noise from spike propagation might pose a significant constraint on the rate at which information could be transmitted between neurons. However, the magnitude and functional significance of this noise source in actual cells remains poorly understood. We measured variability in conduction time along the axons of identified neurons in the cercal sensory system of the cricket Acheta domesticus, and used information theory to calculate the effects of this variability on sensory coding. We found that the variability in spike propagation speed is not large enough to constrain the accuracy of neural encoding in this system.