The Visual Systems of Zebrafish.

The zebrafish visual system has become a paradigmatic preparation for behavioral and systems neuroscience. Around 40 types of retinal ganglion cells (RGCs) serve as matched filters for stimulus features, including light, optic flow, prey, and objects on a collision course. RGCs distribute their signals via axon collaterals to 12 retinorecipient areas in forebrain and midbrain. The major visuomotor hub, the optic tectum, harbors nine RGC input layers that combine information on multiple features. The retinotopic map in the tectum is locally adapted to visual scene statistics and visual subfield-specific behavioral demands. Tectal projections to premotor centers are topographically organized according to behavioral commands. The known connectivity in more than 20 processing streams allows us to dissect the cellular basis of elementary perceptual and cognitive functions. Visually evoked responses, such as prey capture or loom avoidance, are controlled by dedicated multistation pathways that-at least in the larva-resemble labeled lines. This architecture serves the neuronal code's purpose of driving adaptive behavior.

Synchronous inhibitory pathways create both efficiency and diversity in the retina.

Sensory receptive fields combine features that originate in different neural pathways. Retinal ganglion cell receptive fields compute intensity changes across space and time using a peripheral region known as the surround, a property that improves information transmission about natural scenes. The visual features that construct this fundamental property have not been quantitatively assigned to specific interneurons. Here, we describe a generalizable approach using simultaneous intracellular and multielectrode recording to directly measure and manipulate the sensory feature conveyed by a neural pathway to a downstream neuron. By directly controlling the gain of individual interneurons in the circuit, we show that rather than transmitting different temporal features, inhibitory horizontal cells and linear amacrine cells synchronously create the linear surround at different spatial scales and that these two components fully account for the surround. By analyzing a large population of ganglion cells, we observe substantial diversity in the relative contribution of amacrine and horizontal cell visual features while still allowing individual cells to increase information transmission under the statistics of natural scenes. Established theories of efficient coding have shown that optimal information transmission under natural scenes allows a diverse set of receptive fields. Our results give a mechanism for this theory, showing how distinct neural pathways synthesize a sensory computation and how this architecture both generates computational diversity and achieves the objective of high information transmission.

Divisive normalization is an efficient code for multivariate Pareto-distributed environments.

Divisive normalization is a canonical computation in the brain, observed across neural systems, that is often considered to be an implementation of the efficient coding principle. We provide a theoretical result that makes the conditions under which divisive normalization is an efficient code analytically precise: We show that, in a low-noise regime, encoding an n-dimensional stimulus via divisive normalization is efficient if and only if its prevalence in the environment is described by a multivariate Pareto distribution. We generalize this multivariate analog of histogram equalization to allow for arbitrary metabolic costs of the representation, and show how different assumptions on costs are associated with different shapes of the distributions that divisive normalization efficiently encodes. Our result suggests that divisive normalization may have evolved to efficiently represent stimuli with Pareto distributions. We demonstrate that this efficiently encoded distribution is consistent with stylized features of naturalistic stimulus distributions such as their characteristic conditional variance dependence, and we provide empirical evidence suggesting that it may capture the statistics of filter responses to naturalistic images. Our theoretical finding also yields empirically testable predictions across sensory domains on how the divisive normalization parameters should be tuned to features of the input distribution.

Representation of Motion Direction in Visual Area MT Accounts for High Sensitivity to Centripetal Motion, Aligning with Efficient Coding of Retinal Motion Statistics.

The overrepresentation of centrifugal motion in the middle temporal visual area (area MT) has long been thought to provide an efficient coding strategy for optic flow processing. However, this overrepresentation compromises the detection of approaching objects, which is essential for survival. In the present study, we revisited this long-held notion by reanalyzing motion selectivity in area MT of three macaque monkeys (two males, one female) using random-dot stimuli instead of spot stimuli. We found no differences in the number of neurons tuned to centrifugal versus centripetal motion; however, centrifugally tuned neurons showed stronger tuning than centripetally tuned neurons. This was attributed to the heightened suppression of responses in centrifugal neurons to centripetal motion compared with that of centripetal neurons to centrifugal motion. Our modeling implies that this intensified suppression accounts for superior detection performance for weak centripetal motion stimuli. Moreover, through Fisher information analysis, we establish that the population sensitivity to motion direction in peripheral vision corresponds well with retinal motion statistics during forward locomotion. While these results challenge established concepts, considering the interplay of logarithmic Gaussian receptive fields and spot stimuli can shed light on the previously documented overrepresentation of centrifugal motion. Significantly, our findings reconcile a previously found discrepancy between MT activity and human behavior, highlighting the proficiency of peripheral MT neurons in encoding motion direction efficiently.SIGNIFICANCE STATEMENT The efficient coding hypothesis states that sensory neurons are tuned to specific, frequently experienced stimuli. Whereas previous work has found that neurons in the middle temporal (MT) area favor centrifugal motion, which results from forward locomotion, we show here that there is no such bias. Moreover, we found that the response of centrifugal neurons for centripetal motion was more suppressed than that of centripetal neurons for centrifugal motion. Combined with modeling, this provides a solution to a previously known discrepancy between reported centrifugal bias in MT and better detection of centripetal motion by human observers. Additionally, we show that population sensitivity in peripheral MT neurons conforms to an efficient code of retinal motion statistics during forward locomotion.

Scene statistics and noise determine the relative arrangement of receptive field mosaics.

Many sensory systems utilize parallel ON and OFF pathways that signal stimulus increments and decrements, respectively. These pathways consist of ensembles or grids of ON and OFF detectors spanning sensory space. Yet, encoding by opponent pathways raises a question: How should grids of ON and OFF detectors be arranged to optimally encode natural stimuli? We investigated this question using a model of the retina guided by efficient coding theory. Specifically, we optimized spatial receptive fields and contrast response functions to encode natural images given noise and constrained firing rates. We find that the optimal arrangement of ON and OFF receptive fields exhibits a transition between aligned and antialigned grids. The preferred phase depends on detector noise and the statistical structure of the natural stimuli. These results reveal that noise and stimulus statistics produce qualitative shifts in neural coding strategies and provide theoretical predictions for the configuration of opponent pathways in the nervous system.

Nonlinear convergence boosts information coding in circuits with parallel outputs.

Neural circuits are structured with layers of converging and diverging connectivity and selectivity-inducing nonlinearities at neurons and synapses. These components have the potential to hamper an accurate encoding of the circuit inputs. Past computational studies have optimized the nonlinearities of single neurons, or connection weights in networks, to maximize encoded information, but have not grappled with the simultaneous impact of convergent circuit structure and nonlinear response functions for efficient coding. Our approach is to compare model circuits with different combinations of convergence, divergence, and nonlinear neurons to discover how interactions between these components affect coding efficiency. We find that a convergent circuit with divergent parallel pathways can encode more information with nonlinear subunits than with linear subunits, despite the compressive loss induced by the convergence and the nonlinearities when considered separately.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons.

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.

Prior Expectations in Visual Speed Perception Predict Encoding Characteristics of Neurons in Area MT.

Bayesian inference provides an elegant theoretical framework for understanding the characteristic biases and discrimination thresholds in visual speed perception. However, the framework is difficult to validate because of its flexibility and the fact that suitable constraints on the structure of the sensory uncertainty have been missing. Here, we demonstrate that a Bayesian observer model constrained by efficient coding not only well explains human visual speed perception but also provides an accurate quantitative account of the tuning characteristics of neurons known for representing visual speed. Specifically, we found that the population coding accuracy for visual speed in area MT ("neural prior") is precisely predicted by the power-law, slow-speed prior extracted from fitting the Bayesian observer model to psychophysical data ("behavioral prior") to the point that the two priors are indistinguishable in a cross-validation model comparison. Our results demonstrate a quantitative validation of the Bayesian observer model constrained by efficient coding at both the behavioral and neural levels.SIGNIFICANCE STATEMENT Statistical regularities of the environment play an important role in shaping both neural representations and perceptual behavior. Most previous work addressed these two aspects independently. Here we present a quantitative validation of a theoretical framework that makes joint predictions for neural coding and behavior, based on the assumption that neural representations of sensory information are efficient but also optimally used in generating a percept. Specifically, we demonstrate that the neural tuning characteristics for visual speed in brain area MT are precisely predicted by the statistical prior expectations extracted from psychophysical data. As such, our results provide a normative link between perceptual behavior and the neural representation of sensory information in the brain.

Learning heterogeneous delays in a layer of spiking neurons for fast motion detection.

The precise timing of spikes emitted by neurons plays a crucial role in shaping the response of efferent biological neurons. This temporal dimension of neural activity holds significant importance in understanding information processing in neurobiology, especially for the performance of neuromorphic hardware, such as event-based cameras. Nonetheless, many artificial neural models disregard this critical temporal dimension of neural activity. In this study, we present a model designed to efficiently detect temporal spiking motifs using a layer of spiking neurons equipped with heterogeneous synaptic delays. Our model capitalizes on the diverse synaptic delays present on the dendritic tree, enabling specific arrangements of temporally precise synaptic inputs to synchronize upon reaching the basal dendritic tree. We formalize this process as a time-invariant logistic regression, which can be trained using labeled data. To demonstrate its practical efficacy, we apply the model to naturalistic videos transformed into event streams, simulating the output of the biological retina or event-based cameras. To evaluate the robustness of the model in detecting visual motion, we conduct experiments by selectively pruning weights and demonstrate that the model remains efficient even under significantly reduced workloads. In conclusion, by providing a comprehensive, event-driven computational building block, the incorporation of heterogeneous delays has the potential to greatly improve the performance of future spiking neural network algorithms, particularly in the context of neuromorphic chips.

Normative Principles for Decision-Making in Natural Environments.

The decisions we make are shaped by a lifetime of learning. Past experience guides the way that we encode information in neural systems for perception and valuation, and determines the information we retrieve when making decisions. Distinct literatures have discussed how lifelong learning and local context shape decisions made about sensory signals, propositional information, or economic prospects. Here, we build bridges between these literatures, arguing for common principles of adaptive rationality in perception, cognition, and economic choice. We discuss how a single common framework, based on normative principles of efficient coding and Bayesian inference, can help us understand a myriad of human decision biases, including sensory illusions, adaptive aftereffects, choice history biases, central tendency effects, anchoring effects, contrast effects, framing effects, congruency effects, reference-dependent valuation, nonlinear utility functions, and discretization heuristics. We describe a simple computational framework for explaining these phenomena.

Active efficient coding explains the development of binocular vision and its failure in amblyopia.

The development of vision during the first months of life is an active process that comprises the learning of appropriate neural representations and the learning of accurate eye movements. While it has long been suspected that the two learning processes are coupled, there is still no widely accepted theoretical framework describing this joint development. Here, we propose a computational model of the development of active binocular vision to fill this gap. The model is based on a formulation of the active efficient coding theory, which proposes that eye movements as well as stimulus encoding are jointly adapted to maximize the overall coding efficiency. Under healthy conditions, the model self-calibrates to perform accurate vergence and accommodation eye movements. It exploits disparity cues to deduce the direction of defocus, which leads to coordinated vergence and accommodation responses. In a simulated anisometropic case, where the refraction power of the two eyes differs, an amblyopia-like state develops in which the foveal region of one eye is suppressed due to inputs from the other eye. After correcting for refractive errors, the model can only reach healthy performance levels if receptive fields are still plastic, in line with findings on a critical period for binocular vision development. Overall, our model offers a unifying conceptual framework for understanding the development of binocular vision.

From likely to likable: The role of statistical typicality in human social assessment of faces.

Humans readily form social impressions, such as attractiveness and trustworthiness, from a stranger's facial features. Understanding the provenance of these impressions has clear scientific importance and societal implications. Motivated by the efficient coding hypothesis of brain representation, as well as Claude Shannon's theoretical result that maximally efficient representational systems assign shorter codes to statistically more typical data (quantified as log likelihood), we suggest that social "liking" of faces increases with statistical typicality. Combining human behavioral data and computational modeling, we show that perceived attractiveness, trustworthiness, dominance, and valence of a face image linearly increase with its statistical typicality (log likelihood). We also show that statistical typicality can at least partially explain the role of symmetry in attractiveness perception. Additionally, by assuming that the brain focuses on a task-relevant subset of facial features and assessing log likelihood of a face using those features, our model can explain the "ugliness-in-averageness" effect found in social psychology, whereby otherwise attractive, intercategory faces diminish in attractiveness during a categorization task.

The bounded rationality of probability distortion.

In decision making under risk (DMR) participants' choices are based on probability values systematically different from those that are objectively correct. Similar systematic distortions are found in tasks involving relative frequency judgments (JRF). These distortions limit performance in a wide variety of tasks and an evident question is, Why do we systematically fail in our use of probability and relative frequency information? We propose a bounded log-odds model (BLO) of probability and relative frequency distortion based on three assumptions: 1) log-odds: probability and relative frequency are mapped to an internal log-odds scale, 2) boundedness: the range of representations of probability and relative frequency are bounded and the bounds change dynamically with task, and 3) variance compensation: the mapping compensates in part for uncertainty in probability and relative frequency values. We compared human performance in both DMR and JRF tasks to the predictions of the BLO model as well as 11 alternative models, each missing one or more of the underlying BLO assumptions (factorial model comparison). The BLO model and its assumptions proved to be superior to any of the alternatives. In a separate analysis, we found that BLO accounts for individual participants' data better than any previous model in the DMR literature. We also found that, subject to the boundedness limitation, participants' choice of distortion approximately maximized the mutual information between objective task-relevant values and internal values, a form of bounded rationality.

Optimal Population Coding for Dynamic Input by Nonequilibrium Networks.

The efficient coding hypothesis states that neural response should maximize its information about the external input. Theoretical studies focus on optimal response in single neuron and population code in networks with weak pairwise interactions. However, more biological settings with asymmetric connectivity and the encoding for dynamical stimuli have not been well-characterized. Here, we study the collective response in a kinetic Ising model that encodes the dynamic input. We apply gradient-based method and mean-field approximation to reconstruct networks given the neural code that encodes dynamic input patterns. We measure network asymmetry, decoding performance, and entropy production from networks that generate optimal population code. We analyze how stimulus correlation, time scale, and reliability of the network affect optimal encoding networks. Specifically, we find network dynamics altered by statistics of the dynamic input, identify stimulus encoding strategies, and show optimal effective temperature in the asymmetric networks. We further discuss how this approach connects to the Bayesian framework and continuous recurrent neural networks. Together, these results bridge concepts of nonequilibrium physics with the analyses of dynamics and coding in networks.

Information Flow in Biological Networks for Color Vision.

Biological neural networks for color vision (also known as color appearance models) consist of a cascade of linear + nonlinear layers that modify the linear measurements at the retinal photo-receptors leading to an internal (nonlinear) representation of color that correlates with psychophysical experience. The basic layers of these networks include: (1) chromatic adaptation (normalization of the mean and covariance of the color manifold); (2) change to opponent color channels (PCA-like rotation in the color space); and (3) saturating nonlinearities to obtain perceptually Euclidean color representations (similar to dimension-wise equalization). The Efficient Coding Hypothesis argues that these transforms should emerge from information-theoretic goals. In case this hypothesis holds in color vision, the question is what is the coding gain due to the different layers of the color appearance networks? In this work, a representative family of color appearance models is analyzed in terms of how the redundancy among the chromatic components is modified along the network and how much information is transferred from the input data to the noisy response. The proposed analysis is performed using data and methods that were not available before: (1) new colorimetrically calibrated scenes in different CIE illuminations for the proper evaluation of chromatic adaptation; and (2) new statistical tools to estimate (multivariate) information-theoretic quantities between multidimensional sets based on Gaussianization. The results confirm that the efficient coding hypothesis holds for current color vision models, and identify the psychophysical mechanisms critically responsible for gains in information transference: opponent channels and their nonlinear nature are more important than chromatic adaptation at the retina.

Multiplicative mixing of object identity and image attributes in single inferior temporal neurons.

Object recognition is challenging because the same object can produce vastly different images, mixing signals related to its identity with signals due to its image attributes, such as size, position, rotation, etc. Previous studies have shown that both signals are present in high-level visual areas, but precisely how they are combined has remained unclear. One possibility is that neurons might encode identity and attribute signals multiplicatively so that each can be efficiently decoded without interference from the other. Here, we show that, in high-level visual cortex, responses of single neurons can be explained better as a product rather than a sum of tuning for object identity and tuning for image attributes. This subtle effect in single neurons produced substantially better population decoding of object identity and image attributes in the neural population as a whole. This property was absent both in low-level vision models and in deep neural networks. It was also unique to invariances: when tested with two-part objects, neural responses were explained better as a sum than as a product of part tuning. Taken together, our results indicate that signals requiring separate decoding, such as object identity and image attributes, are combined multiplicatively in IT neurons, whereas signals that require integration (such as parts in an object) are combined additively.

Toward a unified theory of efficient, predictive, and sparse coding.

A central goal in theoretical neuroscience is to predict the response properties of sensory neurons from first principles. To this end, "efficient coding" posits that sensory neurons encode maximal information about their inputs given internal constraints. There exist, however, many variants of efficient coding (e.g., redundancy reduction, different formulations of predictive coding, robust coding, sparse coding, etc.), differing in their regimes of applicability, in the relevance of signals to be encoded, and in the choice of constraints. It is unclear how these types of efficient coding relate or what is expected when different coding objectives are combined. Here we present a unified framework that encompasses previously proposed efficient coding models and extends to unique regimes. We show that optimizing neural responses to encode predictive information can lead them to either correlate or decorrelate their inputs, depending on the stimulus statistics; in contrast, at low noise, efficiently encoding the past always predicts decorrelation. Later, we investigate coding of naturalistic movies and show that qualitatively different types of visual motion tuning and levels of response sparsity are predicted, depending on whether the objective is to recover the past or predict the future. Our approach promises a way to explain the observed diversity of sensory neural responses, as due to multiple functional goals and constraints fulfilled by different cell types and/or circuits.

Adaptive Efficient Coding of Correlated Acoustic Properties.

Natural sounds such as vocalizations often have covarying acoustic attributes, resulting in redundancy in neural coding. The efficient coding hypothesis proposes that sensory systems are able to detect such covariation and adapt to reduce redundancy, leading to more efficient neural coding. Recent psychoacoustic studies have shown the auditory system can rapidly adapt to efficiently encode two covarying dimensions as a single dimension, following passive exposure to sounds in which temporal and spectral attributes covaried in a correlated fashion. However, these studies observed a cost to this adaptation, which was a loss of sensitivity to the orthogonal dimension. Here we explore the neural basis of this psychophysical phenomenon by recording single-unit responses from the primary auditory cortex in awake ferrets exposed passively to stimuli with two correlated attributes, similar in stimulus design to the psychoacoustic experiments in humans. We found: (1) the signal-to-noise ratio of spike-rate coding of cortical responses driven by sounds with correlated attributes remained unchanged along the exposure dimension, but was reduced along the orthogonal dimension; (2) performance of a decoder trained with spike data to discriminate stimuli along the orthogonal dimension was equally reduced; (3) correlations between neurons tuned to the two covarying attributes decreased after exposure; and (4) these exposure effects still occurred if sounds were correlated along two acoustic dimensions, but varied randomly along a third dimension. These neurophysiological results are consistent with the efficient coding hypothesis and may help deepen our understanding of how the auditory system encodes and represents acoustic regularities and covariance.SIGNIFICANCE STATEMENT The efficient coding (EC) hypothesis (Attneave, 1954; Barlow, 1961) proposes that the neural code in sensory systems efficiently encodes natural stimuli by minimizing the number of spikes to transmit a sensory signal. Results of recent psychoacoustic studies in humans are consistent with the EC hypothesis in that, following passive exposure to stimuli with correlated attributes, the auditory system rapidly adapts so as to more efficiently encode the two covarying dimensions as a single dimension. In the current neurophysiological experiments, using a similar stimulus design and the experimental paradigm to the psychoacoustic studies of Stilp et al. (2010) and Stilp and Kluender (2011, 2012, 2016), we recorded responses from single neurons in the auditory cortex of the awake ferret, showing adaptive efficient neural coding of two correlated acoustic attributes.

Olfactory Navigation and the Receptor Nonlinearity.

The demands on a sensory system depend not only on the statistics of its inputs but also on the task. In olfactory navigation, for example, the task is to find the plume source; allocation of sensory resources may therefore be driven by aspects of the plume that are informative about source location, rather than concentration per se. Here we explore the implications of this idea for encoding odor concentration. To formalize the notion that sensory resources are limited, we considered coding strategies that partitioned the odor concentration range into a set of discriminable intervals. We developed a dynamic programming algorithm that, given the distribution of odor concentrations at several locations, determines the partitioning that conveys the most information about location. We applied this analysis to planar laser-induced fluorescence measurements of spatiotemporal odor fields with realistic advection speeds (5-20 cm/s), with or without a nearby boundary or obstacle. Across all environments, the optimal coding strategy allocated more resources (i.e., more and finer discriminable intervals) to the upper end of the concentration range than would be expected from histogram equalization, the optimal strategy if the goal were to reconstruct the plume, rather than to navigate. Finally, we show that ligand binding, as captured by the Hill equation, transforms odorant concentration into response levels in a way that approximates information maximization for navigation. This behavior occurs when the Hill dissociation constant is near the mean odor concentration, an adaptive set-point that has been observed in the olfactory system of flies.SIGNIFICANCE STATEMENT The first step of olfactory processing is receptor binding, and the resulting relationship between odorant concentration and the bound receptor fraction is a saturating one. While this Hill nonlinearity can be viewed as a distortion that is imposed by the biophysics of receptor binding, here we show that it also plays an important information-processing role in olfactory navigation. Specifically, by combining a novel dynamic-programming algorithm with physical measurements of turbulent plumes, we determine the optimal strategy for encoding odor concentration when the goal is to determine location. This strategy is distinct from histogram equalization, the strategy that maximizes information about plume concentration, and is closely approximated by the Hill nonlinearity when the binding constant is near the ambient mean.

A roadmap to integrate astrocytes into Systems Neuroscience.

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease.