Resource-rational account of sequential effects in human prediction

An abundant literature reports on 'sequential effects' observed when humans make predictions on the basis of stochastic sequences of stimuli. Such sequential effects represent departures from an optimal, Bayesian process. A prominent explanation posits that humans are adapted to changing environments, and erroneously assume non-stationarity of the environment, even if the latter is static. As a result, their predictions fluctuate over time. We propose a different explanation in which sub-optimal and fluctuating predictions result from cognitive constraints (or costs), under which humans however behave rationally. We devise a framework of costly inference, in which we develop two classes of models that differ by the nature of the constraints at play: in one case the precision of beliefs comes at a cost, resulting in an exponential forgetting of past observations, while in the other beliefs with high predictive power are favored. To compare model predictions to human behavior, we carry out a prediction task that uses binary random stimuli, with probabilities ranging from 0.05 to 0.95. Although in this task the environment is static and the Bayesian belief converges, subjects' predictions fluctuate and are biased toward the recent stimulus history. Both classes of models capture this 'attractive effect', but they depart in their characterization of higher-order effects. Only the precision-cost model reproduces a 'repulsive effect', observed in the data, in which predictions are biased away from stimuli presented in more distant trials. Our experimental results reveal systematic modulations in sequential effects, which our theoretical approach accounts for in terms of rationality under cognitive constraints.

Human inference in changing environments with temporal structure

To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on situations in which the statistics of observations are history-independent. Yet, temporal structure is everywhere in nature and yields history-dependent observations. Do humans modify their inference processes depending on the latent temporal statistics of their observations? We investigate this question experimentally and theoretically using a change-point inference task. We show that humans adapt their inference process to fine aspects of the temporal structure in the statistics of stimuli. As such, humans behave qualitatively in a Bayesian fashion but, quantitatively, deviate away from optimality. Perhaps more importantly, humans behave suboptimally in that their responses are not deterministic, but variable. We show that this variability itself is modulated by the temporal statistics of stimuli. To elucidate the cognitive algorithm that yields this behavior, we investigate a broad array of existing and new models that characterize different sources of suboptimal deviations away from Bayesian inference. While models with "output noise" that corrupts the response-selection process are natural candidates, human behavior is best described by sampling-based inference models, in which the main ingredient is a compressed approximation of the posterior, represented through a modest set of random samples and updated over time. This result comes to complement a growing literature on sample-based representation and learning in humans. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Biases and Variability from Costly Bayesian Inference

When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are updated as a function of sequential observations. We introduce a theoretical framework in which biases and variability emerge from a trade-off between Bayesian inference and the cognitive cost of carrying out probabilistic computations. We consider two forms of the cost: a precision cost and an unpredictability cost; these penalize beliefs that are less entropic and less deterministic, respectively. We apply our framework to the case of a Bernoulli variable: the bias of a coin is inferred from a sequence of coin flips. Theoretical predictions are qualitatively different depending on the form of the cost. A precision cost induces overestimation of small probabilities, on average, and a limited memory of past observations, and, consequently, a fluctuating bias. An unpredictability cost induces underestimation of small probabilities and a fixed bias that remains appreciable even for nearly unbiased observations. The case of a fair (equiprobable) coin, however, is singular, with non-trivial and slow fluctuations in the inferred bias. The proposed framework of costly Bayesian inference illustrates the richness of a 'resource-rational' (or 'bounded-rational') picture of seemingly irrational human cognition.

The Geometry of Information Coding in Correlated Neural Populations

Neurons in the brain represent information in their collective activity. The fidelity of this neural population code depends on whether and how variability in the response of one neuron is shared with other neurons. Two decades of studies have investigated the influence of these noise correlations on the properties of neural coding. We provide an overview of the theoretical developments on the topic. Using simple, qualitative, and general arguments, we discuss, categorize, and relate the various published results. We emphasize the relevance of the fine structure of noise correlation, and we present a new approach to the issue. Throughout this review, we emphasize a geometrical picture of how noise correlations impact the neural code.

Functional Diversity in the Retina Improves the Population Code

Within a given brain region, individual neurons exhibit a wide variety of different feature selectivities. Here, we investigated the impact of this extensive functional diversity on the population neural code. Our approach was to build optimal decoders to discriminate among stimuli using the spiking output of a real, measured neural population and compare its performance against a matched, homogeneous neural population with the same number of cells and spikes. Analyzing large populations of retinal ganglion cells, we found that the real, heterogeneous population can yield a discrimination error lower than the homogeneous population by several orders of magnitude and consequently can encode much more visual information. This effect increases with population size and with graded degrees of heterogeneity. We complemented these results with an analysis of coding based on the Chernoff distance, as well as derivations of inequalities on coding in certain limits, from which we can conclude that the beneficial effect of heterogeneity occurs over a broad set of conditions. Together, our results indicate that the presence of functional diversity in neural populations can enhance their coding fidelity appreciably. A noteworthy outcome of our study is that this effect can be extremely strong and should be taken into account when investigating design principles for neural circuits.

How Diverse Retinal Functions Arise from Feedback at the First Visual Synapse

Many brain regions contain local interneurons of distinct types. How does an interneuron type contribute to the input-output transformations of a given brain region? We addressed this question in the mouse retina by chemogenetically perturbing horizontal cells, an interneuron type providing feedback at the first visual synapse, while monitoring the light-driven spiking activity in thousands of ganglion cells, the retinal output neurons. We uncovered six reversible perturbation-induced effects in the response dynamics and response range of ganglion cells. The effects were enhancing or suppressive, occurred in different response epochs, and depended on the ganglion cell type. A computational model of the retinal circuitry reproduced all perturbation-induced effects and led us to assign specific functions to horizontal cells with respect to different ganglion cell types. Our combined experimental and theoretical work reveals how a single interneuron type can differentially shape the dynamical properties of distinct output channels of a brain region.

Interpretation of correlated neural variability from models of feed-forward and recurrent circuits

Neural populations respond to the repeated presentations of a sensory stimulus with correlated variability. These correlations have been studied in detail, with respect to their mechanistic origin, as well as their influence on stimulus discrimination and on the performance of population codes. A number of theoretical studies have endeavored to link network architecture to the nature of the correlations in neural activity. Here, we contribute to this effort: in models of circuits of stochastic neurons, we elucidate the implications of various network architectures—recurrent connections, shared feed-forward projections, and shared gain fluctuations—on the stimulus dependence in correlations. Specifically, we derive mathematical relations that specify the dependence of population-averaged covariances on firing rates, for different network architectures. In turn, these relations can be used to analyze data on population activity. We examine recordings from neural populations in mouse auditory cortex. We find that a recurrent network model with random effective connections captures the observed statistics. Furthermore, using our circuit model, we investigate the relation between network parameters, correlations, and how well different stimuli can be discriminated from one another based on the population activity. As such, our approach allows us to relate properties of the neural circuit to information processing.

The response of neurons to a stimulus is variable across trials. A natural solution for reliable coding in the face of noise is the averaging across a neural population. The nature of this averaging depends on the structure of noise correlations in the neural population. In turn, the correlation structure depends on the way noise and correlations are generated in neural circuits. It is in general difficult to identify the origin of correlations from the observed population activity alone. In this article, we explore different theoretical scenarios of the way in which correlations can be generated, and we relate these to the architecture of feed-forward and recurrent neural circuits. Analyzing population recordings of the activity in mouse auditory cortex in response to sound stimuli, we find that population statistics are consistent with those generated in a recurrent network model. Using this model, we can then quantify the effects of network properties on average population responses, noise correlations, and the representation of sensory information.

Noise correlations in the human brain and their impact on pattern classification

Multivariate decoding methods, such as multivoxel pattern analysis (MVPA), are highly effective at extracting information from brain imaging data. Yet, the precise nature of the information that MVPA draws upon remains controversial. Most current theories emphasize the enhanced sensitivity imparted by aggregating across voxels that have mixed and weak selectivity. However, beyond the selectivity of individual voxels, neural variability is correlated across voxels, and such noise correlations may contribute importantly to accurate decoding. Indeed, a recent computational theory proposed that noise correlations enhance multivariate decoding from heterogeneous neural populations. Here we extend this theory from the scale of neurons to functional magnetic resonance imaging (fMRI) and show that noise correlations between heterogeneous populations of voxels (i.e., voxels selective for different stimulus variables) contribute to the success of MVPA. Specifically, decoding performance is enhanced when voxels with high vs. low noise correlations (measured during rest or in the background of the task) are selected during classifier training. Conversely, voxels that are strongly selective for one class in a GLM or that receive high classification weights in MVPA tend to exhibit high noise correlations with voxels selective for the other class being discriminated against. Furthermore, we use simulations to show that this is a general property of fMRI data and that selectivity and noise correlations can have distinguishable influences on decoding. Taken together, our findings demonstrate that if there is signal in the data, the resulting above-chance classification accuracy is modulated by the magnitude of noise correlations.

A central challenge in cognitive neuroscience is decoding mental representations from patterns of brain activity. With functional magnetic resonance imaging (fMRI), multivariate decoding methods like multivoxel pattern analysis (MVPA) have produced numerous discoveries about the brain. However, what information these methods draw upon remains the subject of debate. Typically, each voxel is thought to contribute information through its selectivity (i.e., how differently it responds to the classes being decoded), with improved sensitivity reflecting the aggregation of selectivity across voxels. We show that this interpretation downplays an important factor: MVPA is also highly attuned to noise correlations between voxels with opposite selectivity. Across several analyses of an fMRI dataset, we demonstrate a positive relationship between the magnitude of noise correlations and multivariate decoding performance. Indeed, voxels more selective for one class, or heavily weighted in MVPA, tend to be more strongly correlated with voxels selective for the opposite class. Furthermore, using a model to simulate different levels of selectivity and noise correlations, we find that the benefit of noise correlations for decoding is a general property of fMRI data. These findings help elucidate the computational underpinnings of multivariate decoding in cognitive neuroscience and provide insight into the nature of neural representations.

Dynamics of 45S rDNA sites in the cell cycle: fragile sites and chromosomal stability in Lolium and Festuca

Analyses carried out with fluorescence in situ hybridization (FISH) in C-metaphases of the Lolium-Festuca complex have shown the occurrence of spontaneous fragile sites (FSs) in 45S rDNA regions. FSs are expressed as gaps but they do not result in breaks or chromosomal fragments in these species. These gaps have high DNA condensation observed as thin chromatin fibers that connect the apparent segments of the fragile chromosome, allowing for genomic stability. Assessing the behavior of these regions in the cell cycle of Lolium and Festuca species may lead to a better understanding of the dynamics that preserve stability during cell division. Furthermore, it is interesting to track the dynamics of chromosomes bearing 45S rDNA sites in the cell cycle as well as to observe the expression of FSs with no effect of the mitotic block. We observed variation in both the number and size of 45S FISH signals from the S/G2 phases of interphase and from prophase to anaphase where gaps in 45S rDNA sites also were observed. The change in the degree of condensation of the 45S site begins in the S/G2 phase and appears to be related to the transcriptional demand. Taking into account that the number of 45S rDNA sites tends to be re-established when cells reach telophase, we suggest that the chromatin fiber goes back to the normal condensation level to the anaphase (after segregation), allowing for the approximation of chromosome segments and ensuring dynamics that favor the genomic stability of these species.

Self-assembly and plasticity of synaptic domains through a reaction-diffusion mechanism

Signal transmission across chemical synapses relies crucially on neurotransmitter receptor molecules, concentrated in postsynaptic membrane domains along with scaffold and other postsynaptic molecules. The strength of the transmitted signal depends on the number of receptor molecules in postsynaptic domains, and activity-induced variation in the receptor number is one of the mechanisms of postsynaptic plasticity. Recent experiments have demonstrated that the reaction and diffusion properties of receptors and scaffolds at the membrane, alone, yield spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in neurons. On the basis of these experiments we develop a model describing synaptic receptor domains in terms of the underlying reaction-diffusion processes. Our model predicts that the spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in experiments depends on a few key reactions between receptors and scaffolds. Furthermore, our model suggests novel mechanisms for the alignment of pre- and postsynaptic domains and for short-term postsynaptic plasticity in receptor number. We predict that synaptic receptor domains localize in membrane regions with an increased receptor diffusion coefficient or a decreased scaffold diffusion coefficient. Similarly, we find that activity-dependent increases or decreases in receptor or scaffold diffusion yield a transient increase in the number of receptor molecules concentrated in postsynaptic domains. Thus, the proposed reaction-diffusion model puts forth a coherent set of biophysical mechanisms for the formation, stability, and plasticity of molecular domains on the postsynaptic membrane.

Visual coding with a population of direction-selective neurons

The brain decodes the visual scene from the action potentials of ∼20 retinal ganglion cell types. Among the retinal ganglion cells, direction-selective ganglion cells (DSGCs) encode motion direction. Several studies have focused on the encoding or decoding of motion direction by recording multiunit activity, mainly in the visual cortex. In this study, we simultaneously recorded from all four types of ON-OFF DSGCs of the rabbit retina using a microelectronics-based high-density microelectrode array (HDMEA) and decoded their concerted activity using probabilistic and linear decoders. Furthermore, we investigated how the modification of stimulus parameters (velocity, size, angle of moving object) and the use of different tuning curve fits influenced decoding precision. Finally, we simulated ON-OFF DSGC activity, based on real data, in order to understand how tuning curve widths and the angular distribution of the cells' preferred directions influence decoding performance. We found that probabilistic decoding strategies outperformed, on average, linear methods and that decoding precision was robust to changes in stimulus parameters such as velocity. The removal of noise correlations among cells, by random shuffling trials, caused a drop in decoding precision. Moreover, we found that tuning curves are broad in order to minimize large errors at the expense of a higher average error, and that the retinal direction-selective system would not substantially benefit, on average, from having more than four types of ON-OFF DSGCs or from a perfect alignment of the cells' preferred directions.

High-fidelity coding with correlated neurons

Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes, or at best marginally favorable compared to independent codes. Here, we show that positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude. Likewise, the number of stimuli encoded—the capacity—can be enhanced more than tenfold. These effects do not necessitate unrealistic correlation values, and can occur for populations with a few tens of neurons. We further show that both effects benefit from heterogeneity commonly seen in population activity. Error suppression and capacity enhancement rest upon a pattern of correlation. Tuning of one or several effective parameters can yield a limit of perfect coding: the corresponding pattern of positive correlation leads to a ‘lock-in’ of response probabilities that eliminates variability in the subspace relevant for stimulus discrimination. We discuss the nature of this pattern and we suggest experimental tests to identify it.

Traditionally, sensory neuroscience has focused on correlating inputs from the physical world with the response of a single neuron. Two stimuli can be distinguished solely from the response of one neuron if one stimulus elicits a response and the other does not. But as soon as one departs from extremely simple stimuli, single-cell coding becomes less effective, because cells often respond weakly and unreliably. High fidelity coding then relies upon populations of cells, and correlation among those cells can greatly affect the neural code. While previous theoretical studies have demonstrated a potential coding advantage of correlation, they allowed only a marginal improvement in coding power. Here, we present a scenario in which a pattern of correlation among neurons in a population yields an improvement in coding performance by several orders of magnitude. By “improvement” we mean that a neural population is much better at both distinguishing stimuli and at encoding a large number of them. The scenario we propose does not invoke unrealistic values of correlation. What is more, it is even effective for small neural populations and in subtle cases in which single-cell coding fails utterly. These results demonstrate a previously unappreciated potential for correlated population coding.

Rods in daylight act as relay cells for cone-driven horizontal cell-mediated surround inhibition

Vertebrate vision relies on two types of photoreceptors, rods and cones, which signal increments in light intensity with graded hyperpolarizations. Rods operate in the lower range of light intensities while cones operate at brighter intensities. The receptive fields of both photoreceptors exhibit antagonistic center-surround organization. Here we show that at bright light levels, mouse rods act as relay cells for cone-driven horizontal cell-mediated surround inhibition. In response to large, bright stimuli that activate their surrounds, rods depolarize. Rod depolarization increases with stimulus size, and its action spectrum matches that of cones. Rod responses at high light levels are abolished in mice with nonfunctional cones and when horizontal cells are reversibly inactivated. Rod depolarization is conveyed to the inner retina via postsynaptic circuit elements, namely the rod bipolar cells. Our results show that the retinal circuitry repurposes rods, when they are not directly sensing light, to relay cone-driven surround inhibition.

Dynamical adaptation in photoreceptors

Adaptation is at the heart of sensation and nowhere is it more salient than in early visual processing. Light adaptation in photoreceptors is doubly dynamical: it depends upon the temporal structure of the input and it affects the temporal structure of the response. We introduce a non-linear dynamical adaptation model of photoreceptors. It is simple enough that it can be solved exactly and simulated with ease; analytical and numerical approaches combined provide both intuition on the behavior of dynamical adaptation and quantitative results to be compared with data. Yet the model is rich enough to capture intricate phenomenology. First, we show that it reproduces the known phenomenology of light response and short-term adaptation. Second, we present new recordings and demonstrate that the model reproduces cone response with great precision. Third, we derive a number of predictions on the response of photoreceptors to sophisticated stimuli such as periodic inputs, various forms of flickering inputs, and natural inputs. In particular, we demonstrate that photoreceptors undergo rapid adaptation of response gain and time scale, over ∼ 300[Formula: see text] ms-i. e., over the time scale of the response itself-and we confirm this prediction with data. For natural inputs, this fast adaptation can modulate the response gain more than tenfold and is hence physiologically relevant.

Chemotaxis when bacteria remember: drift versus diffusion

Escherichia coli (E. coli) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles – a fact not borne out by experiment – and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.

The chemotaxis of Escherichia coli is a prototypical model of navigational strategy. The bacterium maneuvers by switching between near-straight motion, termed runs, and tumbles which reorient its direction. To reach regions of high nutrient concentration, the run-durations are modulated according to the nutrient concentration experienced in recent past. This navigational strategy is quite general, in that the mathematical description of these modulations also accounts for the active motility of C. elegans and for thermotaxis in Escherichia coli. Recent studies have pointed to a possible incompatibility between reaching regions of high nutrient concentration quickly and staying there at long times. We use numerical investigations and analytical arguments to reexamine navigational strategy in bacteria. We show that, by accounting properly for the full memory of the bacterium, this paradox is resolved. Our work clarifies the mechanism that underlies chemotaxis and indicates that chemotactic navigation in wild-type bacteria is controlled by drift while in some mutant bacteria it is controlled by a modulation of the diffusion. We also propose a new set of effective, large-scale equations which describe bacterial chemotactic navigation. Our description is significantly different from previous ones, as it results from a conceptually different coarse-graining procedure.

Formation and stability of synaptic receptor domains

Neurotransmitter receptor molecules, concentrated in postsynaptic domains along with scaffold and a number of other molecules, are key regulators of signal transmission across synapses. Combining experiment and theory, we develop a quantitative description of synaptic receptor domains in terms of a reaction-diffusion model. We show that interactions between only receptors and scaffolds, together with the rapid diffusion of receptors on the cell membrane, are sufficient for the formation and stable characteristic size of synaptic receptor domains. Our work reconciles long-term stability of synaptic receptor domains with rapid turnover and diffusion of individual receptors, and suggests novel mechanisms for a form of short-term, postsynaptic plasticity.

Cell types, circuits, computation

How does the connectivity of a neuronal circuit, together with the individual properties of the cell types that take part in it, result in a given computation? We examine this question in the context of retinal circuits. We suggest that the retina can be viewed as a parallel assemblage of many small computational devices, highly stereotypical and task-specific circuits afferent to a given ganglion cell type, and we discuss some rules that govern computation in these devices. Multi-device processing in retina poses conceptual problems when it is contrasted with cortical processing. We lay out open questions both on processing in retinal circuits and on implications for cortical processing of retinal inputs.

Approach sensitivity in the retina processed by a multifunctional neural circuit

The detection of approaching objects, such as looming predators, is necessary for survival. Which neurons and circuits mediate this function? We combined genetic labeling of cell types, two-photon microscopy, electrophysiology and theoretical modeling to address this question. We identify an approach-sensitive ganglion cell type in the mouse retina, resolve elements of its afferent neural circuit, and describe how these confer approach sensitivity on the ganglion cell. The circuit's essential building block is a rapid inhibitory pathway: it selectively suppresses responses to non-approaching objects. This rapid inhibitory pathway, which includes AII amacrine cells connected to bipolar cells through electrical synapses, was previously described in the context of night-time vision. In the daytime conditions of our experiments, the same pathway conveys signals in the reverse direction. The dual use of a neural pathway in different physiological conditions illustrates the efficiency with which several functions can be accommodated in a single circuit.

Steady-state chemotaxis in Escherichia coli

The bacterium E. coli maneuvers itself to regions with high chemoattractant concentrations by performing two stereotypical moves: "runs," in which it moves in near-straight lines, and "tumbles," in which it does not advance but changes direction randomly. The duration of each move is stochastic and depends upon the chemoattractant concentration experienced in the recent past. We relate this stochastic behavior to the steady-state density of a bacterium population, and we derive the latter as a function of chemoattractant concentration. In contrast to earlier treatments, here we account for the effects of temporal correlations and variable tumbling durations. A range of behaviors is obtained that depends subtly upon several aspects of the system -- memory, correlation, and tumbling stochasticity, in particular.