Optimal allocation of finite sampling capacity in accumulator models of multi-alternative decision making

When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally allocate limited sampling time to multiple options, modelled as accumulators of noisy evidence, to determine the most profitable one. We show that the effective sampling capacity of an agent increases with both available time and the discriminability of the options, and optimal policies undergo a sharp transition as a function of it. For small capacity, it is best to allocate time evenly to exactly five options and to ignore all the others, regardless of the prior distribution of rewards. For large capacities, the optimal number of sampled accumulators grows sub-linearly, closely following a power law for a wide variety of priors. We find that allocating equal times to the sampled accumulators is better than using uneven time allocations. Our work highlights that multi-alternative decisions are endowed with breadth-depth tradeoffs, demonstrates how their optimal solutions depend on the amount of limited resources and the variability of the environment, and shows that narrowing down to a handful of options is always optimal for small capacities

Alternation rate in perceptual bistability is maximal at and symmetric around equi-dominance

When an ambiguous stimulus is viewed for a prolonged time, perception alternates between the different possible interpretations of the stimulus. The alternations seem haphazard, but closer inspection of their dynamics reveals systematic properties in many bistable phenomena. Parametric manipulations result in gradual changes in the fraction of time a given interpretation dominates perception, often over the entire possible range of zero to one. The mean dominance durations of the competing interpretations can also vary over wide ranges (from less than a second to dozens of seconds or more), but finding systematic relations in how they vary has proven difficult. Following the pioneering work of W. J. M. Levelt (1968) in binocular rivalry, previous studies have sought to formulate a relation in terms of the effect of physical parameters of the stimulus, such as image contrast in binocular rivalry. However, the link between external parameters and “stimulus strength” is not as obvious for other bistable phenomena. Here we show that systematic relations readily emerge when the mean dominance durations are examined instead as a function of “percept strength,” as measured by the fraction of dominance time, and provide theoretical rationale for this observation. For three different bistable phenomena, plotting the mean dominance durations of the two percepts against the fraction of dominance time resulted in complementary curves with near-perfect symmetry around equi-dominance (the point where each percept dominates half the time). As a consequence, the alternation rate reaches a maximum at equi-dominance. We next show that the observed behavior arises naturally in simple double-well energy models and in neural competition models with cross-inhibition and input normalization. Finally, we discuss the possibility that bistable perceptual switches reflect a perceptual “exploratory” strategy, akin to foraging behavior, which leads naturally to maximal alternation rate at equi-dominance if perceptual switches come with a cost

Auto and crosscorrelograms for the spike response of LIF neurons with slow synapses

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in \cite{Mor+04}. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication.Comment: 5 pages, 3 figure

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

Scaling of sensory information in largeneural populations shows signatures ofinformation-limiting correlations

How is information distributed across large neuronal populations within a given brain area? Information may be distributed roughly evenly across neuronal populations, so that total information scales linearly with the number of recorded neurons. Alternatively, the neural code might be highly redundant, meaning that total information saturates. Here we investigate how sensory information about the direction of a moving visual stimulus is distributed across hundreds of simultaneously recorded neurons in mouse primary visual cortex. We show that information scales sublinearly due to correlated noise in these populations. We compartmentalized noise correlations into information-limiting and nonlimiting components, then extrapolate to predict how information grows with even larger neural populations. We predict that tens of thousands of neurons encode 95% of the information about visual stimulus direction, much less than the number of neurons in primary visual cortex. These findings suggest that the brain uses a widely distributed, but nonetheless redundant code that supports recovering most sensory information from smaller subpopulations.We would like to thank Alexandre Pouget, Peter Latham, and members of the HMSNeurobiology Department for useful discussions and feedback on the work, and RachelWilson and Richard Born for comments on early versions of the manuscript. The workwas supported by a scholar award from the James S. McDonnell Foundation (grant#220020462 to J.D.), grants from the NIH (R01MH115554 to J.D.; R01MH107620 to C.D.H.; R01NS089521 to C.D.H.; R01NS108410 to C.D.H.; F31EY031562 to A.W.J.), theNSF’s NeuroNex program (DBI-1707398. to R.N.), MINECO (Spain; BFU2017-85936-Pto R.M.-B.), the Howard Hughes Medical Institute (HHMI, ref 55008742 to R.M.-B.), theICREA Academia (2016 to R.M.-B.), the Government of Aragon (Spain; ISAAC lab, codT33 17D to I.A.-R.), the Spanish Ministry of Economy and Competitiveness (TIN2016-80347-R to I.A.-R.), the Gatsby Charitable Foundation (to R.N.), and an NSF GraduateResearch Fellowship (to A.W.J.)

Poisson-like spiking in circuits with probabilistic synapses.

Neuronal activity in cortex is variable both spontaneously and during stimulation, and it has the remarkable property that it is Poisson-like over broad ranges of firing rates covering from virtually zero to hundreds of spikes per second. The mechanisms underlying cortical-like spiking variability over such a broad continuum of rates are currently unknown. We show that neuronal networks endowed with probabilistic synaptic transmission, a well-documented source of variability in cortex, robustly generate Poisson-like variability over several orders of magnitude in their firing rate without fine-tuning of the network parameters. Other sources of variability, such as random synaptic delays or spike generation jittering, do not lead to Poisson-like variability at high rates because they cannot be sufficiently amplified by recurrent neuronal networks. We also show that probabilistic synapses predict Fano factor constancy of synaptic conductances. Our results suggest that synaptic noise is a robust and sufficient mechanism for the type of variability found in cortex

Effects of synchronization and synaptic time scales on the neuronal response

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica, Fecha de lectura 02-12-2004