Subdiffusive dynamics of bump attractors: mechanisms and functional roles

Multiple bumps can enhance robustness to noise in continuous attractor networks

A central function of continuous attractor networks is encoding coordinates and accurately updating their values through path integration. To do so, these networks produce localized bumps of activity that move coherently in response to velocity inputs. In the brain, continuous attractors are believed to underlie grid cells and head direction cells, which maintain periodic representations of position and orientation, respectively. These representations can be achieved with any number of activity bumps, and the consequences of having more or fewer bumps are unclear. We address this knowledge gap by constructing 1D ring attractor networks with different bump numbers and characterizing their responses to three types of noise: fluctuating inputs, spiking noise, and deviations in connectivity away from ideal attractor configurations. Across all three types, networks with more bumps experience less noise-driven deviations in bump motion. This translates to more robust encodings of linear coordinates, like position, assuming that each neuron represents a fixed length no matter the bump number. Alternatively, we consider encoding a circular coordinate, like orientation, such that the network distance between adjacent bumps always maps onto 360 degrees. Under this mapping, bump number does not significantly affect the amount of error in the coordinate readout. Our simulation results are intuitively explained and quantitatively matched by a unified theory for path integration and noise in multi-bump networks. Thus, to suppress the effects of biologically relevant noise, continuous attractor networks can employ more bumps when encoding linear coordinates; this advantage disappears when encoding circular coordinates. Our findings provide motivation for multiple bumps in the mammalian grid network.

Synaptic mechanisms of interference in working memory

Information from preceding trials of cognitive tasks can bias performance in the current trial, a phenomenon referred to as interference. Subjects performing visual working memory tasks exhibit interference in their responses: the recalled target location is biased in the direction of the target presented on the previous trial. We present modeling work that develops a probabilistic inference model of this history-dependent bias, and links our probabilistic model to computations of a recurrent network wherein short-term facilitation accounts for the observed bias. Network connectivity is reshaped dynamically during each trial, generating predictions from prior trial observations. Applying timescale separation methods, we obtain a low-dimensional description of the trial-to-trial bias based on the history of target locations. Furthermore, we demonstrate task protocols for which our model with facilitation performs better than a model with static connectivity: repetitively presented targets are better retained in working memory than targets drawn from uncorrelated sequences.

Serial dependence is absent at the time of perception but increases in visual working memory

Recent experiments have shown that visual cognition blends current input with that from the recent past to guide ongoing decision making. This serial dependence appears to exploit the temporal autocorrelation normally present in visual scenes to promote perceptual stability. While this benefit has been assumed, evidence that serial dependence directly alters stimulus perception has been limited. In the present study, we parametrically vary the delay between stimulus and response in a spatial delayed response task to explore the trajectory of serial dependence from the moment of perception into post-perceptual visual working memory. We find that behavioral responses made immediately after viewing a stimulus show evidence of adaptation, but not attractive serial dependence. Only as the memory period lengthens is a blending of past and present information apparent in behavior, reaching its maximum with a delay of six seconds. These results dovetail with other recent findings to bolster the interpretation that serial dependence is a phenomenon of mnemonic rather than perceptual processes. However, even while this pattern of effects in group-averaged data has now been found consistently, we show that the relative strengths of adaptation and serial dependence vary widely across individuals. Finally, we demonstrate that when leading mathematical models of working memory are adjusted to account for these trial-history effects, their fit to behavioral data is substantially improved.

Neural Field Models with Threshold Noise

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.

Dynamic patterns in a two-dimensional neural field with refractoriness

The formation of dynamic patterns such as localized propagating waves is a fascinating self-organizing phenomenon that happens in a wide range of spatially extended systems including neural systems, in which they might play important functional roles. Here we derive a type of two-dimensional neural-field model with refractoriness to study the formation mechanism of localized waves. After comparing this model with existing neural-field models, we show that it is able to generate a variety of localized patterns, including stationary bumps, localized waves rotating along a circular path, and localized waves with longer-range propagation. We construct explicit bump solutions for the two-dimensional neural field and conduct a linear stability analysis on how a stationary bump transitions to a propagating wave under different spatial eigenmode perturbations. The neural-field model is then partially solved in a comoving frame to obtain localized wave solutions, whose spatial profiles are in good agreement with those obtained from simulations. We demonstrate that when there are multiple such propagating waves, they exhibit rich propagation dynamics, including propagation along periodically oscillating and irregular trajectories; these propagation dynamics are quantitatively characterized. In addition, we show that these waves can have repulsive or merging collisions, depending on their collision angles and the refractoriness parameter. Due to its analytical tractability, the two-dimensional neural-field model provides a modeling framework for studying localized propagating waves and their interactions.