Rakesh Sengupta

A Shared, Flexible Neural Map Architecture Reflects Capacity Limits in Both Visual Short-Term Memory and Enumeration

Human cognition is characterized by severe capacity limits: we can accurately track, enumerate, or hold in mind only a small number of items at a time. It remains debated whether capacity limitations across tasks are determined by a common system. Here we measure brain activation of adult subjects performing either a visual short-term memory (vSTM) task consisting of holding in mind precise information about the orientation and position of a variable number of items, or an enumeration task consisting of assessing the number of items in those sets. We show that task-specific capacity limits (three to four items in enumeration and two to three in vSTM) are neurally reflected in the activity of the posterior parietal cortex (PPC): an identical set of voxels in this region, commonly activated during the two tasks, changed its overall response profile reflecting task-specific capacity limitations. These results, replicated in a second experiment, were further supported by multivariate pattern analysis in which we could decode the number of items presented over a larger range during enumeration than during vSTM. Finally, we simulated our results with a computational model of PPC using a saliency map architecture in which the level of mutual inhibition between nodes gives rise to capacity limitations and reflects the task-dependent precision with which objects need to be encoded (high precision for vSTM, lower precision for enumeration). Together, our work supports the existence of a common, flexible system underlying capacity limits across tasks in PPC that may take the form of a saliency map.

A visual sense of number emerges from the dynamics of a recurrent on-center off-surround neural network.

It has been proposed that the ability of humans to quickly perceive numerosity involves a visual sense of number. Different paradigms of enumeration and numerosity comparison have produced a gamut of behavioral and neuroimaging data, but there has been no unified conceptual framework that can explain results across the entire range of numerosity. The current work tries to address the ongoing debate concerning whether the same mechanism operates for enumeration of small and large numbers, through a computational approach. We describe the workings of a single-layered, fully connected network characterized by self-excitation and recurrent inhibition that operates at both subitizing and estimation ranges. We show that such a network can account for classic numerical cognition effects (the distance effect, Fechner׳s law, Weber fraction for numerosity comparison) through the network steady state activation response across different recurrent inhibition values. The model also accounts for fMRI data previously reported for different enumeration related tasks. The model also allows us to generate an estimate of the pattern of reaction times in enumeration tasks. Overall, these findings suggest that a single network architecture can account for both small and large number processing.

From Neural Network To Psychophysics Of Time: Exploring Emergent Properties Of RNNs Using Novel Hamiltonian Formalism

The stability analysis of dynamical neural network systems generally follows the route of finding a suitable Liapunov function after the fashion Hopfield’s famous paper on content addressable memory network or by finding conditions that make divergent solutions impossible. For the current work we focused on biological recurrent neural networks (bRNNs) that require transient external inputs (Cohen-Grossberg networks). In the current work we have proposed a general method to construct Liapunov functions for recurrent neural network with the help of a physically meaningful Hamiltonian function. This construct allows us to explore the emergent properties of the recurrent network (e.g., parameter configuration needed for winner-take-all competition in a leaky accumulator design) beyond that available in standard stability analysis, while also comparing well with standard stability analysis (ordinary differential equation approach) as a special case of the general stability constraint derived from the Hamiltonian formulation. We also show that the Cohen-Grossberg Liapunov function can be derived naturally from the Hamiltonian formalism. A strength of the construct comes from its usability as a predictor for behavior in psychophysical experiments involving numerosity and temporal duration judgements.

Big and small numbers: Empirical support for a single, flexible mechanism for numerosity perception

The existence of perceptually distinct numerosity ranges has been proposed for small (i.e., subitizing range) and larger numbers based on differences in precision, Weber fractions, and reaction times. This raises the question of whether such dissociations reflect distinct mechanisms operating across the two numerosity ranges. In the present work, we explore the predictions of a single-layer recurrent on-center, off-surround network model of attentional priority that has been applied to object individuation and enumeration. Activity from the network can be used to model various phenomena in the domain of visual number perception based on a single parameter: the strength of inhibition between nodes. Specifically, higher inhibition allows for precise representation of small numerosities, while low inhibition is preferred for high numerosities. The model makes novel predictions, including that enumeration of small numerosities following large numerosities should result in longer reaction times than when a small numerosity trial following small numerosities. Moreover, the model predicts underestimation of number when a display containing a large number of items follows a trial with small numerosities. We behaviorally confirmed these predictions in a series of experiments. This pattern of results is consistent with a single, flexible object individuation system, which can be modeled successfully by dynamic on-center, off-surround network model of the attentional priority (saliency) map.

The influence of pre-stimulus brain oscillations on the visual sense of number: an MEG study

The visual system is able to rapidly and accurately enumerate a small number of items (subitizing) or, instead, to estimate less precisely a large number of items (estimation). Recent computational, behavioral (Sengupta et al, 2014) and fMRI (Roggeman et al.2010; Knops et al, 2014) studies are consistent with the idea that a single enumeration mechanism may be able to account for both small and large number perception under different levels of inhibition between nodes. In other words, the visual sense of number can be explained through the dynamics of a single recurrent on-center, off-surround network in which the network produces different regimes of numerosities by modulating the inhibition between nodes of the network. Accurate and precise subitizing would require high levels of inhibition between nodes, while low inhibition would account for performance in the estimation range. In the present study we used MEG recording to study the switches in enumeration ranges across series of small (1-4 items) or large (20-30 items) numerosity trials of different lengths. We found modulation of the pre-stimulus alpha (α) and beta (β) frequency bands as a function of whether the previous trials had involved subitizing or estimation. These results, combined with behavioral results showing a specific pattern of switch costs between small and large numerosity trials, are consistent with a change in the pre-stimulus state that prepares the visual system to most effectively enumerate items as either individuals or as an ensemble. Meeting abstract presented at VSS 2015.