Parametric Representation of Tactile Numerosity in Working Memory

Estimated numerosity perception is processed in an approximate number system (ANS) that resembles the perception of a continuous magnitude. The ANS consists of a right lateralized frontoparietal network comprising the lateral prefrontal cortex (LPFC) and the intraparietal sulcus. Although the ANS has been extensively investigated, only a few studies have focused on the mental representation of retained numerosity estimates. Specifically, the underlying mechanisms of estimated numerosity working memory (WM) is unclear. Besides numerosities, as another form of abstract quantity, vibrotactile WM studies provide initial evidence that the right LPFC takes a central role in maintaining magnitudes. In the present fMRI multivariate pattern analysis study, we designed a delayed match-to-numerosity paradigm to test what brain regions retain approximate numerosity memoranda. In line with parametric WM results, our study found numerosity-specific WM representations in the right LPFC as well as in the supplementary motor area and the left premotor cortex extending into the superior frontal gyrus, thus bridging the gap in abstract quantity WM literature

Subitizing with Variational Autoencoders

Numerosity, the number of objects in a set, is a basic property of a given visual scene. Many animals develop the perceptual ability to subitize: the near-instantaneous identification of the numerosity in small sets of visual items. In computer vision, it has been shown that numerosity emerges as a statistical property in neural networks during unsupervised learning from simple synthetic images. In this work, we focus on more complex natural images using unsupervised hierarchical neural networks. Specifically, we show that variational autoencoders are able to spontaneously perform subitizing after training without supervision on a large amount images from the Salient Object Subitizing dataset. While our method is unable to outperform supervised convolutional networks for subitizing, we observe that the networks learn to encode numerosity as basic visual property. Moreover, we find that the learned representations are likely invariant to object area; an observation in alignment with studies on biological neural networks in cognitive neuroscience

Interaction of numerosity and time in prefrontal and parietal cortex

It has been proposed that numerical and temporal information are processed by partially overlapping magnitude systems. Interactions across different magnitude domains could occur both at the level of perception and decision-making. However, their neural correlates have been elusive. Here, using functional magnetic resonance imaging in humans, we show that the right intraparietal cortex (IPC) and inferior frontal gyrus (IFG) are jointly activated by duration and numerosity discrimination tasks, with a congruency effect in the right IFG. To determine whether the IPC and the IFG are involved in response conflict (or facilitation) or modulation of subjective passage of time by numerical information, we examined their functional roles using transcranial magnetic stimulation (TMS) and two different numerosity-time interaction tasks: duration discrimination and time reproduction tasks. Our results show that TMS of the right IFG impairs categorical duration discrimination, whereas that of the right IPC modulates the degree of influence of numerosity on time perception and impairs precise time estimation. These results indicate that the right IFG is specifically involved at the categorical decision stage, whereas bleeding of numerosity information on perception of time occurs within the IPC. Together, our findings suggest a two-stage model of numerosity-time interactions whereby the interaction at the perceptual level occurs within the parietal region and the interaction at categorical decisions takes place in the prefrontal cortex

Commentary: From 'sense of number' to 'sense of magnitude' - The role of continuous magnitudes in numerical cognition

Unlike abstract ones in mathematics, concrete sets of elements in the real world have continuous physical properties, such as overall area and density. The dominant view has it that humans can estimate the discrete numerosities of such sets independently of the co-varying continuous magnitudes; i.e., that humans have a “sense of number”. It has indeed been claimed that various animals, ranging from monkeys to tiny fish, have this sense too. A recent paper by Leibovich et al. (2016) questions all of this (see also Gebuis et al., 2016; Morgan et al., 2014) and argues convincingly that numerosity estimation is not independent from continuous magnitudes but relies on them; that we have not a “sense of number” but a “sense of magnitude”. Yet the authors fail to cite a classic article that made the very same argument 25 years ago, and—unlike Leibovich et al.—supported it with a quantitative model (Allik and Tuulmets, 1991). Although neither density, nor overall area, nor any other single continuous magnitude can provide reliable information about numerosity, Leibovich et al. imply that all of them together can; they suggest that “statistical learning” will take care of extracting this information and turn numerosity estimates out of it. How statistical learning achieves this feat and whether the resulting numerosity estimates will fit observed ones remains, unfortunately, unclear. Allik and Tuulmets’s alternative “occupancy” model has its limits (e.g., Bertamini et al., 2016; Kramer et al., 2011) but it is specific, it is quantitative, and it predicts observed numerosity estimation surprisingly well with just a single free parameter

An emergentist perspective on the origin of number sense

open2noopenZorzi, Marco; Testolin, AlbertoZorzi, Marco; Testolin, Albert

How illusory is the solitaire illusion? Assessing the degree of misperception of numerosity in adult humans

open3siopenAgrillo, Christian; Parrish, Audrey E.; Beran, Michael J.Agrillo, Christian; Parrish, Audrey E.; Beran, Michael J

Enumeration in Alzheimer's disease and other late life psychiatric syndromes

Previous studies suggest that visual enumeration is spared in normal aging but impaired in abnormal aging (late stage Alzheimer's disease, AD), raising the task's potential as a marker of dementia. Experiment 1 compared speeded enumeration of 1–9 random dots in early stage AD, vascular dementia (VAD), depression, and age-matched controls. Previous deficits were replicated but they were not specific to AD, with the rate of counting larger numerosities similarly slowed relative to controls by both AD and VAD. Determination of subitizing span was complicated by the surprisingly slower enumeration of one than of two items, especially in AD patients. Experiment 2 showed that AD patients’ relative difficulty with one item persisted with further practice and extended to the enumeration of targets among distractors. However, it was abolished when pattern recognition was possible (enumerating dots on a die). Although an enumeration test is unlikely to help differentiate early AD from other common dementias, the unexpected pattern of patients’ performance challenges current models of enumeration and requires further investigation