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

Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism

Traditionally, the visual enumeration of a small number of items (1 to about 4), referred to as subitizing, has been thought of as a parallel and pre-attentive process and functionally different from the serial attentive enumeration of larger numerosities. We tested this hypothesis by employing a dual task paradigm that systematically manipulated the attentional resources available to an enumeration task. Enumeration accuracy for small numerosities was severely decreased as more attentional resources were taken away from the numerical task, challenging the traditionally held notion of subitizing as a pre-attentive, capacity-independent process. Judgement of larger numerosities was also affected by dual task conditions and attentional load. These results challenge the proposal that small numerosities are enumerated by a mechanism separate from large numerosities and support the idea of a single, attention-demanding enumeration mechanism

China's post-coal growth

Slowing GDP growth, a structural shift away from heavy industry, and more proactive policies on air pollution and clean energy have caused China's coal use to peak. It seems that economic growth has decoupled from growth in coal consumption

Insatiability and Crisis: Using Interdisciplinarity to Understand (and Denaturalize) Contemporary Humans

This chapter illustrates how collaboration between different social sciences can encourage students to think critically about prevailing assumptions regarding human nature. Both the chapter and the pedagogical experience on which it is based investigate the distinctive type of human created by capitalist society. In so doing, it takes a heterodox approach to analyzing the concept of an insatiable human nature through a case study that invites students to critically assess this perspective. This discussion then leads to an investigation and critique of traditional neoclassical Economic assumptions about human behavior, which forms the basis for a case study on the causes of the global economic and financial crisis of 2008. The goal is to facilitate students’ development of a more grounded perspective on real world events

Environment change, economy change and reducing conflict at source

At a time when fossil fuel burning, nationalism, ethnic and religious intolerance, and other retrograde steps are being promoted, the prospects for world peace and environmental systems stability may appear dim. Yet now is it the more important to continue to examine the sources of conflict. A major obstacle to general progress is the currently dominant economic practice and theory, which is here called the economy-as-usual, or economics-as-usual, as appropriate. A special obstacle to constructive change is the language in which economic matters are usually discussed. This language is narrow, conservative, technical and often obscure. The rapid changes in the environment (physical and living) are largely kept in a separate compartment. If, however, the partition is removed, economics -as-usual, with its dependence on growth and its widening inequality, is seen to be unsustainable. Radical economic change, for better or worse, is to be expected. Such change is here called economy change. The change could be for the better if it involved an expansion of the concept of economics itself, along the lines of oikonomia, a modern revival of a classical Greek term for management or household. In such an expanded view, not everything of economic value can be measured. It is argued that economics-as-usual is the source of much strife. Some features are indicated of a less conflictual economy - more just, cooperative and peaceful. These features include a dignified life available to all people as of right, the word 'wealth' being reconnected with weal, well and well-being, and 'work' being understood as including all useful activity

Marx’s metaphysics of human labour in the light of Sraffa : labour theory of value reconsidered

In this chapter, I analyse the foundations of Marx’s analysis of a capitalist economy in terms of labour time to locate the root cause of Marx’s problem of relating values to prices and surplus values to profits, and then show how Sraffa succeeds in solving the problem by liberating Marx from his metaphysics of “human labour.

The Effect of Viewing Eccentricity on Enumeration

Visual acuity and contrast sensitivity progressively diminish with increasing viewing eccentricity. Here we evaluated how visual enumeration is affected by visual eccentricity, and whether subitizing capacity, the accurate enumeration of a small number (∼3) of items, decreases with more eccentric viewing. Participants enumerated gratings whose (1) stimulus size was constant across eccentricity, and (2) whose stimulus size scaled by a cortical magnification factor across eccentricity. While we found that enumeration accuracy and precision decreased with increasing eccentricity, cortical magnification scaling of size neutralized the deleterious effects of increasing eccentricity. We found that size scaling did not affect subitizing capacities, which were nearly constant across all eccentricities. We also found that size scaling modulated the variation coefficients, a normalized metric of enumeration precision, defined as the standard deviation divided by the mean response. Our results show that the inaccuracy and imprecision associated with increasing viewing eccentricity is due to limitations in spatial resolution. Moreover, our results also support the notion that the precise number system is restricted to small numerosities (represented by the subitizing limit), while the approximate number system extends across both small and large numerosities (indexed by variation coefficients) at large eccentricities