An emergentist perspective on the origin of number sense

McClelland

2020

Psychon Bull Rev

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Both humans and nonhuman animals can exhibit sensitivity to the approximate number of items in a visual array or events in a sequence, and across various paradigms, uncertainty in numerosity judgments increases with the number estimated or produced. The pattern of increase is usually described as exhibiting approximate adherence to Weber’s law, such that uncertainty increases proportionally to the mean estimate, resulting in a constant coefficient of variation. Such a pattern has been proposed to be a signature characteristic of an innate “number sense.” We reexamine published behavioral data from two studies that have been cited as prototypical evidence of adherence to Weber’s law and observe that in both cases variability increases less than this account would predict, as indicated by a decreasing coefficient of variation with an increase in number. We also consider evidence from numerosity discrimination studies that show deviations from the constant coefficient of variation pattern. Though behavioral data can sometimes exhibit approximate adherence to Weber’s law, our findings suggest that such adherence is not a fixed characteristic of the mechanisms whereby humans and animals estimate numerosity. We suggest instead that the observed pattern of increase in variability with number depends on the circumstances of the task and stimuli, and reflects an adaptive ensemble of mechanisms composed to optimize performance under these circumstances.

Section: Discussionmentioning

confidence: 99%

Do estimates of numerosity really adhere to Weber’s law? A reexamination of two case studies

McClelland

2020

Psychon Bull Rev

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“…Previous work has shown that deep belief networks can indeed simulate basic numerical abilities 39 . However, in the original model only cumulative area was taken into account as possible confound, and subsequent simulations presented anectodical evidence that stronger congruency manipulations can affect model's responses 40 . Here we push this modeling approach one step further.…”

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confidence: 98%

Visual sense of number vs. sense of magnitude in humans and machines

Dolfi

Rochus

et al. 2020

Sci Rep

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Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment.

“…Is there a set of fundamental properties underlying the structure and dynamics of deep neural networks?Some insights into these challenging questions have been gained by inspecting deep learning systems with methods borrowed from neuroscience. For example, response profiles of individual neurons in deep networks often exhibit an impressive match with neurophysiological data [31,54,56,61]. Similarly, at the neuronal population level it has been shown that the representational space developed by deep networks has a striking overlap with that observed in the inferior temporal cortex of the primate brain [15,26].…”

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confidence: 99%

Deep learning systems as complex networks

Journal of Complex Networks

Piccolini²,

Suweis

2019

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Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods have greatly improved the state-of-the-art in many challenging cognitive tasks, such as visual object recognition, speech processing, natural language understanding and automatic translation. In particular, one class of deep learning models, known as deep belief networks, can discover intricate statistical structure in large data sets in a completely unsupervised fashion, by learning a generative model of the data using Hebbian-like learning mechanisms. Although these self-organizing systems can be conveniently formalized within the framework of statistical mechanics, their internal functioning remains opaque, because their emergent dynamics cannot be solved analytically. In this article we propose to study deep belief networks using techniques commonly employed in the study of complex networks, in order to gain some insights into the structural and functional properties of the computational graph resulting from the learning process. IntroductionRecent strides in artificial intelligence research have opened tremendous opportunities for technological development. In particular, the last decade has been marked by the so-called "deep learning revolution", which is having strong impact both for scientific investigation and for engineering applications [30].Deep learning allows building artificial neural networks composed of many processing layers, which can learn high-level representations of the data by exploiting multiple levels of abstraction [18]. To differ from conventional machine-learning techniques, this allows to automatically discover intricate statistical structure in large datasets without the need for domain expert knowledge: the relevant features needed to 1 arXiv:1809.10941v1 [cond-mat.dis-nn] 28 Sep 2018 describe the data distribution are directly learned by the machine from the raw input (e.g., pixels values in a digital image). An intriguing aspect of deep learning systems is that they are inspired by neuronal networks in biological brains: information processing occurs in a parallel and distributed fashion [46], thereby allowing cognitive abilities to emerge from the orchestrated operation of many simple, non-linear processing units [35,58].Deep learning has dramatically improved the state-of-the-art in challenging cognitive tasks, such as image classification [16,27], speech recognition [40], natural language understanding [11] and even highlevel reasoning [39,51]. It is currently employed by all major IT companies (Google, Facebook, Microsoft, Apple, just to mention a few) to automatically extract knowledge from large digital datasets, and it is achieving impressive performance also in many other domains such as drug discovery [34], genomics [60], high-energy physics [5] and telecommunications [57,63].However, despite the continuous progress and the widespread d...