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# Numerical ordering of zero in honey bees

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Science  08 Jun 2018:
Vol. 360, Issue 6393, pp. 1124-1126
DOI: 10.1126/science.aar4975

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• RE: Neural Network Understanding the Concept of Zero
• Adrian Dyer, Visual ecology researcher, RMIT University

This is a very interesting finding showing that whilst an implemented compting solution does not instantly enable the processing of an empty set as zero; the neural network can efficiently acquire through experience the concept to solve the problem with a high degree of accuracy. This is consistent with the position that to learn the basics of zero does not demand a highly sophisticated brain, and environmental exposure is probably the key factor in whether the ability to process zero is evidenced in an animal (or other) system.

Competing Interests: I was an author of the original publication is Science.
• ﻿A Simple Neural Network Understanding the Concept of Zero the Way Honey Bees Do

“Numerical ordering of zero in honey bees” describes a careful experiment showing that honey bees understand some concept of zero (1). Applying the experimental setup to a neural network gives similar results.
We used the 97 different cards from the “Supplementary Materials” and scaled them to 64x64 pixels (1, 2). 64x64 is roughly the resolution honey bees see (Fig. 2 in (1)). The cards are randomly shifted (+/- 2 pixels), rotated (+/- 30°), and downscaled (factor 0.6 to 1.0) to increase the number of images. One could argue: Honey bees fly to the cards and see them shifted, rotated and scaled. The neural network takes two images as input and is trained with a label indicating which of the cards contains more objects.
We used a standard neural network (3). Each image is processed by three convolutional layers with kernel size 7, padding 3 and 64 filters, each followed by a ReLU activation layer and fed into one fully connected layer with two outputs. Training is done with a softmax layer.
We followed the procedure of the original article beginning with training the neural network using cards of one to four non-circular objects. After training with about four million randomly chosen combinations, we determined the accuracy with 19000 independent combinations to 98.7%.
The prediction accuracy for one to four circular objects using the already trained network was 97.8%. The generalization to a higher number of objects was tested using cards of one to f...

Competing Interests: None declared.
• RE: When zero understanding is more than understanding zero

In their report “Numerical ordering of zero in honey bees”(8 June, p. 1124) S.R. Howard et al. claim that honeybees show “an understanding that an empty set is lower than one, which is challenging for some other animals”. My alternative hypothesis explains the discrepancy between bees and these animals by a less-is-more effect (1): bees have less understanding of zero than the other animals; this facilitates treating zero like other numbers.
Bees readily extrapolate their conditioning by a less-than rule from non-empty-set stimuli to an empty-set stimulus in pairwise comparison. They understand that the empty-set stimulus displays less elements. They are even sensitive to numerical distance. Yet they ignore the “something” versus “nothing” contrast between empty-set and non-empty-set stimuli. Hence they are not placed within the following basic stages of understanding zero (2): understanding zero as nothing (the absence of a stimulus), categorical understanding of zero as “nothing” versus “something”, and understanding zero as a quantity that is at the very end of the positive numerical continuum and not just lower than some others.
In contrast, animals with a more developed understanding of zero as well understand “that an empty set is lower than one”. Yet the overriding “something” versus “nothing” contrast prevents them from extrapolating their conditioning by non-empty-set stimuli to empty-set stimuli.

1. D. Goldstein, G. Gigerenzer, Models of Ecolo...

Competing Interests: None declared.
• RE: Brightness as a confound
• Adrian Dyer, Researcher/Visual ecologist, RMIT University

The supplementary material shows full modelling for all stimuli which had equal surface area of elements; with the exception of the zero stimulus that contained no elements. Thus stimulus intensity was matched during training. Bees have also been very poor or incapable of intensity discrimination. Bees have been shown, however, to be good at counting. Finally, in the critical transfer test bees had to extrapolate the acquired (e.g. less than) rule to demonstrate a significant preference for the zero stimulus. An associative stimulus intensity explanation to the bees ability to discriminate the visual problem (which were intensity matched anyway) would have led to the opposite behaviour in transfer testing; i.e. bees would have just chosen a stimulus with elements as it would have been a much closer match to the training stimuli. This point is also confirmed with the conflict testing. Thus, the control experiments and design of stimuli exclude stimulus intensity (brightness) as a confounding explanation to our findings. This is shown in the modelling in the supplementary material.

Competing Interests: I am an author of the study.
• RE: Numerical ordering of zero in honey bees

The published result can better be explained as bees differentiating the cards by lightness/darkness rather than arithmetic. The claim that the bees understood "zero" may be a misreading of the bees learning that the darker card offered no reward. This experiment needed to include dark cards with light markings to prove that the bees counted.

Competing Interests: None declared.