Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition. This has, if true, far reaching significance to the fields of machine learning and cognitivesciencealike.

Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition. This has, if true, far reaching significance to the fields of machine learning and cognitive science alike. In this paper, we prove the above claim to be unfortunately incorrect. The statistical analysis to support the claim is flawed in that the sample set used to identify number-aware neurons is too small, compared to the huge number of neurons in the object recognition network. By this flawed analysis one could mistakenly identify number-sensing neurons in any randomly initialized deep neural networks that are not trained at all. With the above critique we ask the question what if a deep convolutional neural network is carefully trained for numerosity?

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition.

We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal physiology that orchestrates responses to maintain a dynamic equilibrium in bodily needs and internal states. In this paper, we focus on an application in numerical cognition, where a bump of activity in an attractor network is used as a spatial numerical representation. While existing neural networks can maintain persistent states, to date, there is no unified framework for dynamically controlling spatial changes in neuronal activity in response to environmental changes. To address this, we couple a well known allostatic microcircuit, the Hammel model, with a ring attractor, resulting in a Spiking Neural Network architecture that can modulate the location of the bump as a function of some reference input. This localized activity in turn is used as a perceptual belief in a simulated subitization task a quick enumeration process without counting. We provide a general procedure to fine-tune the model and demonstrate the successful control of the bump location. We also study the response time in the model with respect to changes in parameters and compare it with biological data. Finally, we analyze the dynamics of the network to understand the selectivity and specificity of different neurons to distinct categories present in the input. The results of this paper, particularly the mechanism for moving persistent states, are not limited to numerical cognition but can be applied to a wide range of tasks involving similar representations.

Summary and Contributions: Update after author response: I would like to thank the authors for the detailed response. I am changing my score from 4 to 5 based on the reviewer discussion and the author response. Some more detailed thoughts follow. While I agree that the negative results here are quite interesting and a step towards slowing the trickle of overreaching conclusions, I am still unconvinced about the positive results. Essentially, a network trained for a simple task does well on the task, and fails to generalize in a robust manner.

This paper demonstrates that an analysis relied upon in a previous paper (Nasr et al., 2019) to identify number-sensitive units in a neural network trained for object recognition is flawed, and that indeed the same network with randomly initialized weights also has a large number of number sensitive units. Moreover, the number of units detected depends strongly on the sample size of the statistical test, with larger sample sizes detecting no number sensitive units. The paper additionally performs some analyses on a network trained specifically to predict number. The reviewers generally felt that the demonstration of Nasr et al.'s flawed analysis was important, with R2 arguing that the work is "imperative to publish" and R1 and R3 finding the experiments in the first part of the paper convincing. However, R1, R3, and R4 all had concerns with the second part of the paper, in which it is claimed that a network trained to classify number (Nu-Net) can learn to subitize. I feel that the results in the first part of the paper are sufficiently impactful that the paper should be accepted.

Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition. This has, if true, far reaching significance to the fields of machine learning and cognitive science alike. In this paper, we prove the above claim to be unfortunately incorrect. The statistical analysis to support the claim is flawed in that the sample set used to identify number-aware neurons is too small, compared to the huge number of neurons in the object recognition network. By this flawed analysis one could mistakenly identify number-sensing neurons in any randomly initialized deep neural networks that are not trained at all.

Humans can readily judge the number of objects in a visual scene, even without counting, and such a skill has been documented in a variety of animal species and in babies prior to language development and formal schooling. Numerical judgments are error-free for small sets, while for larger collections responses become approximate, with variability increasing proportionally to the target number. This response pattern is observed for items of all kinds, despite variation in object features (such as color or shape), suggesting that our visual number sense relies on abstract representations of numerosity. Here, we investigated whether generative Artificial Intelligence (AI) models based on large-scale transformer architectures can reliably name the number of objects in simple visual stimuli or generate images containing a target number of items in the 1-10 range. Surprisingly, none of the foundation models considered performed in a human-like way: They all made striking errors even with small numbers, the response variability often did not increase in a systematic way, and the pattern of errors varied with object category. Our findings demonstrate that advanced AI systems still lack a basic ability that supports an intuitive understanding of numbers, which in humans is foundational for numeracy and mathematical development.