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arxiv: 1906.12213 · v1 · pith:BENTX52Pnew · submitted 2019-06-27 · 💻 cs.CV · cs.AI

On the notion of number in humans and machines

Norbert B\'atfai , D\'avid Papp , Gerg\H{o} Bogacsovics , M\'at\'e Szab\'o , Viktor Szil\'ard Simk\'o , M\'ari\'o Bersenszki , Gergely Szab\'o , Lajos Kov\'acs
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Ferencz Kov\'acs Erik Szilveszter Varga
This is my paper

Pith reviewed 2026-05-25 14:58 UTC · model grok-4.3

classification 💻 cs.CV cs.AI
keywords numerosity classificationsubitizingobject file systemsemantic MNISTdeep learningimage classificationartificial neural networkscognitive psychology
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The pith

Artificial neural networks distinguish numerosities more accurately when below the human object file system capacity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs two sets of Semantic MNIST experiments to compare numerosity classification across humans and machines. Human trials produce results that match the established object file system limit from cognitive psychology. Machine trials apply the same image-based counting task to existing deep learning models originally built for other purposes. The central finding is that these networks achieve higher accuracy on smaller numerosities that fall under the human capacity. The authors close by sketching a framework for studying the concept of number in both biological and artificial systems.

Core claim

The main thesis states that image classification artificial neural networks can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of the object file system in humans, with Semantic MNIST for Humans confirming the known cognitive limit and Semantic MNIST for Machines yielding comparable measurements that support the same pattern in trained models.

What carries the argument

The Semantic MNIST task, which requires determining the number of objects placed in an image, functions as the shared measurement tool that allows direct comparison of human object file system performance with machine classification accuracy.

If this is right

  • Existing deep learning programs can be tested for numerosity discrimination using the same image task applied to humans.
  • Machine accuracy improves specifically for counts that remain under the human object file system limit.
  • The outlined conceptual framework provides a method to examine how the notion of number arises in both humans and machines.
  • Results from machine experiments can be interpreted in the same terms as human cognitive measurements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The pattern may appear in other vision architectures if they are trained on the same object-counting images.
  • Varying the density or arrangement of objects in Semantic MNIST images could test whether the accuracy drop is tied to count alone or to visual crowding.
  • If the effect holds, training regimes that emphasize small counts first might produce models with more human-like numerosity behavior across larger ranges.

Load-bearing premise

The Semantic MNIST task for machines measures a capacity comparable to the human object file system.

What would settle it

A trained image classification network that shows equal accuracy on numerosity tasks across the full range from one to ten objects would falsify the central claim.

Figures

Figures reproduced from arXiv: 1906.12213 by D\'avid Papp, Erik Szilveszter Varga, Ferencz Kov\'acs, Gergely Szab\'o, Gerg\H{o} Bogacsovics, Lajos Kov\'acs, M\'ari\'o Bersenszki, M\'at\'e Szab\'o, Norbert B\'atfai, Viktor Szil\'ard Simk\'o.

Figure 1
Figure 1. Figure 1: Two typical input images for MNIST and SMNIST. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SMNIST for Humans screenshots. As it can be seen in Fig. 2a, the program draws a given number of dots 4 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: This figure shows the relationship between the theoretical and mea [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The well-known visualizations of weights of regression MNIST tuto [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SMNIST for Anyone, Series 1. Both images contain exactly 6 ’X’s. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SMNIST for Anyone, Series 2. Images contain exactly 6 or 9 symbols [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: This Haeckel-like figure contains four timelines. Intuitively, the first [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

In this paper, we performed two types of software experiments to study the numerosity classification (subitizing) in humans and machines. Experiments focus on a particular kind of task is referred to as Semantic MNIST or simply SMNIST where the numerosity of objects placed in an image must be determined. The experiments called SMNIST for Humans are intended to measure the capacity of the Object File System in humans. In this type of experiment the measurement result is in well agreement with the value known from the cognitive psychology literature. The experiments called SMNIST for Machines serve similar purposes but they investigate existing, well known (but originally developed for other purpose) and under development deep learning computer programs. These measurement results can be interpreted similar to the results from SMNIST for Humans. The main thesis of this paper can be formulated as follows: in machines the image classification artificial neural networks can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of OFS in humans. Finally, we outline a conceptual framework to investigate the notion of number in humans and machines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper reports two types of SMNIST experiments on numerosity classification (subitizing). Human SMNIST experiments are claimed to measure Object File System (OFS) capacity and align with cognitive psychology literature (~3-4 items). Machine SMNIST experiments on image-classification ANNs are interpreted analogously, supporting the central thesis that these networks achieve higher accuracy on numerosities below human OFS capacity. A conceptual framework for the notion of number in humans and machines is outlined.

Significance. If the empirical results hold under rigorous controls, the work would provide a testable, falsifiable comparison between human subitizing and ANN performance on small numerosities, potentially informing interdisciplinary research at the intersection of cognitive science and machine learning. The explicit framing of the thesis as an empirical claim rather than a mechanistic equivalence is a positive feature.

major comments (1)
  1. [Abstract] Abstract: the central thesis that ANNs 'can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of OFS in humans' cannot be evaluated because no model architectures, training protocols, accuracy values, error bars, statistical tests, or controls for confounding factors (e.g., object size, density, or training distribution) are described for the SMNIST-for-Machines experiments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for recognizing the potential value of a falsifiable comparison between human subitizing and ANN performance. We address the single major comment below. We agree that the current manuscript does not supply enough experimental detail for the SMNIST-for-Machines results to be evaluated.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central thesis that ANNs 'can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of OFS in humans' cannot be evaluated because no model architectures, training protocols, accuracy values, error bars, statistical tests, or controls for confounding factors (e.g., object size, density, or training distribution) are described for the SMNIST-for-Machines experiments.

    Authors: We accept this criticism. The original manuscript reports that SMNIST-for-Machines experiments were performed on image-classification ANNs but does not provide the requested methodological and statistical details. In the revised version we will (1) specify the exact architectures and training protocols, (2) report accuracy values together with error bars and appropriate statistical tests, and (3) describe controls for object size, density, and training-distribution confounds. The abstract will be expanded to summarize these elements while remaining within length limits. These additions will make the central thesis evaluable. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper describes empirical SMNIST experiments measuring numerosity classification in humans (aligning with known OFS capacity from cognitive literature) and machines (ANNs), with the main thesis being an empirical observation that machines achieve higher accuracy for numerosities below human OFS capacity. No equations, derivations, fitted parameters presented as predictions, self-definitional structures, or load-bearing self-citations appear in the abstract or described framework. The claim is framed as falsifiable via the tasks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities can be identified from the abstract alone.

pith-pipeline@v0.9.0 · 5779 in / 906 out tokens · 19602 ms · 2026-05-25T14:58:08.011405+00:00 · methodology

discussion (0)

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Reference graph

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