Insights into neural architectures for learning numerical concepts from simple visual data

The paper reports some results on neural architectures for learning numerical concepts from visual data. We use datasets of small images with single-pixel dots (one to six per image) to learn the abstraction of small integers, and other numerical concepts (e.g. even versus odd numbers). Both fully-connected and convolutional architectures are investigated. The obtained results indicate that two categories of numerical properties apparently exist (in the context of discussed problems). In the first category, the properties can be learned without acquiring the counting skills, e.g. the notion of small, medium and large numbers. In the second category, explicit counting is embedded into the architecture so that the concepts are learned from numbers rather than directly from visual data. In general, we find that CNN architectures (if properly crafted) are more efficient in the discussed problems and (additionally) come with more plausible explainability.

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1. Short article

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2. Track 3: 4th International Workshop on Artificial Intelligence in Machine Vision and Graphics

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3. Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).