Prime Convolutional Model: Breaking the Ground for Theoretical Explainability
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917945649659904 |
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| author | Panelli, Francesco Almhaithawi, Doaa Cerquitelli, Tania Bellini, Alessandro |
| author_facet | Panelli, Francesco Almhaithawi, Doaa Cerquitelli, Tania Bellini, Alessandro |
| contents | In this paper, we propose a new theoretical approach to Explainable AI. Following the Scientific Method, this approach consists in formulating on the basis of empirical evidence, a mathematical model to explain and predict the behaviors of Neural Networks. We apply the method to a case study created in a controlled environment, which we call Prime Convolutional Model (p-Conv for short). p-Conv operates on a dataset consisting of the first one million natural numbers and is trained to identify the congruence classes modulo a given integer $m$. Its architecture uses a convolutional-type neural network that contextually processes a sequence of $B$ consecutive numbers to each input. We take an empirical approach and exploit p-Conv to identify the congruence classes of numbers in a validation set using different values for $m$ and $B$. The results show that the different behaviors of p-Conv (i.e., whether it can perform the task or not) can be modeled mathematically in terms of $m$ and $B$. The inferred mathematical model reveals interesting patterns able to explain when and why p-Conv succeeds in performing task and, if not, which error pattern it follows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prime Convolutional Model: Breaking the Ground for Theoretical Explainability Panelli, Francesco Almhaithawi, Doaa Cerquitelli, Tania Bellini, Alessandro Artificial Intelligence Machine Learning In this paper, we propose a new theoretical approach to Explainable AI. Following the Scientific Method, this approach consists in formulating on the basis of empirical evidence, a mathematical model to explain and predict the behaviors of Neural Networks. We apply the method to a case study created in a controlled environment, which we call Prime Convolutional Model (p-Conv for short). p-Conv operates on a dataset consisting of the first one million natural numbers and is trained to identify the congruence classes modulo a given integer $m$. Its architecture uses a convolutional-type neural network that contextually processes a sequence of $B$ consecutive numbers to each input. We take an empirical approach and exploit p-Conv to identify the congruence classes of numbers in a validation set using different values for $m$ and $B$. The results show that the different behaviors of p-Conv (i.e., whether it can perform the task or not) can be modeled mathematically in terms of $m$ and $B$. The inferred mathematical model reveals interesting patterns able to explain when and why p-Conv succeeds in performing task and, if not, which error pattern it follows. |
| title | Prime Convolutional Model: Breaking the Ground for Theoretical Explainability |
| topic | Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2503.02773 |