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Prime convolutional model: Breaking the ground for theoretical explainability
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AI
DOI：10.1016/j.ins.2025.122815.png)
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Abstract
En 中文
In this paper, we propose a new theoretical approach to Explainable AI. Following the Scientific Method, this approach consists of 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 for 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.
Keywords:
Explainable AI
Convolutional neural networks (CNN)
Prime grid
Natural numbers
Journal
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6.8
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540
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6.2W