Papers › Classification of integers based on residue classes via modern deep learning algorithms

Classification of integers based on residue classes via modern deep learning algorithms

3 Apr 2023arXiv:2304.01333archive 2025-07-28

Da Wu, Jingye Yang, Mian Umair Ahsan, Kai Wang

Judging whether an integer can be divided by prime numbers such as 2 or 3 may appear trivial to human beings, but can be less straightforward for computers. Here, we tested multiple deep learning architectures and feature engineering approaches on classifying integers based on their residues when divided by small prime numbers. We found that the ability of classification critically depends on the feature space. We also evaluated Automated Machine Learning (AutoML) platforms from Amazon, Google and Microsoft, and found that they failed on this task without appropriately engineered features. Furthermore, we introduced a method that utilizes linear regression on Fourier series basis vectors, and demonstrated its effectiveness. Finally, we evaluated Large Language Models (LLMs) such as GPT-4, GPT-J, LLaMA and Falcon, and demonstrated their failures. In conclusion, feature engineering remains an important task to improve performance and increase interpretability of machine-learning models, even in the era of AutoML and LLMs.

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Absolute Position EncodingsAdamAttentionBPEDense ConnectionsDropoutGPT-4Label SmoothingLayer NormalizationLinear LayerLinear RegressionMulti-Head AttentionPosition-Wise Feed-Forward LayerResidual ConnectionSoftmaxTransformer

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