arXiv:2506.01075v2 Announce Type: replace-cross Abstract: The Boolean Fourier representation has been widely used in learning theory, particularly for learning Disjunctive Normal Form (DNF) under uniform and product distributions. Extending these results to non-product distributions has remained a longstanding open problem. We address this challenge by introducing a generalized Fourier representation that enables learning under a broad class of non-product distributions. Our approach represents any distribution $D$ as a Bayesian network (BN) and derives a corresponding Fourier expansion. We sh
The increasing complexity of AI models and the need for more robust learning algorithms under diverse data distributions drive research into foundational mathematical tools. This paper addresses a long-standing challenge in learning theory.
Improved learning algorithms, especially for complex logical forms and non-uniform data, will enhance the capabilities and reliability of AI systems across various applications.
The ability to learn DNF under non-product distributions using generalized Fourier representations could lead to more efficient and adaptable machine learning models.
- · AI researchers
- · Machine learning developers
- · Data scientists
- · Sectors using complex AI models
- · AI models reliant on simplified distribution assumptions
This research provides a theoretical advancement in learning Disjunctive Normal Form (DNF) using a generalized Fourier representation for non-product distributions.
The improved understanding of learning under complex data distributions could lead to more robust and less biased AI models in real-world scenarios.
These foundational improvements might enable breakthroughs in areas where current AI struggles with highly varied or non-uniform data, leading to new AI applications or enhanced performance in existing ones.
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