Papers › SAND: One-Shot Feature Selection with Additive Noise Distortion

SAND: One-Shot Feature Selection with Additive Noise Distortion

6 May 2025arXiv:2505.03923archive 2025-07-28

Pedram Pad, Hadi Hammoud, Mohamad Dia, Nadim Maamari, L. Andrea Dunbar

Feature selection is a critical step in data-driven applications, reducing input dimensionality to enhance learning accuracy, computational efficiency, and interpretability. Existing state-of-the-art methods often require post-selection retraining and extensive hyperparameter tuning, complicating their adoption. We introduce a novel, non-intrusive feature selection layer that, given a target feature count k, automatically identifies and selects the k most informative features during neural network training. Our method is uniquely simple, requiring no alterations to the loss function, network architecture, or post-selection retraining. The layer is mathematically elegant and can be fully described by: x̃ᵢ = aᵢ xᵢ + (1-aᵢ)zᵢ where xᵢ is the input feature, x̃ᵢ the output, zᵢ a Gaussian noise, and aᵢ trainable gain such that ∑ᵢaᵢ²=k. This formulation induces an automatic clustering effect, driving k of the aᵢ gains to $1$ (selecting informative features) and the rest to $0$ (discarding redundant ones) via weighted noise distortion and gain normalization. Despite its extreme simplicity, our method delivers state-of-the-art performance on standard benchmark datasets and a novel real-world dataset, outperforming or matching existing approaches without requiring hyperparameter search for k or retraining. Theoretical analysis in the context of linear regression further validates its efficacy. Our work demonstrates that simplicity and performance are not mutually exclusive, offering a powerful yet straightforward tool for feature selection in machine learning.

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