Polynomial Perceptrons for Compact, Robust, and Interpretable Machine Learning Models.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Computational Neuroscience

Background:

• Classical perceptrons are limited in modeling nonlinear interactions.
• Deep learning models often lack transparency and require extensive parameters.

Purpose of the Study:

• Introduce the Polynomial Perceptron (PP) as a structured extension of the classical perceptron.
• Model nonlinear interactions with analytical transparency and parameter efficiency.
• Evaluate PP's performance and interpretability across diverse datasets.

Main Methods:

• Incorporating explicit polynomial feature expansions into the perceptron architecture.
• Expressing feature interactions in closed functional form for higher-order dependency capture.
• Evaluating PP against parameter-matched baselines on text, image, and structured data tasks.

Main Results:

• Low-degree PP models achieve competitive accuracy with significantly fewer parameters than MLPs and CNNs.
• Ablation studies show diminishing returns in accuracy beyond moderate polynomial degrees.
• PP demonstrates favorable efficiency-accuracy trade-offs.

Conclusions:

• The Polynomial Perceptron provides a lightweight, interpretable, and computationally efficient alternative to standard neural architectures.
• PP's intrinsic interpretability allows direct analytical insight without post-hoc methods.
• PP is well-suited for resource-constrained environments and applications prioritizing transparency.