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

This paper introduces the Polynomial Perceptron (PP), a structured extension of the classical perceptron that incorporates explicit polynomial feature expansions to model nonlinear interactions while preserving analytical transparency. By expressing feature interactions in closed functional form, PP captures higher-order dependencies through a compact set of learned coefficients, establishing a principled trade-off between expressivity and parameter efficiency. The proposed architecture is evaluated across heterogeneous domains, including text, image, and structured data tasks, under controlled experimental settings with parameter-matched baselines. Performance is assessed using standard metrics such as classification accuracy and model complexity (parameter count). Empirical results demonstrate that low-degree PP models achieve competitive accuracy compared to multilayer perceptrons and convolutional neural networks, while requiring significantly fewer parameters. An ablation study further analyzes the impact of polynomial degree on predictive performance, revealing diminishing returns beyond moderate degrees and highlighting favorable efficiency-accuracy trade-offs. A key advantage of PP lies in its intrinsic interpretability. Unlike conventional deep learning models that rely on post hhoc explanation methods, PP provides direct analytical insight through its explicit polynomial structure, enabling decomposition of predictions into feature-, token-, or patch-level contributions without surrogate approximations. Overall, the results indicate that PP offers a lightweight, interpretable, and computationally efficient alternative to standard neural architectures, particularly well-suited for resource-constrained environments and applications where transparency is critical.