Correlation Effects between Physical Feature Dimension and Feature Expansion Order in Classification

The extraction of physical features constitutes the cornerstone of deep learning models, and revealing the correlation effects between feature dimension and feature expansion order is one key to constructing trustworthy artificial intelligence models. Drawing on energy perturbation theory in physics, this paper proposes a feature energy analysis method based on polynomial expansion, aiming to explore the physical correlation between feature dimension and feature expansion order. Simulation results show that, with the increase of the expansion order, the classification accuracy of the energy analysis method exhibits a monotonically increasing trend. Higher-order nonlinear correlations can effectively capture the complex nonlinear structure of data in low-dimensional projections, thereby significantly improving discriminative ability. Parameter-space analysis shows that the energy analysis method can spontaneously learn the geometric morphology of the target data and form significant clustering behavior according to sample similarity. Visualization of decision boundaries further confirms that higher-order terms improve classification performance by shaping finer decision boundaries that better fit the geometric shapes of samples. These findings provide an effective analytical perspective for building physics-mechanism-inspired explainable deep learning frameworks, thereby enhancing the trustworthiness of deep learning models.