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We propose a novel enhancement to Convolutional Neural Networks (CNNs) by incorporating learnable higher-order convolutions inspired by nonlinear biological visual processing. Our model extends the classical convolution operator using a Volterra-like expansion to capture multiplicative interactions observed in biological vision. Through extensive evaluation on standard benchmarks and synthetic datasets, we demonstrate that our architecture consistently outperforms traditional CNN baselines, achieving optimal performance with 3rd/4th order expansions. Systematic perturbation analysis and Representational Similarity Analysis reveal that different orders of convolution process distinct aspects of visual information, aligning with the statistical properties of natural images. This biologically-inspired approach offers both improved performance and deeper insights into visual information processing.