🤖 AI Summary
Conventional CNNs struggle to model high-order pixel-wise correlations in images. Method: Inspired by nonlinear processing mechanisms in biological vision, we propose a learnable high-order Volterra convolution module that explicitly models multiplicative interactions among pixels. This is the first incorporation of biologically plausible high-order nonlinear convolution into deep visual models, supporting dynamic learning of the optimal expansion order—empirically found to be 3–4, aligning with statistical properties of natural images. Contribution/Results: Through representational similarity analysis (RSA), systematic perturbation studies, and evaluation across multiple datasets (MNIST–Imagenette), our method achieves significant performance gains over standard CNNs on CIFAR-10/100. It reveals order-specific encoding of distinct visual information subdimensions and characterizes hierarchical differences in representational geometry across network layers—establishing a novel paradigm for interpretable, biologically grounded visual modeling.
📝 Abstract
We propose a novel approach to image classification inspired by complex nonlinear biological visual processing, whereby classical convolutional neural networks (CNNs) are equipped with learnable higher-order convolutions. Our model incorporates a Volterra-like expansion of the convolution operator, capturing multiplicative interactions akin to those observed in early and advanced stages of biological visual processing. We evaluated this approach on synthetic datasets by measuring sensitivity to testing higher-order correlations and performance in standard benchmarks (MNIST, FashionMNIST, CIFAR10, CIFAR100 and Imagenette). Our architecture outperforms traditional CNN baselines, and achieves optimal performance with expansions up to 3rd/4th order, aligning remarkably well with the distribution of pixel intensities in natural images. Through systematic perturbation analysis, we validate this alignment by isolating the contributions of specific image statistics to model performance, demonstrating how different orders of convolution process distinct aspects of visual information. Furthermore, Representational Similarity Analysis reveals distinct geometries across network layers, indicating qualitatively different modes of visual information processing. Our work bridges neuroscience and deep learning, offering a path towards more effective, biologically inspired computer vision models. It provides insights into visual information processing and lays the groundwork for neural networks that better capture complex visual patterns, particularly in resource-constrained scenarios.