Convolution goes higher-order: a biologically inspired mechanism empowers image classification

TL;DR

This paper introduces a biologically inspired higher-order convolutional neural network that captures complex visual interactions, improving image classification performance and providing insights into visual processing akin to biological systems.

Contribution

The paper presents a novel higher-order convolution mechanism inspired by biological visual processing, enhancing CNN performance and interpretability.

Findings

Outperforms traditional CNNs on standard benchmarks

Optimal performance achieved with 3rd/4th order expansions

Reveals distinct visual information processing modes

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.