Trainable Spectrally Initializable Matrix Transformations in Convolutional Neural Networks

TL;DR

This paper introduces trainable, spectrally initializable matrix transformations for convolutional neural networks, demonstrating improved accuracy and faster convergence across diverse datasets with an open-source implementation.

Contribution

The work presents a novel trainable spectral matrix transformation method that enhances CNN performance and convergence speed, applicable to various architectures and datasets.

Findings

Average accuracy increase of 2.2 points across datasets

Spectral initialization leads to faster convergence

Transformations are easily integrated into existing architectures

Abstract

In this work, we investigate the application of trainable and spectrally initializable matrix transformations on the feature maps produced by convolution operations. While previous literature has already demonstrated the possibility of adding static spectral transformations as feature processors, our focus is on more general trainable transforms. We study the transforms in various architectural configurations on four datasets of different nature: from medical (ColorectalHist, HAM10000) and natural (Flowers, ImageNet) images to historical documents (CB55) and handwriting recognition (GPDS). With rigorous experiments that control for the number of parameters and randomness, we show that networks utilizing the introduced matrix transformations outperform vanilla neural networks. The observed accuracy increases by an average of 2.2 across all datasets. In addition, we show that the benefit of spectral initialization leads to significantly faster convergence, as opposed to randomly initialized matrix transformations. The transformations are implemented as auto-differentiable PyTorch modules that can be incorporated into any neural network architecture. The entire code base is open-source.