On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognition

TL;DR

This paper reveals that small eigenvalues in global covariance pooling are crucial for fine-grained visual recognition, and proposes a method to amplify them, leading to state-of-the-art results on multiple benchmarks.

Contribution

It introduces a novel approach to magnify small eigenvalues in covariance pooling, improving fine-grained recognition without extra parameters.

Findings

Small eigenvalues are vital for discriminative features.

Amplifying small eigenvalues improves recognition accuracy.

The method achieves state-of-the-art results on fine-grained benchmarks.

Abstract

The Fine-Grained Visual Categorization (FGVC) is challenging because the subtle inter-class variations are difficult to be captured. One notable research line uses the Global Covariance Pooling (GCP) layer to learn powerful representations with second-order statistics, which can effectively model inter-class differences. In our previous conference paper, we show that truncating small eigenvalues of the GCP covariance can attain smoother gradient and improve the performance on large-scale benchmarks. However, on fine-grained datasets, truncating the small eigenvalues would make the model fail to converge. This observation contradicts the common assumption that the small eigenvalues merely correspond to the noisy and unimportant information. Consequently, ignoring them should have little influence on the performance. To diagnose this peculiar behavior, we propose two attribution methods whose visualizations demonstrate that the seemingly unimportant small eigenvalues are crucial as they are in charge of extracting the discriminative class-specific features. Inspired by this observation, we propose a network branch dedicated to magnifying the importance of small eigenvalues. Without introducing any additional parameters, this branch simply amplifies the small eigenvalues and achieves state-of-the-art performances of GCP methods on three fine-grained benchmarks. Furthermore, the performance is also competitive against other FGVC approaches on larger datasets. Code is available at \href{https://github.com/KingJamesSong/DifferentiableSVD}{https://github.com/KingJamesSong/DifferentiableSVD}.