FwNet-ECA: Facilitating Window Attention with Global Receptive Fields through Fourier Filtering Operations

Windowed attention mechanisms were introduced to mitigate the issue of excessive computation inherent in global attention mechanisms. However, In this paper, we present FwNet-ECA, a novel method that utilizes Fourier transforms paired with learnable weight matrices to enhance the spectral features of images. This strategy facilitates inter-window connectivity, thereby maximizing the receptive field. Additionally, we incorporate the Efficient Channel Attention (ECA) module to improve communication between different channels. Instead of relying on physically shifted windows, our approach leverages frequency domain enhancement to implicitly bridge information across spatial regions. We validate our model on the iCartoonFace dataset and conduct downstream tasks on ImageNet, demonstrating that our model achieves lower parameter counts and computational overheads compared to shifted window approaches, while maintaining competitive accuracy. This work offers a more efficient and effective alternative for leveraging attention mechanisms in visual processing tasks, alleviating the challenges associated with windowed attention models. Code is available at https://github.com/qingxiaoli/FwNet-ECA.

Intrinsic dimension estimation of data by principal component analysis

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however, becomes ineffective when data have a nonlinear structure. In this paper, we propose a new PCA-based method to estimate intrinsic dimension of data with nonlinear structures. Our method works by first finding a minimal cover of the data set, then performing PCA locally on each subset in the cover and finally giving the estimation result by checking up the data variance on all small neighborhood regions. The proposed method utilizes the whole data set to estimate its intrinsic dimension and is convenient for incremental learning. In addition, our new PCA procedure can filter out noise in data and converge to a stable estimation with the neighborhood region size increasing. Experiments on synthetic and real world data sets show effectiveness of the proposed method.