Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of parameters poses many challenges such as limited representational power and the vanishing/exploding gradients problem of recursively shared parameters. In this paper, we present a recursive convolution block design and training method, in which a recursively shareable part, or a filter basis, is separated and learned while effectively avoiding the vanishing/exploding gradients problem during training. We show that the unwieldy vanishing/exploding gradients problem can be controlled by enforcing the elements of the filter basis orthonormal, and empirically demonstrate that the proposed orthogonality regularization improves the flow of gradients during training. Experimental results on image classification and object detection show that our approach, unlike previous parameter-sharing approaches, does not trade performance to save parameters and consistently outperforms overparameterized counterpart networks. This superior performance demonstrates that the proposed recursive convolution block design and the orthogonality regularization not only prevent performance degradation, but also consistently improve the representation capability while a significant amount of parameters are recursively shared.

Multi-head-self-attention (MHSA)-equipped models have achieved notable performance in computer vision. Their computational complexity is proportional to quadratic numbers of pixels in input feature maps, resulting in slow processing, especially when dealing with high-resolution images. New types of token-mixer are proposed as an alternative to MHSA to circumvent this problem: an FFT-based token-mixer involves global operations similar to MHSA but with lower computational complexity. However, despite its attractive properties, the FFT-based token-mixer has not been carefully examined in terms of its compatibility with the rapidly evolving MetaFormer architecture. Here, we propose a novel token-mixer called Dynamic Filter and novel image recognition models, DFFormer and CDFFormer, to close the gaps above. The results of image classification and downstream tasks, analysis, and visualization show that our models are helpful. Notably, their throughput and memory efficiency when dealing with high-resolution image recognition is remarkable. Our results indicate that Dynamic Filter is one of the token-mixer options that should be seriously considered. The code is available at https://github.com/okojoalg/dfformer