Basis sharing and coefficient pruning for efficient neural network compression

Network compression is essential for deploying deep neural networks on resource-constrained devices, yet existing approaches often focus on either filter pruning or weight sharing in isolation. In this work, we propose a unified compression framework, SaP, that jointly leverages basis sharing and coefficient pruning to reduce redundancies in both convolutional filters and their resulting feature maps. By representing filters as linear combinations of a reduced set of shared basis filters and removing redundant coefficients, SaP achieves higher compression ratios while preserving discriminative information. This hybrid design mitigates the bottleneck problem inherent in sole basis-sharing methods, reduces computational complexity, and enables efficient fine-tuning in the coefficient subspace. We further provide a theoretical analysis showing that, under the orthonormal basis induced by the singular value decomposition, distances between filters are preserved in the coefficient space, justifying redundancy analysis and pruning in this low-dimensional representation. Extensive experiments on image classification, object detection, instance segmentation, and keypoint detection demonstrate that SaP consistently outperforms state-of-the-art baselines in terms of compression, accuracy retention, and practical efficiency. Ablation studies further validate the effectiveness of the joint approach and provide insights into hyperparameter selection and feature preservation. Our results highlight the potential of combining complementary compression strategies to create highly efficient, deployable neural networks.