Factorized Dynamic Fully-Connected Layers for Neural Networks

The design of neural network layers plays a crucial role in determining the efficiency and performance of various computer vision tasks. However, most existing layers compromise between fast feature extraction and reasoning abilities, resulting in suboptimal outcomes. In this paper, we propose a novel and efficient operator for representation learning that can dynamically adjust to the underlying data structure. We introduce a general Dynamic Fully-Connected (DFC) layer, a non-linear extension of a Fully-Connected layer that has a learnable receptive field, is instance-adaptive, and spatially aware. We propose to use CP decomposition to reduce the complexity of the DFC layer without compromising its expressivity. Then, we leverage Summed Area Tables and Modulation to create an adaptive receptive field that can process the input with constant complexity. We evaluate the effectiveness of our method on image classification and other downstream vision tasks using both hierarchical and isotropic architectures. Our results demonstrate that our method outperforms other commonly used layers by a significant margin while keeping a fixed computational budget, therefore establishing a new strategy to efficiently design neural architectures that can capture the multi-scale features of the input without increasing complexity.