Multi-scale Spatial Representation Learning via Recursive Hermite Polynomial Networks

Multi-scale representation learning aims to leverage diverse features from different layers of Convolutional Neural Networks (CNNs) for boosting the feature robustness to scale variance. For dense prediction tasks, two key properties should be satisfied: the high spatial variance across convolutional layers, and the sub-scale granularity inside a convolutional layer for fine-grained features. To pursue the two properties, this paper proposes Recursive Hermite Polynomial Networks (RHP-Nets for short). The proposed RHP-Nets consist of two major components: 1) a dilated convolution to maintain the spatial resolution across layers, and 2) a family of Hermite polynomials over a subset of dilated grids, which recursively constructs sub-scale representations to avoid the artifacts caused by naively applying the dilation convolution. The resultant sub-scale granular features are fused via trainable Hermite coefficients to form the multi-resolution representations that can be fed into the next deeper layer, and thus allowing feature interchanging at all levels. Extensive experiments are conducted to demonstrate the efficacy of our design, and reveal its superiority over state-of-the-art alternatives on a variety of image recognition tasks. Besides, introspective studies are provided to further understand the properties of our method.