HomCn

HomCn, short for Homogeneous Convolutional Network, is a conceptual family of neural network architectures designed to exploit homogeneous structure in data. The central idea is to apply convolution-like operations in settings where the data encounters uniform, repeating patterns across dimensions, such as regular grids, time series with uniform sampling, or multi-channel signals with consistent dimensionality. In HomCn, the convolution operators are derived to preserve certain symmetries across the entire input, enabling shared weights to generalize across spatial or feature axes and reducing the total number of learnable parameters compared to conventional networks.

Design and variants: Early formulations use a fixed, stationary kernel applied uniformly across the input, with optional adaptations such as depthwise or separable components to control computational cost. Some variants incorporate basis expansion or group-theoretic constraints to enforce invariances, while others integrate pooling or normalization tailored to homogeneous domains.

Applications: Prototypes have been explored for image-like data with strict grid regularity, environmental sensing grids, and audio or time-series tasks that benefit from uniform treatment across axes. In practice, HomCn aims to deliver efficient learning on moderate-sized datasets where data symmetry can be leveraged to reduce overfitting.

Limitations: The approach is less suited to irregular or highly heterogeneous data, where standard CNNs or graph-based methods may better capture local variation. Future work focuses on extending HomCn to partially homogeneous domains and integrating it with attention mechanisms.

See also: Convolutional neural networks, group-equivariant networks, depthwise separable convolutions.