Kronecker Generative Networks: A General Neural Architecture for Parameter-Efficient Learning Across Classification Tasks

Modern neural networks derive much of their effectiveness from rich connectivity patterns. Yet, existing architectures often fix the topology at either the sparse or dense extremes, thereby limiting structural flexibility and analysis. We propose Kronecker Generative Networks (KGNs), an algebraic framework that constructs neural network topologies via recursive generation rules, treating topology as a first-class design object. KGNs generate families of directed acyclic graphs with controllable connectivity complexity, enabling systematic interpolation between sparse and dense aggregation regimes. Under this formulation, architectures such as FractalNet and DenseNet arise as specific instantiations corresponding to different generation rules. We provide theoretical analysis of acyclicity, connectivity scaling, and expressiveness, and demonstrate experimentally that KGN instantiations achieve favorable accuracy-efficiency trade-offs across multiple domains.

The performance of deep learning models is largely dictated by their architecture's connectivity. Unfortunately, existing frameworks treat architecture design rigidly, forcing a choice between sparse or dense connectivity. To solve this, we introduce Kronecker Generative Networks (KGNs), an algebraic framework that generates network structures recursively. Think of it as a master key for network topology: by changing a few initial rules, KGNs can smoothly transition between highly sparse and heavily dense networks. We show that classic architectures like DenseNet are actually just specific branches of the KGN family tree. Ultimately, KGNs provide a mathematically rigorous way to design new neural networks that strike an optimal balance between computational efficiency and predictive accuracy.