A Compositional Framework for Neural Network Modeling Using Typed Petri Nets

The increasing complexity of modern neural networks impedes systematic understanding and formal analysis,often resulting in “black box” behavior. Our paper introduces Typed Petri Nets (TPNs) as a formal framework formodeling the structure and dynamics of neural networks, aiming to address these challenges. We define the corecomponents of TPNs―places, transitions, arcs, a type system (e.g., for tensors), and computation assignments―anddemonstrate how they can compositionally represent basic network layers. Furthermore, we illustrate the capability ofTPNs to model advanced architectures, including convolutional layers, skip connections, and multi-branch structures.TPN dynamics naturally simulate forward propagation through markings and firing rules. The framework’sformal semantics can be rigorously explored using category theory, as illustrated by applications in probabilistic contextsusing Markov Categories. Key advantages of the TPN approach include modularity through compositionality,explicit information flow representation, type safety, and a foundation for formal analysis. This work establishesTPN as a structured, mathematically grounded perspective for understanding complex neural networks, offering apromising basis for future research into learning dynamics, verification, and tool development.