Compositional Dynamics in Learning and Mechanics

📰 ArXiv cs.AI

Learn how compositional dynamics unifies gradient-based learning and Hamiltonian mechanics in a single framework, enabling new insights into adaptive systems

advanced Published 30 Jun 2026
Action Steps
  1. Define the operad Arr with input-output interfaces as objects and smooth adaptive arrangements as morphisms
  2. Construct a functorial semantics for gradient-based learning and Hamiltonian mechanics using the operad Arr
  3. Apply the compositional dynamics framework to a specific problem in learning or mechanics, such as optimizing a neural network or modeling a physical system
  4. Analyze the resulting adaptive arrangements and potential functions to gain insights into the system's behavior
  5. Implement the compositional dynamics framework using a programming language, such as Python or Julia, and a library, such as TensorFlow or PyTorch
Who Needs to Know This

Researchers in AI, machine learning, and physics can benefit from this framework to develop more efficient and adaptive systems, while software engineers and data scientists can apply these concepts to improve model performance and robustness

Key Insight

💡 Compositional dynamics provides a single framework for understanding and analyzing adaptive systems in both learning and mechanics

Share This
🤖💡 Compositional dynamics unifies learning and mechanics! 📚 Learn how to apply this framework to develop more efficient and adaptive systems #AI #MachineLearning #Physics

Full Article

Title: Compositional Dynamics in Learning and Mechanics

Abstract:
arXiv:2606.28984v1 Announce Type: cross Abstract: We give a single compositional setting in which gradient-based learning and Hamiltonian-style mechanics appear as functorial semantics. The syntax is an operad Arr whose objects are input-output interfaces (pairs of manifolds) and whose morphisms are *smooth adaptive arrangements*, which consist of a reactive parameter space, a lens given by smooth output and input maps, and a real-valued potential. The main technical result of the paper is what
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