The field of algorithmic regulation is moving towards a deeper understanding of the relationship between controllers and the systems they regulate. Recent work has focused on the idea that controllers must embody a model of the system they regulate, and has explored the implications of this principle for our understanding of complex systems. One key area of innovation is the development of new frameworks for analyzing and designing controllers, such as those based on algorithmic complexity and compositional symmetry. These frameworks are allowing researchers to better understand the fundamental limits and tradeoffs involved in controlling complex systems, and are opening up new possibilities for the design of more efficient and effective controllers. Notable papers in this area include: The algorithmic regulator, which proves that a good algorithmic regulator reduces the algorithmic complexity of the readout relative to a null baseline. Compositional Symmetry as Compression, which proposes a framework for understanding the structural priors that underlie natural streams and shows how these priors can be used to impose constraints on the behavior of agents.