Just to make sure I’m understanding the concept of causal networks with symmetry correctly, since I’m more used to thinking of dynamical systems: I could in principle think of a dynamical system that I simulate on my computer as a DAG with symmetry, ie using Euler’s method to simulate dx/dt = f(x) I get a difference equation x(t+1) = /delta T * f(x(t)) that I then use to simulate my dynamical system on a computer, and I can think of that as a DAG where x(t) /arrow x(t+1), for all t, and of course theres a symmetry over time since f(x(t)) is constant over time. If I have a spatially distributed dynamical system, like a network, then there might also be symmetries in space. In this way your causal networks with symmetry can capture any dynamical system (and I guess more since causal dependencies need not be deterministic)? Does that sound right?
Just to make sure I’m understanding the concept of causal networks with symmetry correctly, since I’m more used to thinking of dynamical systems: I could in principle think of a dynamical system that I simulate on my computer as a DAG with symmetry, ie using Euler’s method to simulate dx/dt = f(x) I get a difference equation x(t+1) = /delta T * f(x(t)) that I then use to simulate my dynamical system on a computer, and I can think of that as a DAG where x(t) /arrow x(t+1), for all t, and of course theres a symmetry over time since f(x(t)) is constant over time. If I have a spatially distributed dynamical system, like a network, then there might also be symmetries in space. In this way your causal networks with symmetry can capture any dynamical system (and I guess more since causal dependencies need not be deterministic)? Does that sound right?
That is exactly correct.