Papers › Reconstructing cellular automata rules from observations at nonconsecutive times
Reconstructing cellular automata rules from observations at nonconsecutive times
Veit Elser
Recent experiments by Springer and Kenyon have shown that a deep neural network can be trained to predict the action of t steps of Conway's Game of Life automaton given millions of examples of this action on random initial states. However, training was never completely successful for t>1, and even when successful, a reconstruction of the elementary rule (t=1) from t>1 data is not within the scope of what the neural network can deliver. We describe an alternative network-like method, based on constraint projections, where this is possible. From a single data item this method perfectly reconstructs not just the automaton rule but also the states in the time steps it did not see. For a unique reconstruction, the size of the initial state need only be large enough that it and the t-1 states it evolves into contain all possible automaton input patterns. We demonstrate the method on 1D binary cellular automata that take inputs from n adjacent cells. The unknown rules in our experiments are not restricted to simple rules derived from a few linear functions on the inputs (as in Game of Life), but include all 2^(2ⁿ) possible rules on n inputs. Our results extend to n=6, for which exhaustive rule-search is not feasible. By relaxing translational symmetry in space and also time, our method is attractive as a platform for the learning of binary data, since the discreteness of the variables does not pose the same challenge it does for gradient-based methods.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections