mcbal

✨ TL;DR: We design a transformer-shaped module built around relaxation steps of a driven disordered spin system after an input “quench”.

✨ Update (August 2026): For the most complete treatment of this framework, read , which carries the vector-spin construction forward into a broader study of quench protocols, relaxation, stability, and controllable nonequilibrium dynamics. ✨ TL;DR: We int…

✨ Update (August 2026): For the latest and most comprehensive version of this idea, read , which develops the spin-system intuition into a concrete design space for driven dynamics, relaxation, stability, and control.

✨ Update (August 2026): For a more developed framework, read , which moves beyond the equilibrium free-energy assumptions used here and replaces them with a broader account of driven relaxation and nonequilibrium computation.

✨ Update (August 2026): For a more complete development of this collective-response perspective, read , which situates the mean-field intuition within a quench-and-relax framework for nonequilibrium dynamics.

✨ Update (August 2026): If the energy-landscape intuition here is useful, continue with , which turns that static picture into a broader framework for driven, controllable quench-and-relax computation.

✨ Update (August 2026): For the more mature account, read , which moves beyond implicit equilibrium energy models to a dynamical picture of how spin-model transformers compute, relax, and remain controllable.

XKCD 793: A physicist encountering machine learning for the first time ✨ Update (August 2026): For the fuller picture, read , which develops this early energy-based view into a more comprehensive framework built around driven mean-field dynamics, relaxati…