Symmetry in Time: A Representation Theory of Linear Recurrent Memory
HyperSSM solves order-sensitive group benchmarks with at most five state numbers and generalizes to sequences 25 times longer than its training examples.
The authors show that diagonal real- and complex-valued state transitions commute, limiting which group operations those models can track. Their HyperSSM adds quaternion channels while retaining linear-time inference and parallel training. Trained only on final answers, it solves the tested group tasks exactly, including an S₅ task with 32 generators where previous SSMs perform at chance. The authors also interpret learned recurrence weights to recover gyroscope calibration, imperfect qubit-gate rotations and protein-backbone geometry.
ArXiv · AI/CL/LG's note
The authors show that diagonal real- and complex-valued state transitions commute, limiting which group operations those models can track. Their HyperSSM adds quaternion channels while retaining linear-time inference and parallel training. Trained only on final answers, it solves the tested group tasks exactly, including an S₅ task with 32 generators where previous SSMs perform at chance. The authors also interpret learned recurrence weights to recover gyroscope calibration, imperfect qubit-gate rotations and protein-backbone geometry.
ArXiv · AI/CL/LG's note
score 5