arXiv:2607.06942 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper gives a constructive way to turn a finite-state Mealy automaton into a well-defined bi-infinite sequence evolution by scanning tokens with a carrier state, together with an explicit local conservation law. This is transferable as a lightweight recurrent token-mixing layer whose state transition table can be constrained to be bijective and particle-preserving, yielding stable reversible dynamics rather than an unconstrained learned recurrence. The invariant-measure perspective suggests an additional training diagnostic or regularizer: calibrate the layer so that Bernoulli or two-sided Markov input statistics are preserved after the scan. The most practical first target is a binary or low-bit activation mixer replacing part of an SSM or Transformer block.
Replace a recurrent token-mixing operation with a finite-state carrier scan over binary or quantized token features. The local transition table is constrained to conserve a scalar token weight and to be bijective, making the mixer reversible, constant-memory, and less prone to activation drift than a generic recurrent layer.