arXiv:2608.01253 2026 Dynamics 1 ideas extracted · analyzed Aug 31, 2026
The paper constructs an entire complex-time flow W_z=e^{zK} whose generator preserves a bilinear form, with complex orthogonality replacing ordinary unitary evolution. This structure transfers to recurrent and state-space neural networks as an exactly norm-preserving transition, preventing hidden-state explosion or decay across long sequences. The most practical implementation is a low-rank skew-transpose generator combined with a Cayley step, which avoids computing a matrix exponential while retaining the preservation guarantee. The supplied mathematics does not include enough detail to transfer the Markov-chain parity decoding, so the orthogonal-flow construction is the strongest concrete idea.
Replace an unconstrained recurrent or state-space transition with a complex-orthogonal flow generated by a skew-transpose matrix. The transition preserves a bilinear quadratic quantity exactly, preventing repeated application across long sequences from causing norm explosion or decay in the linear dynamics.