arXiv:2608.15895 2026 Architecture 2 ideas extracted · analyzed Sep 1, 2026
The paper exposes an SU(1,1) scattering transform whose state evolution preserves an indefinite Hermitian form exactly, rather than merely approximately. This gives a concrete recipe for recurrent or sequence-processing layers built from structure-preserving hyperbolic matrix updates, with no exploding norm caused by discretization drift. Its nonlinear Fourier amplitude H_f also obeys a constant-one Hausdorff–Young bound, suggesting a spectral regularizer whose strength is calibrated by the input L^p norm instead of an arbitrary coefficient. The most practical transfer is to implement an SU(1,1)-constrained scan layer and compare its stability and long-context behavior against unconstrained linear recurrence and unitary baselines.
Replace an unconstrained recurrent transition by a sequence of exact SU(1,1) hyperbolic updates. The layer processes each token with a 2-complex-dimensional state and preserves the indefinite energy |a|^2-|b|^2=1 exactly, preventing numerical drift while retaining non-unitary amplification and attenuation.
Use the logarithmic transmission amplitude of an SU(1,1) scan as a differentiable spectral penalty. The paper's constant-one nonlinear Hausdorff–Young inequality provides a principled upper budget for this amplitude in terms of the input L^p norm, replacing an arbitrary spectral-weight penalty with a scale-aware constraint.