arXiv:2607.26331 2026 Architecture 1 ideas extracted · analyzed Aug 31, 2026
The paper gives a constructive mechanism for selecting a nonzero spatial wavelength through a mode-dependent instability, rather than relying on unconstrained learned convolutions. Its most transferable asset is the explicit stability ratio for opposite Fourier modes: damping, rotation, and pair-coupling jointly determine whether a mode decays or amplifies. This suggests a Fourier-domain recurrent layer whose gain is deliberately peaked at a learnable nonzero wave number and whose nonlinear saturation prevents divergence, yielding controllable stripe, spot, or labyrinthine feature patterns.
Replace one spatial convolution block by a recurrent Fourier-domain layer that couples every mode k to its opposite mode -k and gives the strongest amplification to a nonzero selected wave number k*. The layer crosses a controlled Turing-like instability at k* and uses cubic saturation to produce bounded structured features instead of unbounded activation growth.