arXiv:2607.18334 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper gives an explicitly solvable signed adjacency operator on an even cyclic graph whose Fourier spectrum is known and whose spectral radius is exactly 2√2, compared with spectral radius 4 for the analogous unsigned two-step circulant. The transferable asset is a structured sign pattern that creates a two-mode Fourier coupling and reduces the operator norm without generic spectral normalization. This can serve as a fixed graph-convolution or sequence-mixing layer, enabling deeper stable compositions or larger raw mixing coefficients under the same Lipschitz budget. The construction is specialized to cyclic or approximately periodic data, so it should first be tested on ring-structured synthetic tasks and one-dimensional sequence benchmarks.
Replace an unsigned two-hop cyclic mixer by the paper's alternating signed circulant. The sign pattern preserves one-step and two-step interactions while reducing the exact spectral radius from 4 to 2√2, allowing a larger raw mixing coefficient under the same operator-norm stability constraint.