arXiv:2608.04133 2026 Architecture 1 ideas extracted · analyzed Aug 31, 2026
The paper identifies a structural reduction for binary optimization: maximizing the norm of a signed vector sum does not require searching all 2^N sign patterns. Any global optimizer is generated by thresholding vector projections onto one common direction, so the search can be reduced to hyperplane cells on a sphere. This can transfer to neural modules with binary latent gates, signed residual branches, or quantized mixture-of-experts routing. In two projected dimensions, the candidate configurations can be enumerated exactly; in higher dimensions, the same characterization gives a principled directional sampler.
Replace exhaustive optimization of N binary gates by the geometrically admissible sign patterns induced by projections onto a common direction. For two-dimensional gate vectors, enumerate angular cells exactly; for higher-dimensional vectors, sample directions and evaluate only the induced configurations.