arXiv:2607.06795 2026 Architecture 1 ideas extracted · analyzed Aug 30, 2026
The paper develops a ternary analogue of a formal group law in which three inputs are combined through four signed linear forms and symmetric functions of their exponentials. The transferable construction is an explicit, permutation-symmetric feature mixer that generates pairwise and higher-order interactions without learning a full trilinear tensor. Its motivic coefficient-ring results are not directly useful for neural networks, but the four-root algebra gives a concrete structured architecture. The best first test is to replace selected three-way fusion MLPs or graph message-passing updates with a truncated four-root mixer at matched parameter and FLOP budgets.
Replace a generic three-input concatenation MLP with a permutation-symmetric mixer built from the four signed combinations x+y-z, x-y+z, -x+y+z, and -x-y-z. Apply a shared truncated exponential to these combinations and aggregate symmetric pairwise products, producing controlled quadratic and higher-order interactions without materializing a full trilinear tensor.