Canonical-row Chern flow on Bott--Samelson towers: realizable-volume models for Schubert, Grothendieck, and Lascoux polynomials
arXiv:2609.02850
2026
Architecture
2 ideas extracted · analyzed Sep 3, 2026
What the math gives to ML
The paper gives constructive realizable-volume models for factorially normalized homogeneous polynomials, connecting their coefficients to Lorentzian Hessian signatures and discrete-convex supports. The transferable assets are explicit curvature inequalities and exchange-closed support structures, rather than the specific Schubert or Grothendieck applications. A practical neural adaptation is to constrain positive higher-order routing or interaction polynomials toward Lorentzian curvature, while using polymatroid-style exchange rules for structured pruning. These are most plausible in higher-order MoE routers, tensorized MLPs, and polynomial attention biases, not as replacements for standard dense Transformer blocks.
Ideas from this paper
Unverified
2026
Replace an unconstrained positive higher-order gating function by a factorially normalized homogeneous polynomial whose coefficients are trained toward the Lorentzian Hessian signature. This gives multiplicative routing or attention interactions a controlled curvature pattern instead of allowing arbitrary unstable higher-order amplification.
Useful6/10
Difficulty6/10
Novelty8/10
Unverified
2026
Prune higher-order tensor or polynomial interactions while preserving an exchange-closed support instead of independently retaining the largest weights. The resulting sparse interaction pattern avoids arbitrary holes and retains structured substitutions between coordinates, potentially improving parameter efficiency and robustness after pruning.
Useful5/10
Difficulty5/10
Novelty9/10