Topology Inference for Immune System Networks by Using Cell Amount Data

arXiv:2608.07403 2026 Dynamics 1 ideas extracted · analyzed Sep 1, 2026

What the math gives to ML

The paper offers a constructive topology-inference mechanism based on three measurable requirements: nonnegative states, convergence to a finite equilibrium with prescribed component ratios, and signed interaction constraints. Its transferable asset is the conversion of these qualitative properties into a constrained quadratic program with explicit dynamical guarantees. A useful neural-network transfer is a positive, ratio-stable recurrent or state-space module whose transition matrix is fitted or projected under sign, contraction, and equilibrium constraints.

Ideas from this paper

Failed on benchmark 2026

Ratio-Stable Positive Recurrent Core

Replace an unconstrained recurrent transition with a positive linear state-space core whose equilibrium has a prescribed composition vector. Fit or project its interaction matrix using a quadratic program with sign, sparsity, diagonal-dominance, and equilibrium constraints, then use the resulting stable dynamics as the hidden-state update.

Useful7/10
Difficulty5/10
Novelty7/10
Paper: Topology Inference for Immune System Networks by Using Cell Amount Data arXiv:2608.07403