On the Representational Geometry of Dynamic Programs
Standard neural architectures often fail to generalize to longer inputs for dynamic programming (DP) targets. We investigate what makes this hard geometrically. Every finite min-plus DP is a shortest path on a DAG, which is equivalently a tropical polynomial whose extended Newton polyhedron encodes the decision boundary of which path wins. We prove these three descriptions (graph, polynomial, polyhedron) form isomorphic semirings at two levels --- formal polynomials and their computed functions --- connected by operations that characterize all structural redundancies. We then address the length-generalization question geometrically: does the decision boundary at length $T$ decide the boun...
| Authors | Richard F. M. Lim, Ruriko Yoshida |
|---|---|
| Primary category | cs.LG |
| Published | 25 August 2026 |
| Last updated at source | 25 August 2026 |
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