On the Representational Geometry of Dynamic Programs
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:On the Representational Geometry of Dynamic Programs
Abstract: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 boundary at $T+1$? We present two structural negatives. The semiring's two native ways to reduce dimension (setting a variable to each identity) are neither injective nor always closed within the DP. Series and parallel composition fail to construct all DAG topologies from smaller sub-DAGs, and even all terminal-only operations do not capture all DP compositions.
| Comments: | 13 pages, 7 figures; submitted to NeurIPS 2026 Workshop on Symmetry and Geometry in Neural Representations (Extended Abstract Track) |
| Subjects: | Machine Learning (cs.LG); Discrete Mathematics (cs.DM); Algebraic Geometry (math.AG); Combinatorics (math.CO) |
| Cite as: | arXiv:2608.25034 [cs.LG] |
| (or arXiv:2608.25034v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.25034
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
Current browse context:
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
SLM-Conditioned Hierarchical Relation Routing for Labeled Property Graph Learning
Aug 28
-
NeuronFuzz: Safety Neuron Guided Fuzzing for LLM Safety Evaluation
Aug 28
-
Pruning Binarized Neural Networks: A Dedicated Framework and Globally Weighted Algorithms
Aug 28
-
Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
Aug 28
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.