Systematic generalization remains a significant challenge in deep learning. In particular, combinatorial generalization - generalizing to new configurations of known factors of variation - is effortle...
arXiv:2505.09716v4 Announce Type: replace
Abstract: Out-of-distribution (OOD) generalisation through composition requires a system to discover invariant properties from input-output associations and...
By George Dimitriadis, Spyridon Samothrakis
The paper presents a necessary and sufficient condition for provable compositional generalization in neural networks, identifying two key principles: structural alignment and unambiguous minimized representations. It rigorously proves this condition, verifies it in Lean 4, and demonstrates its applicability in few-shot settings, including the SCAN jump task. The authors also outline an algorithmic approach and illustrate it with a minimal example, all derived purely from mathematical analysis without empirical validation.
By Yuanpeng Li
The paper investigates how memorizing long‑tail data can aid generalization when combined with a model’s ability to compose features. It demonstrates theoretically that, in a linear setting, memorization plus composition enables correct predictions on rare test examples that involve unseen combinations of long‑tail features. Experiments with neural networks on simple datasets confirm that this effect extends beyond linear models and that a model’s compositional capability depends on its architecture.
By Mo Zhou, Haoyang Ma, Rong Ge
arXiv:2601. 04509v2 Announce Type: replace Abstract: Mixed-integer linear programming (MILP) is a foundational framework for combinatorial optimization across science and engineering, but remains hard to solve at scale due to NP-hardness.
By Peixin Huang, Yaoxin Wu, Yining Ma, Cathy Wu, Wei Zhang, Wen Song
arXiv:2510.03075v4 Announce Type: replace-cross
Abstract: Compositional generalization, the ability to generate novel combinations of known concepts, is a key ingredient for visual generative models....
By Karim Farid, Rajat Sahay, Yumna Ali Alnaggar, Simon Schrodi, Volker Fischer, Cordelia Schmid, Thomas Brox