arXiv:2410. 06665v4 Announce Type: replace-cross Abstract: This paper explores the characterization of equivariant linear layers for representations of permutations and related groups.
By Yonatan Sverdlov, Ido Springer, Nadav Dym
arXiv:2607. 03551v1 Announce Type: new Abstract: Weight space learning aims to learn representations of neural network (NN) weights, enabling different downstream tasks.
By Aron Asefaw, Konstantinos Tzevelekakis, Damian Falk, L\'eo Meynent, Damian Borth
CrossGMN introduces a graph metanetwork that processes a trained source network and an initialized target network simultaneously, enabling equivariant cross‑architecture weight‑space transformations. By preserving symmetry through cross‑network message passing, CrossGMN can refine target network initializations while remaining invariant to source permutations and equivariant to target permutations. Experiments demonstrate that CrossGMN accelerates knowledge distillation, transfers across datasets without retraining, and unifies compression from diverse source architectures into a common target architecture.
By Adir Dayan, Yam Eitan, Haggai Maron
arXiv:2610.00420v1 Announce Type: new
Abstract: A weight space network (or metanetwork) takes the weights of another neural network as input and predicts properties of it. Most prior work trains such...
By Yuxin Ma, Adir Dayan, Yam Eitan, Haggai Maron, Soledad Villar
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
By Ethan Smith
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