aiqbench analysis
This research advances the theoretical understanding of neural networks by formalizing data-dependent parameter symmetries and providing a framework for their automated discovery. By characterizing loss invariance through infinitesimal conditions, the study offers new analytical tools to explore training dynamics and generalization across various architectures, including pretrained transformers. This work represents a significant step toward decoding the structural properties that govern deep learning model behavior.
Discovering Symmetries in Neural Network Parameter Spaces
arXiv:2609.33527v1 Announce Type: new Abstract: Parameter space symmetries are important for understanding neural networks' loss landscape, training dynamics, and generalization. However, systematically identifying these symmetries remains a challenge. In this paper, we formalize data-dependent parameter symmetries and characterize loss invariance and the group-action axioms through infinitesimal conditions, which provide objectives for jointly learning group generators and nonlinear action maps. Our framework systematically uncovers parameter symmetries, including previously unknown ones. To study larger networks, we establish conditions under which subnetwork symmetries extend to the full model. The same construction gives an explicit family of finite-batch symmetries, providing both analytical examples and a foundation for discovery through small subnetworks. Using the infinitesimal characterization and subnetwork construction, we implement a framework for automated discovery of parameter symmetries, and successfully uncovered symmetries in various architectures, including pretrained transformer models.
Abstract:Parameter space symmetries are important for understanding neural networks' loss landscape, training dynamics, and generalization. However, systematically identifying these symmetries remains a challenge. In this paper, we formalize data-dependent parameter symmetries and characterize loss invariance and the group-action axioms through infinitesimal conditions, which provide objectives for jointly learning group generators and nonlinear action maps. Our framework systematically uncovers parameter symmetries, including previously unknown ones. To study larger networks, we establish conditions under which subnetwork symmetries extend to the full model. The same construction gives an explicit family of finite-batch symmetries, providing both analytical examples and a foundation for discovery through small subnetworks. Using the infinitesimal characterization and subnetwork construction, we implement a framework for automated discovery of parameter symmetries, and successfully uncovered symmetries in various architectures, including pretrained transformer models.
Machine Learning (cs.LG)
arXiv:2609.33527 [cs.LG]
(or arXiv:2609.33527v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.33527 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 224 words
