arXiv:2606. 04754v1 Announce Type: new Abstract: Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged.
By Vincent B\"urgin, Daniel Herbst, Ya-Wei Eileen Lin, Stefanie Jegelka
The paper introduces a general theoretical framework for fibrations on graphs labeled by a commutative monoid, extending the classic theory of graph fibrations to weighted and algebraically labeled graphs. It also accommodates approximate fibrations and demonstrates how this framework can be used to compress arbitrary neural networks, including CNNs, providing a solid theoretical basis for recent findings on fibration symmetries in geometric deep learning.
By Paolo Boldi
The paper investigates how parameter symmetries in overparameterized nonlinear neural networks affect representational geometry. It shows that these symmetries can be described by three basic feature transformations—addition, duplication, and scaling—allowing a closed‑form decomposition of representations into essential and auxiliary parts. The study further demonstrates that implementation‑level selection rules can resolve the resulting degeneracy, producing identifiable geometries that reflect feature contributions to the network’s function.
By Marvin Theiss, Lukas Braun, Andrew M. Saxe, Erin Grant
arXiv:2606. 10913v1 Announce Type: new Abstract: We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks.
By Jakob Galley, Vahid Shahverdi, Axel Flinth
arXiv:2610.17424v1 Announce Type: cross
Abstract: Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks...
By Tomas Karella, Emily Shinkle, Alice Elisabeth Anastasia Allen, Pieter J. Swart, Nicholas Lubbers, Roxana Bujack
The paper introduces a physics-inspired neural framework that combines graph neural networks with statistical‑mechanics principles to solve large‑scale graph coloring problems. By using a planting‑based supervised signal, symmetry‑breaking regularization, and iterative noise‑annealed neural dynamics, the model navigates complex solution landscapes and scales quadratically with graph size. It generalizes from small training graphs to instances up to 20 times larger, demonstrating that neural architectures can learn scalable algorithmic strategies effective in hard connectivity regions.
By Lorenzo Colantonio (Department of Physics, Sapienza University of Rome), Andrea Cacioppo (Department of Physics, Sapienza University of Rome), Federico Scarpati (Department of Physics, Sapienza University of Rome), Maria Chiara Angelini (Department of Physics, Sapienza University of Rome), Federico Ricci-Tersenghi (Department of Physics, Sapienza University of Rome), Stefano Giagu (Department of Physics, Sapienza University of Rome)