The paper investigates the relationship between representation and function in neural networks, using analytical two‑layer linear models and simulations of nonlinear networks. It demonstrates that functional similarity and representational similarity can be dissociated: networks may share representations without sharing functions, and vice versa. The study also finds that robustness to input noise or generalization error does not constrain representations, whereas robustness to parameter noise forces networks to adopt task‑specific representations, indicating that representational alignment reflects computational advantages beyond mere functional alignment.
By Lukas Braun, Erin Grant, Andrew M. Saxe
arXiv:2511. 09432v2 Announce Type: replace Abstract: Machine learning (ML) models achieve remarkable performance but remain hard to interpret due to their scale and complexity.
By Ege Erdogan, Ana Lucic
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
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:2608. 08309v1 Announce Type: cross Abstract: We argue that learning visual representations without labels requires a training signal jointly complete across three non-overlapping objectives: semantic invariance across augmented views, patch-level spatial prediction, and representational non-degeneracy.
By Nikos Giakoumoglou, Paschalis Giakoumoglou, Tania Stathaki
arXiv:2604. 00208v2 Announce Type: replace Abstract: Comparing internal representations is a central goal in neuroscience and machine learning, but standard linear alignment metrics (Representational Similarity Analysis, Centered Kernel Alignment, and linear regression) are frequently applied to neural activity coordinates rather than on the underlying features.
By Sunny Liu, Habon Issa, Andr\'e Longon, Liv Gorton, Meenakshi Khosla, Alex Williams, David Klindt