aiqbench analysis
This study empirically characterizes how deep neural network representations evolve geometrically during training, identifying distinct trajectories such as collapse-and-recovery and a pathological destructive regime. By linking these dynamic representation changes to optimization outcomes across different architectures, the work offers critical insights into the internal learning mechanisms of modern models beyond final convergence states.
Representations Have Trajectories: Characterizing Temporal Representation Dynamics in Neural Networks
arXiv:2610.24571v1 Announce Type: new Abstract: Recent work has shown that deep neural networks exhibit an implicit low-rank simplicity bias. In this paper, we investigate the questions that naturally arise from this observation. What are the temporal consequences of low-rank simplicity bias during optimization? How does representation geometry evolve throughout optimization rather than only at convergence? Do different neural architectures exhibit distinct geometric optimization behaviors? To answer these questions, we conduct a large-scale empirical study tracking representational geometry throughout training. We find that neural networks follow three recurring geometric trajectories: persistent high-rank, collapse-and-recovery, and persistent low-rank. We further identify Destructive Representation Collapse (DRC) as a pathological regime in which representations collapse to rank-one and fail to recover, leading to a sustained loss of representational capacity. While collapse-and-recovery is consistently associated with successful optimization in controlled settings, experiments on real-world models show that the relationship between geometric trajectories and optimization outcomes is configuration dependent. Overall, our findings suggest that representation geometry evolves dynamically during training and provide a new perspective on how deep neural networks learn.
Abstract:Recent work has shown that deep neural networks exhibit an implicit low-rank simplicity bias. In this paper, we investigate the questions that naturally arise from this observation. What are the temporal consequences of low-rank simplicity bias during optimization? How does representation geometry evolve throughout optimization rather than only at convergence? Do different neural architectures exhibit distinct geometric optimization behaviors? To answer these questions, we conduct a large-scale empirical study tracking representational geometry throughout training. We find that neural networks follow three recurring geometric trajectories: persistent high-rank, collapse-and-recovery, and persistent low-rank. We further identify Destructive Representation Collapse (DRC) as a pathological regime in which representations collapse to rank-one and fail to recover, leading to a sustained loss of representational capacity. While collapse-and-recovery is consistently associated with successful optimization in controlled settings, experiments on real-world models show that the relationship between geometric trajectories and optimization outcomes is configuration dependent. Overall, our findings suggest that representation geometry evolves dynamically during training and provide a new perspective on how deep neural networks learn.
Machine Learning (cs.LG)
arXiv:2610.24571 [cs.LG]
(or arXiv:2610.24571v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.24571 Focus to learn more arXiv-issued DOI via DataCite
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