Towards Understanding Gradient Flow Dynamics of Homogeneous Neural Networks Beyond the Origin

Abstract:Recent works exploring the training dynamics of homogeneous neural network weights under gradient flow with small initialization have established that in the early stages of training, the weights remain small and near the origin, but converge in direction. Building on this, the current paper studies the gradient flow dynamics of homogeneous neural networks with locally Lipschitz gradients, after they escape the origin. Insights gained from this analysis are used to characterize the first saddle point encountered by gradient flow after escaping the origin. Also, it is shown that for homogeneous feed-forward neural networks, under certain conditions, the sparsity structure emerging among the weights before the escape is preserved after escaping the origin and until reaching the next saddle point.

Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)

arXiv:2502.15952 [cs.LG]

(or arXiv:2502.15952v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2502.15952 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.