Percolation Dynamics in Optimization: Variance Cascades and Nested Symmetry
We study the dynamics of Stochastic Gradient Descent (SGD), which is known to steer deep neural networks toward invariant sets that correspond to simpler subnetworks. How this steering unfolds over time remains poorly understood. We answer this by modeling the stochastic gradient flow (SGF) as a percolation process, in which nested architectural symmetries force subnetworks to merge in discrete blocks rather than by single-edge attachment. These structural transitions register as variance spikes in a macroscopic order parameter echoing physical phase transitions. We further state sufficient conditions under which the trapping argument carries over to Adam and AdamW under heavy-tailed grad...
| Authors | Sai Niranjan Ramachandran, Suvrit Sra |
|---|---|
| Primary category | cs.LG |
| Published | 2 September 2026 |
| Last updated at source | 27 September 2026 |
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