Variational Structure at the Edge of Stability
When discrete-time optimizers operate at the edge of stability, they exhibit near-two-periodic behavior. These oscillatory dynamics are reminiscent of conservative systems, such as the dynamics generated by symplectic integrators. However, a precise formulation of the connection between discrete-time optimizers at the edge of stability and discrete mechanics remains underexplored. Recently, Litman introduced the "edge coupling": a functional on consecutive gradient descent iterates whose critical points encode the fixed points and two-point orbits of the gradient descent dynamics. Here we extend the edge coupling to heavy-ball and Nesterov momentum. We show that its critical points charac...
| Authors | Eric Regis |
|---|---|
| Primary category | cs.LG |
| Published | 21 August 2026 |
| Last updated at source | 21 August 2026 |
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