A Journey to the Edge of Stability
It has recently been found that deep learning often occurs at the "edge of stability (EoS)," where the maximum Hessian eigenvalue of the model is stabilized at a value reciprocal to the learning rate. However, what happens before we reach that regime? We fix a deep learning problem and vary first order optimization methods with dense learning rate sweeps. We then track the characterizing quantities of a learning trajectory: the loss, the sharpness, and the alignment between consecutive gradients. To our surprise, if we scale the learning rate by the dc gain of the optimizer, these traces from the sweeps from different optimizers almost perfectly overlap across a large range of learning ra...
| Authors | Jaerin Lee, Kyoung Mu Lee |
|---|---|
| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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