Loss Spike in Training Neural Networks
This work addresses the problem of training instability for neural network practitioners, offering incremental insights into loss dynamics and sharpness measures.
The paper investigates the mechanism of loss spikes in neural network training, attributing them to sharp loss landscapes and linking them to the maximum eigenvalue of the Hessian, which is found to measure sharpness but not generalization, with experimental observations showing correlation between loss spikes and weight condensation.
In this work, we investigate the mechanism underlying loss spikes observed during neural network training. When the training enters a region with a lower-loss-as-sharper (LLAS) structure, the training becomes unstable, and the loss exponentially increases once the loss landscape is too sharp, resulting in the rapid ascent of the loss spike. The training stabilizes when it finds a flat region. From a frequency perspective, we explain the rapid descent in loss as being primarily influenced by low-frequency components. We observe a deviation in the first eigendirection, which can be reasonably explained by the frequency principle, as low-frequency information is captured rapidly, leading to the rapid descent. Inspired by our analysis of loss spikes, we revisit the link between the maximum eigenvalue of the loss Hessian ($λ_{\mathrm{max}}$), flatness and generalization. We suggest that $λ_{\mathrm{max}}$ is a good measure of sharpness but not a good measure for generalization. Furthermore, we experimentally observe that loss spikes can facilitate condensation, causing input weights to evolve towards the same direction. And our experiments show that there is a correlation (similar trend) between $λ_{\mathrm{max}}$ and condensation. This observation may provide valuable insights for further theoretical research on the relationship between loss spikes, $λ_{\mathrm{max}}$, and generalization.