Title: Adaptive Preconditioners Trigger Loss Spikes in Adam
Primary area: learning theory
Keywords: loss spike, Adam, training instability

Abstract: Loss spikes commonly emerge during neural network training with the Adam optimizer across diverse architectures and scales, yet their underlying mechanisms remain poorly understood. In this work, we investigate the fundamental causes of Adam spikes. While previous explanations attribute these phenomena to sharper loss landscapes at lower loss values, our analysis reveals that it is Adam's adaptive preconditioners that trigger spikes during training. We identify a key mechanism where the second moment estimate becomes insensitive to current gradients when using large $\beta_2$ values. This insensitivity can push the maximum eigenvalue of the preconditioned Hessian beyond the stability threshold $2/\eta$ for sustained periods, manifesting as dramatic loss spikes. We theoretically and experimentally characterize five distinct stages of spike evolution and propose a predictor for anticipating spikes based on gradient-directional curvature. We further validate our mechanism and demonstrate practical mitigation strategies from small fully connected networks to large-scale Transformers. These findings provide new theoretical insights for understanding and controlling loss spike behavior in Adam optimization.