SoftSignSGD(S3): An Enhanced Optimizer for Practical DNN Training and Loss Spikes Minimization Beyond Adam

TL;DR

This paper introduces SignSoftSGD (S3), a new optimizer that enhances Adam by reducing loss spikes and accelerating convergence through a flexible momentum scheme, leading to faster and more stable deep neural network training.

Contribution

S3 generalizes sign-like updates with a $p$-th order momentum, minimizes loss spikes with unified EMA coefficients, and incorporates Nesterov acceleration, offering theoretical convergence guarantees and practical improvements.

Findings

S3 converges faster and more stably than Adam and AdamW.

S3 reduces loss spikes even with larger learning rates.

S3 achieves comparable or better performance with fewer training steps.

Abstract

Adam has proven remarkable successful in training deep neural networks, but the mechanisms underlying its empirical successes and limitations remain underexplored. In this study, we demonstrate that the effectiveness of Adam stems largely from its similarity to SignSGD in robustly handling large gradient fluctuations, yet it is also vulnerable to destabilizing loss spikes due to its uncontrolled update scaling. To enhance the advantage of Adam and mitigate its limitation, we propose SignSoftSGD (S3), a novel optimizer with three key innovations. \emph{First}, S3 generalizes the sign-like update by employing a flexible $p$-th order momentum ($p \geq 1$) in the denominator, departing from the conventional second-order momentum (variance) preconditioning. This design enables enhanced performance while achieving stable training even with aggressive learning rates. \emph{Second}, S3 minimizes the occurrences of loss spikes through unified exponential moving average coefficients for numerator and denominator momenta, which inherently bound updates to $[-1, 1]$ and simplify hyperparameter tuning. \emph{Third}, S3 incorporates an equivalent Nesterov's accelerated gradient(NAG) module, accelerating convergence without memory overhead. Theoretically, we prove that S3 achieves the optimal convergence rate of $O\left(\frac{1}{T^{\sfrac{1}{4}}}\right)$ for general nonconvex stochastic optimization under weak assumptions. Extensive experiments across a range of vision and language tasks show that \textsf{\small S3} not only converges more rapidly and improves performance but also rarely experiences loss spikes, even with a \textbf{$\bm{10 \times}$} larger learning rate. In fact, S3 delivers performance comparable to or better than AdamW with \textbf{$2 \times$} the training steps, establishing its efficacy in both efficiency and final task performance.