Optimizer Dynamics at the Edge of Stability with Differential Privacy

Deep learning models can reveal sensitive information about individual training examples, and while differential privacy (DP) provides guarantees restricting such leakage, it also alters optimization dynamics in poorly understood ways. We study the training dynamics of neural networks under DP by comparing Gradient Descent (GD), and Adam to their privacy-preserving variants. Prior work shows that these optimizers exhibit distinct stability dynamics: full-batch methods train at the Edge of Stability (EoS), while mini-batch and adaptive methods exhibit analogous edge-of-stability behavior. At these regimes, the training loss and the sharpness--the maximum eigenvalue of the training loss Hessian--exhibit certain characteristic behavior. In DP training, per-example gradient clipping and Gaussian noise modify the update rule, and it is unclear whether these stability patterns persist. We analyze how clipping and noise change sharpness and loss evolution and show that while DP generally reduces the sharpness and can prevent optimizers from fully reaching the classical stability thresholds, patterns from EoS and analogous adaptive methods stability regimes persist, with the largest learning rates and largest privacy budgets approaching, and sometimes exceeding, these thresholds. These findings highlight the unpredictability introduced by DP in neural network optimization.

DeMansia: Mamba Never Forgets Any Tokens

This paper examines the mathematical foundations of transformer architectures, highlighting their limitations particularly in handling long sequences. We explore prerequisite models such as Mamba, Vision Mamba (ViM), and LV-ViT that pave the way for our proposed architecture, DeMansia. DeMansia integrates state space models with token labeling techniques to enhance performance in image classification tasks, efficiently addressing the computational challenges posed by traditional transformers. The architecture, benchmark, and comparisons with contemporary models demonstrate DeMansia's effectiveness. The implementation of this paper is available on GitHub at https://github.com/catalpaaa/DeMansia