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新论文 · v1arXiv:2611.11526

A Stability Analysis of AdamW: Unstable Equilibria and Non-Convergence

Baiyu Su, Lizhang Chen, Qiang Liu

原文摘要

AdamW is ubiquitous in deep learning, yet its behavior remains poorly understood. We analyze its dynamics through the lens of dynamical systems and show that AdamW admits an implicit fixed-point objective: its fixed points coincide with the stationary points of a constrained and regularized optimization problem. However, not all of these fixed points are stable under AdamW's dynamics, and stability depends sensitively on curvature, weight decay, and momentum parameters. Even in one-dimensional settings, equilibria may be unstable, and trajectories can exhibit persistent oscillations rather than convergence to them. We further extend the analysis to higher dimensions, deriving sufficient conditions for local stability of the continuous-time dynamics, and propose a convergent modification that preserves AdamW's fixed points. These results clarify what optimization problem AdamW is associated with, when its convergence can be expected, and how its dynamics could inspire more reliable optimizers.

cs.LG · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.18516

Signed Rectified Flow: Negativity-Controlled Generation

Runlong Liao, Baiyu Su, Lizhang Chen, Qiang Liu

原文摘要

We introduce Signed Rectified Flow (Signed RF), a generalization of Rectified Flow that targets the signed measure $π^{sign} = (1+α)π^+ - απ^-$, where $α>0$, $π^+$ is the distribution to promote, and $π^-$ is the distribution to suppress. Although direct sampling from a signed measure is not well-defined, Signed RF induces a valid generative process that concentrates probability in regions where the signed measure is positive while provably excluding regions dominated by its negative component. It therefore provides a principled framework for incorporating negative information and exclusion constraints into generative modeling. We analyze the signed continuity equation underlying Signed RF and use a charged-particle interpretation to explain how negative mass forms exclusion barriers. This theory further motivates practical adaptive guidance algorithms. Across several applications, Signed RF improves the fidelity-diversity trade-off on ImageNet, reduces nearest-neighbor similarity in anti-memorization experiments, and reduces nudity induced by adversarial prompts in Stable Diffusion 3.5 while preserving CLIP and aesthetic scores.

cs.LG · cs.CV

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.09175

SIFR: Stable Signed Flow Reinforcement

Runlong Liao, Xingqian Xu, Lizhang Chen, Baiyu Su, Yufan Huang, Zhonghao Wang, Akash Gokul, Ming-Yu Liu 等 10 位作者

原文摘要

Reward-based fine-tuning of flow models requires effectively promoting high-reward and suppressing low-reward samples, while maintaining training stability over many rounds of iterative updates. Iterative reward fine-tuning provides a simple starting point, but the positive reward weights give no explicit unfitting signal, and repeated reweighting concentrates the distribution and causes collapse. We propose Stable Signed Flow Reinforcement (SIFR), which replaces the reward weights by signed advantages to supply the missing unfitting signal, and constrains the velocity drift from a reference model to stabilize the updates, with a Lagrange multiplier that adapts the regularization strength to a prescribed drift budget. We further show that existing flow RL methods fall within this framework: they implicitly minimize the signed loss, differing in their regularization choices. We validate SIFR on SD3.5 Medium (2.5B) and FLUX.2 Klein (9B) and scale it to Cosmos 3 Super Text2Image (64B): across all 12 backbone--reward pairs with preference and rule-based rewards, it matches or exceeds existing methods, reaches their peak rewards much faster, and keeps improving over long training where they plateau or collapse.

cs.LG · cs.AI · cs.CV

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arXiv ↗PDF ↗