Generalized Dual-Scale Optimization: Topology-Aware Margin Dynamics in Fine-Grained Vision

We identify that the standard Cross-Entropy loss exhibits a monotonically expanding intrinsic margin, causing gradient saturation in fine-grained tasks. To address this, we propose the Generalized Dual-Scale Loss, a unified framework controlling margin dynamics via a parameter $\lambda$. Experiments with Vision Transformers reveal that optimal dynamics are topology-dependent: rigid, geometric manifolds require aggressive hard mining ($\lambda > 1$) to resolve structural subtleties, whereas noisy, biological manifolds favor robust constant margins ($\lambda \approx 1$) to prevent overfitting to clutter. Our work advocates for aligning optimization dynamics with the intrinsic noise and granularity of the data.