Subspace-based DPSGD has emerged as a robust solution for alleviating excessive noise in high-dimensional, privacy-preserving visual learning. It achieves a favorable privacy-utility balance by projecting privatized gradients onto a low-rank subspace derived from in-distribution public data. However, relying solely on limited public data can narrow the diversity of the anchored subspace and induce over-memorization into model training, leading to suboptimal private optimization.To overcome these limitations, we propose a synthesis-augmented subspace-based DPSGD framework, SAS-DPSGD, which integrates synthetic data into the subspace construction process. We quantitatively analyze the private optimization performance using the subspace derived from the mixed public and synthetic data, revealing the benefits as well as the saturation effects of incorporating synthetic data in private visual learning. To the best of our knowledge, this is the first work to provide a unified theoretical guarantee to synthesis-augmented subspace-based DPSGD. Moreover, we design an early projection mechanism within our framework that projects the gradient onto the subspace before performing gradient clipping. This mechanism effectively reduces the gradient clipping bias and lowers the synthetic data requirement, resulting in a faster convergence rate. Extensive experiments on two real-world datasets validate that SAS-DPSGD outperforms nine baselines by up to 9.78% in accuracy and can reduce the amount of synthetic data required by 66.7%.

Accurate flood forecast is crucial to ensure economic and ecological environment safety. Due to the complex factors affecting flood runoff in the small and medium-sized river basins, the traditional model cannot yield satisfactory prediction results. In this paper, we propose a novel Graph Convolution based spatial-temporal Attention LSTM(AGCLSTM) network to tackle the time series prediction problem in the flood forecasting domain. To be specific, our model contains two major modules: 1) the spatial-temporal GCN module with the dropedge mechanism which adequately captures the spatial and temporal characteristics of topological river graphs; 2) the spatial-temporal LSTM module to effectively extract temporal and spatial dynamic correlation in time series hydrological data. Experiments show that our model has excellent performance in flood peak prediction and flow calibration compared with the existing machine learning methods.