We investigate the convergence guarantee of two-layer neural network training with Gaussian randomly masked inputs. This scenario corresponds to Gaussian dropout at the input level, or noisy input training common in sensor networks, privacy-preserving training, and federated learning, where each user may have access to partial or corrupted features. Using a Neural Tangent Kernel (NTK) analysis, we demonstrate that training a two-layer ReLU network with Gaussian randomly masked inputs achieves linear convergence up to an error region proportional to the mask's variance. A key technical contribution is resolving the randomness within the non-linear activation, a problem of independent interest.

翻译：本研究探讨了在输入层采用高斯随机掩码的双层神经网络训练的收敛性保证。该场景对应于输入层的高斯丢弃操作，或传感器网络、隐私保护训练及联邦学习中常见的噪声输入训练，其中每个用户可能仅能获取部分或受损特征。通过神经正切核分析，我们证明了采用高斯随机掩码输入的双层ReLU网络训练能够实现线性收敛，其误差区域与掩码方差成正比。本研究的核心技术贡献在于解决了非线性激活函数内部的随机性问题，该问题本身具有独立的研究价值。