研究输入加噪下两层神经网络的收敛性，发现误差与噪声方差成正比。
Convergence Analysis of Two-Layer Neural Networks under Gaussian Input Masking
- 用神经正切核分析输入层高斯掩码下的训练过程
- 证明网络线性收敛，最终误差与掩码方差成正比
- 解决非线性激活中随机性难题，适用于隐私保护等场景
我们研究了在高斯随机掩码输入条件下，两层神经网络训练的收敛保证。该场景对应于输入层的高斯丢弃（dropout），或传感器网络、隐私保护训练和联邦学习中常见的带噪声输入，其中每个用户可能只能访问部分或受损特征。通过神经正切核（NTK）分析，我们证明：使用高斯随机掩码输入训练两层ReLU网络，能达到线性收敛，最终误差范围与掩码方差成正比。一个关键的技术贡献是解决了非线性激活中的随机性问题，这一问题本身具有独立研究价值。
原文摘要 · Abstract (English)
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.
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