高斯输入掩码下两层神经网络收敛性分析
Convergence Analysis of Two-Layer Neural Networks under Gaussian Input Masking
AI总结：
本研究分析了高斯输入掩码下两层神经网络的收敛性，通过NTK方法证明其线性收敛性，并解决了非线性激活中的随机性问题。
摘要：
我们研究了在高斯随机掩码输入下训练两层神经网络的收敛性保证。这种场景对应于输入层面的高斯丢弃，或在传感器网络、隐私保护训练和联邦学习中常见的噪声输入训练，其中每个用户可能只访问部分或损坏的特征。通过神经切线核（NTK）分析，我们证明了使用高斯随机掩码输入训练两层ReLU网络可以达到线性收敛，误差区域与掩码的方差成比例。关键的技术贡献是解决了非线性激活中的随机性问题，这是一个独立感兴趣的课题。
英文摘要：
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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