arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 1709.06129cs.LGcs.AIcs.CVmath.OCstat.ML
收藏

什么时候卷积滤波器容易学习?

When is a Convolutional Filter Easy To Learn?

Carnegie Mellon University(卡内基梅隆大学);University of Southern California(南加州大学);Facebook AI Research(Facebook人工智能研究)

Simon S. Du, Jason D. Lee, Yuandong Tian

摘要:

我们分析了用于学习具有整流线性单元(ReLU)激活函数的卷积滤波器的(随机)梯度下降算法的收敛性。我们的分析不依赖于任何特定形式的输入分布,我们的证明仅使用ReLU的定义,与之前的作品相比,这些作品仅限于标准高斯输入。我们证明了随机初始化的(随机)梯度下降可以在多项式时间内学习卷积滤波器,并且收敛速度取决于输入分布的平滑度和补丁的紧密程度。据我们所知,这是基于梯度的卷积滤波器算法在非高斯输入分布上的第一个恢复保证。我们的理论还证明了深度神经网络中的两阶段学习率策略的合理性。虽然我们的重点是理论,我们也提出了实验,说明我们的理论研究结果。

英文摘要:

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑