arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2003.13058cs.LGstat.ML
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分层降低训练代价的高维神经特征设计

High-dimensional Neural Feature Design for Layer-wise Reduction of Training Cost

KTH Royal Institute of Technology(瑞典皇家理工学院)

Alireza M. Javid, Arun Venkitaraman, Mikael Skoglund, Saikat Chatterjee

摘要:

我们设计了一个基于ReLU的多层神经网络,将每一层的特征向量映射到一个更高的维度空间。我们在每一层中设计权重矩阵,以确保随着层数的增加,训练成本降低。如果凸成本最小化,则在高维空间中向目标的线性投影导致较低的训练成本。在最小化过程中使用了$\ell_2$ -范数凸约束,以减小泛化误差并避免过拟合。网络的正则化超参数是解析推导的,以保证训练成本的单调递减,因此,它消除了交叉验证来找到每一层中的正则化超参数的需要。我们表明,所提出的架构是范数保持的,并提供了一个可逆的特征向量,因此,可以用来减少训练成本的任何其他学习方法,采用线性投影来估计目标。

英文摘要:

We design a ReLU-based multilayer neural network by mapping the feature vectors to a higher dimensional space in every layer. We design the weight matrices in every layer to ensure a reduction of the training cost as the number of layers increases. Linear projection to the target in the higher dimensional space leads to a lower training cost if a convex cost is minimized. An $\ell_2$-norm convex constraint is used in the minimization to reduce the generalization error and avoid overfitting. The regularization hyperparameters of the network are derived analytically to guarantee a monotonic decrement of the training cost, and therefore, it eliminates the need for cross-validation to find the regularization hyperparameter in each layer. We show that the proposed architecture is norm-preserving and provides an invertible feature vector, and therefore, can be used to reduce the training cost of any other learning method which employs linear projection to estimate the target.

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。

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