A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Method
This provides an incremental improvement for researchers and practitioners in data science and PDE modeling by enabling efficient parallel training with reduced computational costs.
The paper tackles the problem of high-dimensional training data in supervised machine learning by applying the Empirical Interpolation Method (EIM) to reduce dimensionality, resulting in significant training time gains without accuracy loss, with parallel networks requiring fewer than ten times the training weights.
Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine learning. This is termed as DNN-EIM. Applications in data science (e.g., MNIST) and parameterized (and time-dependent) partial differential equations (PDEs) are considered. The proposed DNNs in case of classification are trained in parallel for each class. This approach is sequential, i.e., new classes can be added without having to retrain the network. In case of PDEs, a DNN is designed corresponding to each EIM point. Again, these networks can be trained in parallel, for each EIM point. In all cases, the parallel networks require fewer than ten times the number of training weights. Significant gains are observed in terms of training times, without sacrificing accuracy.