Wearing a MASK: Compressed Representations of Variable-Length Sequences Using Recurrent Neural Tangent Kernels
Sina AlEMohammad, Hossein Babaei, Randall Balestriero, Matt Y. Cheung, Ahmed Imtiaz Humayun, Daniel LeJeune, Naiming Liu, Lorenzo Luzi, Jasper Tan, Zichao Wang, Richard G. Baraniuk
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Abstract
High dimensionality poses many challenges to the use of data, from visualization and interpretation, to prediction and storage for historical preservation. Techniques abound to reduce the dimensionality of fixed-length sequences, yet these methods rarely generalize to variable-length sequences. To address this gap, we extend existing methods that rely on the use of kernels to variable-length sequences via use of the Recurrent Neural Tangent Kernel (RNTK). Since a deep neural network with ReLu activation is a Max-Affine Spline Operator (MASO), we dub our approach Max-Affine Spline Kernel (MASK). We demonstrate how MASK can be used to extend principal components analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) and apply these new algorithms to separate synthetic time series data sampled from second-order differential equations.