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  • title: Eliminating the Invariance on the Loss Landscape of Linear Autoencoders
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            Eliminating the Invariance on the Loss Landscape of Linear Autoencoders
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            Eliminating the Invariance on the Loss Landscape of Linear Autoencoders

            Jul 12, 2020

            Speakers

            RO

            Reza Oftadeh

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            JS

            Jiayi Shen

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            DS

            Dylan Shell

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            About

            In this paper, we propose a new loss function for linear autoencoders (LAEs) and then analytically identify the structure of the loss surface. Optimizing the conventional Mean Square Error (MSE) loss results in a decoder matrix that spans the principal subspace of the sample covariance of the data, but fails to identify the exact eigenvectors. This shortcoming originates from an invariance that cancels out in the global map. Here, we prove that our loss function eliminates this issue, i.e., the…

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