<ul><li>Deep neural networks (DNNs) trained through end-to-end learning have achieved remarkable success across diverse machine learning tasks, but they are not designed to adhere to the Minimum Description Length (MDL) principle.</li><li>A novel theoretical framework for designing and evaluating deep Variational Autoencoders (VAEs) based on MDL is introduced.</li><li>The Spectrum VAE, a specific VAE architecture, is designed and its MDL can be rigorously evaluated under given conditions.</li><li>This work lays the foundation for future research on designing deep learning systems that explicitly adhere to information-theoretic principles.</li></ul>

Minimum Description Length of a Spectrum Variational Autoencoder: A Theory

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