mlsanityData to 7 Oct 2026

On the Stochastic Stability of Deep Markov Models

arXiv 2111.04601 ↗First posted 8 Nov 2021cs.LG cs.SY eess.SYcited by 4

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Abstract (arXiv)

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 34 of its 73 references that are in the map. First posted on arXiv 8 Nov 2021.

Builds on

34 of 73 references.

References · 34

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22 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 2; 2026: 1.

4 papers.

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