Summary of State-space Systems As Dynamic Generative Models, by Juan-pablo Ortega and Florian Rossmannek
State-space systems as dynamic generative models
by Juan-Pablo Ortega, Florian Rossmannek
First submitted to arxiv on: 12 Apr 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Dynamical Systems (math.DS); Probability (math.PR); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper presents a probabilistic framework to study the relationship between input and output processes in discrete-time state-space systems. It introduces general sufficient conditions for the existence and uniqueness of output processes, known as the echo state property. When these conditions are met, the system becomes a generative model for probabilistic dependences between sequence spaces. The results also show that the output depends continuously on the input using the Wasserstein metric. The paper’s stochastic echo state property generalizes sufficient conditions from deterministic situations, allowing state-space systems to induce probabilistic dependence structures without functional relationships. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way is developed to understand how inputs and outputs are connected in a type of system called state-space systems. This connection is special because it only depends on probability, not on specific values. The researchers show that if certain conditions are met, there will be an output process for every input process, and this output will depend continuously on the input. This means that these systems can create random connections between inputs and outputs even when there’s no direct link. |
Keywords
* Artificial intelligence * Generative model * Probability
