The paper "HEAT DEATH OF GENERATIVE MODELS IN CLOSED-LOOP LEARNING" by Matteo Marchi, Stefano Soatto, Pratik Chaudhari, and Paulo Tabuada explores the stability and degeneration of generative models when they are trained on data they generate themselves. The authors investigate the phenomenon of "generative closed-loop learning," where models are iteratively trained using their own generated content, which can lead to mode collapse or the production of gibberish data. Key findings include: 1. **Empirical Observations**: Small-scale experiments show that closed-loop training can lead to degeneration, where models produce only a subset of the desired data distribution. 2. **Theoretical Analysis**: Using dynamical systems tools, the authors show that without sufficient external data at each iteration, any non-trivial temperature (a parameter controlling the randomness of sampling) will cause the model to asymptotically degenerate. 3. **Degeneration Types**: Depending on the temperature regime, the degeneration can result in either a small set of outputs being produced uniformly or a large set of outputs being produced uniformly. 4. **Implications**: The loss of initial dataset knowledge is inevitable unless explicit steps are taken to preserve and reintroduce fresh data. The paper provides insights into the stability of generative models in closed-loop learning, highlighting the importance of maintaining a high fraction of fresh data to prevent degeneration. This research adds to the growing concern about data self-ingestion and the potential for models to lose their original distributional knowledge.The paper "HEAT DEATH OF GENERATIVE MODELS IN CLOSED-LOOP LEARNING" by Matteo Marchi, Stefano Soatto, Pratik Chaudhari, and Paulo Tabuada explores the stability and degeneration of generative models when they are trained on data they generate themselves. The authors investigate the phenomenon of "generative closed-loop learning," where models are iteratively trained using their own generated content, which can lead to mode collapse or the production of gibberish data. Key findings include: 1. **Empirical Observations**: Small-scale experiments show that closed-loop training can lead to degeneration, where models produce only a subset of the desired data distribution. 2. **Theoretical Analysis**: Using dynamical systems tools, the authors show that without sufficient external data at each iteration, any non-trivial temperature (a parameter controlling the randomness of sampling) will cause the model to asymptotically degenerate. 3. **Degeneration Types**: Depending on the temperature regime, the degeneration can result in either a small set of outputs being produced uniformly or a large set of outputs being produced uniformly. 4. **Implications**: The loss of initial dataset knowledge is inevitable unless explicit steps are taken to preserve and reintroduce fresh data. The paper provides insights into the stability of generative models in closed-loop learning, highlighting the importance of maintaining a high fraction of fresh data to prevent degeneration. This research adds to the growing concern about data self-ingestion and the potential for models to lose their original distributional knowledge.