Entropy-Reservoir Bregman Projection: An Information-Geometric Unification of Model Collapse
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917150821711872 |
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| author | Chen, Jingwei |
| author_facet | Chen, Jingwei |
| contents | Self-referential learning -- training a model on data it generated itself -- promises boundless scalability but chronically suffers from model collapse: language models degenerate into repetitive text, GANs drop modes, and reinforcement-learning policies over-exploit. Although practitioners employ ad~hoc fixes such as real-data mixing, entropy bonuses, knowledge distillation, or retrieval-augmented generation, a single principle that explains both the failure mode and the success of these fixes has remained elusive. We present Entropy-Reservoir Bregman Projection (ERBP), an information-geometric framework that unifies these phenomena. We model the closed loop as a stochastic Bregman projection sequence in distribution space. Without external coupling, finite-sample noise forces the system to project onto an ever-shrinking empirical support, causing exponential entropy decay and eventual collapse. Introducing an Entropy Reservoir -- a high-entropy distribution mixed into each projection -- injects a controllable entropy flux that provably stabilises the dynamics. Our theory yields (i) a necessary condition for collapse, (ii) a sufficient condition that guarantees a non-trivial entropy floor, and (iii) closed-form rates that depend only on sample size and the strong-convexity/Lipschitz constants of the Bregman generator. Experiments on large-language-model self-training, Soft Actor-Critic in reinforcement learning, and GAN optimisation validate our predictions and show that disparate stabilisation heuristics correspond to specific reservoir choices and coupling coefficients. ERBP thus transforms a collection of folk remedies into a single, quantitative design rule: monitor and budget your entropy flux. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy-Reservoir Bregman Projection: An Information-Geometric Unification of Model Collapse Chen, Jingwei Machine Learning Artificial Intelligence I.2.6; I.2.7; H.1.1 Self-referential learning -- training a model on data it generated itself -- promises boundless scalability but chronically suffers from model collapse: language models degenerate into repetitive text, GANs drop modes, and reinforcement-learning policies over-exploit. Although practitioners employ ad~hoc fixes such as real-data mixing, entropy bonuses, knowledge distillation, or retrieval-augmented generation, a single principle that explains both the failure mode and the success of these fixes has remained elusive. We present Entropy-Reservoir Bregman Projection (ERBP), an information-geometric framework that unifies these phenomena. We model the closed loop as a stochastic Bregman projection sequence in distribution space. Without external coupling, finite-sample noise forces the system to project onto an ever-shrinking empirical support, causing exponential entropy decay and eventual collapse. Introducing an Entropy Reservoir -- a high-entropy distribution mixed into each projection -- injects a controllable entropy flux that provably stabilises the dynamics. Our theory yields (i) a necessary condition for collapse, (ii) a sufficient condition that guarantees a non-trivial entropy floor, and (iii) closed-form rates that depend only on sample size and the strong-convexity/Lipschitz constants of the Bregman generator. Experiments on large-language-model self-training, Soft Actor-Critic in reinforcement learning, and GAN optimisation validate our predictions and show that disparate stabilisation heuristics correspond to specific reservoir choices and coupling coefficients. ERBP thus transforms a collection of folk remedies into a single, quantitative design rule: monitor and budget your entropy flux. |
| title | Entropy-Reservoir Bregman Projection: An Information-Geometric Unification of Model Collapse |
| topic | Machine Learning Artificial Intelligence I.2.6; I.2.7; H.1.1 |
| url | https://arxiv.org/abs/2512.14879 |