Parametric PDEs consider different system conditions as well as an underlying solution operator characterized by a set of finite-dimensional parameters.

Designing efficient exploration is central to Reinforcement Learning due to the fundamental problem posed by the exploration-exploitation dilemma.

Since it is difficult to directly optimize the marginal likelihood due to the sum inside the log function, we resort to the Expectation-Maximization (EM) algorithm, where we iterate between the expectation and maximization steps. In practice, we draw a mini-batch of size M to estimate this quantity. In other words, we assign each data point to its closest centroid. We report the average accuracy from three independent runs. We do not perform any additional hyper-parameter searches.

Current methods like membership inference or active IP protection either work only in settings where the suspected text is known or do not provide reliable statistical guarantees. We discover that, on the contrary, it is possible to reliably determine if a language model was trained on synthetic data if that data is output by a watermarked LLM.