In this work, we propose a new flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods that rely on random sampling within the Bayesian framework, our approach first leverages flow matching posterior estimation (FMPE) to efficiently constrain the prior range of physical parameters, and then employs MCMC to accurately infer the posterior distribution. For example, in the orbital parameter inference of beta Pictoris b, our model achieved a substantial speed-up while maintaining comparable accuracy-running 77.8 times faster than Parallel Tempered MCMC (PTMCMC) and 365.4 times faster than nested sampling. Moreover, our FM-MCMC method also attained the highest average log-likelihood among all approaches, demonstrating its superior sampling efficiency and accuracy. This highlights the scalability and efficiency of our approach, making it well-suited for processing the massive datasets expected from future exoplanet surveys. Beyond astrophysics, our methodology establishes a versatile paradigm for synergizing deep generative models with traditional sampling, which can be adopted to tackle complex inference problems in other fields, such as cosmology, biomedical imaging, and particle physics.

We cast nested named entity recognition (NNER) as a sequence labeling task by leveraging prior work that linearizes constituency structures, effectively reducing the complexity of this structured prediction problem to straightforward token classification. By combining these constituency linearizations with pretrained encoders, our method captures nested entities while performing exactly n tagging actions. Our approach achieves competitive performance compared to less efficient systems, and it can be trained using any off-the-shelf sequence labeling library.

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior sub ject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

Nested named entity recognition (nested NER) is a fundamental task in natural language processing. Various span-based methods have been proposed to detect nested entities with span representations. However, span-based methods do not consider the relationship between a span and other entities or phrases, which is helpful in the NER task. Besides, span-based methods have trouble predicting long entities due to limited span enumeration length. To mitigate these issues, we present the Propose-and-Refine Network (PnRNet), a two-stage set prediction network for nested NER. In the propose stage, we use a span-based predictor to generate some coarse entity predictions as entity proposals. In the refine stage, proposals interact with each other, and richer contextual information is incorporated into the proposal representations. The refined proposal representations are used to re-predict entity boundaries and classes. In this way, errors in coarse proposals can be eliminated, and the boundary prediction is no longer constrained by the span enumeration length limitation. Additionally, we build multi-scale sentence representations, which better model the hierarchical structure of sentences and provide richer contextual information than token-level representations. Experiments show that PnRNet achieves state-of-the-art performance on four nested NER datasets and one flat NER dataset.

We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization and mapping (SLAM). Although the Gaussian approximation often works well, in other more challenging SLAM situations, the posterior distribution is non-Gaussian and cannot be explicitly represented with standard distributions. Our technique applies to settings where the posterior distribution is substantially non-Gaussian (e.g., multi-modal) and thus needs a more expressive representation. NSFG exploits nested sampling methods to directly sample the posterior to represent the distribution without parametric density models. While nested sampling methods are known for their powerful capability in sampling multi-modal distributions, the application of the methods to SLAM factor graphs is not straightforward. NSFG leverages the structure of factor graphs to construct informative prior distributions which are efficiently sampled and provide notable computational benefits for nested sampling methods. We present simulated experiments which demonstrate that NSFG is more robust and computes solutions over an order of magnitude faster than state-of-the-art sampling techniques. Similarly, we compare NSFG to state-of-the-art Gaussian and non-Gaussian SLAM approaches and demonstrate that NSFG is notably more robust in describing non-Gaussian posteriors.

Nested named entity recognition (NER) aims to identify the entity boundaries and recognize categories of the named entities in a complex hierarchical sentence. Some works have been done using character-level, word-level, or lexicon-level based models. However, such researches ignore the role of the complementary annotations. In this paper, we propose a trigger-based graph neural network (Trigger-GNN) to leverage the nested NER. It obtains the complementary annotation embeddings through entity trigger encoding and semantic matching, and tackle nested entity utilizing an efficient graph message passing architecture, aggregation-update mode. We posit that using entity triggers as external annotations can add in complementary supervision signals on the whole sentences. It helps the model to learn and generalize more efficiently and cost-effectively. Experiments show that the Trigger-GNN consistently outperforms the baselines on four public NER datasets, and it can effectively alleviate the nested NER.

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison. One technical obstacle to using nested sampling in practice is the requirement (for most common implementations) that prior distributions be provided in the form of transformations from the unit hyper-cube to the target prior density. For many applications - particularly when using the posterior from one experiment as the prior for another - such a transformation is not readily available. In this letter we show that parametric bijectors trained on samples from a desired prior density provide a general-purpose method for constructing transformations from the uniform base density to a target prior, enabling the practical use of nested sampling under arbitrary priors. We demonstrate the use of trained bijectors in conjunction with nested sampling on a number of examples from cosmology.

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

Nested sampling is a new Monte Carlo method by Skilling [1] intended forgeneral Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement isan ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration withthe Potts model, an undirected graphical model.