Multivariate zero-inflated count data arise in a wide range of areas such as economics, social sciences, and biology.

This paper introduces "Media of Langue," a novel dictionary visualizing Inter-lingual semantic network/space. Our proposed Inter-lingual semantic network/space is formed solely from the accumulation of translation practices between two or more language systems, in contrast to existing semantic networks/spaces that explicitly use "intra"-lingual relations. By visualizing this network/space for humans, an Inter-lingual dictionary can be realized that points to the semantic place of many words at once with a chain of mutual translation, which also contains the functions of existing dictionaries such as bilingual and synonym dictionaries. We implemented and published this interface as a web application, focusing on seven language pairs. In this paper, we first describe Inter-lingual semantic network/space with its basic features and the way to develop it from bilingual corpora, then details the design of "Media of Langue," with a quick analysis and illustrative examples of use cases. Our website is www.media-of-langue.org. A demonstration video is available at https://youtu.be/98lXuX4yjsU.

This paper introduces a new simulation-based inference procedure to model and sample from multi-dimensional probability distributions given access to i.i.d. samples, circumventing usual approaches of explicitly modeling the density function or designing Markov chain Monte Carlo. Motivated by the seminal work of M\'emoli (2011) and Sturm (2012) on distance and isomorphism between metric measure spaces, we propose a new notion called the Reversible Gromov-Monge (RGM) distance and study how RGM can be used to design new transform samplers in order to perform simulation-based inference. Our RGM sampler can also estimate optimal alignments between two heterogenous metric measure spaces $(\mathcal{X}, \mu, c_{\mathcal{X}})$ and $(\mathcal{Y}, \nu, c_{\mathcal{Y}})$ from empirical data sets, with estimated maps that approximately push forward one measure $\mu$ to the other $\nu$, and vice versa. Analytic properties of RGM distance are derived; statistical rate of convergence, representation, and optimization questions regarding the induced sampler are studied. Synthetic and real-world examples showcasing the effectiveness of the RGM sampler are also demonstrated.

Network spaces have been known as a critical factor in both handcrafted network designs or defining search spaces for Neural Architecture Search (NAS). However, an effective space involves tremendous prior knowledge and/or manual effort, and additional constraints are required to discover efficiency-aware architectures. In this paper, we define a new problem, Network Space Search (NSS), as searching for favorable network spaces instead of a single architecture. We propose an NSS method to directly search for efficient-aware network spaces automatically, reducing the manual effort and immense cost in discovering satisfactory ones. The resultant network spaces, named Elite Spaces, are discovered from Expanded Search Space with minimal human expertise imposed. The Pareto-efficient Elite Spaces are aligned with the Pareto front under various complexity constraints and can be further served as NAS search spaces, benefiting differentiable NAS approaches (e.g. In CIFAR-100, an averagely 2.3% lower error rate and 3.7% closer to target constraint than the baseline with around 90% fewer samples required to find satisfactory networks). Moreover, our NSS approach is capable of searching for superior spaces in future unexplored spaces, revealing great potential in searching for network spaces automatically.