The Universal Dependencies (UD) project has significantly expanded linguistic coverage across 161 languages, yet Luxembourgish, a West Germanic language spoken by approximately 400,000 people, has remained absent until now. In this paper, we introduce LuxBank, the first UD Treebank for Luxembourgish, addressing the gap in syntactic annotation and analysis for this `low-research' language. We establish formal guidelines for Luxembourgish language annotation, providing the foundation for the first large-scale quantitative analysis of its syntax. LuxBank serves not only as a resource for linguists and language learners but also as a tool for developing spell checkers and grammar checkers, organising existing text archives and even training large language models. By incorporating Luxembourgish into the UD framework, we aim to enhance the understanding of syntactic variation within West Germanic languages and offer a model for documenting smaller, semi-standardised languages. This work positions Luxembourgish as a valuable resource in the broader linguistic and NLP communities, contributing to the study of languages with limited research and resources.

Recently, Handwritten Mathematical Expression Recognition (HMER) has gained considerable attention in pattern recognition for its diverse applications in document understanding. Current methods typically approach HMER as an image-to-sequence generation task within an autoregressive (AR) encoder-decoder framework. However, these approaches suffer from several drawbacks: 1) a lack of overall language context, limiting information utilization beyond the current decoding step; 2) error accumulation during AR decoding; and 3) slow decoding speed. To tackle these problems, this paper makes the first attempt to build a novel bottom-up Non-AutoRegressive Modeling approach for HMER, called NAMER. NAMER comprises a Visual Aware Tokenizer (VAT) and a Parallel Graph Decoder (PGD). Initially, the VAT tokenizes visible symbols and local relations at a coarse level. Subsequently, the PGD refines all tokens and establishes connectivities in parallel, leveraging comprehensive visual and linguistic contexts. Experiments on CROHME 2014/2016/2019 and HME100K datasets demonstrate that NAMER not only outperforms the current state-of-the-art (SOTA) methods on ExpRate by 1.93%/2.35%/1.49%/0.62%, but also achieves significant speedups of 13.7x and 6.7x faster in decoding time and overall FPS, proving the effectiveness and efficiency of NAMER.

Recently, most handwritten mathematical expression recognition (HMER) methods adopt the encoder-decoder networks, which directly predict the markup sequences from formula images with the attention mechanism. However, such methods may fail to accurately read formulas with complicated structure or generate long markup sequences, as the attention results are often inaccurate due to the large variance of writing styles or spatial layouts. To alleviate this problem, we propose an unconventional network for HMER named Counting-Aware Network (CAN), which jointly optimizes two tasks: HMER and symbol counting. Specifically, we design a weakly-supervised counting module that can predict the number of each symbol class without the symbol-level position annotations, and then plug it into a typical attention-based encoder-decoder model for HMER. Experiments on the benchmark datasets for HMER validate that both joint optimization and counting results are beneficial for correcting the prediction errors of encoder-decoder models, and CAN consistently outperforms the state-of-the-art methods. In particular, compared with an encoder-decoder model for HMER, the extra time cost caused by the proposed counting module is marginal. The source code is available at https://github.com/LBH1024/CAN.