A gentle tutorial and a structured reformulation of Bock's algorithm for minimum directed spanning trees

This paper presents a gentle tutorial and a structured reformulation of Bock's 1971 Algol procedure for constructing minimum directed spanning trees. Our aim is to make the original algorithm readable and reproducible for modern readers, while highlighting its relevance as an exact decoder for nonprojective graph based dependency parsing. We restate the minimum arborescence objective in Bock's notation and provide a complete line by line execution trace of the original ten node example, extending the partial trace given in the source paper from initialization to termination. We then introduce a structured reformulation that makes explicit the procedure's phase structure, maintained state, and control flow, while preserving the logic of the original method. As a further illustration, we include a worked example adapted from {jurafsky-martin-2026-book} for dependency parsing, showing how a maximum weight arborescence problem is reduced to Bock's minimum cost formulation by a standard affine transformation and traced under the same state variables.

A tree interpretation of arc standard dependency derivation

We show that arc-standard derivations for projective dependency trees determine a unique ordered tree representation with surface-contiguous yields and stable lexical anchoring. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition corresponds to a deterministic tree update, and the resulting hierarchical object uniquely determines the original dependency arcs. We further show that this representation characterizes projectivity: a single-headed dependency tree admits such a contiguous ordered representation if and only if it is projective. The proposal is derivational rather than convertive. It interprets arc-standard transition sequences directly as ordered tree construction, rather than transforming a completed dependency graph into a phrase-structure output. For non-projective inputs, the same interpretation can be used in practice via pseudo-projective lifting before derivation and inverse decoding after recovery. A proof-of-concept implementation in a standard neural transition-based parser shows that the mapped derivations are executable and support stable dependency recovery.

Learning Constituent Headedness

Headedness is widely used as an organizing device in syntactic analysis, yet constituency treebanks rarely encode it explicitly and most processing pipelines recover it procedurally via percolation rules. We treat this notion of constituent headedness as an explicit representational layer and learn it as a supervised prediction task over aligned constituency and dependency annotations, inducing supervision by defining each constituent head as the dependency span head. On aligned English and Chinese data, the resulting models achieve near-ceiling intrinsic accuracy and substantially outperform Collins-style rule-based percolation. Predicted heads yield comparable parsing accuracy under head-driven binarization, consistent with the induced binary training targets being largely equivalent across head choices, while increasing the fidelity of deterministic constituency-to-dependency conversion and transferring across resources and languages under simple label-mapping interfaces.

TREX: Tokenizer Regression for Optimal Data Mixture

Building effective tokenizers for multilingual Large Language Models (LLMs) requires careful control over language-specific data mixtures. While a tokenizer's compression performance critically affects the efficiency of LLM training and inference, existing approaches rely on heuristics or costly large-scale searches to determine optimal language ratios. We introduce Tokenizer Regression for Optimal Data MiXture (TREX), a regression-based framework that efficiently predicts the optimal data mixture for tokenizer training. TREX trains small-scale proxy tokenizers on random mixtures, gathers their compression statistics, and learns to predict compression performance from data mixtures. This learned model enables scalable mixture search before large-scale tokenizer training, mitigating the accuracy-cost trade-off in multilingual tokenizer design. Tokenizers trained with TReX's predicted mixtures outperform mixtures based on LLaMA3 and uniform distributions by up to 12% in both inand out-of-distribution compression efficiency, demonstrating strong scalability, robustness, and practical effectiveness.

Constituency Structure over Eojeol in Korean Treebanks

The design of Korean constituency treebanks raises a fundamental representational question concerning the choice of terminal units. Although Korean words are morphologically complex, treating morphemes as constituency terminals conflates word internal morphology with phrase level syntactic structure and creates mismatches with eojeol based dependency resources. This paper argues for an eojeol based constituency representation, with morphological segmentation and fine grained part of speech information encoded in a separate, non constituent layer. A comparative analysis shows that, under explicit normalization assumptions, the Sejong and Penn Korean treebanks can be treated as representationally equivalent at the eojeol based constituency level. Building on this result, we outline an eojeol based annotation scheme that preserves interpretable constituency and supports cross treebank comparison and constituency dependency conversion.

Multilingual Grammatical Error Annotation: Combining Language-Agnostic Framework with Language-Specific Flexibility

Grammatical Error Correction (GEC) relies on accurate error annotation and evaluation, yet existing frameworks, such as $\texttt{errant}$, face limitations when extended to typologically diverse languages. In this paper, we introduce a standardized, modular framework for multilingual grammatical error annotation. Our approach combines a language-agnostic foundation with structured language-specific extensions, enabling both consistency and flexibility across languages. We reimplement $\texttt{errant}$ using $\texttt{stanza}$ to support broader multilingual coverage, and demonstrate the framework's adaptability through applications to English, German, Czech, Korean, and Chinese, ranging from general-purpose annotation to more customized linguistic refinements. This work supports scalable and interpretable GEC annotation across languages and promotes more consistent evaluation in multilingual settings. The complete codebase and annotation tools can be accessed at https://github.com/open-writing-evaluation/jp_errant_bea.

Enriching the Korean Learner Corpus with Multi-reference Annotations and Rubric-Based Scoring

Despite growing global interest in Korean language education, there remains a significant lack of learner corpora tailored to Korean L2 writing. To address this gap, we enhance the KoLLA Korean learner corpus by adding multiple grammatical error correction (GEC) references, thereby enabling more nuanced and flexible evaluation of GEC systems, and reflects the variability of human language. Additionally, we enrich the corpus with rubric-based scores aligned with guidelines from the Korean National Language Institute, capturing grammatical accuracy, coherence, and lexical diversity. These enhancements make KoLLA a robust and standardized resource for research in Korean L2 education, supporting advancements in language learning, assessment, and automated error correction.

Proposing TAGbank as a Corpus of Tree-Adjoining Grammar Derivations

The development of lexicalized grammars, particularly Tree-Adjoining Grammar (TAG), has significantly advanced our understanding of syntax and semantics in natural language processing (NLP). While existing syntactic resources like the Penn Treebank and Universal Dependencies offer extensive annotations for phrase-structure and dependency parsing, there is a lack of large-scale corpora grounded in lexicalized grammar formalisms. To address this gap, we introduce TAGbank, a corpus of TAG derivations automatically extracted from existing syntactic treebanks. This paper outlines a methodology for mapping phrase-structure annotations to TAG derivations, leveraging the generative power of TAG to support parsing, grammar induction, and semantic analysis. Our approach builds on the work of CCGbank, extending it to incorporate the unique structural properties of TAG, including its transparent derivation trees and its ability to capture long-distance dependencies. We also discuss the challenges involved in the extraction process, including ensuring consistency across treebank schemes and dealing with language-specific syntactic idiosyncrasies. Finally, we propose the future extension of TAGbank to include multilingual corpora, focusing on the Penn Korean and Penn Chinese Treebanks, to explore the cross-linguistic application of TAG's formalism. By providing a robust, derivation-based resource, TAGbank aims to support a wide range of computational tasks and contribute to the theoretical understanding of TAG's generative capacity.

Foundations and Evaluations in NLP

This memoir explores two fundamental aspects of Natural Language Processing (NLP): the creation of linguistic resources and the evaluation of NLP system performance. Over the past decade, my work has focused on developing a morpheme-based annotation scheme for the Korean language that captures linguistic properties from morphology to semantics. This approach has achieved state-of-the-art results in various NLP tasks, including part-of-speech tagging, dependency parsing, and named entity recognition. Additionally, this work provides a comprehensive analysis of segmentation granularity and its critical impact on NLP system performance. In parallel with linguistic resource development, I have proposed a novel evaluation framework, the jp-algorithm, which introduces an alignment-based method to address challenges in preprocessing tasks like tokenization and sentence boundary detection (SBD). Traditional evaluation methods assume identical tokenization and sentence lengths between gold standards and system outputs, limiting their applicability to real-world data. The jp-algorithm overcomes these limitations, enabling robust end-to-end evaluations across a variety of NLP tasks. It enhances accuracy and flexibility by incorporating linear-time alignment while preserving the complexity of traditional evaluation metrics. This memoir provides key insights into the processing of morphologically rich languages, such as Korean, while offering a generalizable framework for evaluating diverse end-to-end NLP systems. My contributions lay the foundation for future developments, with broader implications for multilingual resource development and system evaluation.

Chinese Grammatical Error Correction: A Survey

Chinese Grammatical Error Correction (CGEC) is a critical task in Natural Language Processing, addressing the growing demand for automated writing assistance in both second-language (L2) and native (L1) Chinese writing. While L2 learners struggle with mastering complex grammatical structures, L1 users also benefit from CGEC in academic, professional, and formal contexts where writing precision is essential. This survey provides a comprehensive review of CGEC research, covering datasets, annotation schemes, evaluation methodologies, and system advancements. We examine widely used CGEC datasets, highlighting their characteristics, limitations, and the need for improved standardization. We also analyze error annotation frameworks, discussing challenges such as word segmentation ambiguity and the classification of Chinese-specific error types. Furthermore, we review evaluation metrics, focusing on their adaptation from English GEC to Chinese, including character-level scoring and the use of multiple references. In terms of system development, we trace the evolution from rule-based and statistical approaches to neural architectures, including Transformer-based models and the integration of large pre-trained language models. By consolidating existing research and identifying key challenges, this survey provides insights into the current state of CGEC and outlines future directions, including refining annotation standards to address segmentation challenges, and leveraging multilingual approaches to enhance CGEC.