## 2 Background and Related Work
### Machine Learning and Natural Language Processing in Legal Applications  
Applying machine learning (ML) and AI methods to law have been a topic for speculation and experimentation since at least the 1960s [29]. As computational power and algorithmic sophistication have rapidly improved, exemplified by the emergence of natural language processing (NLP) as a practical tool, ML and AI applications in the legal domain have become more prevalent [30]. As such, the background that we provide here will not be exhaustive, and will focus particularly on the most relevant work, particularly the analysis of patent review proceedings and predicting litigation outcomes. The earliest work in modeling judicial decisions was based on Boolean equations and logical rule-based approaches [31,32]. Prior to the development of more computational resources and capacity for machine learning, much quantitative legal analytics work was based on analyzing citations to case law and statutes [33]. In the United States, the use of text and other features to predict the outcome of judicial proceedings has often focused on the federal Supreme Court, for which there exist readily (and freely) accessible opinions, notable interest issues of legal importance, quantifiable divisions in legal philosophy and ideology, and consistency in the judges (Justices) who make decisions [34,35]. Recent outcome prediction modeling has been able to achieve up to 70% accuracy at the level of predicting Supreme Court Justices' votes based on various features [36]. Other work has looked at other closed legal universes, where there is a known body of statutes and a constrained body of facts, such as tax law [37,38]. Notably, besides simple outcome prediction, other work has used computational text analysis or NLP methods, such as document vectorization, to examine measures of judicial sentiment and modes of reasoning in U.S. appellate courts, where again there are often jurisdictional (philosophical) and ideological divisions [39]. Researchers have also sought to analyze the writing style of jurists using NLP, such as U.S. Supreme Court Justice [PERSON] [40]. A popular way to summarize and classify documents has been to represent them as a vector of the TF-IDF values of document terms [41]. In this approach, a training set of documents defines a vocabulary of terms that appear in those documents. In each document, each term in the vocabulary is assigned the ratio of the frequency of that term in the document to the frequency of the term in all documents. This method and its variants have been extensively used in many fields, including legal document analysis [42, 43, 44]. Another approach that has emerged for translating documents to linguistic features is representing terms by pretrained embedding vectors. These pretrained word embeddings, which are generated by self-supervised machine learning on a large corpus of documents, resulting in vectors in a space where distances reflect semantic relationships between the words. Foundational approaches include GloVe and Word2 vec [45,46]. While these embeddings have generally been trained on large corpora such as Wikipedia articles or news articles, recent work has sought to train specialized word embeddings on legal corpora [47]. In the European context, several researchers have studied litigation prediction problems. [PERSON] et al. applied support vector machines (SVM) to n-grams (small groups of words) to predict the outcome of European Court of Human Rights (ECHR) decisions, obtaining a level of prediction accuracy of over 70%, although accuracy appeared to decline over time, suggesting drift in case law [13]. [PERSON] et al. more recently applied SVMwith TF-IDF (term frequency-inverse document frequency) and n-gram vectorization to ECHR decisions [48].