Phonetic Reconstruction of the Consonant System of Middle C hinese via Mixed Integer Optimization (2025)

Abstract: This paper is concerned with phonetic reconstruction of the consonant system of Middle Chinese. We propose to cast the problem as a Mixed Integer Programming problem, which is able to automatically explore homophonic information from ancient rhyme dictionaries and phonetic information from modern Chinese dialects, the descendants of Middle Chinese. Numerical evaluation on a wide range of synthetic and real data demonstrates the effectiveness and robustness of the new method. We apply the method to information from Guǎngyùn and 20 modern Chinese dialects to obtain a new phonetic reconstruction result. A linguistically motivated discussion of this result is also provided.1

## introduction phonological reconstruction is one main concern in historical linguistics. there are two fundamental goals: reconstructing phonological categories and reconstructing phonetic values of these categories or individual phonemes. the classic linguistic and philological approach applies a comparative strategy to solve both problems by connecting cognates in different languages. previous research in computational linguistics demonstrates the possibility to automate the comparative approach to some extent. see, e.g., @xcite @xcite , @xcite , and @xcite , among others. the comparative approach developed out of attempts to reconstruct proto-indo-european, the common ancestor of the indo-european language family. however, the comparative method itself is not well equipped to handle the special challenges of reconstructing chinese. on the one hand, a key step in the comparative method is to identify as many cognates as possible, which is relatively straightforward for chinese but can be extremely challenging in other languages. on the other hand, documentary materials predominantly use chinese characters to annotate other characters (such as fǎnqiē , a tradition that has continued for thousands of years. for example, rhyme dictionaries such as qiēyùn extensively use this unique annotation method and systematically represent the phonological system of chinese during a specific period. such precious materials are relatively rare in other languages. this information is invaluable for the reconstruction of proto-languages, but the comparative method itself cannot adequately handle it. in fact, throughout chinese history, numerous works similar to the qiēyùn have existed in different periods, each reflecting the phonological system of its time. the purpose of this paper is to address the question of how to systematically utilize these phonetic materials. in the practice of phonological reconstruction for ancient chinese, linguists have been overwhelmingly exploring alternative information to spelling and hence alternative methods to the comparative one @xcite . their work heavily relies on philological documents, especially rhyme dictionaries, which have a unique way to record homophonic information, i.e., fǎnqiē. a basic consensus on the phonological categories of middle chinese (mc) 2 has been reached-there were 35-38 initials in mc, with minor disagreement only on some categories' merging or splitting @xcite @xcite . ancient rhyme dictionaries, however, do not provide phonetic information, and phonetic reconstruction is still extremely challenging. the relevant research is limited and there figure 1 : disagreement among scholars on phonetic reconstruction. bk: @xcite , fl: @xcite , lw: @xcite , rl: @xcite , rs: @xcite , ep: @xcite , td @xcite , wp: @xcite , xc: @xcite , wb: @xcite . 3 the number in each cell represents the percentage of initials on which the corresponding two scholars disagree. this paper is concerned with developing a computational model for phonetic reconstruction of the consonant system of mc. we propose to cast phonetic reconstruction as a mixed integer optimization problem ( §4). a particular goal is to conveniently integrate heterogeneous information. we consider two major information sources: (1) philological documents and (2) modern chinese dialects, 4 the descendants of mc. following generative phonology @xcite , we introduce a novel compact set of chinese-specific distinctive features to represent consonants ( §3). based on the feature-oriented precise phonetic representation, we formalize the optimization goal as minimizing the overall distance between possible homophonic characters and the overall distance between mc and modern dialects. measuring the distance is a key element to the success of the new architecture. to this end, we design a new mathematically sound distance/metric function to suit our feature representation. evaluating the goodness of the reconstruction result is uniquely challenging because of the lack of ground-truth. instead, we evaluate the reconstruction method. we consider two types of experiments: experiments on synthetic data ( §5), where the ground-truth is known, and experiments with held-out data ( §6), where partial information transformed from the ground-truth is known. to create representative synthetic data, we start from a pre-defined consonant system, derive homophonic information that matches fǎnqiē, and derive varieties by introducing stochastic change as well as random noise. we consider three types of consonant systems: 1) purely artificial systems that randomly select elements, e.g., from an ipa chart, 2) natural systems of modern languages, including english, german, and mandarin, and 3) the reconstructed system of latin. numerical evaluation demonstrates the effectiveness and robustness of the new method. it is able to successfully reconstruct most consonants when natural and reconstructed consonant systems are considered. for the experiments with real data, we consider a wide range of representative chinese characters with relevant information from guǎngyùn and 20 modern dialects. given the absence of ground-truth in phonetic reconstruction, to validate the effectiveness of the reconstruction method, we employ the strategy to hold out some fǎnqiē information. in particular, we apply our method to 70% fǎnqiē annotations and compare the automatically reconstructed result with the other 30%. the reconstructed phonemes predict around 68% fǎnqiē. considering that fǎnqiē annotations themselves are not fully consistent, the result is quite promising and the method has a potential use to detect inconsistent fǎnqiē annotations. based on the entire real data set, we provide a new phonetic reconstruction for middle chinese. we present both numerical and linguistic comparison to previous philologist work ( §7). our phonetic reconstruction aligns to the well-studied phonological category reconstruction to a great extent-it obtains an adjusted mutual information @xcite score of over 0.8. a linguistic analysis of the reconstruction result suggests some future research venues. 2 linguistic and philological basis ## representing phonemes representing phonemes in a formal way plays an essential role in computational reconstruction. following generative phonology (chomsky and halle, 1968), we use distinctive features to represent phonemes. @xcite proposes a feature set for all human languages. any specific language only uses a subset of it to mark phonemic contrasts. to compactly represent chinese and its modern varieties, we propose a chinese-specific set. reducing the total number of distinctive features can also boost the efficiency in solving the corresponding optimisation problem. ## the optimization model mixed integer programming (mip) is an optimization problem in which some but not necessarily all variables are constrained to be integers. mip has been widely applied in many nlp tasks, e.g., dependency parsing @xcite , semantic role labeling @xcite , coreference resolution @xcite , as well as some more recent applications, e.g., exemplar selection for in-context learning @xcite we introduce our mip model for phonetic reconstruction as follows. the objective function and constraints are detailed in §4.1 and §4.3 separately. an essential component of the objective function is measuring the distance between two phonetic feature vectors, for which we propose a mathematically sound distance function in name value manner feature sonority 5: vowel, 4: glide, 3: liquid, 2: nasal, 1: obstruent continuant 1: fricatives, liquids, glides, laterals -1: stops, affricates, nasals delayed release 1 1: fricatives, affricates, -1: stops place feature labial 1: articulated with the lips labiodental 2 1: articulated by touching the lower lip to the upper teeth coronal 1: articulated with the tongue blade and/or tip anterior 3 1: (front) dental, alveolar, -1: (post) palato-alveolar, retroflex distributed 3 1: (blade, laminal) dental, palato-alveolar -1: (tip, apical) alveolar, retroflex lateral 1: distinguishes [l] from other coronal liquids and [ì, lz] from other coronal fricatives. dorsal 1: articulated with the tongue body high 4 3: velar, 2: uvular, 1: pharyngeal front 4 3: fronted velar, 2: central velar, 1: back velar, uvular, pharyngeal laryngeal feature voice 1: voiced, -1: voiceless spread glottis 1: [h], breathy vowels, and aspirated consonants. x character of which the initial is to be reconstructed x u upper speller of character x, with its initial to be reconstructed ## validation experiments on synthetic data since language reconstruction lacks a definitive ground-truth, it is challenging to discuss the 'correctness' of any reconstruction result. we validate our method on a wide range of synthetic datasets, which hopefully mirror diachronic phonetic change. starting from a predefined consonant system, we create varieties of it by introducing systematic change and random noise. we then extract character-speller pairs to mimic the fǎnqiē information. in order to evaluate the effectiveness in reconstructing the predefined consonant system, we apply our model to the varieties as well as character-speller data. the idea of experimentation with synthetic data has been utilized to simulate lexical semantic change @xcite . ## reconstruction results and discussion we obtain our final reconstruction result by applying the method to all available data introduced in §6.1. our reconstruction is based on individual characters, while existing results are based on phonological categories. a straightforward way to obtain category-centric result is averaging phonetic feature vectors of all characters belonging to the same phonological category. the nearest ipa phonemes to the averaged vectors can be directly used for comparison to previous manual results by philologists. 12