\begin{table*}[h]
\centering
{
\small
\tabcolsep=0.11cm
\begin{tabular}{lrrrrrrrrrrrrrrrrr}
                                                               & G            & O            & P            & CD           & FJ           & PJ           & A            & CP           & AA           & S            & L            & CA           & Ap           & P            & SE           & DC           & other        \\ \hline
Galenus                                                        & \textbf{416} & 7            & 5            & 1            & 1            & 4            & 5            & 5            & 6            & 3            & 3            & 5            & 1            & 0            & 6            & 10           & 22           \\ \hline
Origenes                                                       & 2            & \textbf{396} & 0            & 1            & 6            & 4            & 5            & 12           & 1            & 3            & 0            & 24           & 0            & 0            & 6            & 5            & 35           \\ \hline
Plutarchus                                                     & 6            & 3            & \textbf{390} & 3            & 9            & 8            & 17           & 2            & 2            & 5            & 2            & 5            & 12           & 1            & 6            & 13           & 16           \\ \hline
\begin{tabular}[c]{@{}l@{}}Cassius\\ Dio\end{tabular}          & 1            & 0            & 8            & \textbf{428} & 5            & 2            & 2            & 0            & 7            & 8            & 2            & 1            & 17           & 6            & 0            & 7            & 6            \\ \hline
\begin{tabular}[c]{@{}l@{}}Flavius\\ Josephus\end{tabular}     & 3            & 3            & 10           & 5            & \textbf{418} & 2            & 4            & 6            & 8            & 9            & 6            & 1            & 8            & 0            & 4            & 9            & 4            \\ \hline
\begin{tabular}[c]{@{}l@{}}Philo\\ Judaeus\end{tabular}        & 5            & 10           & 13           & 3            & 16           & \textbf{403} & 3            & 3            & 2            & 3            & 3            & 12           & 0            & 0            & 11           & 8            & 5            \\ \hline
Athenaeus                                                      & 11           & 6            & 17           & 4            & 4            & 2            & \textbf{368} & 4            & 7            & 11           & 9            & 7            & 2            & 6            & 6            & 14           & 22           \\ \hline
\begin{tabular}[c]{@{}l@{}}Claudius \\ Ptolemaeus\end{tabular} & 3            & 0            & 0            & 0            & 0            & 1            & 0            & \textbf{480} & 0            & 8            & 0            & 0            & 0            & 0            & 5            & 0            & 3            \\ \hline
\begin{tabular}[c]{@{}l@{}}Aelius\\ Aristides\end{tabular}     & 7            & 6            & 6            & 6            & 7            & 2            & 5            & 0            & \textbf{368} & 8            & 10           & 6            & 1            & 3            & 3            & 40           & 22           \\ \hline
Strabo                                                         & 4            & 5            & 9            & 0            & 3            & 2            & 7            & 1            & 9            & \textbf{432} & 4            & 1            & 3            & 6            & 4            & 4            & 6            \\ \hline
Lucianus                                                       & 2            & 3            & 6            & 1            & 5            & 4            & 9            & 0            & 13           & 9            & \textbf{360} & 12           & 5            & 6            & 6            & 30           & 29           \\ \hline
\begin{tabular}[c]{@{}l@{}}Clemens\\ Alexandrinus\end{tabular} & 8            & 28           & 3            & 4            & 10           & 14           & 4            & 1            & 6            & 5            & 8            & \textbf{349} & 0            & 5            & 17           & 11           & 27           \\ \hline
Appianus                                                       & 1            & 0            & 10           & 18           & 8            & 2            & 2            & 1            & 3            & 2            & 5            & 3            & \textbf{437} & 0            & 0            & 3            & 5            \\ \hline
Pausanias                                                      & 0            & 1            & 1            & 2            & 0            & 0            & 2            & 0            & 4            & 3            & 2            & 3            & 2            & \textbf{472} & 0            & 3            & 5            \\ \hline
\begin{tabular}[c]{@{}l@{}}Sextus\\ Empiricus\end{tabular}     & 2            & 4            & 6            & 0            & 1            & 1            & 4            & 1            & 2            & 2            & 1            & 11           & 0            & 0            & \textbf{446} & 7            & 12           \\ \hline
\begin{tabular}[c]{@{}l@{}}Dio\\ Chrysostomus\end{tabular}     & 2            & 4            & 12           & 9            & 5            & 3            & 7            & 0            & 9            & 10           & 10           & 9            & 6            & 4            & 2            & \textbf{398} & 10           \\ \hline
other                                                          & 17           & 23           & 22           & 7            & 6            & 15           & 32           & 14           & 10           & 6            & 12           & 18           & 6            & 9            & 40           & 21           & \textbf{242} \\ \hline
\end{tabular}}
\caption{The confusion matrix of the obtained authorship classifier. Every horizontal line sums up to 500 sentences by the corresponding author that were set aside for validation. Every column shows the number of sentences labelled by classifier as sentences authored by the corresponding author.}
\label{tab:ac}
\end{table*}
\begin{itemize}
    \item we use a transfer learning approach to train BERT for Ancient Greek;
    \item we demonstrate that this language model is useful for authorship attribution of Ancient Greek texts;
    \item we obtain results that may be used as evidence in the process of authorship attribution of the Pseudo-Plutarchean texts;
    \item we obtain new insights into the paths along which the reception of ancient philosophy was developed.
\end{itemize}

\section{Data}
The data were taken from the digital history projects at the Chair of
Ancient History of the University of Leipzig. The Plutarch texts were transformed into a digital representation under professional supervision. Data can be obtained from the following free repositories Perseus Digital Library\footnote{https://github.com/PerseusDL/canonical-greekLit} and First Thousand Years of Greek\footnote{https://github.com/ThomasK81/TEItoCEX} as part of Open Greek and Latin\footnote{https://opengreekandlatin.org}. The resulting representation was stored in XML format (TEI guidelines) and enriched with metadata. The XML structure and metadata were removed. The strings were transferred into lowercase letters. The diacritics were removed. We did not touch hyphenation, punctuation, or any multilingual remains, nor did we apply any special language-related transformations.
The resulting data set consists of 1 244 documents with 199 809 paragraphs or 14 373 311 words.

\subsection{Tokenizers}
The tokenization of words into sub-word tokens is a crucial preprocessing step that can affect the performance of the model. Up to this point, we were using "words" as a linguistic term, whereas we understand tokens as the output of a tokenization algorithm. Thus, there would be one or more tokens that represent every word. Counting the number of tokens used on average to represent a word or, conversely, an average number of words per token gives an estimate of how fit  the tokenization is for the data set. In particular, the average number of words per token varies from 0 to 1, and the closer it is to 1, the more words are represented with one token. Various researchers have shown that corpus-specific tokenization could be beneficial for an NLP task. For example, \citet{sennrich-etal-2016-neural} show that optimal vocabulary is dependent on the frequencies of the words in the target corpus. \citet{lakew2019controlling} and \citet{aji2020neural} partially discuss the tokenization in the setting of cross-language transfer. Though \citet{aji2020neural} demonstrate that there is no clear evidence that one parent is better than another for cross-lingual transfer learning, they also show that token matching and joint vocabulary \cite{nguyen2017transfer} are the best ways to handle the embedding layer during transfer learning. 

\subsection{Training Ancient Greek BERT via Transfer Learning}
If related tasks are available, we can fine-tune the model first on a related task with more data before fine-tuning it on the target task, see \cite{ruder2019transfer}. This helps particularly for tasks with limited data \cite{phang2018sentence} and improves sample efficiency on the target task \cite{yogatama2019learning}. Since we have a limited amount of Ancient Greek texts, we want to do language transfer from Modern Greek to Ancient Greek training a masked language
model (MLM)\footnote{https://github.com/huggingface/transformers/blob/master/ examples/language-modeling/run\_language\_modeling.py} of the Ancient Greek text. 

From Dio Chrysostomus we had only 5580 sentences available for training, but this amount of data could be sufficient \cite{zhang2020revisiting} to train a well-performing BERT-based classifier. For the author classifier, to avoid bias from different sentences,  we sample 5 580 sentences from every author in this list. We also include the  label "Others" for 5 580
random sentences by less prolific authors who were not included in this shortlist. The choice of the number of authors balances the requirement to have enough data to train the classifier and the wish to include as many authors in the authorship attribution classifier as possible. 

We use this data set to train BERT Classifiers similarly to \cite{fabien2020bertaa}. Table \ref{tab:au} shows the validation accuracy for Modern Greek and Multilingual BERTs after MLM on Ancient Greek and 10 epochs of classifier training\footnote{AdamW, LR = 2e-5, eps = 1e-8,  linear\_schedule}. Table \ref{tab:au}  also shows a standard NLTK Naive Bayes Classifier trained on the 2 000 most frequent unigrams as a reference point for authorship attribution accuracy.

Since Modern Greek BERT fine-tuned for authorship attribution after MLM shows the best validation accuracy, we use it for the subsequent analysis. Table \ref{tab:ac} shows the confusion matrix of the resulting classifier on 500 validation sentences by every author.

Table \ref{tab:ac} shows that the authorship attribution model works rather well. The errors mostly happen in sentences that have a topical affinity to another author or on authors with similar regional backgrounds. That observation suggests developing a separate regional classifier that might help authorship attribution. This classifier is described in detail in the next Subsection.
{"value": "416", "type": "Other"} {"value": "7", "type": "Other"} {"value": "5", "type": "Other"} {"value": "1", "type": "Other"} {"value": "1", "type": "Other"} {"value": "4", "type": "Other"} {"value": "5", "type": "Other"} {"value": "5", "type": "Other"} {"value": "6", "type": "Other"} {"value": "3", "type": "Other"} {"value": "3", "type": "Other"} {"value": "5", "type": "Other"} {"value": "1", "type": "Other"} {"value": "0", "type": "Other"} {"value": "6", "type": "Other"} {"value": "10", "type": "Other"} {"value": "22", "type": "Other"} {"value": "2", "type": "Other"} {"value": "396", "type": "Other"} {"value": "0", "type": "Other"} {"value": "1", "type": "Other"} {"value": "6", "type": "Other"} {"value": "4", "type": "Other"} {"value": "5", "type": "Other"} {"value": "12", "type": "Other"} {"value": "1", "type": "Other"} {"value": "3", "type": "Other"} {"value": "0", "type": "Other"} {"value": "24", "type": "Other"} {"value": "0", "type": "Other"} {"value": "0", "type": "Other"} 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{"value": "1", "type": "Other"} {"value": "0", "type": "Other"} {"value": "480", "type": "Other"} {"value": "0", "type": "Other"} {"value": "8", "type": "Other"} {"value": "0", "type": "Other"} {"value": "0", "type": "Other"} {"value": "0", "type": "Other"} {"value": "0", "type": "Other"} {"value": "5", "type": "Other"} {"value": "0", "type": "Other"} {"value": "3", "type": "Other"} {"value": "7", "type": "Other"} {"value": "6", "type": "Other"} {"value": "6", "type": "Other"} {"value": "6", "type": "Other"} {"value": "7", "type": "Other"} {"value": "2", "type": "Other"} {"value": "5", "type": "Other"} {"value": "0", "type": "Other"} {"value": "368", "type": "Other"} {"value": "8", "type": "Other"} {"value": "10", "type": "Other"} {"value": "6", "type": "Other"} {"value": "1", "type": "Other"} {"value": "3", "type": "Other"} {"value": "3", "type": "Other"} {"value": "40", "type": "Other"} {"value": "22", "type": "Other"} {"value": "4", "type": "Other"} {"value": "5", "type": "Other"} 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