\begin{table*}[]
\centering
\begin{tabular}{lrrrrrrr}
\hline
		& \multicolumn{1}{l}{Sample} 	& \multicolumn{1}{l}{Top 1} 	& \multicolumn{1}{l}{Top 1} 	& \multicolumn{1}{l}{Top 2} 	& \multicolumn{1}{l}{Top 2} 	& \multicolumn{1}{l}{Top 3} 	& \multicolumn{1}{l}{Top 3} \\ 
		& \multicolumn{1}{l}{Size} 	& 	& \multicolumn{1}{l}{Share} 	& 	& \multicolumn{1}{l}{Share} 	& & \multicolumn{1}{l}{Share} \\ 

\hline
De Fluviis  & 310 						& Athenaeus 				& 22\% 						& Others 					& 21\% 						& Strabo 					&  19\%                                       \\
\hline
   & 						&  				&  						&				& 					& Sextus  			&             \\ 
De Musica   & 285 						& Athenaeus 				& 21\% 						& Plutarch 				& 18\%						& Empiricus 			&     14\%         \\ 
\hline
Placita  &  				&  					&						& Claudius  		&  						& Sextus  			&    \\
Philosophorum  & 928 				& Others 					& 36\% 						& Ptolemaeus  		& 20\% 						& Empiricus  			& 11 \%   \\
\hline
\end{tabular}
\caption{The most frequently attributed authors in the three Pseudo-Plutarchean texts.}
\label{tab:p}
\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. 

Since each model has its own specific tokenizer before pretraining, one wants to measure how well each of them works with Ancient Greek. To do that, one could take two sample data sets: a sample of Modern Greek
Wikipedia (referred to in Table \ref{tab:tok} as “modern”) and a comparable sample of Ancient Greek (“ancient”  in Table \ref{tab:tok}). Each data sample is tokenized with both the Modern Greek BERT tokenizer\footnote{https://huggingface.co/nlpaueb/bert-base-greek-uncased-v} and the Multilingual BERT tokenizer\footnote{https://huggingface.co/bert-base-multilingual-cased}. One can speculate that the model uses shorter tokens to adopt grammatical information and deal with longer, rarely observed words. In contrast, the representations with longer tokens could be useful for semantically intensive problems. These longer, semantically charged tokens may vary significantly on various downstream tasks. Thus, the average length of a token and the average number of words per token, shown in Table \ref{tab:tok}, could be coarsely used as an estimate of the resulting tokenization. One could claim that the higher these values, the more apt the tokenizer is for the task. Indeed, higher average length of a token and number of words per token mean that longer, more semantically charged tokens could be matched for transfer; see \cite{singh2019bert,aji2020neural,samenko2021fine} for a detailed discussion of various tokenization properties.

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 Ancient Greek was used in various regions and territories, one might expect that the texts also show regional peculiarities. Such peculiarities
then should also be detectable by a dedicated regional BERT Classifier. We constructed three coarse regions for the origins of the authors in the data set: a region surrounding Delphi, where Plutarch was working, a region in the proximity of Alexandria, and the region of ancient Ionia, namely the ancient region on the central part of the western coast of modern Anatolia, see Figure \ref{fig:map}. After balancing texts written by authors in these three regions with the fourth label that includes random sentences from authors outside of these regions, we train another BERT-based classifier to achieve a $0.79$ validation accuracy for the region of the author. Table \ref{tab:region} shows the results of the obtained classifier on the validation set.

Let us now split these three Pseudo-Plutarchean texts into the separate sentences and apply the author classifier described above to these texts.
Table \ref{tab:p} shows the authors that are most frequently attributed within a particular document, along with the share of sentences attributed to them. We have double-checked these results using an alternative scoring method. Instead of classifying every sentence in a document and then averaging the classifier's results across all sentences, one could obtain probability scores for every author that the model estimates for every sentence. Averaging those probabilities throughout the document, one could obtain the three most-probable author candidates. These three most-probable authors turn out to be exactly the same for all three documents as the ones in Table \ref{tab:p}. Moreover, the resulting probabilities of the authorship are also the same for all three most probable authors across all three documents under examination. 

Table \ref{tab:p}  demonstrates that the resulting authorship profiles differ for all three documents. However, the sample size for De Fluviis and De Musica is smaller than the sample size for Placita Philosophorum. Plutarch ends up being in the top three of the most frequently predicted authors only in De Musica. For De Fluviis and De Musica Athenaeus ends up being the most frequent guess of the BERT authorship classifier, while for Placita Philosophorum "other" is the most frequent attribution. Claudius Ptolemaeus and Sextus Empiricus are, respectively, the second and the third most frequent guesses. 
{"value": "310", "type": "Data Stat.", "dataset": "De Fluviis", "sub-set/group name": "xx", "attribute name": "Sample Size", "dataset features": {"xx": "yy"}} {"value": "22", "type": "Result", "training data/set": "xx", "test data/set": "De Fluviis", "task": "authorship attribution", "metric": "Top 1 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "21", "type": "Result", "training data/set": "xx", "test data/set": "De Fluviis", "task": "authorship attribution", "metric": "Top 2 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "19", "type": "Result", "training data/set": "xx", "test data/set": "De Fluviis", "task": "authorship attribution", "metric": "Top 3 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "285", "type": "Data Stat.", "dataset": "De Musica", "sub-set/group name": "xx", "attribute name": "Sample Size", "dataset features": {"xx": "yy"}} {"value": "21", "type": "Result", "training data/set": "xx", "test data/set": "De Musica", "task": "authorship attribution", "metric": "Top 1 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "18", "type": "Result", "training data/set": "xx", "test data/set": "De Musica", "task": "authorship attribution", "metric": "Top 2 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "14", "type": "Result", "training data/set": "xx", "test data/set": "De Musica", "task": "authorship attribution", "metric": "Top 3 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "928", "type": "Data Stat.", "dataset": "Placita Philosophorum", "sub-set/group name": "xx", "attribute name": "Sample Size", "dataset features": {"xx": "yy"}} {"value": "36", "type": "Result", "training data/set": "xx", "test data/set": "Placita Philosophorum", "task": "authorship attribution", "metric": "Top 1 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "20", "type": "Result", "training data/set": "xx", "test data/set": "Placita Philosophorum", "task": "authorship attribution", "metric": "Top 2 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}} {"value": "11", "type": "Result", "training data/set": "xx", "test data/set": "Placita Philosophorum", "task": "authorship attribution", "metric": "Top 3 Share", "experimental settings": {"xx": "yy"}, "model": "Ancient Greek BERT", "model settings": {"xx": "yy"}}