\section{Training Parameters}
We train SG models for 15 epochs and AE models for 5; in this manner, we ensure similar exposure to data, as AE models see each data instance several times per epoch, albeit with varying labels. We consistently use $lr = 1\mathrm{e}{-5}$.

In the SG setting, we use log-scaled class weights in training, so as to mitigate the effect of data imbalance; this modification is not applied to AE due to a different architecture.

\newpage
\section{Illustrations}
\label{sec:app2}

\begin{figure*}[ht]
    \centering \small
    \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl1_sg_label_breakdown.jpg}
    \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl1_sg_conf_vs_var_color_agreement_factor.jpg}
     \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl2_sg_label_breakdown.jpg}
     \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl2_sg_conf_vs_var_color_agreement_factor.jpg}
     \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl3_sg_label_breakdown.jpg}
     \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl3_sg_conf_vs_var_color_agreement_factor.jpg}
    \caption{\small Data maps for the majority label classifier, DeBERTa-v3-base, granularity levels 1, 2, and 3 (top to bottom). X- and Y-axis correspond to \textbf{variability} and \textbf{confidence}, respectively. Left column: class-wise breakdown; right column: breakdown by agreement (ratio of the majority label per instance).}
    \label{fig:sg_agr}
\end{figure*}

\begin{figure*}[ht]
    \centering \small
    \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl1_AE_label_breakdown.jpg}
    \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl1_conf_vs_var_color_agreement_factor.jpg}
     \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl2.5_AE_label_breakdown.jpg}
     \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl2.5_AE_conf_vs_var_color_agreement_factor.jpg}
     \includegraphics[width=0.52\linewidth]{IDRR_Perspectives/figures/lvl3.5_AE_label_breakdown.jpg}
     \includegraphics[width=0.47\linewidth]{IDRR_Perspectives/figures/lvl3.5_AE_conf_vs_var_color_agreement_factor.jpg}
    \caption{\small Data maps for the Annotator Embeddings model \cite{deng-etal-2023-annotate}, DeBERTa-v3-base, granularity levels 1, 2, and 3 (top to bottom). X- and Y-axis correspond to \textbf{variability} and \textbf{confidence}, respectively. Left column: class-wise breakdown; right column: breakdown by agreement (ratio of the majority label per instance).}
    \label{fig:AE_agr}
\end{figure*}

\begin{figure*}[ht]
    \centering \small
    \includegraphics[width=0.1825\linewidth]{IDRR_Perspectives/figures/feats/feats1.jpg}
     \includegraphics[width=0.1825\linewidth]{IDRR_Perspectives/figures/feats/feats2.jpg}
     \includegraphics[width=0.1825\linewidth]{IDRR_Perspectives/figures/feats/feats3.jpg}
     \includegraphics[width=0.1825\linewidth]{IDRR_Perspectives/figures/feats/feats4.jpg}
     \includegraphics[width=0.1825\linewidth]{IDRR_Perspectives/figures/feats/feats5.jpg}
    \caption{\small Top positive and negative logistic regression features for the \textit{precedence} probe at level-3 across 5 validation folds. Each column corresponds to a different fold. The token \textbf{sep} marks the Arg1/Arg2 boundary, i.e., "sep after" indicates that Arg2 starts with "after".}
    \label{fig:feats}
\end{figure*}

\begin{figure*}[ht]
    \centering \small
    \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_l1.jpg}
    \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_AE_l1.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_l2.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_AE_l2.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_l3.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/npmi/cms_AE_l3.jpg}
    \caption{\small Normalized pointwise mutual information (nPMI) for \textit{precedence}-related bigrams and most frequent labels for each sense level. Left: majority labels; right: raw labels. Top to bottom: levels 1, 2, and 3.}
    \label{fig:bigram_npmi}
\end{figure*}

\begin{figure*}[ht]
    \centering \small
    \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/sg-l1_rare_label_vs_conf.jpg}
    \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/AE-l1_rare_label_vs_conf.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/sg-l2_rare_label_vs_conf.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/AE-l2.5_rare_label_vs_conf.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/sg-l3_rare_label_vs_conf.jpg}
     \includegraphics[width=0.485\linewidth]{IDRR_Perspectives/figures/boxplots/AE-l3.5_rare_label_vs_conf.jpg}
    \caption{\small Confidence boxplots for frequent vs rare labels (relative frequency greater than /less than 0.33). '****' indicates statistical significance per the Mann-Whitney test with $p \le 1\mathrm{e}{-4}$. Left: SG; right: AE. Top to bottom: levels 1, 2, and 3.}
    \label{fig:freq_boxplots}
\end{figure*}