\documentclass[aspectratio=169,11pt]{beamer}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{amsmath,amssymb,graphicx,booktabs}
\pdfstringdefDisableCommands{\def\\{ }\def\translate#1{#1}}
\definecolor{AcademicBlue}{RGB}{26,57,86}
\definecolor{AcademicTeal}{RGB}{0,105,112}
\setbeamercolor{structure}{fg=AcademicBlue}
\setbeamercolor{frametitle}{fg=AcademicBlue,bg=white}
\setbeamercolor{title}{fg=AcademicBlue}
\setbeamercolor{alerted text}{fg=AcademicTeal}
\setbeamercolor{block title}{fg=white,bg=AcademicBlue}
\setbeamercolor{block body}{fg=black,bg=AcademicBlue!5}
\setbeamertemplate{navigation symbols}{}
\setbeamertemplate{itemize items}[circle]
\setbeamertemplate{footline}{\hfill\usebeamerfont{page number in head/foot}\insertframenumber\,/\,\inserttotalframenumber\hspace{4mm}\vspace{3mm}}
\setbeamersize{text margin left=8mm,text margin right=8mm}
\setbeamerfont{frametitle}{size=\Large,series=\bfseries}
\setbeamerfont{title}{size=\LARGE,series=\bfseries}
\addtobeamertemplate{frametitle}{\vspace{2mm}}{}
\setlength{\tabcolsep}{7pt}
\newcommand{\papersource}[1]{\par\smallskip{\scriptsize\color{gray}#1\par}}
\newcommand{\fig}[2][0.66]{\centering\includegraphics[width=0.96\linewidth,height=#1\textheight,keepaspectratio]{figures/#2.pdf}\par}
\newcommand{\sft}{\mathcal L_{\mathrm{SFT}}}
\newcommand{\rec}{\mathcal L_{\mathrm{rec}}}
\newcommand{\attn}{\mathcal L_{\mathrm{attn}}}
\title[Balancing Memory Pathways]{Balancing Memory Pathways}
\subtitle{Analyzing and Improving Memory Utilization in Hybrid LMs}
\author{Paper by Hyunji Lee, Joykirat Singh, Zaid Khan,\\Justin Chih-Yao Chen, Elias Stengel-Eskin,\\Alessandro Sordoni, Arman Cohan, and Mohit Bansal}
\date{\href{https://arxiv.org/abs/2610.06750v1}{arXiv:2610.06750v1} (5 October 2026)\\Research reading \textbullet\ 13 November 2026}
\begin{document}

\begin{frame}
\titlepage
\end{frame}

\begin{frame}{Multiple memory pathways need targeted training}
\begin{block}{Takeaway}
Ordinary SFT mainly strengthens attention. A recurrent-only auxiliary pass makes recurrent memory more useful and improves the full model.
\end{block}
\begin{itemize}
\item QA micro-average: \alert{34.6 $\to$ 38.5} (Qwen3.5); \alert{31.0 $\to$ 36.2} (Nemotron-H).
\item Benefits are strongest on longer-context QA and longer agent trajectories.
\end{itemize}
\smallskip
{\small Publication not found as of 2026-11-13: \href{https://arxiv.org/abs/2610.06750}{arXiv record}, \href{https://joykirat18.github.io/}{author list}.\\
\href{https://github.com/amy-hyunji/Balancing-Memory-Pathways}{Official public code}: training, data preparation, and pathway evaluation.}
\papersource{Paper, Secs. 1, 5; Table 1, PDF pp. 1--3, 7. Scores follow dataset-specific EM/F1.}
\end{frame}

\begin{frame}{Two pathways offer different ways to use the past}
\fig[0.76]{fig1_v3}
\papersource{Paper, Fig. 1, PDF p. 2. Original schematic: direct token access versus compact recurrent state.}
\end{frame}

\begin{frame}{Attention and recurrence have different strengths}
\begin{columns}[c]
\begin{column}{0.56\textwidth}
\fig[0.64]{hybrid_pathway_bar_paper}
\end{column}
\begin{column}{0.41\textwidth}
\begin{itemize}
\item Higher $\Delta$NLL means the removed component mattered more.
\item Based NQ retrieval depends more on attention.
\item PG19 language modeling depends more on recurrence.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 2.2; Fig. 2, PDF pp. 3--4. Qwen3.5; whole-layer ablation.}
\end{frame}

\begin{frame}{Information needs change the relative dependence}
\begin{columns}[c]
\begin{column}{0.56\textwidth}
\fig[0.64]{base_store_f1_barplot}
\end{column}
\begin{column}{0.41\textwidth}
\[
R_{\mathrm{attn}}=\frac{\text{Attention-only score}}{\text{Full score}}
\]
\begin{itemize}
\item Higher retention for verbatim and single-evidence QA.
\item Lower retention when inference or evidence integration is needed.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Fig. 3, PDF p. 4; Appendix A, p. 14. Category counts are balanced within each comparison.}
\end{frame}

\begin{frame}{Interventions isolate cross-segment information flow}
Divide each input into \alert{past} and \alert{current} segments.\\
For QA: document $\mid$ question and subsequent prediction.
\medskip
\begin{center}
\begin{tabular}{lcc}
\toprule
Condition & Past attention & Past recurrent state\\
\midrule
Full & Available & Available\\
Recurrent-only & Blocked & Available\\
Attention-only & Available & Reset at boundary\\
\bottomrule
\end{tabular}
\end{center}
\medskip
All layers remain active \emph{within} each segment.\\
``Only'' describes the mechanism that carries information across the boundary.
\papersource{Paper, Sec. 4.1, PDF p. 5. Different from the whole-layer ablation in Fig. 2.}
\end{frame}

\begin{frame}{Recurrent-only masks attention across the boundary}
\[
M_{t,s}=\begin{cases}
0,&s\leq t\ \text{and}\ \sigma(s)=\sigma(t),\\
-\infty,&\text{otherwise}.
\end{cases}
\]
\begin{itemize}
\item $t$: query position; $s$: key position; $\sigma$: segment identity.
\item Add $M$ to attention scores before normalization.
\item Keep causal attention within each segment; recurrent state remains continuous over the entire sequence.
\end{itemize}
\begin{block}{Effect}
Past information must enter recurrent state to influence the current answer.
\end{block}
\papersource{Paper, Sec. 4.1, PDF p. 5; unnumbered equation.}
\end{frame}

\begin{frame}{Attention-only resets the recurrent history}
\[
S_t=\mathbf{1}[\sigma(t)=\sigma(t-1)]\,\mathcal A_t(S_{t-1})+w_t,
\quad S_0=0.
\]
\begin{itemize}
\item $S_t$: recurrent state; $\mathcal A_t$: transition; $w_t$: current-token write.
\item For $t>1$: at a boundary, the old state contribution becomes zero.
\item Standard causal attention can still retrieve preceding tokens.
\end{itemize}
\medskip
This is a general intervention on state propagation, rather than a replacement of the model's recurrent update rule.
\papersource{Paper, Sec. 4.1, PDF p. 5; unnumbered equation.}
\end{frame}

\begin{frame}{Standard SFT leaves recurrent-only performance low}
\fig[0.65]{qwen3.5_qa_agentic}
\smallskip
Full and Attention-only improve; Recurrent-only barely changes.\\
QA: $5.1\to5.0$; Quest: $2.5\to4.0$.
\papersource{Paper, Sec. 4.2; Fig. 4, PDF p. 6. Qwen3.5-4B, percent scores.}
\end{frame}

\begin{frame}{Train the full model and a recurrent-only pass jointly}
\[
\boxed{\mathcal L(\theta)=\sft(\theta)+\lambda\rec(\theta)},\qquad\lambda=0.25.
\]
\begin{itemize}
\item Same supervised next-token target in both passes.
\item Full pass: both pathways can carry past information.
\item Auxiliary pass: attention to past segments is masked; recurrence is continuous.
\item Full model at inference; no auxiliary inference pass.
\end{itemize}
\begin{block}{Compute-matched comparison}
Auxiliary runs use half as many optimization steps to offset the extra computation per step.
\end{block}
\papersource{Paper, Secs. 3, 5.1; Appendix C.1, PDF pp. 4, 7, 14--15.}
\end{frame}

\begin{frame}{Evaluation tests task quality and pathway utilization}
\begin{columns}[t]
\begin{column}{0.49\textwidth}
\textbf{Models and adaptation}
\begin{itemize}
\item Qwen3.5-4B: 24 Gated DeltaNet + 8 attention layers.
\item Nemotron-H-4B-Instruct: 24 Mamba2 + 4 attention layers.
\item All-layer LoRA: rank 16, scaling 32, dropout 0.05.
\end{itemize}
\end{column}
\begin{column}{0.49\textwidth}
\textbf{Tasks and metrics}
\begin{itemize}
\item QA: 12k train / 2k validation; 8.2k test, mean context 84k tokens.
\item Six datasets; dataset-specific EM/F1; micro-average.
\item Agents: TextWorld and BabyAI; success within step limit.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 3; Appendix B, PDF pp. 4--5, 14. Five epochs with early stopping; auxiliary step adjustment applies.}
\end{frame}

\begin{frame}{Recurrent auxiliary supervision improves QA overall}
\begin{center}
\begin{tabular}{lrrrr}
\toprule
&\multicolumn{2}{c}{Qwen3.5}&\multicolumn{2}{c}{Nemotron-H}\\
Dataset&SFT&+Rec&SFT&+Rec\\
\midrule
DROP&48.6&46.9&42.4&44.5\\
MuSR&45.6&44.8&40.9&38.1\\
HotpotQA&43.1&44.0&38.7&42.1\\
Qasper&30.1&35.9&28.1&34.1\\
NarrativeQA&24.4&33.7&21.9&31.7\\
MINTEval&21.1&28.9&18.8&27.8\\
\midrule
Micro-average&34.6&\textbf{38.5}&31.0&\textbf{36.2}\\
\bottomrule
\end{tabular}
\end{center}
\papersource{Paper, Table 1, PDF p. 7. +Rec means SFT + recurrent auxiliary loss. QA ``accuracy'' combines EM and F1.}
\end{frame}

\begin{frame}{Gains concentrate on longer-context datasets}
\begin{center}
\begin{tabular}{lrr}
\toprule
Gain over SFT (percentage points)&Qwen3.5&Nemotron-H\\
\midrule
Qasper&+5.8&+6.0\\
NarrativeQA&+9.3&+9.8\\
MINTEval&+7.8&+9.0\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Longer-context group: about \alert{+8.0 pp}; other three datasets: about \alert{+0.2 pp}.
\item These summarize equal-weight dataset/model gains, rather than the micro-average.
\item Some shorter tasks regress: Qwen DROP/MuSR and Nemotron MuSR.
\end{itemize}
\papersource{Paper, Secs. 1, 5.2; Table 1, PDF pp. 2, 7. Dataset differences do not isolate length alone.}
\end{frame}

\begin{frame}{The improvement accompanies much stronger recurrent use}
\fig[0.61]{qwen3.5_qa_memory_comparison}
\medskip
SFT $\to$ SFT+Rec: recurrent-only \alert{$5.0\to22.8$};\\
attention-only $25.0\to23.7$; full score $34.6\to38.5$.
\papersource{Paper, Fig. 6, PDF p. 8. Qwen3.5-4B. Restricted losses alone reduce full-model performance.}
\end{frame}

\begin{frame}{Agent gains are largest on BabyAI}
\begin{center}
\begin{tabular}{llrrrr}
\toprule
Model&Objective&Quest&Treasure&PutNext&GoToMaze\\
\midrule
Qwen&SFT&78.5&44.0&46.0&63.0\\
& SFT+Rec&\textbf{80.5}&\textbf{56.0}&\textbf{73.0}&\textbf{83.0}\\
Nemotron&SFT&70.5&40.5&30.0&77.0\\
& SFT+Rec&\textbf{75.5}&\textbf{47.0}&\textbf{47.0}&\textbf{84.0}\\
\midrule
\multicolumn{2}{l}{Mean gain (pp)}&+3.5&+9.3&\alert{+22.0}&\alert{+13.5}\\
\bottomrule
\end{tabular}
\end{center}
\medskip
Mean trajectory length: BabyAI 134.0 vs. TextWorld 42.2 steps.\\
Longer trajectories are consistent with larger memory benefits.
\papersource{Paper, Table 2, PDF p. 8. PutNext = PutNextLocal; GoToMaze = GoToObjMaze. Success rates (\%).}
\end{frame}

\begin{frame}{Auxiliary training improves use of past trajectories}
\fig[0.62]{failure_recovery_and_successful_demonstrations}
\smallskip
Failure recovery: larger gains on multi-evidence QA.\\
Successful demonstrations: more often produce a successful, shorter trajectory.
\papersource{Paper, Fig. 7, PDF p. 9. Left: attempt budget; right: demonstration length relative to optimal.}
\end{frame}

\begin{frame}{Experience helps when it must be integrated}
\begin{columns}[c]
\begin{column}{0.52\textwidth}
\fig[0.60]{failure_recovery_accumulated}
\end{column}
\begin{column}{0.45\textwidth}
\begin{itemize}
\item TextWorld: prior failures in context, up to 7 attempts; reported mean recovery gain \alert{+19.2 pp}.
\item QA group means: multi-evidence \alert{+30.3 pp}; single-evidence +2.8 pp.
\item Five successful demonstrations: \alert{+6.0 pp} rate of beating the shortest demonstration.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 6, Fig. 7; Appendix C.2, Fig. 10, PDF pp. 9, 14--15. QA overall aggregation caveat: backup slide 30.}
\end{frame}

\begin{frame}{The same imbalance appears in text + latent memory}
\begin{columns}[c]
\begin{column}{0.54\textwidth}
\fig[0.63]{explicit_hybrid}
\end{column}
\begin{column}{0.43\textwidth}
\begin{itemize}
\item Qwen3-4B-Instruct: 8k-token text summary + 128 latent KV slots.
\item Naive joint SFT: 24.1, below text-only 25.9.
\item Auxiliary training: \alert{28.6}.
\item Oracle 32.0 selects the better single-memory prediction per example.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 6, Fig. 8; Appendix C.3, PDF pp. 9, 15--16. Oracle is a hindsight reference.}
\end{frame}

\begin{frame}{Role-based supervision makes the other memory irrelevant}
\[
\ell(T_i,L_i)=-\log p_\theta(y_i\mid q_i,T_i,L_i)
\]
\[
\mathcal L_i=\ell(T_i,L_i)+\lambda\mathcal L_i^{\mathrm{aux}},\quad
\mathcal L_i^{\mathrm{aux}}=\begin{cases}
\ell(T_i,\operatorname{sg}[L_j]),&\mathrm{role}(i)=\mathrm{text},\\
\ell(T_j,L_i),&\mathrm{role}(i)=\mathrm{latent}.
\end{cases}
\]
\begin{itemize}
\item $T_i,L_i$: correct text/latent memories; $j$: unrelated context.
\item $q_i,y_i$: question/target; $\operatorname{sg}$: stop gradient; $\lambda=0.25$.
\item Best rule: verbatim $\to$ text; non-verbatim $\to$ latent.
\item Role labels supervise training; full inference has both memories.
\end{itemize}
\papersource{Paper, Appendix C.3.3, Eq. (1), PDF p. 17. Unrelated memories are matched by dataset and similar document length.}
\end{frame}

\begin{frame}{Choosing the right role matters more than adding more losses}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Variant&Score&$\Delta$Latent&$\Delta$Text\\
\midrule
Naive SFT&24.1&$-2.4$&$+11.4$\\
Verbatim&\textbf{28.6}&\textbf{$+4.7$}&$+10.4$\\
Reverse&24.5&$+1.1$&$+7.2$\\
Random&23.9&$-1.0$&$+10.5$\\
Latent-aux for all&26.1&$+3.4$&$+8.5$\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item $\Delta$: score drop after replacing that memory with unrelated content.
\item Verbatim routing increases latent use while largely retaining text use.
\item Random roles and indiscriminate auxiliary objectives fail to match this gain.
\end{itemize}
\papersource{Paper, Table 3; Appendix C.3.3, PDF pp. 17--18. Positive $\Delta$ indicates sensitivity to the correct memory.}
\end{frame}

\begin{frame}{Train complementary use, then measure the tradeoff}
\begin{enumerate}
\item \textbf{Diagnose:} task improvement can hide an underused memory pathway.
\item \textbf{Intervene:} forcing information through that pathway during training improves full-model performance.
\item \textbf{Coordinate:} text/latent experiments show that role assignment can preserve complementary strengths.
\end{enumerate}
\medskip
\textbf{Scope and costs}
\begin{itemize}
\item Evidence: 4B-scale models, LoRA SFT; some short QA datasets regress.
\item Compute matched by fewer steps; wall-clock costs are not measured.
\item Interventions reveal dependence, rather than a unique additive contribution of each pathway.
\end{itemize}
\papersource{Paper, Secs. 3--7, PDF pp. 4--10; interpretation based on reported protocols and ablations.}
\end{frame}

\begin{frame}{Sources and discussion prompts}
\textbf{Primary sources}
\begin{itemize}
\item Lee et al. (2026), \emph{Balancing Memory Pathways: Analyzing and Improving Memory Utilization in Hybrid LMs}.\\
\href{https://arxiv.org/abs/2610.06750v1}{arXiv:2610.06750v1}, including Appendices A--C.
\item \href{https://github.com/amy-hyunji/Balancing-Memory-Pathways}{Official public implementation} and \href{https://joykirat18.github.io/}{author publication list}.
\end{itemize}
\medskip
\textbf{Questions suggested by this reading}
\begin{itemize}
\item Can role assignment be learned without gold-answer heuristics?
\item How do gains change under fixed FLOPs, fixed examples, and fixed wall-clock budgets?
\item Can length and evidence integration be varied independently within a task?
\end{itemize}
\papersource{Publication/code checked 2026-11-13. Discussion questions are reader analysis. Backup slides follow.}
\end{frame}

\appendix
\begin{frame}{Backup: the restricted objective should remain auxiliary}
\begin{center}
\begin{tabular}{lrr}
\toprule
Training objective&Qwen3.5&Nemotron-H\\
\midrule
$\sft$&34.6&31.0\\
$\sft+\rec$&\textbf{38.5}&\textbf{36.2}\\
$\rec$&30.4&29.8\\
$\attn$&31.6&31.4\\
$\sft+\attn$&35.6&34.1\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Mean gain: recurrent auxiliary +4.6 pp vs. attention auxiliary +2.1 pp.
\item A single restricted loss does not preserve full-model performance as well.
\end{itemize}
\papersource{Paper, Table 1, PDF p. 7. QA micro-average; two-model mean gains rounded to one decimal.}
\end{frame}

\begin{frame}{Backup: Qwen agent objective ablations}
\begin{center}
\begin{tabular}{lrrrr}
\toprule
Objective&Quest&Treasure&PutNext&GoToMaze\\
\midrule
$\sft$&78.5&44.0&46.0&63.0\\
$\sft+\rec$&\textbf{80.5}&\textbf{56.0}&\textbf{73.0}&\textbf{83.0}\\
$\rec$&75.5&45.0&13.0&37.0\\
$\attn$&76.5&44.0&31.0&50.0\\
$\sft+\attn$&77.0&49.0&47.0&70.0\\
\bottomrule
\end{tabular}
\end{center}
\medskip
Restricted-only objectives particularly hurt BabyAI.\\
Preserving the unrestricted training condition matters.
\papersource{Paper, Table 2, PDF p. 8. Success rates (\%). PutNextLocal and GoToObjMaze abbreviated.}
\end{frame}

\begin{frame}{Backup: Nemotron agent objective ablations}
\begin{center}
\begin{tabular}{lrrrr}
\toprule
Objective&Quest&Treasure&PutNext&GoToMaze\\
\midrule
$\sft$&70.5&40.5&30.0&77.0\\
$\sft+\rec$&\textbf{75.5}&\textbf{47.0}&\textbf{47.0}&\textbf{84.0}\\
$\rec$&68.5&40.0&17.0&20.0\\
$\attn$&71.5&42.0&37.0&54.0\\
$\sft+\attn$&72.0&44.5&43.0&80.0\\
\bottomrule
\end{tabular}
\end{center}
\medskip
The recurrent auxiliary advantage also holds with Mamba2-based recurrence.
\papersource{Paper, Table 2, PDF p. 8. Success rates (\%). PutNextLocal and GoToObjMaze abbreviated.}
\end{frame}

\begin{frame}{Backup: the tested nonzero weights all improve Quest}
\begin{columns}[c]
\begin{column}{0.57\textwidth}
\fig[0.65]{lambda_ablation_full}
\end{column}
\begin{column}{0.40\textwidth}
\begin{itemize}
\item Qwen3.5, TextWorld Quest.
\item SFT ($\lambda=0$): 78.5\%.
\item All tested nonzero values improve over this baseline.
\item Authors select $\lambda=0.25$; plot also shows 0.5 at approximately 80.5\%.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Appendix C.1; Fig. 9, PDF pp. 14--15. This is a single task/model sweep.}
\end{frame}

\begin{frame}{Backup: SFT increases attention retention across QA types}
\begin{columns}[c]
\begin{column}{0.59\textwidth}
\fig[0.64]{attention_only_retention_barplot_v2}
\end{column}
\begin{column}{0.38\textwidth}
\begin{itemize}
\item Gains are in \emph{percentage points} of retention.
\item Verbatim / single-evidence mean: +25.5 pp.
\item Non-verbatim / multi-evidence mean: about +19.2 pp.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 4.2; Fig. 5, PDF p. 6. Qwen3.5; retention = Attention-only / Full score.}
\end{frame}

\begin{frame}{Backup: text and latent strengths vary by information type}
\begin{columns}[c]
\begin{column}{0.55\textwidth}
\fig[0.63]{sec4_1_information_types_delta}
\end{column}
\begin{column}{0.42\textwidth}
\begin{itemize}
\item $\Delta$ = latent score minus text score under matched budgets.
\item Text favors verbatim / single evidence.
\item Latent is more competitive on multi-evidence / non-verbatim questions.
\item Latent encoding: document + $K$ memory tokens; retain their layer-wise KV as answer prefix.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Appendix C.3.1; Fig. 11, PDF pp. 15--16. Distinct from the 8k text / 128 latent joint setting.}
\end{frame}

\begin{frame}{Backup: full role-assignment comparison}
\begin{center}
\begin{tabular}{llrrr}
\toprule
Role assignment&Variant&Score&$\Delta$Latent&$\Delta$Text\\
\midrule
--&Naive&24.1&$-2.4$&$+11.4$\\
Per-example&Outcome&26.1&$+0.8$&$+11.5$\\
&Verbatim&\textbf{28.6}&\textbf{$+4.7$}&$+10.4$\\
&Reverse&24.5&$+1.1$&$+7.2$\\
&Random&23.9&$-1.0$&$+10.5$\\
All examples&Latent-aux&26.1&$+3.4$&$+8.5$\\
&Text-aux&24.9&$+0.0$&$+14.5$\\
&Unrouted (both)&24.4&$-1.2$&$+9.1$\\
--&Oracle&32.0&--&--\\
\bottomrule
\end{tabular}
\end{center}
\papersource{Paper, Table 3, PDF p. 17; interpretation p. 18. Outcome chooses latent role when latent-only prediction is correct.}
\end{frame}

\begin{frame}{Backup: interpret QA recovery aggregates with care}
\begin{itemize}
\item Sec. 6 reports a mean QA recovery gain of \textbf{16.6 pp}.
\item Reported group means: single-evidence $14.8\to17.6$; multi-evidence $27.3\to57.6$.
\item The equal-weight mean of these gains is $(2.8+30.3)/2\approx16.6$ pp.
\item Yet the plotted \emph{All} curves differ by only about 6--9 pp at budgets 2, 3, and 7; the aggregation/denominator is not reconciled in the text.
\end{itemize}
\medskip
Use the group-specific results and plotted trend. Treat 16.6 pp as a \emph{reported aggregate}, rather than reading it directly from the All curve.
\papersource{Paper, Sec. 6; Fig. 7, PDF p. 9. Numerical mismatch identified in this reading; curve gaps are approximate.}
\end{frame}
\end{document}
