% Reading presentation, based on the arxiv-paper-reader Beamer template.
\documentclass[aspectratio=169,11pt]{beamer}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{amsmath,amssymb,graphicx,booktabs}
\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}
\newcommand{\papersource}[1]{\par\smallskip{\scriptsize\color{gray}#1\par}}
\newcommand{\q}{\mathbf q}
\newcommand{\kvec}{\mathbf k}
\newcommand{\Q}{\mathbf Q}
\newcommand{\Rseq}{\mathbf R}
\newcommand{\state}{\mathcal S}
\newcommand{\rh}{\boldsymbol\rho}
\title[NoteBank]{History Replays Itself}
\subtitle{Unleashing Long-Context Capability in Linear Attention\\[3mm]\textbf{NoteBank: preserve text, retrieve, replay}}
\author{Paper by Li Nanbo, Firas Laakom, et al.\\King Abdullah University of Science and Technology}
\date{Reading presentation $\cdot$ 2 November 2026\\\href{https://arxiv.org/abs/2610.15715v1}{arXiv:2610.15715v1 $\cdot$ submitted 11 October 2026}}
\begin{document}
\begin{frame}
\titlepage
\end{frame}

\begin{frame}{A small replay budget recovers distant evidence}
\begin{block}{Central result}
Frozen GDN at 1M tokens: \textbf{1.7\% $\rightarrow$ 70.3\%}\\
Mean over six RULER retrieval tasks; replay at most $2\times64$ tokens.
\end{block}
\begin{itemize}
\item Preserve selected text before the question is known.
\item Use the backbone's features to address it, and its forward pass to read it.
\item Distinguish retrieval gains, read adaptation, and state reset.
\end{itemize}
\medskip
{\small Publication not found as of 2026-11-02; \href{https://liangyuwang.github.io/}{author lists a preprint}.\\
\href{https://nanboli.github.io/notebank-page/}{Code forthcoming: official project page}.}
\papersource{Paper, Sec. 4.1 and Fig. 3, PDF p. 6. Lookup date: 2026-11-02.}
\end{frame}

\begin{frame}{A recurrent state must compute and retain evidence}
\[
\mathbf S_t=\mathbf S_{t-1}\mathbf A_t+
\beta_t\mathbf v_t\kvec_t^\top,\qquad
\mathbf o_t=\mathbf S_t\q_t.
\]
\begin{itemize}
\item $\q_t,\kvec_t\in\mathbb R^{d_k}$; $\mathbf v_t\in\mathbb R^{d_v}$;
$\mathbf S_t\in\mathbb R^{d_v\times d_k}$.
\item $\mathbf A_t$ controls retention and transformation;
$\beta_t$ controls writing.
\item Context arrives first; the question arrives later.
\end{itemize}
\begin{block}{The access bottleneck}
Ordinary inference can use history only through the retained state
$\state_T$. Evidence can be lost before its relevance is known.
\end{block}
\papersource{Paper, Sec. 2, Eq. (1), PDF p. 3. Surrounding gates and normalization are omitted.}
\end{frame}

\begin{frame}{NoteBank separates computation from text storage}
\centering
\includegraphics[width=.97\linewidth,height=.61\textheight,keepaspectratio]{figures/fig-02-method.pdf}
\par\medskip\raggedright
\textbf{Write} without the question $\;\rightarrow\;$
\textbf{address} with the question $\;\rightarrow\;$
\textbf{replay} through the same backbone.
\papersource{Paper, Fig. 2, PDF p. 4. Reused author figure. The answer branch starts from a separate state copy.}
\end{frame}

\begin{frame}{Writing selects locally distinctive text}
\[
\overline{\boldsymbol\mu}_{\mathcal C}^{\ell,h}
=\widehat{\frac1{|\mathcal C|}\sum_{t\in\mathcal C}\widehat{\kvec}_t^{\ell,h}},
\qquad
d_t^{\ell,h}=1-\langle\widehat{\kvec}_t^{\ell,h},
\overline{\boldsymbol\mu}_{\mathcal C(t)}^{\ell,h}\rangle.
\]
\begin{itemize}
\item Hats denote $\ell_2$ normalization; average scores across $J$ channels.
\item Score 48-token windows; start with the center token's sentence.
\item Expand to adjacent sentences within the note budget $B$.
\item Exclude overlapping sentences before selecting a second note.
\end{itemize}
\begin{block}{Default short-note configuration}
$W=2$ notes/chunk, $B=64$ tokens/note; $C=512$ for GDN/GDN-2,
$C=256$ for Mamba-2. No future question is used.
\end{block}
\papersource{Paper, Eqs. (3), (8), PDF pp. 4, 18; Apps. B.2 and C.3, pp. 17--21.}
\end{frame}

\begin{frame}{Keys choose positions; queries become addresses}
\[
t_i^{*,\ell,h}=\operatorname*{arg\,max}_{t\in I_i}d_t^{\ell,h},
\qquad
\rh_i^{\ell,h}=P^{\ell,h}\q_{t_i^{*,\ell,h}}^{\ell,h}.
\]
\begin{itemize}
\item $I_i$: positions in note $i$; each channel chooses its own token.
\item $P^{\ell,h}$ selects 16 fixed random coordinates, without replacement.
\item The same coordinate map is used for notes and questions.
\item Store original token IDs plus addresses, not historical full KV tensors.
\end{itemize}
\begin{block}{A useful distinction}
The routing comparison is \textbf{query-to-query} after compaction.
Key distinctiveness determines the representative position.
\end{block}
\papersource{Paper, Eq. (4), PDF p. 4; App. B.3, Eq. (9), PDF p. 19.}
\end{frame}

\begin{frame}{Each channel votes for its best matching note}
\[
\mathbf u_\tau^{\ell,h}=P^{\ell,h}\q_\tau^{\ell,h},
\qquad
s_i^{\ell,h}=\max_\tau
\langle\widehat{\mathbf u}_\tau^{\ell,h},\widehat{\rh}_i^{\ell,h}\rangle
\]
\[
V_i=\sum_{\ell,h}\mathbf1\!
\left[i=\operatorname*{arg\,max}_j s_j^{\ell,h}\right].
\]
\begin{itemize}
\item Probe the question from a temporary copy of $\state_T$.
\item Each channel finds one winning note; retrieve top-$R$ by votes.
\item Ties favor earlier insertion. Replay follows document order.
\end{itemize}
\papersource{Paper, Eq. (5), PDF pp. 4--5. Matching casts BF16 features to FP32 and normalizes them.}
\end{frame}

\begin{frame}{Replay uses a fresh branch of the retained state}
\[
\state_{\mathrm{read}}\gets\operatorname{copy}(\state_T),\quad
\state_{\Rseq}=F_\phi(\state_{\mathrm{read}},\Rseq),\quad
\mathbf Y\sim p_\phi(\cdot\mid\state_{\Rseq},\Q).
\]
\begin{enumerate}
\item Discard the question-probing state after retrieval.
\item Replay at most $RB$ original tokens through the full backbone.
\item Process the question again, then generate the answer.
\end{enumerate}
\medskip
Positions continue from the context boundary; notes are re-encoded at
their new positions.
\begin{block}{Architecture-specific intervention}
Mamba-2 experiments reset recurrent states before replay, retaining
convolution caches and positions. We separate this effect later.
\end{block}
\papersource{Paper, Eq. (6), p. 5; Algorithm 1, p. 18; Apps. B.4/C.3, pp. 19, 21.}
\end{frame}

\begin{frame}{Read adaptation leaves writing and routing frozen}
\begin{columns}[T]
\begin{column}{.47\textwidth}
\begin{block}{NB-TF}
No weight updates.\\[2mm]
Native writing, routing, replay and generation.
\end{block}
\end{column}
\begin{column}{.49\textwidth}
\begin{block}{NB-LoRA}
Adapters enabled during replay, question processing and generation.\\[2mm]
Disabled during context ingestion and retrieval.
\end{block}
\end{column}
\end{columns}
\medskip
\[
\Delta W=(\alpha/r)BA,\qquad
\mathcal L=-\frac1{|\widetilde{\mathbf Y}|}
\sum_t\log p_{\phi,\theta}(\widetilde y_t\mid
\state_{\mathrm{read}},\Rseq,\Q,\widetilde{\mathbf Y}_{<t}).
\]
Answer-only loss; 2,400 adaptation examples; fewer than 9.3M tokens.
\papersource{Paper, App. B.4, Eq. (10), PDF p. 19; App. C.4, p. 21.}
\end{frame}

\begin{frame}{The benchmarks test different kinds of access}
\centering
\begin{tabular}{p{2.6cm}p{5.7cm}p{3.4cm}}
\toprule
Benchmark & Evaluation scope & Replay / metric\\
\midrule
RULER & Six tasks; 100 examples each per length; 4K--1M & Top-2; task mean\\[1.5mm]
LongBench v1 & 12 subsets; 30 examples each; 360 total & GDN top-1; Mamba top-4; macro score\\[1.5mm]
MemoryAgent-\newline Bench & Selected QA tasks; reported 2,100 questions & Top-4; task macro accuracy\\[1.5mm]
LongBench v2 & 375 full-input QA/dialogue examples & Qwen top-8; accuracy\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
Within each backbone: same checkpoint and examples. Qwen uses YaRN
for both Plain and NoteBank.
\papersource{Paper, Sec. 4, PDF pp. 5--7; App. C.2, p. 20. MemoryAgentBench count inconsistency: backup slide.}
\end{frame}

\begin{frame}{Frozen GDN sustains retrieval from 4K to 1M}
\centering
\includegraphics[width=.98\linewidth,height=.62\textheight,keepaspectratio]{figures/fig-03-ruler.pdf}
\par\medskip\raggedright
At 1M, gains over Plain: \textbf{+68.6, +66.6, +37.8 pp}.\\
Top-2 replay; six-task means. Mamba-2 also uses a readout state reset.
\papersource{Paper, Fig. 3 and Sec. 4.1, PDF p. 6. Original figure; JRT repeats the full prompt.}
\end{frame}

\begin{frame}{Natural-language gains vary by task and reader}
\centering
\begin{tabular}{lrrr}
\toprule
LongBench v1, 12-task macro & Plain & NB-TF & NB-LoRA\\
\midrule
GDN, top-1 & 15.49 & 16.07 & 23.03\\
Mamba-2, top-4 & 6.79 & 13.43 & 17.10\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
\begin{itemize}
\item GDN training-free gain: \textbf{+0.58 points}.
\item LoRA improves QA, but hurts summarization relative to NB-TF.
\item Summarization: GDN $13.52\to11.37$;
Mamba-2 $16.51\to7.46$.
\end{itemize}
\medskip
Published Transformer score 16.05 is a contextual reference with a
different training protocol.
\papersource{Paper, Table 1, PDF p. 6; Sec. 4.2, p. 7; Table 5, p. 25. Scores combine task-specific metrics.}
\end{frame}

\begin{frame}{Most GDN LongBench improvement comes from adaptation}
\centering
\begin{tabular}{lrrrr}
\toprule
 & \multicolumn{2}{c}{RULER @ 1M} &
\multicolumn{2}{c}{LongBench v1}\\
\cmidrule(lr){2-3}\cmidrule(lr){4-5}
GDN & Frozen & LoRA & Frozen & LoRA\\
\midrule
Without NoteBank & 1.7 & 1.7 & 15.49 & 22.72\\
With NoteBank, top-1 & 59.8 & 58.4 & 16.07 & 23.03\\
\bottomrule
\end{tabular}
\par\bigskip
\begin{block}{Two different bottlenecks}
RULER: memory access recovers distant evidence.\\[2mm]
LongBench: adaptation drives most of the gain;
adapted models differ by only \textbf{0.31 points}.
\end{block}
\papersource{Paper, Table 4 and Sec. 6.3, PDF p. 10. Adapters trained separately with matched data and budgets.}
\end{frame}

\begin{frame}{A strong hybrid also benefits without training}
\centering
\begin{tabular}{lrrr}
\toprule
Qwen3.5-9B & Plain & NB-TF & Gain\\
\midrule
MemoryAgentBench, top-4 & 55.7 & 56.8 & +1.1 pp\\
LongBench v2, top-8 & 46.1 & 49.3 & +3.2 pp\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
\begin{itemize}
\item 24 GDN blocks + 8 attention blocks.
\item Write and address with GDN features; replay through every block.
\item Both methods use YaRN; LongBench v2 uses 375 selected examples.
\item On MemoryAgentBench, top-1 matches Plain; top-4 improves it.
\end{itemize}
\papersource{Paper, Tables 2/6, PDF pp. 6/25; Apps. C.1/C.2, p. 20.}
\end{frame}

\begin{frame}{State reset explains much of Mamba-2-8B recovery}
\centering
\begin{tabular}{lrr}
\toprule
MemoryAgentBench & Overall & Single-hop FactCon.\\
\midrule
Plain & 0.0 & 0.0\\
Clean start, no replay & 13.0 & 14.0\\
NB-TF, top-1 & 14.5 & 19.0\\
NB-TF, top-4 & 14.7 & 22.0\\
\bottomrule
\end{tabular}
\par\bigskip
\begin{block}{Use the matched control}
Top-4 adds \textbf{1.7 pp} over clean start, versus 14.7 pp over Plain.
The accumulated long-context state can impair readout.
\end{block}
More replay is task-dependent: EventQA drops $17.9\to16.4$ from top-1 to top-4.
\papersource{Paper, Table 6, PDF p. 25; state-reset discussion, pp. 21, 26.}
\end{frame}

\begin{frame}{Extra arithmetic is tiny relative to full ingestion}
\[
\Delta F=F_{\mathrm{write}}+F_{\mathrm{route}}
+(|\Q|+|\Rseq|)f_\phi,\qquad |\Rseq|\le RB.
\]
\[
F_{\mathrm{route}}\approx
2|\Q|N_TJd_\rho+3(|\Q|+N_T)Jd_\rho.
\]
Here $N_T$ counts notes, $d_\rho=16$, and $f_\phi$ is backbone FLOPs per token.
\begin{itemize}
\item GDN at 1M: Plain $\approx2891.4$ TFLOPs;
extra $\approx0.722$ TFLOPs.
\item Added ratio: \textbf{0.025\%}; three backbones span
0.0171\%--0.0250\%.
\item Fixed probing/replay is amortized; writing and exhaustive routing grow with history.
\end{itemize}
\medskip
These estimates exclude many non-arithmetic system costs. Hybrid attention needs additional accounting.
\papersource{Paper, Sec. 5.1, pp. 7--8; App. C.6, Eqs. (12)--(16), PDF pp. 22--23.}
\end{frame}

\begin{frame}{Persistent payload is compact, but grows with history}
\begin{columns}[T]
\begin{column}{.49\textwidth}
\textbf{GDN + NoteBank at 1M}
\begin{itemize}
\item Recurrent state: 48 MiB.
\item Conv. cache: 1.125 MiB.
\item Archive: 24.959 MiB.
\item Helpers: $\approx0.402$ MiB.
\end{itemize}
\medskip
\textbf{Total: $\approx74.49$ MiB}.
\end{column}
\begin{column}{.47\textwidth}
\textbf{The comparison}
\[
M_{\mathrm{MHA}}=4|\mathcal L|DP
\]
$P$: input tokens. BF16 full MHA; 24 layers; width 2048; no KV-head sharing.
\[
\frac{M_{\mathrm{NB}}}{M_{\mathrm{MHA}}}\approx\frac1{2638}.
\]
Reference: $\approx192$ GiB.
\end{column}
\end{columns}
\medskip
Excludes weights, workspace, branch copies and Python-object overhead.
This is a persistent-payload ratio for the specified GDN configuration.
\papersource{Paper, Sec. 5.2, PDF p. 8; App. C.7, Eqs. (17)--(21), p. 23.}
\end{frame}

\begin{frame}{Measured latency overhead is about 12.4\%}
\centering
\begin{tabular}{lrr}
\toprule
GDN at 1M & Plain & NB-TF top-2\\
\midrule
End-to-end time & 125.11 s & 140.64 s\\
Peak GPU memory & 2.93 GiB & 3.27 GiB\\
RULER score (separate quality run) & 1.71 & 70.33\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
\begin{itemize}
\item H100 80GB, BF16, batch 1, exactly 32 generated tokens.
\item Archive rebuilt each run; probing, routing and replay included.
\item Peak memory includes weights and transient allocations.
\end{itemize}
\begin{block}{Practical interpretation}
Very small arithmetic overhead coexists with measurable runtime overhead.
\end{block}
\papersource{Paper, Sec. 5.3, PDF p. 8; App. C.5, pp. 21--22; Table 7, p. 26.}
\end{frame}

\begin{frame}{Stored evidence can remain inaccessible}
\begin{columns}[c]
\begin{column}{.62\textwidth}
\includegraphics[width=\linewidth,height=.60\textheight,keepaspectratio]{figures/fig-05a-coverage.pdf}
\end{column}
\begin{column}{.35\textwidth}
\textbf{Oracle routing at 1M}\\[3mm]
GDN\\
$75.0\to75.7$\\[3mm]
Mamba-2\\
$40.4\to61.6$\\[3mm]
Archive, reader and replay budget held fixed.
\end{column}
\end{columns}
\medskip
GDN retrieves most archived gold values. Mamba-2 leaves a larger
gap between preservation and access.
\papersource{Paper, Fig. 5a/b and Sec. 6.1, PDF pp. 8--9. Original panel; diagnostics differ from top-2 headline results.}
\end{frame}

\begin{frame}{Alternative routers help Mamba-2 on LongBench}
\centering
\begin{tabular}{lrr}
\toprule
LongBench, fixed LoRA reader, top-1 & GDN & Mamba-2\\
\midrule
Random & 21.96 & 13.83\\
Mean input embedding & 22.40 & 16.70\\
Native feature voting & 23.03 & 14.25\\
BM25 & 23.50 & 18.66\\
BGE & 23.77 & 17.24\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
Native routing avoids an auxiliary encoder. Its quality is backbone-dependent.
BM25 realizes some of the observed routing headroom.
\medskip
Reported timing scopes differ: native 26 ms includes probing;
BGE timing includes full-bank encoding.
\papersource{Paper, Tables 3/8, PDF pp. 10/27. Timing values do not form a matched per-query latency comparison.}
\end{frame}

\begin{frame}{The best evidence budget depends on the backbone}
\begin{itemize}
\item \textbf{Write more:} $W=2$ improves coverage over $W=1$;
storage rises, arithmetic changes little.
\item \textbf{Write more often:} small chunks help Mamba-2; very coarse
$C=2048$ hurts both backbones.
\item \textbf{Replay more:} at 1M, $R=1\to4$ gives GDN
$59.5\to75.2$, Mamba-2 $37.1\to40.8$.
\item \textbf{Replay longer:} longer spans are not uniformly better.
The 1M grid peaks at $(B,R)=(128,4)$.
\end{itemize}
\begin{block}{Natural-language interaction}
With LoRA, LongBench peaks at $(256,2)$ for GDN (24.13) and
$(128,4)$ for Mamba-2 (17.81).
\end{block}
\papersource{Paper, App. D.2, Figs. 8--12, PDF pp. 27--30. Ablation scores belong to their own configurations.}
\end{frame}

\begin{frame}{The contribution is a stronger memory interface}
\begin{enumerate}
\item \textbf{Preserve independently.} A fixed recurrent state need not
be the only route to historical evidence.
\item \textbf{Reuse native computation.} Frozen features write and route;
ordinary forward passes read selected text.
\item \textbf{Track the actual bottleneck.} Coverage, routing, read
adaptation and state stability contribute differently.
\end{enumerate}
\begin{block}{Main trade-off}
Sparse query-independent storage can miss evidence. Archive size and
exhaustive matching grow with history; the replay budget stays bounded.
\end{block}
\papersource{Paper, Secs. 3, 6, 7, PDF pp. 3--5, 8--10. Synthesis of reported mechanisms and controls.}
\end{frame}

\begin{frame}{Paper and source links}
\textbf{History Replays Itself: Unleashing Long-Context Capability in Linear Attention}
\par\medskip
{\small Li Nanbo, Firas Laakom, Yilan Zhang, Piotr Pi\k{e}kos,
Yimeng Chen, Liangyu Wang, Yifan Xu, Mateusz Ostaszewski,
Dandan Guo, Wenyi Wang, Yanning Dai, Yuhui Wang,
J\"urgen Schmidhuber.}
\par\medskip
\begin{itemize}
\item \href{https://arxiv.org/abs/2610.15715v1}{arXiv:2610.15715v1}:
the version read in this presentation.
\item \href{https://nanboli.github.io/notebank-page/}{Official project}:
code marked \emph{Coming soon}.
\item \href{https://liangyuwang.github.io/}{Coauthor publication list}:
listed as a 2026 preprint.
\end{itemize}
\medskip
Publication not found as of 2026-11-02.\\
All results are from the paper; teaching explanations and calculations
are identified where used.
\end{frame}

\appendix
\begin{frame}{Backup: the writer has explicit boundary rules}
\begin{itemize}
\item Candidate region includes the preceding chunk's last 32 tokens.
Their original features and scores are retained.
\item A long initial sentence is clipped to a valid contiguous
$B$-token segment.
\item Selecting part of a sentence excludes that entire sentence
from the second selection.
\item Notes from one write operation do not overlap; notes across
chunk boundaries may overlap.
\item A final incomplete chunk is processed but writes no note.
\end{itemize}
\medskip
Teaching calculation: $W=2,B=64,C=512$ permits up to 25\% as many
stored token occurrences as input tokens. At 1M, the observed ratio is
about 22.2\%; replay is at most 128 tokens.
\papersource{Paper, App. B.2, PDF pp. 17--19; Eq. (18), p. 23. Percentages calculated from stated budgets/counts.}
\end{frame}

\begin{frame}{Backup: adaptation is shared across downstream tasks}
\begin{itemize}
\item Natural Questions-derived short-answer corpus: 2,400 examples,
including 678 without supporting evidence.
\item Original gold answers are retained for these no-support examples.
\item Rank $r=8$, scale $\alpha=16$; adapters on four selected layers.
\item 600 AdamW updates; four examples accumulated per update;
learning rate $5\times10^{-4}$.
\item Answer-only loss including EOS; frozen context state and
discrete routing.
\end{itemize}
\medskip
Each backbone/budget adapter is evaluated across all 12 LongBench
tasks without task-specific fine-tuning.
\papersource{Paper, Apps. B.4/C.4, PDF pp. 19/21. Weight decay 0.01; gradient clipping 1.0.}
\end{frame}

\begin{frame}{Backup: more span tokens can reduce retrieval quality}
\textbf{RULER at 1M: six-task mean, NB-TF}
\par\medskip
\begin{columns}[T]
\begin{column}{.47\textwidth}
\centering GDN\\[2mm]
\begin{tabular}{lrrr}
\toprule
 & $B=64$ & 128 & 256\\
\midrule
$R=1$ & 59.5 & 57.2 & 52.8\\
$R=2$ & 70.3 & 72.4 & 71.2\\
$R=4$ & 75.2 & \textbf{76.8} & 74.5\\
\bottomrule
\end{tabular}
\end{column}
\begin{column}{.47\textwidth}
\centering Mamba-2\\[2mm]
\begin{tabular}{lrrr}
\toprule
 & $B=64$ & 128 & 256\\
\midrule
$R=1$ & 37.1 & 33.5 & 33.0\\
$R=2$ & 37.8 & 39.9 & 35.8\\
$R=4$ & 40.8 & \textbf{41.3} & 37.3\\
\bottomrule
\end{tabular}
\end{column}
\end{columns}
\par\bigskip
Longer notes and more notes change different aspects of evidence access.
The best configuration uses more than the default replay budget.
\papersource{Redrawn from Paper, Fig. 11, PDF p. 29 (1M column only). Do not substitute these values for other runs.}
\end{frame}

\begin{frame}{Backup: LoRA does not remove budget sensitivity}
\textbf{LongBench macro score: NB-LoRA}
\par\medskip
\begin{columns}[T]
\begin{column}{.47\textwidth}
\centering GDN\\[2mm]
\begin{tabular}{lrrr}
\toprule
 & $R=1$ & 2 & 4\\
\midrule
$B=64$ & 23.26 & 21.30 & 20.04\\
$B=128$ & 23.20 & 22.12 & 21.19\\
$B=256$ & 22.59 & \textbf{24.13} & 22.86\\
\bottomrule
\end{tabular}
\end{column}
\begin{column}{.47\textwidth}
\centering Mamba-2\\[2mm]
\begin{tabular}{lrrr}
\toprule
 & $R=1$ & 2 & 4\\
\midrule
$B=64$ & 14.26 & 15.77 & 16.88\\
$B=128$ & 16.55 & 17.43 & \textbf{17.81}\\
$B=256$ & 14.25 & 16.20 & 17.18\\
\bottomrule
\end{tabular}
\end{column}
\end{columns}
\par\bigskip
GDN's score averaged over span budgets falls from 23.02 to 21.36
as $R$ increases from 1 to 4. The full grid reveals an interaction
hidden by that average.
\papersource{Redrawn from Paper, Fig. 12, PDF p. 30. These ablation runs differ slightly from the main table.}
\end{frame}

\begin{frame}{Backup: exact payload accounting uses recorded counts}
$P$: input tokens; $N_T$: notes; $U$: stored token occurrences.
\[
\bar P\approx1{,}048{,}019,\qquad
\overline{N_T}\approx4092.3,\qquad
\bar U\approx232{,}514.
\]
\[
M_{\mathrm{archive}}=2N_TJd_\rho+4U+24N_T
\quad\text{bytes}.
\]
\[
\begin{aligned}
M_{\mathrm{NB}}={}&M_{\mathrm{archive}}+4Jd_kd_v\\
&+2c_{\mathrm{conv}}J(2d_k+d_v)+M_{\mathrm{helper}}.
\end{aligned}
\]
\begin{itemize}
\item BF16 addresses, int32 token IDs, three uint64 fields per note.
\item GDN: $J=192$, $d_k=d_v=256$, $c_{\mathrm{conv}}=4$.
\item Payload measured at answer start; exclude transient branch copies.
\end{itemize}
\papersource{Paper, App. C.7, Eqs. (18)--(21), PDF p. 23.}
\end{frame}

\begin{frame}{Backup: preserve the paper's evaluation qualifications}
\begin{itemize}
\item \textbf{MemoryAgentBench count:} the paper reports 2,100 questions,
but its 11-configuration enumeration sums to 2,300.
Keep reported scores without reconstructing the sample set.
\item \textbf{Router reader label:} Table 3 calls readers LoRA;
its GDN RULER value 59.8 is labeled Frozen in Table 4
(LoRA: 58.4). Avoid cross-table configuration equivalence.
\item \textbf{Transformer comparison:} the runtime baseline uses GQA
and unscaled RoPE beyond a configured 4K range.
The 1/2600 payload reference instead assumes full MHA.
\end{itemize}
\papersource{Paper, App. C.2, p. 20; Tables 3/4, p. 10; Apps. C.5/C.7, pp. 22--23.}
\end{frame}

\begin{frame}{Backup: retrieval quality and evidence use interact}
\centering
\begin{tabular}{llrr}
\toprule
Four LongBench QA tasks & Reader & Native top-1 & Oracle-1\\
\midrule
GDN & Frozen & 7.05 & 7.59\\
GDN & LoRA & 19.11 & 22.58\\
Mamba-2 & Frozen & 4.22 & 7.23\\
Mamba-2 & LoRA & 9.09 & 26.43\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
\begin{itemize}
\item Fixed archive, reader and one-note replay budget.
\item Oracle chooses an archived note containing a reference answer.
\item Answer containment is a relevance proxy, not guaranteed support;
these scores are not a strict natural-language upper bound.
\end{itemize}
\papersource{Paper, Fig. 5c, PDF p. 9. Tasks: HotpotQA, 2WikiMQA, MuSiQue, Qasper.}
\end{frame}
\end{document}