% Research discussion, approximately 25 minutes, followed by backup slides.
% Based on the arxiv-paper-reader Beamer template; compile with pdfLaTeX.
\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{\M}{\mathbf M}
\newcommand{\Sstate}{\mathbf S}
\newcommand{\Kmem}{\tilde{\mathbf K}}
\newcommand{\Vmem}{\tilde{\mathbf V}}
\newcommand{\Qmem}{\tilde{\mathbf Q}}
\newcommand{\Hmem}{\tilde{\mathbf H}}
\newcommand{\diag}{\operatorname{diag}}
\newcommand{\softmax}{\operatorname{Softmax}}
\newcommand{\norm}{\operatorname{Norm}}
\setlength{\tabcolsep}{5pt}
\renewcommand{\arraystretch}{1.14}
\title[Metis]{Metis: Memory Foundation Model}
\subtitle{Learning persistent memory inside a frozen language model}
\author{Paper by Zeyu Zhang et al.\\[2mm]\small Independent research discussion}
\date{arXiv:2607.26760v2 (4 August 2026)\\Reading: 9 October 2026}
\hypersetup{pdftitle={Metis: Memory Foundation Model -- Research Discussion},
  pdfauthor={Independent paper reading},pdfsubject={arXiv:2607.26760v2}}

\begin{document}

\begin{frame}
  \titlepage
  \vspace{-5mm}
  \begin{center}
    \small\alert{Fixed-size states support memory without replaying history,\\
    with substantial limits in capacity and controllability.}
  \end{center}
\end{frame}

\begin{frame}{Memory must bridge when facts arrive and matter}
  \begin{block}{Research question}
    Can a model learn what to store, revise, forget, and use across
    interactions through its own forward computation?
  \end{block}
  \begin{columns}[T,onlytextwidth]
    \column{0.48\textwidth}
    \textbf{External textual memory}
    \begin{itemize}
      \item Store history as text.
      \item Retrieve and construct a prompt.
      \item Optimize retrieval and answering through separate stages.
    \end{itemize}
    \column{0.48\textwidth}
    \textbf{Metis}
    \begin{itemize}
      \item Persist a compact internal state.
      \item Read it in the model forward pass.
      \item Learn memory procedures from future-answer supervision.
    \end{itemize}
  \end{columns}
  \papersource{Paper, Secs. 1--2, PDF pp. 1--6.}
\end{frame}

\begin{frame}{Online state changes; learned weights stay frozen}
  \[
    (Y_t,\M_{t+1})=f_\Phi(X_t,\M_t)
  \]
  \begin{itemize}
    \item $X_t$: current input; $Y_t$: current response.
    \item $\M_t$: persistent state, with normalization state
          $\Sstate_t$ suppressed here.
    \item $\Phi$: shared backbone and learned memory read/write weights.
  \end{itemize}
  \begin{block}{Two different kinds of adaptation}
    \textbf{Mid-training:} freeze the backbone and train memory parameters.\\
    \textbf{Inference:} freeze all learned weights; update state by forward computation.
  \end{block}
  \papersource{Paper, Secs. 2.1--2.3 and 5.1, PDF pp. 3--5, 16--17; Appendix A, p. 33.}
\end{frame}

\begin{frame}{A layer reads old memory and writes the next state}
  \begin{center}
    \includegraphics[width=0.99\linewidth,height=0.62\textheight,keepaspectratio]
      {figures/fig-02-block.pdf}
  \end{center}
  \small The original attention branch handles the current step.
  Memory readout adds history; the write branch prepares future state.
  \papersource{Paper, Fig. 2(c), PDF p. 7, cropped from the author figure.
  The diagram shows LU; the final model uses GDU.}
\end{frame}

\begin{frame}{Select informative tokens before compressing them}
  \[
    \mathbf p_t=\softmax\!\left(\Hmem_t\tilde{\mathbf w}_{\rm agg}/\tau\right)
  \]
  \[
    L'_t=\operatorname{clip}\!\left(
      \min\left\{k:\sum_{r=1}^{k}p_{(r)}\ge\rho\right\},K_{\min},L
    \right)
  \]
  \begin{itemize}
    \item Sort importance scores; retain enough positions to cover mass $\rho$.
    \item Gather $L'_t$ hidden states and project them to $\Kmem_t,\Vmem_t$.
    \item A straight-through estimator trains the scorer through the dense distribution.
  \end{itemize}
  \begin{block}{The key distinction}
    Top-$\rho$ controls probability mass, not a fixed fraction of tokens.
  \end{block}
  \papersource{Paper, Sec. 3.3, PDF pp. 8--9. Layer indices omitted.}
\end{frame}

\begin{frame}{The linear update exposes the storage trade-off}
  \[
    \M_{t+1}=\lambda\M_t+
    \frac{1-\lambda}{L'_t\sqrt{d_k}}\,\Kmem_t^\top\Vmem_t
  \]
  \[
    \Sstate_{t+1}=\lambda\Sstate_t+
    \frac{1-\lambda}{L'_t\sqrt{d_k}}\,\Kmem_t^\top\mathbf 1
  \]
  \begin{itemize}
    \item $\M_t\in\mathbb R^{d_k\times d_v}$ stores key--value associations;
          $\Sstate_t\in\mathbb R^{d_k}$ tracks normalization.
    \item Fixed state size; old and new associations share the same matrix.
    \item Global decay alone does not implement selective semantic forgetting.
  \end{itemize}
  \small\alert{Final Metis uses Gated Delta Update (GDU).}
  The paper does not expand its complete recurrence.
  \papersource{Paper, Eqs. (2)--(3), Sec. 3.3, PDF p. 9; Appendix C, pp. 35--36.}
\end{frame}

\begin{frame}{A separate query learns how to use historical state}
  \[
    \Qmem_t=\Hmem_t\tilde{\mathbf W}_Q,\qquad
    \tilde{\mathbf A}_t=
      \diag(\Qmem_t\Sstate_t)^{-1}\Qmem_t\M_t
  \]
  \[
    \mathbf A_t=\gamma\,\mathbf A_{\rm current}
                 +(1-\gamma)\norm(\tilde{\mathbf A}_t)
  \]
  \begin{itemize}
    \item Learned $\tilde{\mathbf W}_Q$ can suppress irrelevant historical keys.
    \item Query--key normalization controls the readout denominator.
    \item Output normalization aligns the scale of the two branches.
  \end{itemize}
  \small Implementation adds a unit vector to the denominator for stability;
  the displayed paper equation omits it.
  \papersource{Paper, Eqs. (4)--(5), PDF p. 9. Current-step attention is retained.}
\end{frame}

\begin{frame}{Supervision teaches operations and their side effects}
  \begin{columns}[T,onlytextwidth]
    \column{0.51\textwidth}
    \textbf{Primary: 357,137 samples}
    \begin{itemize}
      \item Remember: fact $\to$ query.
      \item Update: old $\to$ new $\to$ query.
      \item Forget: fact $\to$ revoke $\to$ query.
      \item Reflect: facts $\to$ composed answer.
    \end{itemize}
    \small 27 source benchmarks; 406.1M tokens.\\
    Explicit, implicit, and distractor variants.
    \column{0.45\textwidth}
    \textbf{Auxiliary: 609,443 samples}
    \begin{itemize}
      \item Bind similar facts to different entities.
      \item Forget one fact while retaining another.
      \item Return to ordinary conversation.
      \item Ignore memory when irrelevant.
    \end{itemize}
  \end{columns}
  \papersource{Paper, Sec. 4, Tables 1--4, PDF pp. 13--16.
  Reflect means composition of stored facts in these tasks.}
\end{frame}

\begin{frame}{Three objectives share the same answer likelihood}
  \[
    \ell(s,t)=-\frac1{|Y_t|}\sum_k
       \log P(y_{t,k}\mid X_t,Y_{t,<k};\theta_t)
  \]
  \[
    \mathcal L=\sum_{\tau}\pi_\tau(e)\,
    \mathbb E_{s\sim\mathcal D_\tau}
       \left[\sum_{t\in\mathcal Q_s}\ell(s,t)\right]
  \]
  \begin{itemize}
    \item \textbf{Reconstruction:} recover the earlier passage from state.
    \item \textbf{Operations:} answer according to the revised memory.
    \item \textbf{Regularization:} avoid interference and memory pollution.
  \end{itemize}
  \small Five data subsets; annealed sampling weights $\pi_\tau(e)$.
  Only selected answer steps are directly supervised.
  \papersource{Paper, Sec. 5, Eqs. (12)--(17), PDF pp. 16--18.}
\end{frame}

\begin{frame}{No context means no history replay at query time}
  \begin{center}
  \begin{tabular}{p{2.7cm}p{8.9cm}}
    \toprule
    Setting & Historical information available to the query \\
    \midrule
    Full Context & All evidence text supplied by the benchmark setting \\
    Partial Context & DenseRAG top-5 sentence chunks \\
    No Context & State or adapted weights after an information phase \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Each instance resets state, ingests evidence, then answers questions.
    \item MemOps Gold supplies oracle turns; LoCoMo Gold supplies evidence sessions.
    \item Main scores: per-example median of 3 judge calls, then micro-average.
  \end{itemize}
  \papersource{Paper, Sec. 6.1 and Appendices E--F, PDF pp. 18--19, 37--40.
  Judge: gpt-4.1-mini; scores allow partial credit.}
\end{frame}

\begin{frame}{Memory-only gains leave a large full-context gap}
  \begin{center}
  \small
  \begin{tabular}{lrrrr}
    \toprule
    Method & MemOps & Metis Test & LoCoMo & NextMem \\
    \midrule
    Qwen3.5-4B, no history & 1.65 & 16.96 & 0.18 & 11.86 \\
    Temp-LoRA-4B & 8.85 & 19.34 & 9.99 & 24.20 \\
    $\delta$-Mem & 4.38 & 15.03 & 10.79 & 20.42 \\
    \textbf{Metis-4B} & \textbf{17.84} & \textbf{56.72} & \textbf{16.31} & \textbf{41.69} \\
    \textbf{Metis-27B} & \textbf{24.76} & \textbf{73.77} & \textbf{26.74} & \textbf{50.82} \\
    \midrule
    Qwen3.5-27B, full context & 87.90 & 78.87 & 65.03 & 78.80 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Metis is strongest on the four main averages within the no-context group.
    \item Exact evidence remains much more effective on external memory tasks.
  \end{itemize}
  \papersource{Paper, Tables 5--6, PDF pp. 19--20. MemOps and LoCoMo use Gold;
  scores on a 0--100 scale. $\delta$-Mem uses a different Qwen3-4B backbone.}
\end{frame}

\begin{frame}{Forgetting remains hard outside the synthetic test}
  \begin{columns}[T,onlytextwidth]
    \column{0.47\textwidth}
    \begin{block}{Metis-27B: Forget score}
      \large Metis Test: \textbf{77.50}\\[2mm]
      MemOps Gold: \textbf{10.91}\\[2mm]
      MemOps Full: \textbf{3.86}
    \end{block}
    \column{0.49\textwidth}
    \textbf{A Metis-4B timing failure}
    \begin{enumerate}
      \item Store Alice's food preference.
      \item Ask the model to forget it.
      \item The immediate reply repeats it.
      \item A later query receives no answer.
    \end{enumerate}
  \end{columns}
  \medskip
  \small Operation-step responses and subsequent memory behavior are
  separate targets for controllability.
  \papersource{Paper, Table 5, p. 19; Table 12, p. 35; Fig. 5 and Sec. 6.9, p. 26.
  Case sequence paraphrased.}
\end{frame}

\begin{frame}{Token selection is the largest measured contributor}
  \begin{center}
  \begin{tabular}{lrr}
    \toprule
    Metis-4B variant & Overall & Relative change \\
    \midrule
    Full model & 33.14 & -- \\
    No auxiliary data (MS+MP) & 26.74 & $-19.31\%$ \\
    Linear update instead of GDU & 32.95 & $-0.58\%$ \\
    Last token instead of adaptive selection & 12.93 & $-60.98\%$ \\
    Reuse original query & 29.09 & $-12.23\%$ \\
    No query--key normalization & 23.72 & $-28.44\%$ \\
    \bottomrule
  \end{tabular}
  \end{center}
  \small Accurate input selection and controlled memory readout matter more
  than the update-rule change in this 4B aggregate.
  \papersource{Paper, Table 7, PDF p. 22. Overall: equal-weight mean of four benchmarks.
  Changes are relative percentages, not percentage points.}
\end{frame}

\begin{frame}{Transfer is strong on ATM and mixed on MemDaily}
  \begin{center}
  \begin{tabular}{lrr}
    \toprule
    Method & ATM-Bench Gold & MemDaily Gold \\
    \midrule
    Temp-LoRA-4B / Metis-4B & 2.57 / \textbf{10.22} & 44.92 / \textbf{52.54} \\
    Temp-LoRA-9B / Metis-9B & 2.86 / \textbf{16.49} & \textbf{51.42} / 47.29 \\
    Temp-LoRA-27B / Metis-27B & 2.57 / \textbf{18.56} & \textbf{59.45} / 59.04 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Neither benchmark was used for training-data construction.
    \item ATM number questions use exact match; MemDaily uses single-choice accuracy.
    \item Removing LoCoMo/LongMemEval training sources reduces the six-benchmark
          mean by 0.76--2.69 points across scales.
  \end{itemize}
  \papersource{Paper, Tables 8--9, PDF pp. 22--23. All methods query without context replay.
  ATM mixes Jaccard, exact match, and judge scores.}
\end{frame}

\begin{frame}{Capacity degrades with both longer writes and history}
  \begin{center}
    \includegraphics[width=0.98\linewidth,height=0.54\textheight,keepaspectratio]
      {figures/fig-03-capacity.pdf}
  \end{center}
  \small
  Left: reset and write all facts once. Right: accumulate state across writes.\\
  Solid: Metis-4B; dashed: full context. Earlier facts weaken; newer facts also fluctuate.
  \papersource{Paper, Fig. 3, p. 23; protocol, pp. 23--24. Left axis counts words.
  Right Group Count labels do not align with 40 facts grouped by 5;
  interpret the trend, not an exact update threshold.}
\end{frame}

\begin{frame}{Activating irrelevant memory hurts instruction following}
  \begin{center}
  \begin{tabular}{lrrr}
    \toprule
    Active stage & Qwen3.5-4B & Metis-4B & Gap (pp) \\
    \midrule
    MMLU-Pro & 46.00 & 40.90 & $-5.10$ \\
    IFEval (strict) & 76.71 & 54.53 & \alert{$-22.18$} \\
    GSM8K & 84.53 & 78.92 & $-5.61$ \\
    MMMLU & 59.90 & 56.60 & $-3.30$ \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Empty-state scores are close to the original backbone.
    \item Active stage: store one fixed task-irrelevant evaluation message;
          the backbone sees the same message in its prompt.
    \item Frozen weights do not prevent activation-level interference.
  \end{itemize}
  \papersource{Paper, Table 10, p. 24; exact active-stage protocol, Appendix F.4, p. 40.}
\end{frame}

\begin{frame}{Rank 64 preserves short-task scores at one-eighth storage}
  \begin{columns}[c,onlytextwidth]
    \column{0.59\textwidth}
    \includegraphics[width=\linewidth,height=0.50\textheight,keepaspectratio]
      {figures/fig-04-lowrank.pdf}
    \column{0.37\textwidth}
    \textbf{Metis-4B}\\[2mm]
    Full score: 33.14\\
    Rank-64 score: 33.10\\
    Recovery: 99.9\%\\[3mm]
    Full state: 16.79 MB\\
    Rank 64: 2.11 MB
  \end{columns}
  \medskip
  \[
    \hat{\M}=\mathbf U_{:,1:k}\boldsymbol{\Sigma}_{1:k,1:k}\mathbf V_{:,1:k}^\top
  \]
  \small Store the factors, then reconstruct before use.
  This is a persistence result, not an eightfold compute speedup.
  \papersource{Paper, Fig. 4 / Table 11, p. 25; storage measurements, Appendix G.3, p. 43.}
\end{frame}

\begin{frame}{Cold-start latency improves modestly over full context}
  \begin{center}
  \begin{tabular}{lrrr}
    \toprule
    4B method & Mean E2E (s) & P95 E2E (s) & Mean query (s) \\
    \midrule
    Full Context & 0.607 & 3.012 & 0.607 \\
    RAG top-5 & 0.268 & 0.456 & 0.223 \\
    Temp-LoRA & 1.567 & 3.292 & 0.305 \\
    $\delta$-Mem & 0.884 & 1.600 & 0.656 \\
    Metis & 0.562 & 0.926 & 0.360 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Metis vs.\ Full Context: mean $-7.4\%$, P95 $-69.3\%$.
    \item RAG is fastest among history-using methods in this protocol.
    \item Natural stopping yields unequal output lengths: Metis 8.3 tokens,
          Full Context 5.7 on average.
  \end{itemize}
  \papersource{Paper, Appendix G.1, Table 16, p. 41.
  1,527 LoCoMo Gold instances; state reset and evidence processing included in E2E.}
\end{frame}

\begin{frame}{Long-history speedups include a real ingestion cost}
  \begin{center}
    \includegraphics[width=0.99\linewidth,height=0.54\textheight,keepaspectratio]
      {figures/fig-07-latency.pdf}
  \end{center}
  \small
  First measured E2E crossover: \textbf{64K}. At 128K: \textbf{1.497$\times$}
  and \textbf{1.595$\times$} faster than Full Context for 32/128 outputs.\\
  Most ingestion time is backbone encoding; the query path stays nearly flat.
  \papersource{Paper, Figs. 7--8, pp. 42--43. Single A800, batch 1, fixed outputs.
  Generation-only timing: no answer-quality scoring in this sweep.}
\end{frame}

\begin{frame}{Users share weights and carry compact separate states}
  \begin{columns}[T,onlytextwidth]
    \column{0.48\textwidth}
    \textbf{Memory-as-Adapter}
    \begin{itemize}
      \item Share frozen model and memory parameters.
      \item Swap each user's state from storage.
      \item Stack equal-shape states along the batch dimension.
      \item Use batched matrix multiplication for readout.
    \end{itemize}
    \column{0.48\textwidth}
    \textbf{Measured operating points}
    \begin{itemize}
      \item At 32K: Full Context 1,118.86 MB/session; Metis 16.79 MB.
      \item $B=8$: TTFT 88--91 ms with prebuilt states.
      \item $B=64$: 1,585.6 decode tokens/s; 30\% latency overhead vs.\ raw backbone.
    \end{itemize}
  \end{columns}
  \papersource{Paper, Appendix G.3--G.4, pp. 43--46.
  Single-node static batches; serving state writes are performed in advance.}
\end{frame}

\begin{frame}{A useful memory primitive with three open bottlenecks}
  \begin{enumerate}
    \item \textbf{Capacity:} fixed state avoids growing caches, but long writes
      and repeated updates lose information.
    \medskip
    \item \textbf{Control:} semantic operations emerge, but external forgetting
      and active-state instruction following remain weak.
    \medskip
    \item \textbf{Evaluation:} short-task quality and long-history throughput
      should be tested jointly on persistent, interleaved interactions.
  \end{enumerate}
  \begin{block}{Discussion takeaway}
    Native memory is a promising learned component for future hybrid memory systems.
  \end{block}
  \papersource{Synthesis of Secs. 6 and 8 and Appendix G, PDF pp. 18--28, 40--46.
  Joint evaluation is a reader-proposed direction.}
\end{frame}

\begin{frame}{Paper and discussion sources}
  \textbf{Zeyu Zhang et al.}\\
  \emph{Metis: Memory Foundation Model}\\
  arXiv:2607.26760v2, revised 4 August 2026.
  \medskip
  \begin{itemize}
    \item \href{https://arxiv.org/abs/2607.26760v2}{Versioned arXiv record}
    \item \href{https://arxiv.org/pdf/2607.26760v2}{Paper PDF}
    \item \href{https://github.com/MemTensor/Metis}{Project link supplied in the paper}
    \item \href{https://huggingface.co/collections/IAAR-Shanghai/metis}{Model collection supplied in the paper}
  \end{itemize}
  \medskip
  \small Source locators refer to 1-based PDF pages. Reused figures are author
  figures; numerical tables select and reorganize the reported results.
  \medskip
  \par\alert{Backup slides: derivation, datasets, supplementary results, serving.}
\end{frame}

\appendix

\begin{frame}{Backup: virtual-prefix attention motivates the state}
  Exact attention over current tokens and a virtual memory prefix can be split:
  \[
    \mathbf A=\boldsymbol{\Lambda}_{\rm cur}\mathbf A_{\rm cur}
      +(\mathbf I-\boldsymbol{\Lambda}_{\rm cur})\mathbf A_{\rm prefix}.
  \]
  \begin{itemize}
    \item $\boldsymbol{\Lambda}_{\rm cur}$ depends on each query's softmax partition masses.
    \item Replace the query-dependent matrix by a global mixture weight $\gamma$.
    \item Replace the exponential similarity kernel with a dot product.
  \end{itemize}
  \[
    \mathbf A_{\rm prefix}\ \leadsto\
    \diag\!\left(\mathbf Q\mathbf K^\top\mathbf 1/\sqrt{d_k}\right)^{-1}
    \mathbf Q\left(\mathbf K^\top\mathbf V/\sqrt{d_k}\right)
  \]
  \small These are architectural approximations.
  The kernel replacement is not the first-order expansion $1+z$ of $\exp(z)$.
  \papersource{Paper, Sec. 3.4, PDF pp. 9--11.
  No uniform softmax-approximation bound is given.}
\end{frame}

\begin{frame}{Backup: LU mixes value interference and normalization}
  \small Let $D_c$ and $\mathbf R_c$ be the target step's denominator and
  numerator contributions; $D_o,R_o$ collect other steps.
  \normalsize
  \[
  \begin{aligned}
    \tilde{\mathbf A}
      &=(D_c+D_o)^{-1}(\mathbf R_c+R_o)\\
      &\approx D_c^{-1}\mathbf R_c
        +\underbrace{D_c^{-1}R_o}_{\text{value interference}}\\
      &\quad-\underbrace{D_c^{-1}D_oD_c^{-1}\mathbf R_c}_{\text{target dilution}}
        -\underbrace{D_c^{-1}D_oD_c^{-1}R_o}_{\text{cross term}}.
  \end{aligned}
  \]
  \begin{itemize}
    \item Expansion requires invertible $D_c$ and small $D_c^{-1}D_o$.
    \item Independent memory queries can reduce off-target similarities.
    \item Many individually small off-target terms can still accumulate.
  \end{itemize}
  \papersource{Paper, Sec. 3.5, PDF pp. 11--13. $D_c,D_o,R_o$ are teaching shorthand.
  This analysis uses LU, not the final GDU recurrence.}
\end{frame}

\begin{frame}{Backup: data scale and training progress differ}
  \begin{center}
  \begin{tabular}{lrr}
    \toprule
    Primary operation & Samples & Tokens (M) \\
    \midrule
    Remember & 56,855 & 362.0 \\
    Forget & 136,271 & 21.7 \\
    Update & 81,501 & 11.0 \\
    Reflect & 82,510 & 11.4 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Remember contributes about 89.1\% of primary tokens.
    \item 4B: 14K steps / 1 epoch; 27B: 14K / about 0.4 epoch.
    \item 9B: validation-based early stopping at 8K / about 0.5728 epoch.
    \item AdamW, learning rate $2\cdot10^{-4}$, BF16, $8\times$H100; backbone frozen.
  \end{itemize}
  \papersource{Paper, Table 2, p. 15; training configuration, Sec. 6.1, p. 19.
  A further 609,443 auxiliary samples support interference control.}
\end{frame}

\begin{frame}{Backup: MemOps Full is harder for native memory}
  \begin{center}
  \begin{tabular}{lrrr}
    \toprule
    No-context method & 4B & 9B & 27B \\
    \midrule
    Temp-LoRA & 9.98 & 12.19 & 10.83 \\
    Metis & 9.70 & 11.53 & 15.35 \\
    \midrule
    Full-context Qwen3.5 reference & 83.52 & 85.69 & 87.19 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Full evidence: three complete segments, 24 utterances.
    \item Metis-4B and 9B do not beat matching Temp-LoRA averages here.
    \item Metis-27B leads the no-context average, with strong reflection
          but weak forgetting.
  \end{itemize}
  \papersource{Paper, Appendix B, Table 12, PDF pp. 34--35.
  Micro-averaged judge scores, 0--100 scale.}
\end{frame}

\begin{frame}{Backup: GDU and LU favor different tasks}
  \begin{center}
  \begin{tabular}{llrrr}
    \toprule
    Scale & Update & LoCoMo Gold & Metis Test & Overall \\
    \midrule
    4B & GDU / LU & 16.31 / 11.97 & 56.72 / 58.54 & 33.14 / 32.95 \\
    9B & GDU / LU & 16.81 / 15.37 & 57.92 / 68.66 & 34.44 / 35.59 \\
    27B & GDU / LU & 26.74 / 14.16 & 73.77 / 75.32 & 44.02 / 41.50 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item GDU leads on LoCoMo at every scale; LU leads on the synthetic test.
    \item 9B comparison also changes training duration: GDU 8K, LU 14K steps.
    \item Under LU, removing MS slightly improves Overall (32.95 to 33.67);
          removing all auxiliary data lowers it to 28.85.
  \end{itemize}
  \papersource{Paper, Appendix C, Tables 13--14, PDF pp. 35--36.
  Overall is the equal-weight mean of four benchmarks.}
\end{frame}

\begin{frame}{Backup: removing sources redistributes performance}
  \begin{center}
  \begin{tabular}{lrrrr}
    \toprule
    Scale & Six-bench mean & Change & LoCoMo change & NextMem change \\
    \midrule
    4B & 30.90 & $-1.66$ & $-3.13$ & $-4.39$ \\
    9B & 32.83 & $-0.76$ & $-1.09$ & $-1.85$ \\
    27B & 39.59 & $-2.69$ & $-5.59$ & $+2.49$ \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Exclude all instances synthesized from LoCoMo and LongMemEval.
    \item About 2.61\% of instances are removed, concentrated in selected task slices.
    \item Overall capability largely survives; individual tasks move differently.
    \item Entity coverage and supervision mixture both change.
  \end{itemize}
  \papersource{Paper, Sec. 6.5, Table 9, PDF pp. 22--23.
  Changes are score points; the six-benchmark mean includes the two OOD benchmarks.}
\end{frame}

\begin{frame}{Backup: the architecture transfers across backbones}
  \begin{center}
  \begin{tabular}{lrrr}
    \toprule
    Backbone & No history & Metis & Full Context \\
    \midrule
    Llama3.1-8B & 10.69 & 36.03 & 70.61 \\
    Gemma4-12B & 8.36 & 37.68 & 77.30 \\
    Gemma4-31B & 5.40 & 33.44 & 78.18 \\
    Llama3.1-70B & 12.71 & 39.29 & 75.06 \\
    \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Each backbone receives memory-specific mid-training; checkpoint at 14K steps.
    \item Every tested family benefits from the internal memory state.
    \item Scaling is non-monotonic under the shared training recipe.
  \end{itemize}
  \papersource{Paper, Appendix D, Table 15, PDF pp. 36--37.
  Equal-weight average over the four main benchmarks.}
\end{frame}

\begin{frame}{Backup: persistence cost is fixed, but quality also differs}
  \begin{center}
    \includegraphics[width=0.76\linewidth,height=0.61\textheight,keepaspectratio]
      {figures/fig-09-storage.pdf}
  \end{center}
  \small At 32K: Full Context / Metis Full / Metis rank 64 =
  1,118.86 / 16.79 / 2.11 MB. $\delta$-Mem is much smaller at 4.6 KB.
  \papersource{Paper, Fig. 9 and Appendix G.3, PDF pp. 43--44.
  Runtime per-session storage, not total model or peak inference memory.
  The paper's 128K storage ratios are extrapolations.}
\end{frame}

\begin{frame}{Backup: prebuilt states make the serving path flat}
  \begin{center}
    \includegraphics[width=0.99\linewidth,height=0.47\textheight,keepaspectratio]
      {figures/fig-10-serving.pdf}
  \end{center}
  \begin{itemize}
    \item Batch 8; 128 output tokens/user; 1K--64K historical tokens/user.
    \item Metis includes loading and state injection, but history writes are prebuilt.
    \item Full Context includes both resident-KV and no-cache variants;
          both run out of memory at 64K in this batch.
  \end{itemize}
  \papersource{Paper, Fig. 10 and Appendix G.4, PDF pp. 44--46.
  Synthetic, single-node, static-batch workload; medians over five runs.}
\end{frame}

\begin{frame}{Backup: memory adds overhead while preserving batching}
  \begin{center}
    \includegraphics[width=0.99\linewidth,height=0.49\textheight,keepaspectratio]
      {figures/fig-11-overhead.pdf}
  \end{center}
  \small
  Relative to the raw backbone with identical prompts:
  about 14\% latency overhead through $B=8$, 30\% at $B=64$.\\[1mm]
  Continuous batching and interleaved read/write consistency remain future systems work.
  \papersource{Paper, Fig. 11 and Appendix G.4, PDF pp. 45--46.
  Throughput is aggregate decode throughput; state loading/re-stacking is counted.}
\end{frame}

\end{document}