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\newcommand{\LA}{\mathrm{LA}}
\newcommand{\SWA}{\mathrm{SWA}}
\newcommand{\AVG}{\mathrm{AVG}}
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\title[Component imbalance]{Untangling Component Imbalance in\\Hybrid Linear Attention\\Conversion Methods}
\subtitle{HedgeCATs, SSD, and the meaning of successful conversion}
\author{Research paper discussion}
\date{arXiv:2510.05901v2 \;|\; 15 October 2026}

\begin{document}

% Main talk: frames 1--21, approximately 25 minutes.
\begin{frame}
  \titlepage
  \vspace{-5mm}
  {\small Paper authors: Martin Benfeghoul, Teresa Delgado, Adnan Oomerjee,\\
  Haitham Bou-Ammar, Jun Wang, and Zafeirios Fountas.}
  \papersource{Huawei Noah's Ark Lab and University College London. Paper revised 10 October 2025.}
\end{frame}

\begin{frame}[t]{A high hybrid score can hide a failed linear branch}
  \begin{block}{The central question}
    After converting a pretrained Transformer, does linear attention
    actually contribute to the model's performance?
  \end{block}
  \par\medskip
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Mistral-7B & Hybrid & SWA only & LA only \\
    \midrule
    Six-task average (\%) & 65.48 & \alert{65.56} & 34.78 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Removing LA slightly improves the reported average.
    \item Removing all attention gives 34.40: close to LA only.
    \item Overall recovery and component usefulness need separate tests.
  \end{itemize}
  \vfill
  \papersource{Paper, Sec. 3.2 and Table 1, PDF pp. 4--5. Mistral results use the authors' implementation.}
\end{frame}

\begin{frame}[t]{LA compresses history; SWA retains local detail}
  \[
    \mathbf S_t=\sum_{i\le t}\phi(\mathbf k_i)\mathbf v_i^\top,
    \qquad \mathbf z_t=\sum_{i\le t}\phi(\mathbf k_i),
    \qquad \mathbf o_t^\LA=
    \frac{\phi(\mathbf q_t)^\top\mathbf S_t}{\phi(\mathbf q_t)^\top\mathbf z_t}
  \]
  \begin{itemize}
    \item $\phi:\mathbb R^d\to\mathbb R^{d'}$;
      $\mathbf S_t\in\mathbb R^{d'\times d_v}$ and $\mathbf z_t\in\mathbb R^{d'}$.
    \item Each new token adds one outer product and one vector.
  \end{itemize}
  \begin{block}{The hybrid studied here}
    Recent $w$ tokens $\longrightarrow$ SWA\quad;
    older tokens $\longrightarrow$ LA state
    \par\smallskip
    Hybrid output: $\mathbf o_t=\tfrac12\mathbf o_t^\SWA+\tfrac12\mathbf o_t^\LA$.
  \end{block}
  Fixed $w$ and feature size give linear sequence scaling. Equal
  coefficients do not imply equal functional contributions.
  \vfill
  \papersource{Paper, Eqs. (2)--(3), Sec. 3.1, PDF pp. 2--4. Causal form above is an explanatory rewrite.}
\end{frame}

\begin{frame}[t]{Feature capacity and transfer objective are separate choices}
  \[
    \phi(\mathbf x)=
    [\,\sigma(\mathbf W_\phi^\top\mathbf x+\mathbf b)
    \oplus\sigma(-\mathbf W_\phi^\top\mathbf x-\mathbf b)\,]
  \]
  \par\medskip
  \centering
  \begin{tabular}{lll}
    \toprule
    Projection & $\mathbf W_\phi$ shape & Output dimension \\
    \midrule
    Square & $h_d\times h_d$ & $d'=2h_d$ \\
    Rectangular & $h_d\times(h_d/2)$ & $d'=h_d$ \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Positive and negative projections preserve both directional responses.
    \item Default activation: softmax over feature coordinates.
    \item RoPE is applied before $\phi$; smaller $d'$ also reduces state size.
  \end{itemize}
  \vfill
  \papersource{Paper, Eq. (4), Secs. 3.1 and 3.4.2, PDF pp. 3--4 and 6. $h_d$: query/key head dimension.}
\end{frame}

\begin{frame}[t]{The hybrid loss can let SWA carry the approximation}
  With teacher weights $A^\mathrm{soft}$ and output $O^\mathrm{soft}$:
  \begin{align*}
    \mathcal L_\mathrm{weights}
      &= -\sum_{t,i\le t} A^\mathrm{soft}_{ti}\log A^\phi_{ti}
      &&\text{LA weights} \\
    \mathcal L_\mathrm{LA-out}
      &= \|O^\mathrm{soft}-O^\LA\|_F^2
      &&\text{LA output} \\
    \mathcal L_\mathrm{hybrid-out}
      &= \|O^\mathrm{soft}-[gO^\SWA+(1-g)O^\LA]\|_F^2
      &&\text{joint output}
  \end{align*}
  \begin{itemize}
    \item The first two objectives require LA to perform the approximation.
    \item The third supervises only the combined result.
    \item Weight transfer materializes pairwise weights; a linear student
      output still does not remove the softmax teacher's quadratic work.
  \end{itemize}
  \vfill
  \papersource{Paper, Sec. 3.4.1, PDF p. 6. Equations organize the stated objectives; averaging factors omitted.}
\end{frame}

\begin{frame}[t]{The experiments isolate conversion under a small data budget}
  \begin{columns}[T,onlytextwidth]
    \column{0.49\textwidth}
    \begin{block}{Models and training}
      \begin{itemize}
        \item Mistral-7B, Llama3-8B, Llama3.1-8B: instruction-tuned models.
        \item FineWeb-Edu; 1,024-token samples; about 25M tokens/epoch.
        \item Transfer: 1 epoch.
        \item LoRA: 1--5 epochs; $r=8$, $\alpha=16$ on $Q,K,V,O$ projections.
      \end{itemize}
    \end{block}
    \column{0.48\textwidth}
    \begin{block}{Evaluation}
      \begin{itemize}
        \item Zero-shot PIQA, ARC-E, ARC-C, HellaSwag, WinoGrande, MMLU.
        \item ARC-C and HellaSwag: normalized accuracy.
        \item AVG: equal mean of six task accuracies.
        \item Recovery: converted AVG divided by original AVG.
      \end{itemize}
    \end{block}
  \end{columns}
  \vfill
  \papersource{Paper, Sec. 3.1, PDF p. 4. Default $g=0.5$, SWA window 64; LA excludes the local window.}
\end{frame}

\begin{frame}[t]{SWA carries most of the LoLCATs-style hybrid performance}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Active attention & Mistral-7B & Llama3-8B & Llama3.1-8B$^*$ \\
    \midrule
    Original model & 68.26 & 71.32 & 73.01 \\
    Hybrid & 65.48 & 67.55 & 71.08 \\
    SWA only & \alert{65.56} & 66.08 & \alert{71.45} \\
    LA only & 34.78 & 33.55 & 33.96 \\
    No attention & 34.40 & 34.17 & 33.93 \\
    \midrule
    Hybrid $-$ SWA only (pp) & $-0.08$ & $+1.47$ & $-0.37$ \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item LA alone is close to the no-attention control in all three cases.
    \item Llama3 retains a positive LA contribution; complete bypass is not universal.
  \end{itemize}
  \vfill
  \papersource{Paper, Table 1, PDF p. 5. Accuracy in \%; differences calculated from reported AVG.}
  \papersource{$^*$Official LoLCATs checkpoints and code; the other two columns use the authors' implementation.}
\end{frame}

\begin{frame}[t]{Pure LA works better for Mistral than for the Llama models}
  \centering
  \includegraphics[width=0.97\linewidth,height=0.49\textheight,keepaspectratio]{figures/fig-01-la-only.pdf}
  \begin{itemize}
    \item Mistral: 46.94 after weight transfer $\to$ 50.75 after 2 LoRA epochs.
    \item Llama3: 34.59 $\to$ 36.05; Llama3.1: 34.82 $\to$ 39.36.
    \item LoRA is not intrinsically incompatible with LA, but conversion
      difficulty depends strongly on the starting model.
  \end{itemize}
  \vfill
  \papersource{Paper, Fig. 1 and Sec. 3.3, PDF p. 5; Table 6, PDF p. 15. Original author figure.}
\end{frame}

\begin{frame}[t]{A larger map does not rescue hybrid-output transfer}
  Mistral-7B; evaluate LA only after one transfer epoch, without LoRA.
  \par\medskip
  \centering
  \begin{tabular}{lrr}
    \toprule
    Transfer target & $d'=2h_d$ & $d'=h_d$ \\
    \midrule
    Attention weights (CE) & 46.94 & 43.25 \\
    LA outputs (MSE) & \alert{47.23} & 42.60 \\
    Hybrid outputs (MSE) & 35.41 & 34.59 \\
    No attention & 34.40 & 34.40 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item At $d'=2h_d$, pure-output transfer beats hybrid transfer by 11.82 pp.
    \item Reducing capacity hurts both successful transfer objectives.
    \item Output MSE can work: the hybrid target is the critical distinction.
  \end{itemize}
  \vfill
  \papersource{Paper, Tables 2--3 and Secs. 3.4.1--3.4.2, PDF p. 6. AVG in \%; pp = percentage points.}
\end{frame}

\begin{frame}[t]{Exponential-family feature maps transfer more successfully}
  Mistral-7B; square projection; one weight-transfer epoch; LA-only evaluation.
  \par\medskip
  \centering
  \begin{tabular}{lrr}
    \toprule
    Activation & AVG (\%) & Above no attention (pp) \\
    \midrule
    Softmax & \alert{46.94} & 12.54 \\
    Exponential & 46.11 & 11.71 \\
    ReLU & 36.07 & 1.67 \\
    $1+\mathrm{ELU}$ & 35.12 & 0.72 \\
    None & 34.81 & 0.41 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  Softmax and exponential activations are close in this protocol;
  the alternatives are much closer to the no-attention score of 34.40.
  \vfill
  \papersource{Paper, Table 4 and Sec. 3.4.3, PDF p. 7. Differences calculated from reported AVG.}
\end{frame}

\begin{frame}[t]{Three interventions change when SWA can take over}
  \begin{block}{1. Inference-time hybrid}
    Train LA first; add SWA only at inference.\par
    No additional hybrid training is needed.
  \end{block}
  \begin{block}{2. HedgeCATs}
    LA weight transfer $\longrightarrow$ brief hybrid LoRA.\par
    Early stopping limits the drift back toward SWA dependence.
  \end{block}
  \begin{block}{3. Scheduled Sliding-window Dropout (SSD)}
    Randomly suppress SWA during hybrid LoRA.\par
    The linear path must operate when the local branch is unavailable.
  \end{block}
  \vfill
  \papersource{Paper, Secs. 4.1--4.3, PDF pp. 7--8. ``Zero-shot hybrid'' still includes prior LA training.}
\end{frame}

\begin{frame}[t]{Adding SWA at inference reveals useful complementarity}
  After weight transfer, with no LoRA; default window 64.
  \par\medskip
  \centering
  \begin{tabular}{lrrrr}
    \toprule
    Model & LA only & Hybrid & Overlap & SWA only \\
    \midrule
    Mistral-7B & 46.94 & \alert{66.02} & 63.34 & 61.66 \\
    Llama3-8B & 34.59 & \alert{67.91} & 51.41 & 61.83 \\
    Llama3.1-8B & 34.82 & \alert{68.71} & 56.04 & 62.57 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Removing LA costs 4.36, 6.08, and 6.14 pp, respectively.
    \item Weak standalone LA can still complement SWA.
    \item Overlap hurts at fixed $g=0.5$; adaptive mixing is suggested as a remedy.
    \item Llama3.1 recovery is 94.11\%, below the paper's broad 95\% claim.
  \end{itemize}
  \vfill
  \papersource{Paper, Table 8, PDF p. 16; Sec. 4.1, PDF pp. 7--8. AVG in \%; recovery as reported for this row.}
\end{frame}

\begin{frame}[t]{HedgeCATs needs a short hybrid fine-tuning schedule}
  \centering
  \includegraphics[width=0.76\linewidth,height=0.55\textheight,keepaspectratio]{figures/fig-03-hedgecats.pdf}
  \begin{itemize}
    \item Best tested epoch: 1. AVG = 65.85 for Mistral, 68.99 for Llama3.
    \item LA ablation gap shrinks from 0.76 to 0.44 pp for Mistral,
      and from 2.97 to 1.72 pp for Llama3 (epochs 1 $\to$ 5).
  \end{itemize}
  \vfill
  \papersource{Paper, Fig. 3, PDF p. 8; Table 9, PDF p. 17. Original author figure; dashed lines are original models.}
\end{frame}

\begin{frame}[t]{SSD removes the local shortcut during training}
  \begin{block}{At epoch $k$}
    Drop the SWA branch with probability $p_k$ and use window $w_k$.
    Hold the last schedule value after the schedule ends.
  \end{block}
  \par\medskip
  \centering
  \begin{tabular}{lll}
    \toprule
    Experiment & Drop probability $p_k$ & Window $w_k$ \\
    \midrule
    Dropout schedule & $0.9\to0.75\to0.5$ & 32 \\
    Window schedule & 0.5 & $4\to8\to16\to32\to64$ \\
    Fixed setting & 0.5 & 16 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Heavy early dropout forces more training through LA.
    \item Mask granularity and branch rescaling are not fully specified;
      standard inverted-dropout scaling should not be assumed.
  \end{itemize}
  \vfill
  \papersource{Paper, Sec. 4.3, PDF p. 8. Tables 10--12, PDF pp. 17--18.}
\end{frame}

\begin{frame}[t]{Scheduled dropout sustains accuracy and a positive LA gap}
  \centering
  \includegraphics[width=0.76\linewidth,height=0.55\textheight,keepaspectratio]{figures/fig-04a-ssd-dropout.pdf}
  \begin{itemize}
    \item At 5 epochs: Mistral 66.30 vs. 64.04 SWA-only; Llama3 68.58 vs. 64.65.
    \item LA adds 2.26 and 3.93 pp, but the gaps still shrink with training.
    \item Setting: $p=0.9\to0.75\to0.5$, fixed window 32.
  \end{itemize}
  \vfill
  \papersource{Paper, Fig. 4a, PDF p. 9; Table 10, PDF p. 17. Original author figure; AVG accuracy in \%.}
\end{frame}

\begin{frame}[t]{Growing the window does not improve this conversion}
  \centering
  \begin{tabular}{llrrr}
    \toprule
    Model & SSD configuration & 1 epoch & 2 epochs & 5 epochs \\
    \midrule
    Mistral & Scheduled $p$, $w=32$ & 66.15 & 66.14 & 66.30 \\
            & Fixed $p=0.5$, $w=16$ & 64.34 & 65.99 & 64.97 \\
            & Fixed $p$, growing $w$ & 64.03 & 62.43 & \alert{61.42} \\
    \midrule
    Llama3 & Scheduled $p$, $w=32$ & 68.12 & 68.29 & 68.58 \\
           & Fixed $p=0.5$, $w=16$ & 68.18 & 68.03 & 68.45 \\
           & Fixed $p$, growing $w$ & 67.85 & 67.51 & 67.45 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Fixed dropout already works reasonably well.
    \item The experiments also change window size: they do not isolate
      the benefit of scheduling dropout at a matched window.
  \end{itemize}
  \vfill
  \papersource{Paper, Tables 10--12, PDF pp. 17--18. Hybrid AVG in \%. Growing $w$: 4, 8, 16, 32, 64.}
\end{frame}

\begin{frame}[t]{Average recovery hides a persistent MMLU deficit}
  Llama3-8B; SSD dropout schedule, window 32, 5 LoRA epochs.
  \par\medskip
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Task & Original model & SSD hybrid & SWA only \\
    \midrule
    PIQA & 78.13 & 78.13 & 77.48 \\
    ARC-Easy & 81.69 & 80.72 & 80.43 \\
    ARC-Challenge & 56.66 & 56.23 & 55.12 \\
    HellaSwag & 75.94 & 72.84 & 56.11 \\
    WinoGrande & 71.67 & 72.61 & 72.61 \\
    MMLU & 63.85 & \alert{50.97} & 46.16 \\
    \midrule
    AVG & 71.32 & 68.58 & 64.65 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  HellaSwag gains 16.73 pp from LA; MMLU still trails the original by 12.88 pp.
  \vfill
  \papersource{Paper, Table 10, PDF p. 17. Accuracy in \%; ARC-C and HellaSwag use normalized accuracy.}
\end{frame}

\begin{frame}[t]{Accuracy and LA dependence favor different choices}
  \centering
  \begin{tabular}{lrrrr}
    \toprule
    & \multicolumn{2}{c}{Mistral-7B} & \multicolumn{2}{c}{Llama3-8B} \\
    Method & AVG & $\gap$ & AVG & $\gap$ \\
    \midrule
    LoLCATs-style diagnostic & 65.48 & $-0.08$ & 67.55 & $+1.47$ \\
    Inference hybrid; no LoRA & 66.02 & $+4.36$ & 67.91 & $+6.08$ \\
    HedgeCATs; 1 epoch & 65.85 & $+0.76$ & 68.99 & $+2.97$ \\
    SSD; 5 epochs & 66.30 & $+2.26$ & 68.58 & $+3.93$ \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item $\gap=\AVG_\mathrm{hybrid}-\AVG_\mathrm{SWA-only}$, in percentage points.
    \item Inference hybrid: no joint training; largest gaps in these rows.
    \item HedgeCATs: highest selected Llama3 score with brief LoRA.
    \item SSD: longer adaptation, smaller window (32 vs. 64).
  \end{itemize}
  \vfill
  \papersource{Paper, Tables 1, 8--10, PDF pp. 5, 16--17. Selected settings, not a matched-budget ranking.}
\end{frame}

\begin{frame}[t]{The evidence supports useful components in specific settings}
  \begin{itemize}
    \item \textbf{Functional dependence:} removing LA tests its usefulness
      in a trained hybrid. A 50/50 coefficient does not establish equal contribution.
    \medskip
    \item \textbf{Context and efficiency:} six zero-shot tasks establish the
      reported accuracy effects; long-context retrieval, latency, and memory
      savings are not measured here.
    \medskip
    \item \textbf{Recovery depends on the setting:} Llama3.1 inference hybrid
      reaches 94.11\%; the growing-window SSD can be substantially worse.
    \medskip
    \item \textbf{Reporting conflicts matter:} some recovery ratios and prose
      trends disagree with the appendix. Use the explicit AVG rows for comparisons.
  \end{itemize}
  \vfill
  \papersource{Paper, Secs. 4--5, PDF pp. 7--10; Tables 8--12, PDF pp. 16--18. Specific conflicts in backup slide 26.}
\end{frame}

\begin{frame}[t]{Conversion needs accuracy and useful components}
  \begin{enumerate}
    \item \textbf{Diagnose the complete model.}\par
      Report hybrid, SWA-only, LA-only, and no-attention controls.
    \medskip
    \item \textbf{Give LA an independent learning signal.}\par
      Weight transfer and pure-LA output transfer both outperform
      hybrid-output transfer in the main diagnostic.
    \medskip
    \item \textbf{Control later competition between branches.}\par
      Delayed hybridization, early stopping, and branch dropout offer
      different accuracy, attribution, and budget trade-offs.
  \end{enumerate}
  \medskip
  \begin{block}{A concrete next experiment}
    Combine component ablations with distance-controlled retrieval and
    measured inference costs at matched training budgets.
  \end{block}
  \vfill
  \papersource{Synthesis of the paper's results; the proposed next experiment is this reading's analysis.}
\end{frame}

\begin{frame}[t]{Paper and presentation scope}
  \textbf{Untangling Component Imbalance in Hybrid Linear Attention Conversion Methods}
  \medskip

  Martin Benfeghoul, Teresa Delgado, Adnan Oomerjee, Haitham Bou-Ammar,
  Jun Wang, and Zafeirios Fountas.
  \medskip

  \href{https://arxiv.org/abs/2510.05901v2}{arXiv:2510.05901v2}, revised 10 October 2025.
  \medskip

  \begin{itemize}
    \item All experimental values come from this version of the paper.
    \item Figures retain the authors' original plots and legends.
    \item Tables select relevant rows; derived gaps are labeled in percentage points.
    \item Backup slides: mixing weights, additional model results,
      complete inference curves, fixed SSD, and reporting conflicts.
  \end{itemize}
  \vfill
  \papersource{Research discussion prepared 15 October 2026. The presentation author is not a paper author.}
\end{frame}

\appendix

\begin{frame}[t]{Backup: a fixed mixing coefficient is not a softmax partition}
  Partition the history into a recent window and older positions.
  If both branches were exact softmax:
  \[
    Z_{\rm near}=\sum_{i\in\mathcal W_t}e^{\mathbf q_t^\top\mathbf k_i/\sqrt d},
    \qquad
    Z_{\rm far}=\sum_{i\notin\mathcal W_t,\ i\le t}e^{\mathbf q_t^\top\mathbf k_i/\sqrt d}
  \]
  \[
    \mathbf o_t^{\rm full}
    =\alpha_t\mathbf o_t^{\rm near}+(1-\alpha_t)\mathbf o_t^{\rm far},
    \qquad \alpha_t=\frac{Z_{\rm near}}{Z_{\rm near}+Z_{\rm far}}.
  \]
  \begin{itemize}
    \item $\alpha_t$ depends on the query and history; it is generally not $0.5$.
    \item An overlapping LA branch sends recent tokens through both paths.
    \item This motivates adaptive mixing, but does not establish its benefit
      or eliminate LA approximation error.
  \end{itemize}
  \vfill
  \papersource{Explanatory derivation from softmax normalization; related to the authors' discussion in Sec. 4.1, PDF p. 7.}
\end{frame}

\begin{frame}[t]{Backup: pure-output transfer also helps the Llama models}
  After one transfer epoch; square projection; no LoRA; LA-only evaluation.
  \par\medskip
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Transfer target & Mistral-7B & Llama3-8B & Llama3.1-8B \\
    \midrule
    Weights & 46.94 & 34.59 & 34.82 \\
    LA outputs & 47.23 & \alert{38.22} & 35.45 \\
    Hybrid outputs & 35.41 & 33.86 & 33.87 \\
    No attention & 34.40 & 34.17 & 34.11 \\
    \bottomrule
  \end{tabular}\par
  \medskip
  \begin{itemize}
    \item Llama3 benefits more from pure-output than from weight transfer.
    \item LA conversion remains far below the original Llama model scores.
    \item HedgeCATs uses weight transfer, but the evidence does not make
      that objective uniformly best.
  \end{itemize}
  \vfill
  \papersource{Paper, Table 7, PDF p. 15. AVG accuracy in \%.}
\end{frame}

\begin{frame}[t]{Backup: no-LoRA hybridization is not uniformly the best row}
  \centering
  \includegraphics[width=0.98\linewidth,height=0.47\textheight,keepaspectratio]{figures/fig-02-inference-hybrid.pdf}
  \begin{itemize}
    \item Mistral hybrid: 66.02 $\to$ 65.48 $\to$ 64.99 as pure-LA LoRA proceeds.
    \item Table 8 lists Llama3 as 67.91 $\to$ 67.91 $\to$ 68.40,
      and Llama3.1 as 68.71 $\to$ 68.78 $\to$ 68.16.
    \item These rows do not support a universal ``best without fine-tuning''
      claim; the Llama3 repeated rows and ratios also warrant caution.
  \end{itemize}
  \vfill
  \papersource{Paper, Fig. 2, PDF p. 8; Table 8, PDF p. 16. Original author figure.}
\end{frame}

\begin{frame}[t]{Backup: fixed dropout already preserves a useful linear path}
  \centering
  \includegraphics[width=0.76\linewidth,height=0.55\textheight,keepaspectratio]{figures/fig-04c-ssd-fixed.pdf}
  \begin{itemize}
    \item Fixed $p=0.5$, $w=16$: Mistral peaks at epoch 2 (65.99).
    \item Llama3 reaches 68.45 at epoch 5 vs. 64.52 for SWA only.
    \item Scheduled dropout should be compared at the same window
      before attributing an improvement specifically to scheduling.
  \end{itemize}
  \vfill
  \papersource{Paper, Fig. 4c, PDF p. 9; Table 11, PDF p. 18. Original author figure.}
\end{frame}

\begin{frame}[t]{Backup: several reporting conflicts change the interpretation}
  \begin{itemize}
    \item \textbf{Inference hybrid, Table 8:}\par
      Llama3, 2 epochs: AVG 68.40 / original 71.32 implies about 95.91\%
      recovery; the table prints 95.27\%.
    \medskip
    \item \textbf{SSD, Table 10:}\par
      Llama3, 5 epochs: AVG 68.58 / 71.32 implies about 96.16\%;
      the table prints 95.97\%.
    \medskip
    \item \textbf{Window scheduling, Table 12 and Fig. 4b:}\par
      Llama3 hybrid falls 67.85 $\to$ 67.51 $\to$ 67.45.
      Sec. 4.3 describes a mild late recovery.
    \medskip
    \item These slides retain the reported AVG values and flag the conflicts;
      they do not infer corrected experimental measurements.
  \end{itemize}
  \vfill
  \papersource{Paper, Sec. 4.3, PDF p. 8; Fig. 4b, PDF p. 9; Tables 8, 10, 12, PDF pp. 16--18.}
\end{frame}

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