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\title[PartRep]{PARTREP: Learning What to Repeat\\for Decoder-only LLMs}
\subtitle{A learned selector for selective prompt repetition}
\author{Research group reading\\[2mm]
  \small Paper authors: Andikawati P Widjaja, Yongjun Kim,\\
  \small Hyounghun Kim, and Jaeho Lee}
\date{\small arXiv:2607.01792v1 \enspace|\enspace 2 July 2026\\
  Reading prepared: 29 September 2026}
\hypersetup{pdftitle={PartRep: Research Group Reading},
  pdfauthor={Paper reading presentation},
  pdfsubject={Analysis of arXiv:2607.01792v1}}
\begin{document}

\begin{frame}
  \titlepage
  \vspace{-3mm}
  \begin{center}
    \color{AcademicTeal}\small
    Keep the original prompt; learn which tokens deserve a second appearance.
  \end{center}
\end{frame}

\begin{frame}{The main result is a quality--cost trade-off}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{0.49\textwidth}
      \begin{block}{Qwen2.5-3B: seven-task average}
        \centering
        \begin{tabular}{lr}
          No repetition & 66.9\%\\
          Full repetition & 68.5\%\\
          \textbf{PartRep} & \textbf{68.3\%}
        \end{tabular}
      \end{block}
    \end{column}
    \begin{column}{0.47\textwidth}
      \begin{block}{Relative to full repetition}
        \centering
        {\Large 59.5\%}\quad KV tokens\\[2mm]
        {\Large 79.0\%}\quad prefill FLOPs
      \end{block}
    \end{column}
  \end{columns}
  \bigskip
  \begin{itemize}
    \item Select only a fraction of the prompt, using a learned gate.
    \item The original prompt is retained in full.
    \item Savings are measured against \alert{full repetition}; cost still rises
      relative to no repetition.
  \end{itemize}
  \papersource{Paper, Table 1, PDF p.6; $\tau=0.15$. Ratios recomputed from the displayed table.
  The abstract reports 59.4\% KV, a small unexplained discrepancy.}
\end{frame}

\begin{frame}{A late copy can read the entire original prompt}
  \begin{columns}[c,onlytextwidth]
    \begin{column}{0.60\textwidth}
      \includegraphics[width=\linewidth,height=4.1cm,keepaspectratio]{figures/fig-01.pdf}
    \end{column}
    \begin{column}{0.36\textwidth}
      \begin{itemize}
        \item Early tokens cannot see later context.
        \item A repeated token has a new, later representation.
        \item That copy can attend to all of the first prompt.
      \end{itemize}
    \end{column}
  \end{columns}
  \medskip
  \begin{block}{Mechanistic intuition}
    Repetition creates additional information paths under the same causal mask.
    It does not retroactively update the original prefix.
  \end{block}
  \papersource{Paper, Sections 1 and 3, PDF pp.1--3; original Figure 1.
  Figure arrows are conceptual, not per-task guarantees.}
\end{frame}

\begin{frame}{Choose a subsequence under an explicit budget}
  Let $\mathbf t=(t_1,\ldots,t_L)$ be the original prompt.
  \[
    \mathbf t_{\rm FR}=\mathbf t\oplus\mathbf t,
    \qquad
    \mathbf t_{\rm PR}=\mathbf t\oplus f(\mathbf t).
  \]
  \[
    \max_f\ \operatorname{acc}\bigl(\mathbf t\oplus f(\mathbf t)\bigr)
    \quad\text{subject to}\quad |f(\mathbf t)|\leq\tau L.
  \]
  \begin{itemize}
    \item $f(\mathbf t)$ is an \alert{order-preserving subsequence}.
    \item Default short-task budget: $\tau=0.15$.
    \item The selector adds information cues; it does not remove original input.
  \end{itemize}
  \begin{block}{A different objective from cache eviction}
    A token can be valuable to retain but provide little benefit when repeated.
    Evicting after a full repeat also retains the longer prefill cost.
  \end{block}
  \papersource{Paper, Equations (2)--(5), Section 3, PDF p.3; Section 3.1, p.4.
  Connector and window expansion are omitted from this idealized length constraint.}
\end{frame}

\begin{frame}{Select during prefill, then append the chosen tokens}
  \centering
  \includegraphics[width=\linewidth,height=3.8cm,keepaspectratio]{figures/fig-02.pdf}
  \medskip
  \begin{enumerate}
    \item Extract original-prompt hidden states at layer $l^\star$.
    \item Score positions and select the top-$\tau$ fraction.
    \item Append selected tokens; reuse prefix computation and finish prefill.
  \end{enumerate}
  \papersource{Paper, original Figure 2, PDF p.4; Sections 4.2 and 4.4, pp.5--6.
  Qwen layer-choice ablation selects layer 18.}
\end{frame}

\begin{frame}{High NLL supplies labels for what to repeat}
  \[
    \operatorname{NLL}(t_i)=-\log P(t_i\mid t_{<i}).
  \]
  \begin{itemize}
    \item High NLL: the target model finds a token hard to predict from its prefix.
    \item Training positives: positions in the highest-NLL $\tau$ fraction
      of each sequence.
    \item At inference, a small gate predicts membership in that group.
  \end{itemize}
  \begin{block}{What this signal does and does not establish}
    Surprisal is an empirical proxy for repetition value.
    It is not a direct estimate of a token's causal effect on answer accuracy.
  \end{block}
  \papersource{Paper, Equations (6)--(8), Section 4.1, PDF pp.4--5.
  Top-$\tau$ means the upper tail; the paper's $\tau$-quantile wording is ambiguous.}
\end{frame}

\begin{frame}{The gate reads learned prototypes, one token at a time}
  \[
    \mathbf q=W_2\,\operatorname{SiLU}(W_1\mathbf h),\qquad
    p=g(\mathbf h)=\sigma\!\left[
    \mathbf v^\top\operatorname{Softmax}
    \!\left(\frac{\mathbf qK^\top}{\sqrt{d_h}}\right)\right].
  \]
  \begin{columns}[T,onlytextwidth]
    \begin{column}{0.50\textwidth}
      \begin{itemize}
        \item $\mathbf h\in\mathbb R^d$: base-model hidden state.
        \item $W_1$: $d\to 2d_h$.
        \item $W_2$: $2d_h\to d_h$.
        \item $d_h=64$.
      \end{itemize}
    \end{column}
    \begin{column}{0.46\textwidth}
      \begin{itemize}
        \item $K\in\mathbb R^{s\times d_h}$: learned keys.
        \item $\mathbf v\in\mathbb R^s$: learned values.
        \item $s=64$ by default.
        \item $p$: one score per input position.
      \end{itemize}
    \end{column}
  \end{columns}
  \medskip
  \alert{No additional $L\times L$ input self-attention in the gate.}
  \papersource{Paper, Equations (9)--(11), PDF p.5; Table 7, p.13.
  Query orientation follows the paper's row-vector attention notation.}
\end{frame}

\begin{frame}{Train the gate; keep the base language model frozen}
  \[
    \ell(\mathbf t)=\frac{1}{L}\sum_{j=1}^{L}
        \lambda_j\,\ell_{\rm CE}(p_j,y_j),
    \qquad
    \lambda_j=
    \begin{cases}
      (1-\tau)/\tau,&y_j=1,\\
      1,&y_j=0.
    \end{cases}
  \]
  \begin{itemize}
    \item Store hidden-state/NLL pairs offline; derive binary labels for $\tau$.
    \item 3M training tokens: 2M FineWeb-Edu + 1M Ultra-FineWeb-Edu.
    \item Sequence lengths: 10--1024 tokens.
    \item Adam, learning rate $10^{-3}$, batch size 4096, 25 epochs;
      cosine schedule and early stopping with patience 5.
  \end{itemize}
  \begin{block}{Cost is shifted offline}
    Each target LLM needs its own gate. No cross-model zero-shot transfer is shown.
  \end{block}
  \papersource{Paper, Equations (12)--(15), PDF pp.5--6; Appendix A.1, p.11;
  Limitations, p.9. Validation split and batch unit are not specified.}
\end{frame}

\begin{frame}{The final repeated span depends on formatting and windows}
  \begin{block}{Online input construction}
    Original prompt + connector + selected tokens in original order
    + any required answer formatting.
  \end{block}
  \begin{itemize}
    \item Default connector: \textit{Pay attention to these key tokens:}
    \item Optional expansion restores a whole word or neighboring words.
    \item Fragmented subwords and missing local relations motivate expansion.
    \item Causal prefix computation can be reused when prefix positions stay fixed.
  \end{itemize}
  \[
    N=L+m+w+c,\qquad m\leq\tau L,
  \]
  where $w$ counts extra window tokens and $c$ counts connector/formatting tokens.
  \papersource{Paper, Section 4.4, PDF p.6; Appendix C.3, p.13.
  Length decomposition is a reader explanation.
  Detailed cache scheduling and post-expansion budget rules are not reported.}
\end{frame}

\begin{frame}{The evidence spans different experimental settings}
  \centering
  \begin{tabular}{lll}
    \toprule
    Experiment & Model(s) & Setting\\
    \midrule
    Seven-task main result & Qwen2.5-3B & $\tau=0.15$\\
    Cross-model MMLU & Qwen, Llama, Gemma & Three model families\\
    RULER & Qwen2.5-3B & $\tau=0.3$ + windows\\
    Window ablation & Llama3.2-3B & ARC-Challenge\\
    Other ablations & Qwen2.5-3B & ARC-Challenge\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item Accuracy $\uparrow$; stored prompt KV tokens $\downarrow$;
      reported prefill FLOPs $\downarrow$.
    \item Greedy decoding, one run, bfloat16; no error bars.
    \item RULER: 100 examples per subtask, 1300 total.
    \item Eight benchmarks across the study; not every model on every benchmark.
  \end{itemize}
  \papersource{Paper, Section 5.1, PDF pp.6--7; Sections 5.3--6.1, pp.7--8;
  Appendix A.2, p.11. Model names: Qwen2.5-3B Instruct, Llama3.2-3B Instruct,
  Gemma4-E4B it.}
\end{frame}

\begin{frame}{PartRep approaches full-repeat quality at lower cost}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Method & Avg.\ accuracy & KV tokens & Prefill FLOPs\\
    \midrule
    No repetition & 66.9 & 235.5 & 1.549 T\\
    Append model summary & 67.9 & 277.4 & 3.676 T\\
    Append LLMLingua summary & 67.4 & 277.4 & 2.105 T\\
    Full repetition & 68.5 & 471.1 & 3.140 T\\
    \textbf{PartRep} & \textbf{68.3} & \textbf{280.4} & \textbf{2.481 T}\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item $+1.4$ percentage points over no repetition.
    \item $-0.2$ percentage points versus full repetition.
    \item More accurate than appended LLMLingua, but also more compute.
    \item About 87.5\% of the full-repeat gain, using rounded reported means.
  \end{itemize}
  \papersource{Reorganized from paper, Table 1, PDF p.6.
  Qwen2.5-3B, seven benchmarks, $\tau=0.15$.
  T = $10^{12}$ FLOPs; derived gain fraction is descriptive, not a confidence estimate.}
\end{frame}

\begin{frame}{The average hides meaningful task-level differences}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Benchmark & No repetition & Full repetition & PartRep\\
    \midrule
    ARC-Challenge & 79.8 & 82.8 & 81.4\\
    OpenBookQA & 76.6 & 78.0 & 77.8\\
    MMLU & 62.5 & 60.3 & \alert{63.2}\\
    MedQA & 47.5 & 51.0 & 50.3\\
    SciQ & 90.3 & 92.9 & 92.2\\
    MMLU-Pro & 27.8 & 27.3 & \alert{27.8}\\
    GSM8K & 84.2 & 87.3 & 85.5\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item PartRep improves six tasks over no repetition; one is tied.
    \item It exceeds full repetition on two tasks and trails on five.
    \item Full repetition itself can hurt: MMLU and MMLU-Pro.
  \end{itemize}
  \papersource{Reorganized from paper, Table 1, PDF p.6; accuracy in percent.
  Claims of universal task-wise superiority would overstate these data.}
\end{frame}

\begin{frame}{Separate ideal attention scaling from reported total FLOPs}
  Ignoring selection, formatting and expansion:
  \[
    \frac{M_{\rm PR}}{M_{\rm FR}}\approx\frac{1+\tau}{2},
    \qquad
    \frac{F_{\rm attn,PR}}{F_{\rm attn,FR}}
      \approx\frac{(1+\tau)^2}{4}.
  \]
  \centering
  \begin{tabular}{lrr}
    \toprule
    At $\tau=0.15$ & KV ratio & Compute ratio\\
    \midrule
    Ideal length-based calculation & 57.5\% & 33.1\% (attention only)\\
    Table 1: PartRep / full repeat & 59.5\% & 79.0\% (total prefill)\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item Total compute also includes linear layers and method overhead.
    \item Versus no repetition: KV $+19.1\%$, prefill FLOPs $+60.2\%$.
    \item FLOPs and KV token counts are not latency and peak GPU memory.
  \end{itemize}
  \papersource{Paper, Section 3, PDF p.3; Table 1, p.6. Ratios derived from displayed values.
  Abstract KV claim: 59.4\%; table recomputation: 59.52\%.}
\end{frame}

\begin{frame}{MMLU improves over vanilla across three model families}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Method & Qwen2.5-3B & Llama3.2-3B & Gemma4-E4B\\
    \midrule
    No repetition & 62.5 & 54.1 & 74.0\\
    Full repetition & 60.3 & \alert{54.8} & 72.9\\
    Append LLMLingua & 61.0 & 53.5 & \alert{76.1}\\
    PartRep & \alert{63.2} & 54.3 & 75.8\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item Gains over vanilla: $+0.7$, $+0.2$, $+1.8$ percentage points.
    \item PartRep is not the best method in every model column.
    \item Gemma features must come from a global-attention layer.
    \item Each model has its own trained gate; this is not gate transfer.
  \end{itemize}
  \papersource{Reorganized from paper, Table 2 and Section 5.3, PDF p.7.
  Gemma extraction restriction: Section 5.1, p.6; no exact Gemma layer number given.
  Single-run differences have no reported uncertainty.}
\end{frame}

\begin{frame}{RULER gains use a larger budget and local windows}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Method & 4k & 8k & 16k\\
    \midrule
    No repetition & 77.7 & 80.0 & 72.3\\
    Full repetition & 79.2 & 82.3 & 72.3\\
    LLMLingua & 69.2 & 73.1 & 63.5\\
    \textbf{PartRep} & \textbf{80.0} & \textbf{83.8} & \textbf{73.2}\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{block}{Qwen2.5-3B: $\tau=0.3$ + local-context expansion}
    Gains over full repetition: $+0.8$, $+1.5$, $+0.9$ percentage points.
  \end{block}
  \begin{itemize}
    \item Actual post-expansion cache size and FLOPs are not in this table.
    \item Do not transfer the short-task cost ratios to these results.
    \item The advantage over full repetition is not monotonic in length.
  \end{itemize}
  \papersource{Reorganized from paper, Table 3 and Section 5.4, PDF pp.7--8.
  LLMLingua label follows Table 3; its precise variant is not clarified there.}
\end{frame}

\begin{frame}{High NLL is useful, but does not win at every budget}
  \begin{columns}[c,onlytextwidth]
    \begin{column}{0.70\textwidth}
      \includegraphics[width=\linewidth,height=5.7cm,keepaspectratio]{figures/fig-04.png}
    \end{column}
    \begin{column}{0.27\textwidth}
      \begin{itemize}
        \item Highest NLL generally beats low NLL and random.
        \item Attention is higher at 15\% and 90\%.
        \item This compares scoring signals, not just learned-gate quality.
      \end{itemize}
    \end{column}
  \end{columns}
  \papersource{Paper, original Figure 4, Appendix B.1, PDF p.11.
  Qwen2.5-3B on ARC-Challenge. Curves are single-run results without uncertainty.}
\end{frame}

\begin{frame}{Window expansion repairs cues at an additional token cost}
  \centering
  \begin{tabular}{lrr}
    \toprule
    Expansion & ARC accuracy (\%) & KV tokens\\
    \midrule
    No windowing & 61.5 & 90.1\\
    Complete the word & 64.6 & 94.5\\
    Add one neighboring word on each side & 66.0 & 110.2\\
    \bottomrule
  \end{tabular}
  \bigskip
  \begin{block}{Llama3.2-3B on ARC-Challenge}
    The widest tested window adds 4.5 percentage points and about 22.3\% KV tokens
    relative to no expansion.
  \end{block}
  \begin{itemize}
    \item Lexical integrity and local relations matter.
    \item The selection ratio alone does not determine the final budget.
  \end{itemize}
  \papersource{Reorganized from paper, Table 5, Section 6.1, PDF p.8.
  KV growth is derived from displayed values. This experiment uses Llama, not Qwen.}
\end{frame}

\begin{frame}{The connector is part of the intervention}
  \centering
  \begin{tabular}{lr}
    \toprule
    Connector style & ARC accuracy (\%)\\
    \midrule
    Natural-language cue (default) & \textbf{81.4}\\
    ChatML & 70.6\\
    Natural language + ChatML & 79.5\\
    Raw concatenation & 79.4\\
    XML & 71.6\\
    Technical natural-language cue & 80.9\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item The default cue exceeds raw concatenation by 2.0 percentage points.
    \item Benefits cannot be attributed to token selection alone.
    \item Wrapper effects may depend on model/template interpretation;
      the cause is not isolated.
  \end{itemize}
  \papersource{Values from the labels in paper Figure 7, Appendix B.4, PDF p.12;
  templates in Table 6, p.11. Qwen2.5-3B on ARC-Challenge.}
\end{frame}

\begin{frame}{Estimated prefill cost stays below full repetition}
  \begin{columns}[c,onlytextwidth]
    \begin{column}{0.70\textwidth}
      \includegraphics[width=\linewidth,height=5.7cm,keepaspectratio]{figures/fig-03b.pdf}
    \end{column}
    \begin{column}{0.27\textwidth}
      \begin{itemize}
        \item Dense attention remains $O(L^2)$.
        \item KV remains $O(L)$ at fixed $\tau$ (panel a).
        \item FLOP savings do not establish speedups.
      \end{itemize}
    \end{column}
  \end{columns}
  \papersource{Paper, Figure 3(b), Section 6.2, PDF p.8; author vector panel,
  all axes and legends retained. P = $10^{15}$ FLOPs.
  Panel (a), reproduced in the reading notes, gives the KV scaling comparison.}
\end{frame}

\begin{frame}{The deployment case needs several missing measurements}
  \begin{itemize}
    \item \textbf{Per-model training:} a new target LLM requires a new gate.
    \item \textbf{Statistical scope:} single runs; small gains lack uncertainty.
    \item \textbf{System evidence:} no full-method TTFT, throughput, or peak-memory
      comparison with a common backend.
    \item \textbf{Reproducibility:} cache scheduling, expanded budgets, prompt
      protocols, and exact FLOP accounting are incompletely specified.
    \item \textbf{Generalization:} long real-world documents, larger models,
      and multimodal tokens remain open.
  \end{itemize}
  \begin{block}{A focused follow-up}
    Fix the final appended-token budget and connector, then compare selectors
    on both accuracy and measured end-to-end cost.
  \end{block}
  \papersource{Authors' limitations: PDF p.9. Evaluation protocol: Appendix A, p.11.
  Remaining points and proposed follow-up are reader analysis.}
\end{frame}

\begin{frame}{A compact second look is promising under the tested conditions}
  \begin{enumerate}
    \item \textbf{Core idea:} learn which input tokens benefit from another
      late-context representation.
    \medskip
    \item \textbf{Engineering choice:} distill high-NLL membership into a small
      gate using intermediate hidden states.
    \medskip
    \item \textbf{Observed trade-off:} near full-repeat average accuracy with
      fewer cached tokens and lower reported prefill FLOPs.
    \medskip
    \item \textbf{Qualification:} task, model, connector and window settings
      change the outcome; runtime benefits still need direct validation.
  \end{enumerate}
  \papersource{Synthesis of paper Sections 4--6, PDF pp.4--8, and Appendices A--B, pp.11--13.
  This presentation analyzes the paper; it does not report an independent reproduction.}
\end{frame}

\begin{frame}{Primary source and reading scope}
  \textbf{Andikawati P Widjaja, Yongjun Kim, Hyounghun Kim, Jaeho Lee.}\\[2mm]
  \textit{PARTREP: Learning What to Repeat for Decoder-only LLMs.}\\[2mm]
  arXiv:2607.01792v1, submitted 2 July 2026.\\[2mm]
  \href{https://arxiv.org/abs/2607.01792v1}{arxiv.org/abs/2607.01792v1}
  \bigskip
  \begin{itemize}
    \item Read the author TeX, all substantive sections and Appendices A--E.
    \item Checked equations, seven figures and seven tables against the 15-page PDF.
    \item Original figures are reused; reorganized tables retain source locators.
    \item Ratios and implementation cautions are explicitly marked as reader analysis.
  \end{itemize}
  \papersource{Materials retrieved 29 September 2026.
  Main talk: slides 1--22, approximately 20--30 minutes.
  Remaining slides provide optional discussion details.}
\end{frame}

\appendix

\begin{frame}{Backup: deeper features do not monotonically improve accuracy}
  \begin{columns}[c,onlytextwidth]
    \begin{column}{0.70\textwidth}
      \includegraphics[width=\linewidth,height=5.25cm,keepaspectratio]{figures/fig-05.png}
    \end{column}
    \begin{column}{0.27\textwidth}
      \begin{itemize}
        \item Layers 18 and 30 both reach about 81.4\%.
        \item Layer 18 has lower latency.
        \item Timing scope is not fully specified.
      \end{itemize}
    \end{column}
  \end{columns}
  \papersource{Paper, original Figure 5, Appendix B.2, PDF p.12.
  Qwen2.5-3B on ARC-Challenge; this does not establish a universal layer choice.}
\end{frame}

\begin{frame}{Backup: increasing the repetition budget can reduce accuracy}
  \begin{columns}[c,onlytextwidth]
    \begin{column}{0.70\textwidth}
      \includegraphics[width=\linewidth,height=5.25cm,keepaspectratio]{figures/fig-06.png}
    \end{column}
    \begin{column}{0.27\textwidth}
      \begin{itemize}
        \item Default: $\tau=0.15$.
        \item Accuracy is non-monotonic.
        \item The 64--69-token right-axis accounting is not explained.
      \end{itemize}
    \end{column}
  \end{columns}
  \papersource{Paper, original Figure 6, Appendix B.3, PDF p.12.
  Qwen2.5-3B on ARC-Challenge. Author explanation about cue dilution is a hypothesis.}
\end{frame}

\begin{frame}{Backup: a small gate is a reasonable tested operating point}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{0.57\textwidth}
      \textbf{Architecture}\\[2mm]
      \begin{tabular}{lrr}
        \toprule
        Gate & Acc.\ (\%) & FLOPs\\
        \midrule
        Linear & 80.7 & 270.6 k\\
        Two-layer MLP & 81.4 & 549.0 k\\
        Transformer & 81.3 & 654.3 k\\
        \bottomrule
      \end{tabular}
    \end{column}
    \begin{column}{0.40\textwidth}
      \textbf{Learnable keys}\\[2mm]
      \begin{tabular}{rrr}
        \toprule
        $s$ & Acc.\ (\%) & FLOPs\\
        \midrule
        32 & 80.1 & 544.8 k\\
        64 & 81.4 & 549.0 k\\
        128 & 80.6 & 557.3 k\\
        \bottomrule
      \end{tabular}
    \end{column}
  \end{columns}
  \bigskip
  \begin{itemize}
    \item The reported two-layer configuration includes learned-key attention.
    \item Larger gates do not improve these single-run results.
    \item Gate FLOP normalization is unspecified; do not directly divide
      these values by the main-table request cost.
  \end{itemize}
  \papersource{Reorganized from paper, Table 4, PDF p.8, and Table 7, p.13.
  Qwen2.5-3B on ARC-Challenge. No repetition: 79.8\%.}
\end{frame}

\begin{frame}{Backup: eviction saves cache after paying for a full repeat}
  \centering
  \begin{tabular}{lrrr}
    \toprule
    Method & Avg.\ acc.\ (\%) & KV tokens & Prefill FLOPs\\
    \midrule
    Full repetition & 68.5 & 471.1 & 3.140 T\\
    + Echo eviction & 64.4 & 235.5 & 3.152 T\\
    + H2O eviction & 62.9 & 270.8 & 3.162 T\\
    LLMLingua compression & 14.9 & 78.6 & 1.130 T\\
    PartRep & 68.3 & 280.4 & 2.481 T\\
    \bottomrule
  \end{tabular}
  \medskip
  \begin{itemize}
    \item Echo removes first-copy KV; H2O retains selected heavy hitters.
    \item LLMLingua compression feeds only the compressed repeated input.
    \item Its poor score is specific to this setup, not a general verdict.
    \item Echo/H2O use manual KV decoding; other methods use vLLM.
  \end{itemize}
  \papersource{Reorganized from paper, Table 1, PDF p.6;
  Appendix A.2, p.11, and C.6--C.8, pp.13--14. Qwen2.5-3B, seven tasks.}
\end{frame}

\begin{frame}{Backup: notation does not supply an optimality theorem}
  The paper motivates selection using
  \[
    \max_f H(f(\mathbf t)\mid\mathbf t).
  \]
  \begin{itemize}
    \item For ordinary random variables and deterministic $f$,
      $H(f(X)\mid X)=0$.
    \item The paper acknowledges this and uses a model-based information notion.
    \item It gives no approximation guarantee linking NLL ranking to accuracy.
    \item The selector notation $f$ alternates between scores and a subsequence.
  \end{itemize}
  \begin{block}{Useful operational interpretation}
    Frozen hidden states $\to$ per-position scores $\to$ top-$k$ positions
    $\to$ restore order $\to$ optionally expand $\to$ append.
  \end{block}
  \papersource{Paper, Equations (4), (7)--(9), PDF pp.3--5, especially the footnote on p.5.
  Operational decomposition and caution are reader analysis.}
\end{frame}

\end{document}