% Self-authored research discussion, based on arXiv:2606.04511v1.
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\title[SparDA]{SparDA}
\subtitle{Sparse Decoupled Attention for\\Efficient Long-Context LLM Inference}
\author{\texorpdfstring{Paper authors: Yaosheng Fu, Guangxuan Xiao, Xin Dong,\\Song Han, and Oreste Villa}{Paper authors: Yaosheng Fu, Guangxuan Xiao, Xin Dong, Song Han, and Oreste Villa}}
\date{Paper discussion \quad|\quad 20 October 2026\\
  \href{https://arxiv.org/abs/2606.04511v1}{arXiv:2606.04511v1 \quad (3 June 2026)}}

\begin{document}

\begin{frame}
  \titlepage
  \vspace{-5mm}
  \begin{center}
  \alert{Predict the next layer's KV accesses early enough to overlap transfer and compute.}
  \end{center}
\end{frame}

\begin{frame}{Sparse attention leaves two expensive dependencies}
  \begin{tabular}{lp{0.64\textwidth}}
    \toprule
    KV capacity & The historical cache still grows with context length.\\[2mm]
    CPU--GPU transfer & Offloaded blocks must arrive before attention can run.\\[2mm]
    Block selection & Each query still scores a growing compressed-key index.\\
    \bottomrule
  \end{tabular}
  \vspace{4mm}
  \[
    Q_l \longrightarrow \text{select blocks}
    \longrightarrow \text{fetch KV}
    \longrightarrow \text{attention}_l
  \]
  \begin{block}{The opportunity}
    Produce the memory-access decision before the layer needs its data.
  \end{block}
  \papersource{Paper, Secs. 1 and 3, PDF pp. 1--3.}
\end{frame}

\begin{frame}{InfLLM-V2 selects blocks through a compressed index}
  \[
    \mathcal B_l(i)=
    \mathcal B_{\mathrm{init}}\cup
    \mathcal B_{\mathrm{local}}(i)\cup
    \mathcal B_{\mathrm{topk}}(i)
  \]
  \begin{enumerate}
    \item Mean-pool keys: window $l_{C_1}=32$, stride $s_{C_1}=16$.
    \item Score with all $G$ query heads in each GQA group;\\
          softmax per head, then sum scores within the group.
    \item Max-pool scores to blocks, then select top-$k$.
  \end{enumerate}
  \vspace{3mm}
  \begin{block}{Two granularities}
    A compressed-key position is an index entry.\\
    A fetched KV block contains \alert{64 tokens} in these experiments.
  \end{block}
  \papersource{Paper, Sec. 3.1, Eqs. (1)--(2), PDF p. 3; App. C, pp. 13--14.}
\end{frame}

\begin{frame}{Forecast separates selection from attention}
  \centering
  \includegraphics[width=0.97\linewidth,height=0.73\textheight,keepaspectratio]
    {figures/fig-02-architecture.pdf}
  \papersource{Original Fig. 2, PDF p. 4. Left: baseline; middle: prefill; right: decode.}
\end{frame}

\begin{frame}{Layer $l$ predicts which history layer $l+1$ will read}
  \[
  (\mathbf Q_l,\mathbf K_l,\mathbf V_l,\mathbf F_l)=\phi_l(\mathbf X_l)
  \]
  \[
  \mathcal B_{l+1}=\mathcal B_{\mathrm{init}}\cup\mathcal B_{\mathrm{local}}
    \cup f_{\mathrm{top}}\!\left(\mathbf F_l
        \widetilde{\mathbf K}_{l+1}^{\top},k\right)
  \]
  \[
  \mathbf O_{l+1}=\Attn\!\left(
    \mathbf Q_{l+1},\mathbf K_{l+1}[\mathcal B_{l+1}],
    \mathbf V_{l+1}[\mathcal B_{l+1}]\right)
  \]
  \begin{itemize}
    \item Historical compressed keys for \emph{every layer} already reside on GPU.
    \item Initial/local blocks are excluded from dynamic selection;\\
          the next layer's new key is unnecessary for selecting distant blocks.
    \item Layer 0 uses a same-layer Forecast and keeps its KV on GPU.
  \end{itemize}
  \papersource{Paper, Eqs. (3)--(5), Sec. 4.1, PDF pp. 4--5; App. A, p. 13.}
\end{frame}

\begin{frame}{One Forecast head replaces $G$ selection heads}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
      \begin{block}{Original selector}
      $G$ query heads per KV head\\[2mm]
      Per-head softmax\\[2mm]
      Sum across query heads
      \end{block}
    \end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{Forecast selector}
      One Forecast head per KV head\\[2mm]
      Rank logits directly\\[2mm]
      Original attention heads retained
      \end{block}
    \end{column}
  \end{columns}
  \vspace{3mm}
  \[
  O(H_{\mathrm{kv}}G\,T N_b d_h)
  \;\longrightarrow\;
  O(H_{\mathrm{kv}}\,T N_b d_h),
  \qquad N_b\approx T/16
  \]
  \alert{Prefill selection retains a quadratic length term.}
  \papersource{Paper, Sec. 4.1, PDF p. 5. Complexity above is an explanatory derivation for scoring only.}
\end{frame}

\begin{frame}{Train Forecast to match the target layer's selector}
  \[
  \mathbf S_{l,m}^{\mathrm{tgt}}
    =\sum_{h=1}^{G}
      \sm\!\left(
      \mathbf Q_{l,m,h}
      (\widetilde{\mathbf K}_{l,m}^{\mathrm{tgt}})^\top/\tau
      \right)
  \]
  \[
  \mathbf S_{l,m}^{\mathrm{pred}}
    =\sm\!\left(
      \mathbf F_{l-1,m}
      (\widetilde{\mathbf K}_{l,m}^{\mathrm{pred}})^\top/\tau
      \right)
  \]
  \begin{itemize}
    \item Teacher: actual target-layer query heads; student: previous-layer Forecast.
    \item Apply causal masking and initial/local exclusion.
    \item Match aligned score grids using a partitioned KL objective.
    \item Only \alert{33.5M Forecast parameters} train; the 8B backbone is frozen.
  \end{itemize}
  \papersource{Paper, Sec. 4.2, Eq. (6), PDF pp. 5--6. $m$: GQA group; $\tau$: attention temperature.}
\end{frame}

\begin{frame}{A rest bucket preserves supervision outside top-$k$}
  \[
  \mathcal L_{\mathrm{KL}}=\sum_l
    \KL\!\left(\bar{\mathbf S}^{\mathrm{tgt}}_{l,\mathcal S}
    \,\middle\|\,\bar{\mathbf S}^{\mathrm{pred}}_{l,\mathcal S}\right)
  \]
  \begin{itemize}
    \item Teacher-selected positions define the same partition for both branches.
    \item Keep $k$ selected scores separately; merge all remaining scores.
    \item Normalize each resulting $(k+1)$-way distribution.
  \end{itemize}
  \vspace{3mm}
  \centering
  \begin{tabular}{lcc}
    \toprule
    Teaching example, $k=2$ & Full distribution & Partition\\
    \midrule
    Teacher & $(.40,.30,.20,.10)$ & $(.40,.30,.30)$\\
    Student & $(.35,.25,.15,.25)$ & $(.35,.25,.40)$\\
    \bottomrule
  \end{tabular}
  \vspace{2mm}
  \par\alert{Excess probability outside the selected set still incurs a loss.}
  \papersource{Paper, Eq. (7), PDF pp. 5--6. Numerical example is explanatory, not an experiment.}
\end{frame}

\begin{frame}{Fine-grained supervision improves a coarse indexer}
  \[
  \underbrace{\text{Teacher keys: }(2,1)}_{\text{window, stride}}
  \longrightarrow \text{fine scores}
  \longrightarrow \text{max-pool to the }(32,16)\text{ grid}
  \]
  \[
  \underbrace{\text{Student keys: }(32,16)}_{\text{same at training and inference}}
  \longrightarrow \text{student scores}
  \longrightarrow \text{partitioned KL}
  \]
  \centering
  \begin{tabular}{llrr}
    \toprule
    Model & Teacher window & RULER & Four-family Avg\\
    \midrule
    MiniCPM & $(32,16)\rightarrow(2,1)$ & $75.7\rightarrow78.7$ & $60.4\rightarrow61.7$\\
    NOSA & $(32,16)\rightarrow(2,1)$ & $71.4\rightarrow73.9$ & $50.1\rightarrow51.7$\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \par Strong local matches can survive before coarse key averaging blurs them.
  \papersource{Paper, Sec. 4.2, PDF p. 6; Table 6, p. 15. Higher scores are better.}
\end{frame}

\begin{frame}{A persistent UVA kernel turns lookahead into overlap}
  \begin{enumerate}
    \item Compute current $Q,K,V,F$; update the current cache.
    \item Forecast next-layer blocks; launch their prefetch on another stream.
    \item Wait for current-layer data only if the prior prefetch is incomplete.
    \item Run current attention and FFN while the next-layer transfer proceeds.
  \end{enumerate}
  \vspace{3mm}
  \begin{block}{The system tradeoff}
    Persistent CTAs read pinned CPU memory via UVA.\\
    More CTAs improve transfer throughput but consume compute resources.
  \end{block}
  \[
    t_{\mathrm{transfer}}+t_{\mathrm{compute}}
      \quad\rightsquigarrow\quad
    \max(t_{\mathrm{transfer}},t_{\mathrm{compute}})
  \]
  \papersource{Paper, Sec. 4.3, PDF p. 6; Algorithm 2, p. 13. Timing expression is an idealized overlap illustration.}
\end{frame}

\begin{frame}{Evaluation distinguishes accuracy, latency, and capacity}
  \begin{itemize}
    \item \textbf{Backbones:} MiniCPM4.1-8B and NOSA-8B; both use InfLLM-V2.\\
          NOSA additionally has a query-agnostic eviction head.
    \item \textbf{Accuracy:} HELMET, LongBench, RULER, and reasoning.\\
          Native contexts: 64K / 32K; RULER also extends to 128K.
    \item \textbf{Systems:} H100 80 GB / PCIe Gen5; A100 80 GB / Gen4.\\
          Both have 2 TB host memory; one warmup, two measured runs.
  \end{itemize}
  \begin{block}{Read the baseline labels carefully}
    $\dagger$: all KV on GPU. No $\dagger$: CPU offload.\\
    Decode comparisons at equal batch and at maximum feasible batch answer different questions.
  \end{block}
  \papersource{Paper, Sec. 5.1, PDF pp. 6--7; App. C, pp. 13--15.}
\end{frame}

\begin{frame}{Average quality is preserved, with task-level tradeoffs}
  \centering
  \begin{tabular}{llrrrrr}
    \toprule
    Model & Method & HELMET & LongBench & RULER & Reasoning & Avg\\
    \midrule
    MiniCPM & Sparse & 38.9 & 45.0 & 78.2 & 83.6 & 61.4\\
            & SparDA & 38.3 & 45.1 & 78.7 & 84.7 & \alert{61.7}\\
    \midrule
    NOSA & Sparse & 32.2 & 42.4 & 72.2 & 50.7 & 49.4\\
         & SparDA & 33.4 & 42.3 & 73.9 & 57.2 & \alert{51.7}\\
    \bottomrule
  \end{tabular}
  \vspace{4mm}
  \begin{itemize}
    \item Avg is the \textbf{unweighted mean of four benchmark families}.
    \item Dense averages remain higher: 63.5 / 52.4.
    \item InfiniGen averages: 57.7 / 45.6 under the block-sparse adaptation.
    \item MiniCPM loses 0.6 on HELMET; NOSA gains mostly on reasoning.
  \end{itemize}
  \papersource{Paper, Table 1, PDF p. 7. All scores: higher is better.}
\end{frame}

\begin{frame}{RULER improves at every tested length}
  \centering
  \begin{tabular}{llrrrr}
    \toprule
    Model & Method & 32K & 64K & 96K & 128K\\
    \midrule
    MiniCPM & Sparse & 86.1 & 78.2 & 68.7 & 67.7\\
            & SparDA & 87.6 & 78.7 & 70.8 & 68.8\\
            & Gain (pp) & +1.5 & +0.5 & +2.1 & +1.1\\
    \midrule
    NOSA & Sparse & 72.2 & 56.6 & 48.8 & 40.7\\
         & SparDA & 73.9 & 60.5 & 52.9 & 45.0\\
         & Gain (pp) & +1.7 & +3.9 & +4.1 & \alert{+4.3}\\
    \bottomrule
  \end{tabular}
  \vspace{4mm}
  \begin{itemize}
    \item NOSA's relative advantage grows while its absolute accuracy falls.
    \item LongRoPE factors (MiniCPM) or RoPE-base scaling (NOSA) enable extension.
    \item Positional extension is identical across methods within each model.
  \end{itemize}
  \papersource{Paper, Table 2, PDF p. 7; App. C, p. 14. pp = percentage points.}
\end{frame}

\begin{frame}{Selection savings appear in both inference phases}
  \centering
  \includegraphics[width=0.97\linewidth,height=0.60\textheight,keepaspectratio]
    {figures/fig-03-breakdown.pdf}
  \vspace{2mm}
  \begin{itemize}
    \item At 128K: up to $2.50\times$ faster prefill selection; over $2\times$ in decode.
    \item Similar sparse-attention cost \emph{between methods at the same length}.
    \item Near-flat decode latency reflects GPU underutilization in this regime.
  \end{itemize}
  \papersource{Original Fig. 3, PDF p. 8; discussion p. 7. MiniCPM, batch 4. Units: ms (left), $\mu$s (right).}
\end{frame}

\begin{frame}{Prefill gains grow with context length}
  \centering
  \setlength{\tabcolsep}{8pt}
  \begin{tabular}{llrr}
    \toprule
    Model & Method & 32K & 128K\\
    \midrule
    MiniCPM & Dense$^\dagger$ & 20388.3 & 8085.8\\
            & Sparse & 18548.4 & 13661.8\\
            & SparDA & 19845.6 & \alert{17087.6}\\
    \midrule
    NOSA & Dense$^\dagger$ & 20438.9 & 8118.0\\
         & Sparse & 12778.3 & 9805.2\\
         & SparDA & 13456.0 & \alert{11332.7}\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \begin{itemize}
    \item H100, batch 4, tokens/s. $\dagger$ means no offload.
    \item At 128K: \alert{$1.25\times$ / $1.16\times$} versus Sparse.
    \item Prefill benefits mainly from cheaper selection; KV writeback is asynchronous.
  \end{itemize}
  \papersource{Paper, Table 3 and Sec. 5.3, PDF p. 8.}
\end{frame}

\begin{frame}{At equal batch, decode reaches $1.69\times$ speedup}
  \centering
  \begin{tabular}{llrrrr}
    \toprule
    Model & Method & B4 & B8 & B16 & B64\\
    \midrule
    MiniCPM & Sparse & 167.8 & 279.5 & 447.9 & 788.9\\
            & SparDA & 240.2 & \alert{471.2} & 705.3 & 1000.1\\
    \midrule
    NOSA & Sparse & 173.2 & 285.4 & 529.2 & 1298.3\\
         & SparDA & 219.0 & \alert{399.3} & 735.0 & 1463.3\\
    \bottomrule
  \end{tabular}
  \vspace{4mm}
  \[
  \text{MiniCPM, B8: }\frac{471.2}{279.5}=1.69,
  \qquad
  \text{NOSA, B8: }\frac{399.3}{285.4}=1.40
  \]
  \begin{itemize}
    \item H100, 128K, tokens/s; both methods offload KV.
    \item NOSA already reduces fetch traffic, leaving less room for overlap.
  \end{itemize}
  \papersource{Paper, Table 4, PDF p. 9; interpretation in Sec. 5.3, pp. 8--9.}
\end{frame}

\begin{frame}{The $5.28\times$ result includes a larger feasible batch}
  \centering
  \setlength{\tabcolsep}{8pt}
  \begin{tabular}{lrr}
    \toprule
    MiniCPM, H100, 128K & Batch & Throughput (tokens/s)\\
    \midrule
    Dense$^\dagger$ & 4 & 108.6\\
    Sparse$^\dagger$ & 4 & 189.5\\
    SparDA & 64 & 1000.1\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \[
    \frac{1000.1\;(\mathrm{B64})}{189.5\;(\mathrm{B4})}
      =\alert{5.28\times}\quad\text{versus Sparse}^{\dagger}
  \]
  \begin{itemize}
    \item Resident baselines run out of memory at B8 and above at 128K.
    \item This measures serving throughput across different feasible batches.
    \item When memory suffices, resident Sparse can win:\\
      at 32K/B16, $1073.0$ versus SparDA's $918.5$ tokens/s.
  \end{itemize}
  \papersource{Paper, Table 4, PDF p. 9. $\dagger$: no offload. Ratios calculated from the table.}
\end{frame}

\begin{frame}{High-batch gains depend on asynchronous prefetch}
  \centering
  \begin{tabular}{llrrr}
    \toprule
    Model & Method & B4 & B16 & B64\\
    \midrule
    MiniCPM & Sparse & 167.8 & 447.9 & 788.9\\
            & Forecast, no prefetch & \alert{247.3} & 505.9 & 696.9\\
            & Full SparDA & 240.2 & \alert{705.3} & \alert{1000.1}\\
    \midrule
    NOSA & Sparse & 173.2 & 529.2 & 1298.3\\
         & Forecast, no prefetch & \alert{226.5} & 653.0 & 1063.8\\
         & Full SparDA & 219.0 & \alert{735.0} & \alert{1463.3}\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \begin{itemize}
    \item At B4, pipeline overhead slightly outweighs overlap.
    \item At B64, Forecast alone is slower than Sparse.
    \item Full prefetch adds 43.5\% / 37.6\% over the no-prefetch variant at B64.
  \end{itemize}
  \papersource{Paper, Table 10, PDF p. 16. H100, 128K; tokens/s.}
\end{frame}

\begin{frame}{Prefetch needs a batch-dependent share of the GPU}
  \centering
  \begin{tabular}{lrr}
    \toprule
    Persistent CTAs & B16 & B64\\
    \midrule
    16 & \alert{918.5} & 1255.9\\
    32 & 813.1 & 1328.0\\
    64 & 737.3 & \alert{1380.2}\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \begin{itemize}
    \item H100, MiniCPM, 32K; throughput in tokens/s.
    \item More transfer CTAs can slow attention/FFN by consuming SM resources.
    \item H100 heuristic: 16 CTAs below B32, otherwise 32.\\
          Within 4\% of the best swept choice at every tested batch.
    \item A100 switches from 16 to 32 CTAs at B64.
  \end{itemize}
  \papersource{Paper, Sec. 4.3, PDF p. 6; Table 7 and App. D, p. 15.}
\end{frame}

\begin{frame}{The same design also improves A100 throughput}
  \centering
  \setlength{\tabcolsep}{8pt}
  \begin{tabular}{llrrr}
    \toprule
    Model & Phase / batch & Sparse & SparDA & Ratio\\
    \midrule
    MiniCPM & Prefill / B4 & 6299.2 & 7756.8 & $1.23\times$\\
    NOSA & Prefill / B4 & 4717.1 & 5477.5 & $1.16\times$\\
    MiniCPM & Decode / B8 & 195.1 & 303.3 & $1.55\times$\\
    NOSA & Decode / B16 & 395.6 & 526.3 & $1.33\times$\\
    \bottomrule
  \end{tabular}
  \vspace{4mm}
  \begin{itemize}
    \item All rows: A100 80 GB, 128K context, tokens/s.
    \item Decode gains are smaller than the H100 maxima.
    \item GPU compute, HBM, and PCIe all differ between platforms;\\
          these measurements do not isolate PCIe generation alone.
  \end{itemize}
  \papersource{Paper, Tables 8--9, PDF pp. 15--16; hardware details p. 14. Last point: reader analysis.}
\end{frame}

\begin{frame}{Aggregate quality hides meaningful retrieval tradeoffs}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
      \begin{block}{MiniCPM: selected task changes}
        HELMET Recall: $67.8\rightarrow61.5$\\[2mm]
        HELMET Rerank: $14.7\rightarrow17.0$\\[2mm]
        RULER multi-key 3: $62.0\rightarrow56.0$\\[2mm]
        RULER QA 1: $64.0\rightarrow70.0$
      \end{block}
    \end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{NOSA: reasoning gains}
        MATH-500: $72.2\rightarrow71.6$\\[2mm]
        AIME 2024: $40.0\rightarrow46.7$\\[2mm]
        AIME 2025: $40.0\rightarrow53.3$\\[2mm]
        AIME has 30 problems per year.
      \end{block}
    \end{column}
  \end{columns}
  \vspace{3mm}
  AIME uses sampled generation; +13.3 percentage points is about four additional correct answers.
  \papersource{Paper, Tables 11, 13, 14, PDF pp. 17--18; evaluation protocol p. 14. Sparse $\rightarrow$ SparDA.}
\end{frame}

\begin{frame}{Early memory-access decisions are the central contribution}
  \begin{enumerate}
    \item \textbf{Represent:} a compact Forecast predicts next-layer block demand.
    \item \textbf{Teach:} fine-resolution supervision preserves useful selection quality.
    \item \textbf{Schedule:} persistent UVA prefetch converts lookahead into overlap.
  \end{enumerate}
  \begin{block}{Where the evidence applies}
    Two InfLLM-V2-based 8B models; benefits depend on context and batch.\\
    GPU memory still grows through compressed keys, layer-0 KV, and buffers.\\
    Token-level DSA/CSA and larger models are proposed extensions.
  \end{block}
  \vspace{2mm}
  \textbf{Discussion:} How far ahead should a model predict memory accesses before prediction error outweighs a longer overlap window?
  \papersource{Paper, Secs. 6--7, PDF pp. 9--10; App. C, pp. 14--15. Discussion question: reader analysis.}
  \papersource{Fu et al., SparDA. \href{https://arxiv.org/abs/2606.04511v1}{arXiv:2606.04511v1}.}
\end{frame}

\appendix

\begin{frame}{Backup: training is small in parameters, substantial in compute}
  \begin{tabular}{ll}
    \toprule
    Trainable parameters & 33.5M Forecast weights, 0.41\% of the 8B model\\
    Optimizer & AdamW; $\beta=(0.9,0.95)$, $\epsilon=10^{-6}$\\
    Schedule & Constant $5\times10^{-4}$; 2000 optimizer steps\\
    Batch / precision & Effective batch 32; BF16 mixed precision\\
    Regularization & Weight decay 0.01; gradient norm clipped to 0.5\\
    Data & ProLong-64K\\
    Hardware & 32 H100 GPUs\\
    \bottomrule
  \end{tabular}
  \vspace{3mm}
  \begin{itemize}
    \item Prose reports MiniCPM at 64K in $\leq$48 h; NOSA at 32K in $\leq$24 h.
    \item Table 5 lists 65,536 tokens without a model-specific distinction.\\
          \alert{NOSA's training length needs clarification for reproduction.}
  \end{itemize}
  \papersource{Paper, Sec. 4.2, PDF p. 5; App. B and Table 5, p. 13.}
\end{frame}

\begin{frame}{Backup: benchmark aggregation and generation protocols}
  \begin{itemize}
    \item \textbf{HELMET:} 7 categories, 100 samples each; greedy decoding.
    \item \textbf{LongBench:} 14 English tasks; greedy decoding.
    \item \textbf{RULER:} 13 tasks, 50 examples each; greedy decoding.
    \item \textbf{Reasoning:} 500 MATH problems and 30 problems per AIME year;\\
      sampled generation, GPT-5.2 judging.
  \end{itemize}
  \begin{block}{Reasoning differs across the two backbones}
    MiniCPM: thinking enabled, temperature 0.9, top-p 0.95, up to 64K output.\\
    NOSA: two-shot examples, temperature 1.0, top-p 1.0, up to 8K output.
  \end{block}
  Four-family Avg weights each family equally; reasoning Avg weights each dataset equally.
  \papersource{Paper, App. C, PDF p. 14; Tables 1 and 14, pp. 7 and 18.}
\end{frame}

\begin{frame}{Backup: cache reuse and the first layer affect system gains}
  \begin{itemize}
    \item NOSI caches blocks used in the previous decoding step.\\
      Transfer traffic comes from \alert{newly selected, missing blocks}.
    \item GPU retains compressed keys ($\approx1/16$ of full Key size),\\
      layer-0 KV, and working caches/buffers.
    \item At 96K, Sparse supports B128 while SparDA runs out of memory there;\\
      SparDA's B64 peak throughput still exceeds Sparse's B128 throughput.
    \item InfiniGen is adapted to block selection and performs CPU gather;\\
      its low throughput also reflects this implementation path.
  \end{itemize}
  \begin{block}{Capacity and scheduling remain coupled}
    A larger lookahead window may hide more transfer, but also needs earlier predictions and more buffering.
  \end{block}
  \papersource{Paper, Table 4, PDF p. 9; App. C, pp. 14--15. Final block: reader analysis.}
\end{frame}

\begin{frame}{Backup: prefill and decode use Forecast differently}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
      \begin{block}{Prefill}
        Compute the current layer's keys.\\[2mm]
        Score them with the stored $\mathbf F_{l-1}$.\\[2mm]
        Use the smaller selector on GPU.\\[2mm]
        Write used KV back to CPU asynchronously.
      \end{block}
    \end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{Decode}
        Next-layer historical keys already exist.\\[2mm]
        Score their GPU-resident compressed index using $\mathbf F_l$.\\[2mm]
        Fetch next-layer KV while computing the current layer.
      \end{block}
    \end{column}
  \end{columns}
  \vspace{3mm}
  Selection work still grows with history; flat measured decode latency is a hardware-utilization regime.
  \papersource{Paper, Sec. 4.1, PDF pp. 4--5; Algorithms 1--2, p. 13; Fig. 3, p. 8.}
\end{frame}

\end{document}