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\title{SAS: Learning Context Rankings}
\author{Independent paper reading}
\date{18 September 2026}
\begin{document}
\begin{frame}{SAS: learn which context blocks help prediction}
\begin{center}
{\Large Simple Attention Sparsification via\\[2mm]
End-to-End Optimization of Context Ranking}\par\medskip
Zhiwei Li, Lei Zhu, Hao Gu, Xiang Hu, Yan Wang, Haitao Mi,\\
Sirui Han, Leowei Liang, Zhijiang Guo\par\medskip
\href{https://arxiv.org/abs/2609.13141v1}{arXiv:2609.13141v1}\quad |\quad Reading discussion, 18 September 2026
\end{center}
\begin{block}{Takeaway}
Train block rankings through continuous gates and the LM loss;\newline
use ordinary hard Top-$K$ sparse attention at inference.
\end{block}
\small Independent reading presentation; approximately 25 minutes + backup.
\papersource{Paper title and authors: PDF p. 1. Author spelling follows the PDF.}
\end{frame}
\begin{frame}{The scarce resource is the decode attention budget}
\begin{itemize}
\item Dense decoding reads the growing KV context for each new token.
\item A block selector ranks history, then retains only $K$ blocks.
\item Which blocks best preserve prediction quality under this budget?
\end{itemize}
\[
\underbrace{\operatorname{softmax}(\mathbf q\mathbf K^\top)\mathbf V}_{\text{dense}}
\quad\longrightarrow\quad
\underbrace{\operatorname{softmax}(\mathbf q\mathbf K_{\mathcal S}^\top)\mathbf V_{\mathcal S}}_{\text{selected tokens }\mathcal S}
\]
\begin{block}{Scope}
Post-training adaptation of an existing dense model. The main setting\newline
freezes the backbone and trains only a lightweight selector.
\end{block}
\papersource{Secs. 1, 3 and 5.1, PDF pp. 1--4, 9--10; Eqs. (1)--(3).}
\end{frame}
\begin{frame}{Matching attention mass can miss predictive value}
\begin{columns}[T]
\begin{column}{0.48\textwidth}
\textbf{Attention distillation}
\begin{itemize}
\item Match the dense attention distribution layer by layer.
\item Hard Top-$K$ blocks the direct LM gradient through indices.
\end{itemize}
\end{column}
\begin{column}{0.48\textwidth}
\textbf{The proposed objective}
\begin{itemize}
\item Learn ranking from the final next-token prediction loss.
\item Account for values and interactions across layers.
\end{itemize}
\end{column}
\end{columns}
\bigskip
\begin{block}{Controlled comparison}
SAS and SeerAttention-R share the AttnGate architecture.\newline
The central change is how the selector is supervised.
\end{block}
\papersource{Secs. 1--2 and 5.1, PDF pp. 1--4, 9--10. Predictive relevance is the motivation, not an optimality theorem.}
\end{frame}
\begin{frame}{A continuous gate supplies the missing gradient path}
\centering
\includegraphics[width=0.97\linewidth,height=0.65\textheight,keepaspectratio]{figures/fig1-method.pdf}
\par\medskip Hard selection remains; the differentiable path passes through $\log\mathbf g$.
\papersource{Original Fig. 1, PDF p. 2. Green arrows denote backward flow.}
\end{frame}
\begin{frame}{Training keeps both hard selection and soft scores}
\[
\mathbf s=\mathcal R_\theta\!\left(\mathbf q,\{\mathbf K_{B_m}\}_{m=1}^{C}\right),
\qquad \mathbf g=\operatorname{softmax}(\mathbf s),\qquad g_0=1
\]
\[
\mathcal I=\operatorname{TopK}(\mathbf g,K),\qquad
\mathcal S=B_0\cup\bigcup_{m\in\mathcal I}B_m
\]
\begin{block}{Training attention}
\[
\mathbf o=\operatorname{softmax}\!\left(\mathbf q\mathbf K_{\mathcal S}^{\top}
+\log\mathbf g_{\mathcal S}\right)\mathbf V_{\mathcal S}
\]
\end{block}
$B_0$: current causal block; $B_m$: historical blocks of 64 tokens.\par
Normalize over \textbf{all} historical scores, then broadcast selected gates.\par
Update selector $\theta$ using $\nabla_\theta\mathcal L_{\rm LM}$; backbone frozen.
\papersource{Sec. 4.3, Eq. (9), Algorithm 1, PDF pp. 8--9. Attention scaling is omitted as in the paper.}
\end{frame}
\begin{frame}{Inference removes the gate and keeps the learned ranking}
\[
\mathcal I=\operatorname{TopK}(\mathbf s,K),\qquad
\mathbf o=\operatorname{softmax}(\mathbf q\mathbf K_{\mathcal S}^{\top})\mathbf V_{\mathcal S}
\]
\begin{itemize}
\item No log-gate bias in inference attention.
\item Prefill: dense attention. Decode: select blocks and gather their KV.
\item GQA groups share a selection; SGLang uses FlashInfer kernels.
\item SAS and SeerAttention-R use the same serving backend.
\end{itemize}
\begin{block}{Interpretation}
End-to-end training does not make Top-$K$ indices differentiable.\newline
The continuous training computation is a proxy for discrete inference.
\end{block}
\papersource{Algorithm 2, PDF p. 9; inference implementation, Sec. 5.1, PDF p. 10.}
\end{frame}
\begin{frame}{Inner gates learn relative reallocation of attention}
\[
\widetilde p_i=\frac{g_{b(i)}e^{z_i}}{\sum_j g_{b(j)}e^{z_j}},\qquad z_i=\mathbf q\mathbf k_i^\top
\]
\[
\frac{\partial\mathcal L}{\partial g_m}\bigg|_{\rm inner}
=\sum_{i\in B_m}\frac{\widetilde p_i}{g_m}\,
 d\mathbf o^\top(\mathbf v_i-\mathbf o)
\]
\[
\frac{\partial\mathcal L}{\partial g_m}\bigg|_{\rm outer}
=\sum_{i\in B_m}p_i\,d\mathbf o^\top\mathbf v_i
\]
Inner gating changes normalization; outer gating only rescales values.\par\medskip
$d\mathbf o$ is the upstream loss gradient. The term $\mathbf v_i-\mathbf o$\newline
compares a token's contribution with the current attention output.
\papersource{Eq. (5), PDF p. 7; Appendix D.1, PDF pp. 21--23.}
\end{frame}
\begin{frame}{Normalization calibrates history against the current block}
\[
\log g_m=s_m-\operatorname{LSE}(\mathbf s)\ (m\geq1),\qquad \log g_0=0
\]
\begin{itemize}
\item The common historical offset does \textbf{not} cancel: $B_0$ gets no offset.
\item Softmax gates are invariant to shifting all historical scores.
\item Sigmoid can saturate at 1; raw logits can collapse toward 0.\newline
Both can approach ungated training and learn poor rankings.
\end{itemize}
\begin{block}{Teaching example: equal logits, one token per block}
Two historical blocks + one current block:\newline
softmax historical gates $(1/2,1/2)$ give attention $(1/4,1/4,1/2)$.\newline
Raw scores $(0,0)$ instead give $(1/3,1/3,1/3)$.
\end{block}
\papersource{Eq. (6), Fig. 3, PDF p. 7. Example constructed for explanation; not a paper experiment.}
\end{frame}
\begin{frame}{Continuous scores and sparse scope serve different purposes}
\textbf{Preserve ranking:} binary STE gates discard score magnitudes.\par
A dropped token's surrogate factor can be
\[
\frac{e^{z_i}}{\sum_{j\in\mathcal S}e^{z_j}},\quad i\notin\mathcal S,
\]
which can grow arbitrarily large; it is not its forward probability.
\medskip\par
\textbf{Limit training scope:} compute attention only on selected blocks.
\[
 ds_m^{\rm sparse}=-g_m\sum_{\ell\in\mathcal I}g_\ell dg_\ell\quad(m\notin\mathcal I)
\]
Unselected blocks still get indirect score updates through normalization,\newline
but no independent signal from their own values. Early learning is slower.
\papersource{Eqs. (7)--(8), PDF p. 8; Appendices D.2--D.3, PDF pp. 23--24.}
\end{frame}
\begin{frame}{The ablation isolates three quality-critical choices}
\centering
\begin{tabular}{lrr}
\toprule
Design (one epoch) & GPQA accuracy (\%) & Output tokens\\
\midrule
Full attention reference & 56.1 & 8547\\
Inner + softmax + continuous + full & 54.4 & 7109\\
Outer gate & 41.6 & 13807\\
Sigmoid activation & 17.0 & 28444\\
Raw-logit injection & 18.8 & 26401\\
Binary gate + STE & 46.0 & 7289\\
\textbf{Sparse scope (SAS)} & \textbf{54.8} & 7410\\
Noise-based scope approximation & 52.2 & 7552\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
Qwen3-4B, budget 2048, GPQA avg@16. Other gate variants use full scope.\par
Standard deviations 2.0--2.8 are omitted in the original ablation table.
\papersource{Table 1, PDF p. 6. Sparse scope mainly trades early convergence for lower training cost.}
\end{frame}
\begin{frame}{Fused training avoids a dense attention matrix}
\begin{enumerate}
\item Traverse KV tiles; add the block's log-gate inside attention logits.
\item Mask unselected blocks using a per-query threshold; skip empty tiles.
\item Preserve causal current-block attention and online softmax updates.
\item Recompute probabilities in backward; sum token-logit gradients\newline
to obtain block-level log-gate gradients.
\end{enumerate}
\begin{block}{What the kernel achieves}
FlashAttention-style memory efficiency with learnable block gates.\newline
It does not eliminate scoring all candidates or all selection overhead.
\end{block}
Training memory/throughput comparisons are not fully quantified in the paper.
\papersource{Sec. 4.3, PDF p. 9; Appendix E and Algorithms 3--4, PDF pp. 24--26.}
\end{frame}
\begin{frame}{The main evaluation freezes Qwen3 and tests transfer}
\begin{columns}[T]
\begin{column}{0.49\textwidth}
\textbf{Training}
\begin{itemize}
\item Qwen3: 4B / 8B / 14B.
\item OpenR1-MATH-220K, 1 epoch.
\item AdamW, LR $10^{-3}$, cosine.
\item Batch 32; max length 32768.
\item Block size 64; AttnGate only.
\end{itemize}
\end{column}
\begin{column}{0.49\textwidth}
\textbf{Evaluation}
\begin{itemize}
\item MATH500, GPQA, AIME24/25.
\item LongBench: non-thinking.
\item BFCL Multi-Turn, VitaBench.
\item Agent context: YaRN to 65536.
\item Same trained selector across task families.
\end{itemize}
\end{column}
\end{columns}
\medskip
Main comparator: SeerAttention-R. Reasoning also includes\newline
Sliding Window, StreamingLLM and Quest.
\papersource{Sec. 5.1, PDF pp. 9--10. The controlled ablation specifically uses 93.7K math examples (p. 6).}
\end{frame}
\begin{frame}{GPQA gains are large at a 1024-token budget}
\centering
\begin{tabular}{lrrrr}
\toprule
Backbone & Full & Seer-R & SAS & Gain (pp)\\
\midrule
Qwen3-4B & 56.19 & 39.84 & 50.41 (2.8) & +10.57\\
Qwen3-8B & 60.54 & 39.43 & 53.17 (2.9) & +13.74\\
Qwen3-14B & 65.25 & 45.64 & 61.14 (2.9) & +15.50\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
Accuracy in \%; parentheses: reported SAS standard deviation.\par
At the same budget, MATH500 gains are +5.98 / +7.70 / +6.81 pp.
\begin{block}{What this establishes}
A better training signal substantially improves tight-budget selection.\newline
SAS still falls below full attention on all three GPQA backbones here.
\end{block}
\papersource{Table 2, PDF p. 10. Gains computed from the reported means; pp = percentage points.}
\end{frame}
\begin{frame}{Harder math improves; large budgets narrow the gap}
\centering
\begin{tabular}{llrrr}
\toprule
Budget & Task / backbone & Seer-R & SAS & Gain (pp)\\
\midrule
2048 & AIME24 / 4B & 55.83 & 68.85 & +13.02\\
2048 & AIME24 / 14B & 63.65 & 77.76 & +14.11\\
2048 & AIME25 / 8B & 43.30 & 58.41 & +15.11\\
2048 & AIME25 / 14B & 48.70 & 64.19 & +15.49\\
4096 & MATH500 / 4B & 94.10 & 93.67 & $-0.43$\\
4096 & GPQA / 8B & 60.48 & 60.42 & $-0.06$\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
SAS does not win every cell. AIME standard deviations are substantial.\par
At 4096, 4B AIME24 is 71.72 (6.8) vs. dense 71.25;\newline
this small difference does not establish superiority to dense attention.
\papersource{Table 2, PDF p. 10. Seer-R means above are the original-report rows, not the separate reproduced rows.}
\end{frame}
\begin{frame}{LongBench transfer is positive but modest on average}
\centering
\begin{tabular}{lrrr}
\toprule
Budget / method & 4B Avg. & 8B Avg. & 14B Avg.\\
\midrule
Full & 52.2 & 54.4 & 56.6\\
2048 / Seer-R & 51.2 & 52.6 & 54.9\\
2048 / SAS & 51.5 & 53.4 & 55.8\\
4096 / Seer-R & 51.9 & 53.8 & 55.7\\
4096 / SAS & 52.0 & 53.9 & 56.2\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
At 2048, the 8K+ bucket gains are +0.4 / +1.7 / +2.4 points.\par
Math-only selector training transfers to non-thinking long-context tasks.
\begin{alertblock}{Source inconsistency}
Introduction p. 3 claims +3.2 for 4B / 2048 / 8K+.\newline
Table 3 reports $48.8-48.4=+0.4$; this presentation follows the table.
\end{alertblock}
\papersource{Table 3, PDF p. 10; Sec. 5.2, PDF p. 11.}
\end{frame}
\begin{frame}{BFCL improves throughout; VitaBench has exceptions}
\centering
\begin{tabular}{lrrr}
\toprule
BFCL Multi-Turn & 4B & 8B & 14B\\
\midrule
Full & 35.75 & 42.75 & 44.50\\
2048 / Seer-R & 29.00 & 34.38 & 38.88\\
2048 / SAS & 32.50 & 36.75 & 39.50\\
4096 / SAS & 34.38 & 41.25 & 44.00\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
\textbf{VitaBench, Qwen3-14B:}\par
At 4096, SAS Avg@4 is 34.2 / 28.7 / 12.3 across the three scenarios.\par
But at 2048, Delivery Avg@4 drops: Seer 32.2 $\to$ SAS 30.0.\par
At 4096, OTA Pass@4 is SAS 27.0 vs. Seer 29.0 vs. full 37.0.\par
Average success and repeated-trial metrics should be kept separate.
\papersource{Tables 4--5, PDF p. 11. Selected metrics shown; no claim of uniform dominance.}
\end{frame}
\begin{frame}{Joint continued pretraining is feasible, not uniformly better}
OLMo3-7B; train backbone + a retrieval Q/K selector jointly.\par
About 50B tokens, 8192 context, 13000 steps, batch 512.\par\medskip
\centering
\begin{tabular}{lrr}
\toprule
Model & General average & LongBench average\\
\midrule
OLMo3-Base & 43.88 & 29.0\\
OLMo3-512SWA & 43.24 & 28.0\\
HiLS-Attn-RoPE & 41.68 & 30.0\\
SAS-RoPE & 43.28 & 30.0\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
SAS nearly matches SWA on the general average and ties HiLS on LongBench.\par
Task-level tradeoff: HellaSwag 50.63 is strong, but CRUX 19.25\newline
is below both dense base (24.62) and HiLS (25.62).
\papersource{Sec. 5.3 and Tables 6--7, PDF pp. 11--12. Selector architecture differs from the main AttnGate setting.}
\end{frame}
\begin{frame}{Better task performance can coexist with lower layerwise coverage}
\centering
\includegraphics[width=0.97\linewidth,height=0.53\textheight,keepaspectratio]{figures/fig5a-mass.pdf}
\par\medskip\raggedright
Coverage weights: $e^{z_i}$ or $e^{z_i}\|\mathbf v_i\|_2$.\par
Across early, middle and late layers, SAS generally retains less mass.\par
Matching dense attention mass is therefore an incomplete selection objective.
\papersource{Original Fig. 5(a), Eq. (10), PDF p. 13. Distill = Seer-R; NTP = SAS.}
\end{frame}
\begin{frame}{Cross-layer recall supports a complementarity explanation}
\centering
\includegraphics[width=0.97\linewidth,height=0.48\textheight,keepaspectratio]{figures/fig5b-recall.pdf}
\par\medskip
$\displaystyle \mathrm{Recall}=\frac{|\mathcal I_{\rm all}\cap\mathcal I^\star_{\rm all}|}{|\mathcal I^\star_{\rm all}|}$,
\quad $\displaystyle \mathcal I_{\rm all}=\bigcup_{j=1}^{L}\mathcal I_j$.
\par\medskip\raggedright
Higher union recall is consistent with complementary choices across layers.\par
\textbf{Reading caveat:} recall alone does not control union size or prove causality;\newline
the oracle derives from dense attention on long training sequences.
\papersource{Original Fig. 5(b), PDF p. 13; Eq. (11) and protocol, PDF pp. 13--14. GQA oracle uses within-group voting.}
\end{frame}
\begin{frame}{Shorter reasoning traces also hit the length cap less often}
\centering
\includegraphics[width=0.96\linewidth,height=0.57\textheight,keepaspectratio]{figures/fig6-generation.pdf}
\par\medskip\raggedright
Qwen3-4B, budget 4096, generation cap 32768.\par
AIME25: 19418 $\to$ 16960 tokens; truncation 21.67\% $\to$ 6.67\%.\par
Interpret alongside accuracy: shorter output alone is not better reasoning.
\papersource{Original Fig. 6, Sec. 6.2, PDF p. 14.}
\end{frame}
\begin{frame}{Steady-state decode is faster as context grows}
\begin{columns}
\begin{column}{0.48\textwidth}\centering
\includegraphics[width=\linewidth,height=0.47\textheight,keepaspectratio]{figures/fig7a-latency.pdf}
\end{column}
\begin{column}{0.48\textwidth}\centering
\includegraphics[width=\linewidth,height=0.47\textheight,keepaspectratio]{figures/fig7b-budget.pdf}
\end{column}
\end{columns}
\medskip
Batch 1: 2.4$\times$ at 64K, 4.6$\times$ at 256K, 5.6$\times$ at 512K.\par
Batch 8: approximately 13$\times$ at 64K.\par
Qwen3-4B, single GPU, SGLang, CUDA graphs; time 512 decode tokens.\par
\alert{Prefill excluded; GPU model not specified. These are not quality tests at 512K.}
\papersource{Original Fig. 7(a,b), PDF p. 15; measurement protocol, Sec. 6.3, PDF p. 14.}
\end{frame}
\begin{frame}{Selection becomes the bottleneck at very long context}
\begin{columns}
\begin{column}{0.49\textwidth}\centering
\includegraphics[width=\linewidth,height=0.62\textheight,keepaspectratio]{figures/fig7c-breakdown.pdf}
\end{column}
\begin{column}{0.48\textwidth}
\begin{itemize}
\item Attention reads a fixed KV budget.
\item Scoring still scans all block summaries.
\item Top-$K$ grows from 21\% of this stage at 8K to 90\% at 512K.
\end{itemize}
\medskip
Fixed selected-attention cost does not imply constant total decode cost.
\end{column}
\end{columns}
\papersource{Original Fig. 7(c), Sec. 6.3, PDF p. 15. Breakdown covers the selector + sparse-attention stage.}
\end{frame}
\begin{frame}{Long-context retrieval remains a major limitation}
RULER: separate 0.5B-token selector training on packed 64K sequences.\par
Non-thinking; YaRN extends evaluation to 128K.\par\medskip
\centering
\begin{tabular}{lrrr}
\toprule
Qwen3-14B, budget 4096 & Full & Seer-R & SAS\\
\midrule
16K & 92.91 & 76.77 & 83.35\\
32K & 92.15 & 64.96 & 66.82\\
64K & 92.19 & 42.34 & 45.92\\
128K & 82.23 & 22.36 & 29.95\\
\bottomrule
\end{tabular}
\par\medskip\raggedright
At 128K: +7.59 over Seer, but $-52.28$ relative to full attention.\par
Authors suggest pooled block summaries lose localized needle-like signals.\par
This explanation is plausible; the mechanism is not isolated experimentally.
\papersource{Appendix B, Table 8, PDF p. 21. This is not the main math-only selector training protocol.}
\end{frame}
\begin{frame}{The contribution is a better learning signal for sparse routing}
\begin{enumerate}
\item \textbf{Mechanism:} log-space softmax gates give the selector an LM-loss path while retaining Top-$K$ sparsity.
\item \textbf{Evidence:} strong tight-budget reasoning gains, plus transfer to long-context and agent tasks.
\item \textbf{Boundary:} no universal win, no full recovery of long retrieval, and no constant-cost routing at arbitrary context length.
\end{enumerate}
\begin{block}{Discussion}
Can richer block summaries improve retrieval without making selection\newline
the dominant cost? Can we reduce the train--inference gate mismatch?
\end{block}
\papersource{Synthesis of Secs. 4--6 and Appendix B. Discussion questions are reading analysis.}
\end{frame}
\begin{frame}{Reference and material provenance}
\textbf{Primary source}\par
Zhiwei Li et al.\par
\emph{SAS: Simple Attention Sparsification via End-to-End\newline
Optimization of Context Ranking.}\par
\href{https://arxiv.org/abs/2609.13141v1}{arXiv:2609.13141v1}, submitted 11 September 2026.\par\bigskip
Read the matching author TeX and 26-page PDF, including Appendices A--E.\par
Figures are original author assets; numeric tables are selected transcriptions.\par
The normalization example and methodological caveats are this reading's analysis.\par\medskip
Companion: \texttt{reading-notes.zh.md}.\par
Editable slides: \texttt{slides.en.tex}; local build: pdfLaTeX.\par
No independent model training or benchmark reproduction was performed.
\end{frame}
\begin{frame}{Backup: lower training loss can hide poor discrete rankings}
\centering
\includegraphics[width=0.92\linewidth,height=0.58\textheight,keepaspectratio]{figures/fig8a-loss.pdf}
\par\medskip\raggedright
Sigmoid/raw-logit variants can lower loss by approaching ungated attention.\par
Evaluate the final ungated sparse inference model, not only training loss.
\papersource{Original Fig. 8(a), Appendix A, PDF p. 20; final ablation results, Table 1, PDF p. 6.}
\end{frame}
\begin{frame}{Backup: STE has much larger gradient norms}
\centering
\includegraphics[width=0.92\linewidth,height=0.58\textheight,keepaspectratio]{figures/fig8b-grad.pdf}
\par\medskip\raggedright
Panel III: binary STE produces much larger measured gradient norms.\par
Bounded soft attention probabilities alone are not a global bound\newline
on all gate or model gradients.
\papersource{Original Fig. 8(b), Appendix A, PDF p. 20; gradient analysis, Appendix D, PDF pp. 21--24.}
\end{frame}
\begin{frame}{Backup: sparse scope is comparable, not mathematically equivalent}
\centering
\begin{tabular}{llrr}
\toprule
Budget & Backbone / task & Full scope & Sparse scope\\
\midrule
1024 & 8B / GPQA & 55.62 (2.8) & 53.17 (2.9)\\
2048 & 4B / GPQA & 54.40 (2.9) & 54.86 (2.8)\\
2048 & 14B / AIME24 & 76.67 (6.7) & 77.76 (6.6)\\
4096 & 14B / MATH500 & 94.12 (1.0) & 95.23 (0.8)\\
4096 & 8B / AIME25 & 64.24 (7.1) & 63.41 (7.2)\\
\bottomrule
\end{tabular}
\par\bigskip\raggedright
Most final results are close, with differences in both directions.\par
This supports the practical sparse-scope choice; it is not a convergence proof.\par
For unselected blocks, full scope supplies an own-content gradient,\newline
whereas sparse scope supplies only a normalization-mediated update.
\papersource{Appendix C, Table 9, PDF p. 21. Parentheses: reported standard deviations.}
\end{frame}
\begin{frame}{Backup: comparison details that change the interpretation}
\begin{itemize}
\item Quest at budget 1024: digitized from a prior paper's figure.
\item Seer-R and Seer-R\#: original-report and reproduced rows;\newline
only budget 4096 has a separately listed reproduced row.
\item Main reasoning sampling settings are referenced to Seer-R;\newline
the SAS text does not fully restate them.
\item AIME at budget 1024 is unreported, not zero.
\item A $Kb$ historical budget coexists with an always-kept current block.
\item The abstract page lists Leo Liang; the PDF lists Leowei Liang.
\end{itemize}
\papersource{Table 2 and Sec. 5.1, PDF p. 10; Algorithms 1--2, PDF p. 9; identity, PDF p. 1 and arXiv abstract page.}
\end{frame}
\end{document}