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\title{OpenAttention: One Percent Is Enough with Tail Proxies}
\subtitle{Paper discussion \quad arXiv:2610.30951v1}
\author{\small Hyunwoo Yu, Jongbeom Lee, Hyunbin Kim, Sungjun Park, Jaemin Choi,\\
Jincheol Yang, Seunghun Moon, Bongjoon Hyun, Kyomin Sohn,\\
Kyeongbo Kong, Suk-Ju Kang}
\date{22 October 2026 \quad \href{https://arxiv.org/abs/2610.30951v1}{arxiv.org/abs/2610.30951v1}}

\begin{document}
\begin{frame}
  \titlepage
\end{frame}

\begin{frame}{A 1\% read retains 99\% of dense accuracy}
  \begin{center}
  \begin{tabular}{lc}
  \toprule
  RULER-32K HARD, Llama-3.1-8B & Mean accuracy\\
  \midrule
  Dense (100\% read) & 87.04\\
  Best listed sparse baseline (1\%) & 48.22\\
  \textbf{OpenAttention (1\%)} & \textbf{86.30}\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Exact reads capture selected tokens.
    \item Count-aware proxies represent \emph{every} unread token.
    \item A fused kernel runs the decode attention stage at 0.12 vs.\ 1.20 ms, batch 32.
  \end{itemize}
  \papersource{Paper, Fig. 1, PDF p. 1; Table 11, p. 23; Table 9, p. 22. The 10$\times$ figure is attention-stage time.}
\end{frame}

\begin{frame}{The tail remains after sparse top-$k$ selection}
  \centering
  \includegraphics[width=0.94\linewidth,height=0.62\textheight,keepaspectratio]{figures/figure_2.png}
  \vspace{-0.7em}
  \begin{itemize}
    \item Discarding loses tail mass; sampling can miss residual heavy hitters.
    \item OpenAttention uses cluster proxies to carry the unread tail into softmax.
  \end{itemize}
  \papersource{Paper, Fig. 2, PDF p. 2. Original figure.}
\end{frame}

\begin{frame}{One proxy wins in the low-read head diagnostic}
  \centering
  \includegraphics[width=0.91\linewidth,height=0.60\textheight,keepaspectratio]{figures/tail-error-hash.png}
  \vspace{-0.4em}
  \begin{itemize}
    \item Red: top-$k$ + one proxy; blue: top-$k$; green: top-$k$/sample; brown: sample only.
    \item The four panels in the paper test two heads and two selectors.
  \end{itemize}
  \papersource{Paper, Fig. 3(c,d), PDF p. 3. Original figure cropped to the HashAttention selector. Relative attention-output error.}
\end{frame}

\begin{frame}{The proxy is a virtual token with a count}
  For exact set $X$ and unread tail $T$, $N=|T|$:
  \[
  z_i=d^{-1/2}q^\top k_i,\qquad
  \ell_T=\bar z_T+\log N,\qquad
  v_T^{\mathrm{proxy}}=\bar v_T .
  \]
  \[
  \hat o=
  \frac{\sum_{i\in X}e^{z_i}v_i+
        \underbrace{Ne^{\bar z_T}\bar v_T}_{\text{one virtual token}}}
       {\sum_{i\in X}e^{z_i}+Ne^{\bar z_T}}.
  \]
  \keypoint{The $+\log N$ term makes one token stand for all $N$ members. The mass $Ne^{\bar z_T}$ usually underestimates $\sum_{i\in T}e^{z_i}$.}
  \papersource{Paper, Eq. (1), PDF pp. 3--4; Appendix A, pp. 12--13.}
\end{frame}

\begin{frame}{Sampling nearly doubles a specific weight error}
  Define the \emph{unnormalized} discrepancy
  \[
    \mathcal E=\frac{1}{Z}\sum_i|\hat w_i-w_i|,\quad
    \tau=\frac{\sum_{i\in T}w_i}{Z},\quad w_i=e^{z_i}.
  \]
  For a \emph{fixed} tail of $N$ tokens and a uniform sample of size $m$:
  \[
    \mathcal E_{\rm discard}=\tau,\qquad
    \mathbb E[\mathcal E_{\rm sample}]
      =2\tau\left(1-\frac{m}{N}\right).
  \]
  \keypoint{As $m/N\to0$, the sampling discrepancy approaches $2\tau$. This is not a twofold claim for normalized attention or output error.}
  \papersource{Paper, Eq. (2), PDF p. 4; derivation in Appendix A.2, PDF pp. 17--18.}
\end{frame}

\begin{frame}{Output error also depends on values and mass}
  \begin{columns}[T,onlytextwidth]
  \column{0.52\textwidth}
  \[
  \frac{\sqrt{\mathbb E[(\hat Z_s-Z)^2]}}{Z}
  =\tau\frac{\mathrm{CV}_T}{\sqrt m}
  \sqrt{\frac{N-m}{N-1}} .
  \]
  \begin{itemize}
    \item Smaller $m$ raises normalizer uncertainty.
    \item Concentrated tail weights raise $\mathrm{CV}_T$.
  \end{itemize}
  \column{0.45\textwidth}
  \begin{block}{Diagnostic at a 1\% read}
  Behind HashAttention, the sample includes the heaviest missed token with only about \textbf{0.5\%} probability.
  \end{block}
  \end{columns}
  \papersource{Paper, Appendix A.2, PDF p. 17; Fig. 10, p. 20. The diagnostic uses 137,216 decode rows.}
\end{frame}

\begin{frame}{Four stages make a proxy-based read}
  \centering
  \includegraphics[width=0.98\linewidth,height=0.72\paperheight,keepaspectratio]{figures/method-pipeline.png}
  \papersource{Paper, Fig. 5(a), PDF p. 5. Original figure cropped to the pipeline.}
\end{frame}

\begin{frame}{Exact reads and residual proxies share softmax}
  After selected tokens are removed from each cluster:
  \[
  \hat o=
  \frac{\displaystyle\sum_{i\in X}e^{z_i}v_i+
  \sum_{b\in\mathcal P}n'_be^{\bar z'_b}\bar v'_b}
  {\displaystyle\sum_{i\in X}e^{z_i}+
  \sum_{b\in\mathcal P}n'_be^{\bar z'_b}} .
  \]
  \begin{itemize}
    \item $X$: sink, local window, QGS top-$k$, and ErrorGate expansions.
    \item Primes denote statistics of \emph{unread} cluster members.
    \item Subtracting exact tokens from pooled moments prevents double counting.
  \end{itemize}
  \papersource{Paper, Appendix A, Eq. (8), PDF pp. 12--13; Appendix A.1, p. 16.}
\end{frame}

\begin{frame}{QGC clusters by expected logit distance}
  With query second moment $M=\mathbb E[qq^\top]$:
  \[
  \mathbb E_q[(z_i-z_j)^2]
    =d^{-1}(k_i-k_j)^\top M(k_i-k_j).
  \]
  Its leading eigenpairs $(U_r,\Lambda_r)$ define
  \[
     \Phi=KU_r\Lambda_r^{1/2}\in\mathbb R^{n\times r},
     \qquad r=16.
  \]
  \begin{itemize}
    \item Run $k$-means in this query-weighted key space, once after prefill.
    \item $M$ mixes presampled and current question-query moments 50/50.
  \end{itemize}
  \papersource{Paper, Sec. 3.2.1, Eq. (4), PDF p. 5.}
\end{frame}

\begin{frame}{QGC helps at the same 1\% read}
  \begin{center}
  \begin{tabular}{lcc}
  \toprule
  Clustering & Dimension & Mean accuracy\\
  \midrule
  Token position & -- & 84.37\\
  Key-only $k$-means & 128 & 85.42\\
  \textbf{QGC} & \textbf{16} & \textbf{86.30}\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
    \item Same $C=64$ and total 1\% read.
    \item Decode queries retain an absolute cosine of 0.82 (median) with $M$'s first eigenvector.
    \item The clustering target is logit dispersion, not direct output error.
  \end{itemize}
  \papersource{Paper, Table 1 and Fig. 6, PDF p. 5. RULER-32K HARD.}
\end{frame}

\begin{frame}{QGS finds high-logit tokens from int8 codes}
  \[
  c_i=Q_8(U_{32}^{\top}k_i),\qquad
  \tilde z_i=(U_{32}^{\top}q)^\top c_i .
  \]
  \begin{center}
  \begin{tabular}{lccc}
  \toprule
  Selector & Top-32 recall at $1/16$ & At $1/32$ & ms/layer\\
  \midrule
  HashAttention & 0.74 & 0.63 & 0.24\\
  Double Sparsity & 0.97 & 0.95 & 0.50\\
  \textbf{QGS} & \textbf{0.97} & \textbf{0.94} & \textbf{0.22}\\
  \bottomrule
  \end{tabular}
  \end{center}
  Exact attention recomputes the selected tokens' original logits.
  \papersource{Paper, Eq. (5) and Table 2, PDF p. 6. Same decode rows; selection time is separate from the attention kernel.}
\end{frame}

\begin{frame}{Cluster discrepancy is mass times spread}
  For residual cluster $b$, $\delta_i=z_i-\bar z_b$:
  \[
  \varepsilon_b=n_be^{\bar z_b}
    \underbrace{\frac{1}{n_b}\sum_{i\in b}|e^{\delta_i}-1|}_{D_b},
  \qquad
  Z\mathcal E=\sum_{b\in\mathcal P}\varepsilon_b .
  \]
  \begin{itemize}
    \item Equal logits give $D_b=0$: the proxy is exact in weight space.
    \item Small mass gives small contribution at fixed spread.
    \item Reading a whole cluster exactly removes its nonnegative term.
  \end{itemize}
  \papersource{Paper, Eq. (3), PDF p. 4; Appendix A, PDF p. 13. This is an exact finite-cache identity.}
\end{frame}

\begin{frame}{ErrorGate estimates that discrepancy cheaply}
  Gaussian logit-deviation model + diagonal key variance:
  \[
  \hat\sigma_b^2=d^{-1}\sum_j q_j^2\mathrm{Var}_b(k_j),
  \]
  \[
  \hat\varepsilon_b=n_be^{\bar z_b}
    e^{\hat\sigma_b^2/2}\bigl(2\Phi_{\rm N}(\hat\sigma_b)-1\bigr).
  \]
  \begin{itemize}
    \item Estimated error ranking: 86.30 mean accuracy at 1\%.
    \item Centroid-mass ranking: 85.99; variance-only: 84.81.
    \item Diagonal vs.\ full model scores: Spearman 0.92 in the diagnostic.
  \end{itemize}
  \papersource{Paper, Eq. (6), Tables 3 and Fig. 7, PDF p. 6. The score is neither an exact discrepancy nor a certified output bound.}
\end{frame}

\begin{frame}{The 1\% read is split across three streams}
  \[
    q_b=\min\left(n_b,\lambda
    \frac{\hat\varepsilon_b}{\max_{b'}\hat\varepsilon_{b'}}\right),
    \qquad \sum_b q_b=E .
  \]
  \begin{block}{Deployed 1\% configuration}
  $C=64$ clusters; roughly 9 initial QGS reads; $E=216$ added exact reads. Mean and variance statistics cost $1.5C=96$ KV rows, about 29\% of the read.
  \end{block}
  \begin{itemize}
    \item Water filling spends the token budget exactly.
    \item Proportional partial-token allocation is a heuristic.
  \end{itemize}
  \papersource{Paper, Eq. (7), PDF pp. 6--7; Appendix A.1, p. 17; hyperparameters, Appendix D, pp. 22--23.}
\end{frame}

\begin{frame}{One online softmax handles exact and proxy rows}
  \begin{enumerate}
    \item Gather QGS and expanded-cluster exact KV rows into SRAM.
    \item Subtract those rows from cached cluster moments.
    \item Stream residual cluster means as virtual tokens with logits
      $\ell_b=d^{-1/2}q^\top\bar k'_b+\log n'_b$.
    \item Update one running max, normalizer, and value accumulator.
  \end{enumerate}
  \begin{block}{State and representation}
    At $C=64$, cached cluster statistics occupy about 12 MiB for the 32-layer model, versus a 4.0 GiB KV cache.
  \end{block}
  \papersource{Paper, Sec. 3.4, PDF p. 7; Algorithm 1 and implementation, Appendix C, PDF pp. 20--21.}
\end{frame}

\begin{frame}{The main benchmark charges proxy reads}
  \begin{itemize}
    \item Llama-3.1-8B-Instruct, bf16; seven RULER-32K HARD tasks, 200 samples each.
    \item Context prefill is dense. Sparse attention covers the question chunk and generation.
    \item Read budget: KV rows per query head, including $1.5$ rows per proxy cluster.
    \item HashAttention/vAttention share signatures; MagicPIG uses LSH; OpenAttention uses QGS.
    \item Compressed-index scan is excluded from the read budget for all methods.
  \end{itemize}
  \papersource{Paper, Sec. 4 Setup, PDF p. 7; baseline protocol, Appendix F, PDF pp. 23--25.}
\end{frame}

\begin{frame}{OpenAttention stays near dense down to 1\%}
  \centering
  \begin{tabular}{rcccc}
  \toprule
  Total read & OpenAttention & HashAttention & vAttention & MagicPIG\\
  \midrule
  10\% & \textbf{87.08} & 81.23 & 83.08 & 52.52\\
  5\%  & \textbf{86.82} & 71.55 & 68.86 & 34.42\\
  3\%  & \textbf{86.83} & 63.48 & 55.74 & 24.01\\
  1\%  & \textbf{86.30} & 48.22 & 36.29 & 10.53\\
  \bottomrule
  \end{tabular}
  \vspace{0.7em}
  \begin{block}{Reading the table}
  Dense mean = 87.04. At 1\%, OpenAttention is 0.74 points below dense and 38.08 points above the best listed sparse baseline.
  \end{block}
  \papersource{Paper, Fig. 8, PDF p. 7; Table 11, p. 23. MagicPIG realized reads: 10.0, 5.1, 2.9, 1.1\%.}
\end{frame}

\begin{frame}{Proxies provide the largest ablation gain}
  \centering
  \begin{tabular}{lcc}
  \toprule
  5\% read configuration & Mean accuracy & Gain vs.\ first row\\
  \midrule
  Hash selector + residual sampling & 67.35 & --\\
  Replace sampling with proxies & 77.91 & +10.56\\
  Proxies + ErrorGate & 85.90 & +18.55\\
  Proxies + QGS & 86.73 & +19.38\\
  \textbf{Proxies + ErrorGate + QGS} & \textbf{86.82} & \textbf{+19.47}\\
  \bottomrule
  \end{tabular}
  \vspace{0.7em}
  \keypoint{A tail proxy already matters; clustering, allocation and selection recover most of the remaining loss.}
  \papersource{Paper, Table 4, PDF p. 8; per-task Table 12, p. 24. The ablation's first row is a separate configuration from the main vAttention row.}
\end{frame}

\begin{frame}{The 3\% setting transfers across models}
  \centering
  \begin{tabular}{lccc}
  \toprule
  Method & Llama-8B & DeepSeek-8B & Mistral-7B\\
  \midrule
  Dense & 87.04 & 73.46 & 65.46\\
  HashAttention & 63.48 & 59.85 & 51.24\\
  vAttention & 57.15 & 49.26 & 46.14\\
  \textbf{OpenAttention} & \textbf{86.59} & \textbf{73.49} & \textbf{64.83}\\
  \bottomrule
  \end{tabular}
  \vspace{0.7em}
  \begin{itemize}
    \item Same seven hard RULER tasks at a 3\% read.
    \item OpenAttention remains within 0.7 accuracy points of dense on these models.
  \end{itemize}
  \papersource{Paper, Table 5, PDF p. 8.}
\end{frame}

\begin{frame}{Accuracy tracks dense from 16K to 96K}
  \centering
  \begin{tabular}{lcccc}
  \toprule
  Context & 16K & 32K & 64K & 96K\\
  \midrule
  Dense & 87.14 & 87.75 & 85.49 & 78.01\\
  OpenAttention (3\%) & \textbf{87.49} & \textbf{87.38} & \textbf{84.82} & \textbf{78.10}\\
  HashAttention (3\%) & 67.41 & 63.87 & 49.65 & 27.99\\
  \bottomrule
  \end{tabular}
  \vspace{0.6em}
  \begin{itemize}
    \item 100 samples per task; 64K and 96K are RULER-generated extensions.
    \item Cluster count scales with length; this sweep uses $E=0$.
  \end{itemize}
  \papersource{Paper, Table 7, PDF p. 9; Appendix I, p. 27.}
\end{frame}

\begin{frame}{The 10$\times$ result is an attention-stage timing}
  \centering
  \begin{tabular}{lcc}
  \toprule
  B=32, 32K, H100 NVL & 1\% read & 3\% read\\
  \midrule
  Dense fused SDPA & 1.20 ms & 1.22 ms\\
  OpenAttention.flash & \textbf{0.12 ms} & \textbf{0.24 ms}\\
  Stage speedup & 10.0$\times$ & 5.1$\times$\\
  \bottomrule
  \end{tabular}
  \vspace{0.7em}
  \begin{itemize}
    \item Kernel table uses $E=0$, unlike the 1\% accuracy deployment.
    \item Excludes index scan, selection, ErrorGate scoring, and residual updates.
    \item At $B=1$, 1\% times are 0.06 vs.\ 0.05 ms.
  \end{itemize}
  \papersource{Paper, Table 9, PDF p. 22; discussion of excluded work, PDF p. 21.}
\end{frame}

\begin{frame}{What the evidence supports}
  \begin{enumerate}
    \item At small reads, preserving the unread tail by a few count-aware proxies can retain much more task accuracy than discarding or sampling it.
    \item Query geometry helps both clustering and top-$k$ selection; estimated proxy error guides the exact-read budget.
    \item The weight-error formula is exact for the defined metric, while the Gaussian ErrorGate score and partial-token allocation are approximations.
    \item Full decode latency still requires accounting for index scanning, selection, cluster construction and updates.
  \end{enumerate}
  \papersource{Paper, Secs. 2--4 and 6, PDF pp. 3--9; Appendix C, PDF pp. 20--22.}
\end{frame}

\begin{frame}{Paper and source}
  \begin{block}{Primary source}
  Hyunwoo Yu et al., \emph{OpenAttention: One Percent Is Enough with Tail Proxies}, arXiv:2610.30951v1 (2026).
  \end{block}
  \vspace{0.7em}
  \begin{itemize}
    \item Paper: \href{https://arxiv.org/abs/2610.30951v1}{arxiv.org/abs/2610.30951v1}
    \item Project: \href{https://hyunwoo137.github.io/OpenAttention/}{hyunwoo137.github.io/OpenAttention}
    \item Code: \href{https://github.com/hyunwoo137/OpenAttention}{github.com/hyunwoo137/OpenAttention}
  \end{itemize}
  \papersource{All numerical results and original figures in this deck come from the cited arXiv v1 PDF.}
\end{frame}

\appendix
\begin{frame}{Backup: output error has a value-dependent identity}
  For the residual-proxy estimator:
  \[
  \hat Z(\hat o-o)
    =-\sum_{b\in\mathcal P}\sum_{i\in b}
       (e^{z_i}-e^{\bar z_b})(v_i-o).
  \]
  Hence
  \[
  \|\hat o-o\|_2
   \leq\sum_b \hat a_b^{\mathrm{virt}}V_bD_b,\quad
  V_b=\max_{i\in b}\|v_i-o\|_2 .
  \]
  \begin{itemize}
    \item Exact finite-cache identity and deterministic bound.
    \item Explains why the value-free $\mathcal E$ need not order output errors.
  \end{itemize}
  \papersource{Paper, Appendix A, Lemma 1 and Proposition 1, PDF pp. 13--15.}
\end{frame}

\begin{frame}{Backup: comparisons use specific baselines}
  \begin{itemize}
    \item HashAttention and vAttention share the public HashAttention signatures.
    \item vAttention is tuned per target read under the paper's matched-read accounting.
    \item MagicPIG hash tables are calibrated to realized reads near 1, 3, 5 and 10\%.
    \item Main protocol sparsifies question plus generation; MagicPIG's original protocol keeps the question dense.
    \item The 1\% timing uses $E=0$; the 1\% accuracy configuration uses $E=216$.
  \end{itemize}
  \papersource{Paper, Sec. 4 Setup, PDF p. 7; Appendix F, pp. 23--25; Table 9, p. 22.}
\end{frame}

\begin{frame}{Backup: other tasks and KV compression}
  \begin{columns}[T,onlytextwidth]
  \column{0.49\textwidth}
  \begin{block}{Question-free tasks, 3\% read}
    \begin{tabular}{lcc}
    \toprule
    & Dense & Ours\\
    \midrule
    gov\_report ROUGE-L & 36.08 & 35.53\\
    multi\_news ROUGE-L & 26.61 & 26.80\\
    LongBench-v2 accuracy & 30.00 & 33.30\\
    \bottomrule
    \end{tabular}
  \end{block}
  \column{0.48\textwidth}
  \begin{block}{With 2048-entry KV compression}
    \begin{tabular}{lcc}
    \toprule
    & Alone & + Ours\\
    \midrule
    StreamingLLM & 28.00 & 28.28\\
    SnapKV & 69.98 & 69.49\\
    PyramidKV & 70.34 & 70.14\\
    \bottomrule
    \end{tabular}
  \end{block}
  \end{columns}
  \papersource{Paper, Tables 6 and 15--16, PDF pp. 9, 25--26. LongBench-v2 uses only 60 requests.}
\end{frame}

\end{document}