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\title[BinaryPC]{Training-Free Hashing-Based Attention\\via Binary Principal Components}
\subtitle{BinaryPC: data-aware retrieval with 64-bit key codes}
\author{\small Paper by Daohai Yu, Zhanpeng Zeng, Keyu Chen, Wenhao Li,\\
Zhifeng Shen, Luxi Lin, Ruizhi Qiao, Xing Sun, and Rongrong Ji}
\date{\small arXiv:2608.04405v1 \;|\; ICML 2026\\Research group discussion \;|\; 16 October 2026}

\begin{document}

% Main presentation: approximately 25 minutes, frames 1--22.
\begin{frame}
  \titlepage
  \vspace{-4mm}
  \centering\small
  Reconstruct keys, scan compact codes, then attend to selected original KV.
\end{frame}

\begin{frame}{The expensive step is repeatedly reading long KV histories}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.48\textwidth}
  \fig{1}{fig01-multi-value}
\end{column}
\begin{column}{0.49\textwidth}
  \begin{itemize}
    \item Decode has few queries and many cached keys.
    \item Exact top-$k$ still reads all keys to compute scores.
    \item A compact proxy can reduce the cost of finding useful tokens.
  \end{itemize}
  \medskip
  At 128K on NIAH multi-value:\\
  TOPK / BinaryPC: \alert{92.50};\\
  MagicPIG: 86.00; full: 94.00.
\end{column}
\end{columns}
\papersource{Paper, Sec. 1, Fig. 1, PDF p. 1; exact subtask scores: Table 18, p. 21. TOPK budget: 2\%.}
\end{frame}

\begin{frame}{Data-aware hashing need not require gradient training}
\centering
\begin{tabular}{lll}
\toprule
Approach & Selection / encoding & Main trade-off \\
\midrule
Static KV pruning & Prefill importance & Future evidence can be lost \\
Quest & Query-aware chunks & Coarse selection units \\
MagicPIG & Random LSH projections & Long codes / hash tables \\
Spotlight & Trained nonlinear hash & Model-specific training \\
\textbf{BinaryPC} & \textbf{Binary reconstruction} & \textbf{Greedy approximation} \\
\bottomrule
\end{tabular}
\medskip
\begin{block}{Design question}
Can key activations provide a useful retrieval representation through direct computation?
\end{block}
\papersource{Paper, Secs. 2--3, PDF pp. 2--4; baseline configurations: Appendix A.1, p. 13.}
\end{frame}

\begin{frame}{A compact search stage selects original KV for attention}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.48\textwidth}
\begin{block}{Prefill / preparation}
\begin{enumerate}
\item Obtain projection $\PP$ online or through offline calibration.
\item Encode keys into 64-bit codes.
\item Identify keys with large reconstruction errors.
\end{enumerate}
\end{block}
\end{column}
\begin{column}{0.48\textwidth}
\begin{block}{Each decoding step}
\begin{enumerate}
\item Project and quantize the query.
\item Score all key codes; take top-$k$.
\item Add protected keys, gather KV, and compute subset attention.
\end{enumerate}
\end{block}
\end{column}
\end{columns}
\medskip
\alert{The full KV cache remains stored.} The saving is in access and computation per step.
\papersource{Paper, Sec. 3.2, Algorithms 1--3, PDF pp. 4--5; Appendix B.4, p. 17. Diagram is a teaching summary.}
\end{frame}

\begin{frame}{Reconstructing keys gives an asymmetric score approximation}
\[
\min_{\HH,\PP}\|\K-\HH\PP\|_F,
\qquad
\K\in\R^{N\times D},\quad
\HH\in\{-1,+1\}^{N\times H},\quad
\PP\in\R^{H\times D}.
\]
\begin{block}{From key reconstruction to retrieval}
\[
\kk\approx\hh\PP
\quad\Longrightarrow\quad
\qq\kk^\top\approx(\qq\PP^\top)\hh^\top.
\]
\end{block}
\begin{itemize}
\item $N$: cached tokens; $D$: key dimension; $H$: hash length.
\item Keys use binary coefficients; query coefficients retain magnitude.
\item The implementation uses $D=128$ and $H=64$.
\end{itemize}
\papersource{Paper, Eqs. (2)--(3), PDF pp. 3--4; Appendix A.4, p. 14.}
\end{frame}

\begin{frame}{Extract one binary rank-one component from each residual}
Initialize $\RR=\K$. For each of $H$ bits:
\[
\vv^*\sim\mathcal N(0,\mathbf I_D),\qquad
\uu=\sgn(\RR{\vv^*}^\top),\qquad
\vv=\frac{\uu^\top\RR}{N},\qquad
\RR\leftarrow\RR-\uu\vv.
\]
Store $\uu$ as one column of $\HH$, and $\vv$ as one row of $\PP$.
\begin{block}{Why the residual decreases}
For fixed $\uu$, the update for $\vv$ is least squares:
\[
\|\RR-\uu\vv\|_F^2
=\|\RR\|_F^2-\frac{\|\uu^\top\RR\|_2^2}{N}.
\]
\end{block}
The binary partition uses a random direction. This is a greedy procedure;
it does not compute exact PCA or a global binary optimum.
\papersource{Paper, Algorithm 1, PDF p. 4. Column-vector convention for $\uu$; residual identity is a discussion derivation.}
\end{frame}

\begin{frame}{New keys are encoded sequentially because the basis is not orthogonal}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.49\textwidth}
\[
\begin{aligned}
\rr_0&=\kk,\\
h_i&=\sgn(\rr_{i-1}\PP_{i,:}^\top),\\
\rr_i&=\rr_{i-1}-h_i\PP_{i,:}.
\end{aligned}
\]
Each bit describes what earlier bits have not reconstructed.\medskip

This differs from a single parallel operation $\sgn(\kk\PP^\top)$.
\end{column}
\begin{column}{0.48\textwidth}
\fig{1}{fig03-residual}
\small Left: constructing the basis.\\Right: encoding with a fixed basis.\\The curves show measured residuals.
\end{column}
\end{columns}
\papersource{Paper, Algorithm 2 and Fig. 3, PDF p. 4. Fixed-basis per-key descent is empirical, not unconditional.}
\end{frame}

\begin{frame}{Spend more bits on one query and fewer on every key}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.46\textwidth}
\begin{block}{Key: 8 bytes}
64 binary signs $\longrightarrow$ one 64-bit word per cached key.
\end{block}
\begin{block}{Query projection: 64 bytes}
64 signed quantized values $\longrightarrow$ one sign word and seven magnitude words.
\end{block}
\end{column}
\begin{column}{0.51\textwidth}
Let $\mathbf p=\qq\PP^\top$. After quantization:
\[
\hat p_i=s_i\sum_{j=0}^{6}2^j M_{j,i}.
\]
\begin{itemize}
\item XOR identifies sign agreement.
\item AND and popcount collect contributions by bit plane.
\item Weighted sums approximate inner products, then top-$k$ selects candidates.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Algorithm 3, PDF p. 5; Appendix A.4, pp. 14--15. Zero-based bit indexing used here; details in backup.}
\end{frame}

\begin{frame}{Protect the keys whose compressed scores are least reliable}
\[
e_i=\|\kk_i-\hh_i\PP\|_2,
\qquad
\mathcal S_{\rm attn}=\mathcal S_{\rm hash}\cup\mathcal S_{\rm err}.
\]
\begin{itemize}
\item Error-Aware Safeguard (EAS) retains large-error keys from prefill.
\item Large error means a less reliable proxy, not necessarily large current attention.
\end{itemize}
\begin{block}{Connection to score error}
\[
|\qq\kk^\top-(\qq\PP^\top)\hh^\top|
\leq\|\qq\|_2\,\|\kk-\hh\PP\|_2.
\]
\end{block}
Default: reserve \alert{10\% of the attention budget} for EAS.\\
Example: 100,000 input tokens, 2,000 total budget, about 200 EAS slots.
\papersource{Paper, Eqs. (8)--(9), p. 5; budget setting, p. 6. Bound and numerical example are teaching derivations.}
\end{frame}

\begin{frame}{Offline projection calibration shifts work out of prefill}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.52\textwidth}
\textbf{Online:} construct $\PP$ from the current input keys.\medskip

\textbf{OPC:} collect keys from 180 calibration samples:
\begin{itemize}
\item 60 PG19: literary text;
\item 60 ProofPile: formal reasoning;
\item 60 CodeParrot: code.
\end{itemize}
Apply Algorithm 1 without backpropagation. Inference still encodes incoming keys.
\end{column}
\begin{column}{0.44\textwidth}
\fig{1}{fig07-prefill}
\small OPC prefill latency is close to full attention in this measurement.
\end{column}
\end{columns}
\papersource{Paper, Sec. 3.2, p. 4; Fig. 7 right, p. 14; Appendix B.2, p. 16. Consumer-grade GPU setup.}
\end{frame}

\begin{frame}{The evaluation changes budgets across context regimes}
\centering
\begin{tabular}{lll}
\toprule
Evaluation & Main quantity & BinaryPC budget \\
\midrule
Short tasks & GSM8K / MMLU accuracy; CoQA F1 & 5\% \\
LongBench & Mean of 16 task scores & 2\% and 1K \\
InfiniteBench & Mean of seven task scores & 2\% and 2K \\
LongBench v2 & Multiple-choice accuracy & 2\% and 2K \\
RULER, 8K--128K & 13-task score at each length & 2\% and 2K \\
NIAH & Retrieval by depth and length & 2\% \\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Fixed counts and percentages are different: at 8K, 2K is about 25\%.
\item MagicPIG's effective budget is data-dependent: about 5--7\% on short tasks, 2--3\% elsewhere.
\end{itemize}
\papersource{Paper, Sec. 4.1, pp. 5--7; Appendix A.1--A.2, pp. 13--14. All task scores shown later are higher-is-better.}
\end{frame}

\begin{frame}{OPC substantially improves short-context fidelity on Llama-3}
\centering
\begin{tabular}{lcc}
\toprule
Method & Llama-3-8B & Llama-3.1-8B \\
\midrule
Full attention & 64.92 & 72.74 \\
MagicPIG (default) & 56.46 & 64.23 \\
Spotlight (5\%) & 58.97 & --- \\
BinaryPC (5\%) & 59.31 & 70.81 \\
BinaryPC + OPC (5\%) & \alert{63.82} & \alert{71.16} \\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Llama-3 online average drops by 5.61 points from full attention.
\item Its GSM8K score is 54.50 full, 42.60 online, and 52.00 with OPC.
\end{itemize}
OPC matters for this setting; ``training-free'' does not imply no quality loss.
\papersource{Paper, Table 2, PDF p. 6. Average of GSM8K, CoQA, and MMLU; mixed accuracy / F1 scores.}
\end{frame}

\begin{frame}{LongBench averages remain close to full attention at 2\%}
\centering
\begin{tabular}{lccc}
\toprule
Model & Full & BinaryPC & BinaryPC + OPC \\
\midrule
Llama-3-8B & 30.63 & 30.18 & 30.35 \\
Llama-3.1-8B-Instruct & 49.64 & \alert{49.50} & 49.50 \\
Mistral-7B-Instruct-v0.3 & 47.31 & 47.07 & 47.24 \\
Qwen2.5-7B-Instruct-1M & 47.03 & 46.48 & 46.30 \\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Llama-3.1: a 0.14-point gap at 2\%; 49.66 / 49.67 with a 1K budget.
\item Task-specific gaps remain: Qwen Lcc is 46.19 full vs. 42.01 online and 39.94 with OPC.
\end{itemize}
\papersource{Paper, Table 3, p. 6; Table 9, p. 15. Mean over 16 datasets, not an equal mean of six category averages.}
\end{frame}

\begin{frame}{Long-context quality depends on the model and benchmark}
\centering
\begin{tabular}{llcc}
\toprule
Model & Method & InfiniteBench & LongBench v2 \\
\midrule
Llama-3.1-8B & Full & 43.30 & 29.4 \\
 & BinaryPC, 2\% & 43.21 & 29.8 \\
 & OPC, 2\% & 43.09 & 29.4 \\
\midrule
Qwen2.5-7B & Full & 31.15 & 30.4 \\
 & BinaryPC, 2\% & 29.83 & 31.2 \\
 & OPC, 2\% & 29.31 & 30.4 \\
\bottomrule
\end{tabular}\par
\medskip
Llama tracks the full baseline closely. Qwen loses 1.32 / 1.84 points on InfiniteBench, while maintaining LongBench v2 accuracy.
\papersource{Paper, Table 1, p. 5; Table 8, p. 14. Qwen is the Instruct-1M model; InfiniteBench reports a seven-task mean.}
\end{frame}

\begin{frame}{RULER separates hash approximation from sparse-budget loss}
\centering
\begin{tabular}{lrrrr}
\toprule
Context & Full & Exact TOPK 2\% & BinaryPC 2\% & BinaryPC 2K \\
\midrule
8K & 94.32 & 91.53 & 91.67 & 94.47 \\
16K & 93.96 & 91.37 & 90.86 & 93.98 \\
32K & 87.10 & 88.80 & 87.73 & 88.86 \\
64K & 85.19 & 83.39 & 84.36 & 85.09 \\
128K & 76.49 & 73.62 & \alert{73.23} & 72.89 \\
\midrule
Average & 87.41 & 85.74 & 85.57 & 87.06 \\
\bottomrule
\end{tabular}\par
\medskip
At 128K, BinaryPC is 0.39 points below exact sparse TOPK and 3.26 below full attention. The 2K setting uses much more budget at short lengths.
\papersource{Paper, Table 4, PDF p. 7. Llama-3.1-8B-Instruct. TOPK is an exact-score reference, not a task-score upper bound.}
\end{frame}

\begin{frame}{NIAH retrieval patterns closely follow full attention}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.49\textwidth}
\fig{1}{fig04-niah-full}
\end{column}
\begin{column}{0.49\textwidth}
\fig{1}{fig04-niah-binarypc}
\end{column}
\end{columns}
\medskip
\begin{itemize}
\item Horizontal axis: context length; vertical axis: needle depth; greener is better.
\item Llama-3.1 average: 95.11 full, 95.57 online, 95.85 with OPC.
\item Low-scoring cells remain near the beginning of longer contexts.
\end{itemize}
\papersource{Paper, Fig. 4, p. 7; Fig. 10, p. 20. BinaryPC budget 2\%; Qwen results in Fig. 9 reach 100.00.}
\end{frame}

\begin{frame}{EAS restores passkey retrieval for online BinaryPC}
\centering
\begin{tabular}{lrrrr}
\toprule
EAS share & Online R.PK & Online avg. & OPC R.PK & OPC avg. \\
\midrule
0\% & 64.00 & 41.30 & 99.00 & 46.93 \\
2\% & \alert{99.00} & 47.42 & 99.00 & 47.34 \\
5\% & 99.00 & 47.63 & 99.00 & 47.57 \\
10\% (default) & 99.00 & 47.41 & 99.00 & 47.51 \\
15\% & 99.00 & 47.51 & 99.00 & 47.41 \\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Just 2\% of the attention budget recovers 35 percentage points on R.PK.
\item Authors attribute failures to passkeys being hard-to-encode outliers.
\item This uses 100 samples per subtask; full attention averages 47.92.
\end{itemize}
\papersource{Paper, Sec. 4.3 and Table 5, PDF pp. 8--9. InfiniteBench, Llama-3.1-8B-Instruct.}
\end{frame}

\begin{frame}{64 bits and simple calibration are effective in the tested settings}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.46\textwidth}
\textbf{Hash length: NIAH}
\medskip
\begin{tabular}{lrr}
\toprule
Bits & 104K & Average \\
\midrule
32 & 71.82 & 86.37 \\
64 & 92.73 & \alert{90.18} \\
128 & 90.91 & 90.00 \\
\bottomrule
\end{tabular}
\medskip

64 bits fit in one machine word. Doubling the code gives no mean gain here.
\end{column}
\begin{column}{0.50\textwidth}
\textbf{Calibration: LongBench}
\medskip
\begin{tabular}{lr}
\toprule
Setting & Average \\
\midrule
Full attention & 30.57 \\
OPC, mixed data & 30.39 \\
OPC, PG19 only & \alert{30.43} \\
\bottomrule
\end{tabular}
\medskip

Literary calibration also works on this mix of QA, code, and synthetic tasks.
\end{column}
\end{columns}
\papersource{Paper, Tables 6--7, p. 9. NIAH mean: 88K--120K, Llama-3.1-8B. Table 7 is a separate reported setting.}
\end{frame}

\begin{frame}{A fourfold layer speedup includes retrieval overhead}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.49\textwidth}
\fig{1}{fig06-attention-time}
\end{column}
\begin{column}{0.47\textwidth}
\textbf{At 512K context:}
\begin{itemize}
\item Full attention: 1.814 ms.
\item Subset attention: 0.163 ms.
\item Search + top-$k$ + gather: 0.295 ms.
\end{itemize}
\[
\frac{1.814}{0.163+0.295}\approx\alert{4.0\times}.
\]
The complete layer cost matters, including scanning all key codes.
\end{column}
\end{columns}
\papersource{Paper, Sec. 4.2 and Fig. 6, PDF p. 8. Llama-3.1-8B-Instruct; 2\% attention budget.}
\end{frame}

\begin{frame}{The reported 3.56-fold decoding gain occurs at 2M tokens}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.48\textwidth}
\fig{1}{fig05-context-b2}
\end{column}
\begin{column}{0.49\textwidth}
\begin{itemize}
\item Llama-3.1-8B-Instruct + OPC.
\item Eight data-center GPUs, pipeline parallelism, static KV cache.
\item Batch size 2, 2\% budget.
\item Warm up 32 steps; generate 64 tokens; average three runs.
\end{itemize}
\medskip
\alert{Position encoding is extended and output quality is not evaluated in this throughput experiment.}
\end{column}
\end{columns}
\papersource{Paper, Sec. 4.2, pp. 7--8; Fig. 5, second panel. Decode throughput excludes prefill and offline calibration.}
\end{frame}

\begin{frame}{The largest batch-size gain includes a kernel fallback effect}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.48\textwidth}
\fig{1}{fig05-batch-128k}
\end{column}
\begin{column}{0.49\textwidth}
\begin{itemize}
\item At batch sizes above 15, the full-attention implementation switches from Split-K to a standard kernel.
\item BinaryPC calls attention on a much smaller selected subset.
\item At 128K and batch 16, the measured ratio reaches \alert{5.04$\times$}.
\end{itemize}
\medskip
This ratio combines sparse access with the implementation's kernel-selection behavior.
\end{column}
\end{columns}
\papersource{Paper, Sec. 4.2 and Fig. 5 rightmost, PDF p. 8. Eight data-center GPUs; FlashAttention 2.7.1.}
\end{frame}

\begin{frame}{The useful contribution is the combination of three decisions}
\begin{enumerate}
\item \textbf{Reconstruct before retrieving.} Data-aware binary coefficients yield a useful score proxy without gradients.
\medskip
\item \textbf{Allocate precision asymmetrically.} One 8-byte code per key; a more precise query is reused across the scan.
\medskip
\item \textbf{Protect hard-to-encode evidence.} EAS repairs a substantial online passkey failure.
\end{enumerate}
\medskip
\begin{block}{Practical scope}
Keep the full KV cache, adding about 1.56\% for key codes at $D=128$ BF16.
Long contexts offer the strongest speed benefit; task quality and short-context latency still require attention.
\end{block}
\papersource{Paper, Secs. 3--4; memory calculation: Appendix B.4, p. 17.}
\end{frame}

\begin{frame}{Reference and discussion}
\textbf{Daohai Yu et al.}\\
\emph{Training-Free Hashing-Based Attention via Binary Principal Components}.\\
ICML 2026; arXiv:2608.04405v1, submitted 5 August 2026.
\medskip

\href{https://arxiv.org/abs/2608.04405v1}{arxiv.org/abs/2608.04405v1}\\
\href{https://github.com/yudaohai666/BPC}{Author code: github.com/yudaohai666/BPC}
\medskip
\begin{block}{Questions suggested by the method}
Can gradient-free construction target ranking error more directly?\\
How should a static basis and protected set evolve during long generation?
\end{block}
\papersource{All reported results in this presentation come from the version above. Additional derivations are labeled.}
\end{frame}

\appendix

\begin{frame}{Backup: construction and fixed-basis encoding have different guarantees}
\textbf{Construction, fixed binary $\uu$:}
\[
\vv_{\rm LS}=\frac{\uu^\top\RR}{N},\qquad
\|\RR-\uu\vv_{\rm LS}\|_F^2
=\|\RR\|_F^2-\frac{\|\uu^\top\RR\|_2^2}{N}.
\]
The aggregate reconstruction residual cannot increase in this update.
\medskip

\textbf{New key, fixed component $\vv$:}
\[
\|\rr-\sgn(\rr\vv^\top)\vv\|_2^2-\|\rr\|_2^2
=\|\vv\|_2^2-2|\rr\vv^\top|.
\]
This quantity can be positive. Residual curves for fixed-basis encoding are empirical evidence on the tested data.
\papersource{Discussion derivations from Algorithms 1--2, PDF p. 4; empirical curves: Fig. 3.}
\end{frame}

\begin{frame}{Backup: make the sign convention and bit weights explicit}
Encode $+1$ as 0 and $-1$ as 1 on both sides. Let $W$ be the XOR of the sign words; $W=1$ means disagreement.
\[
\hat p_i=s_i\sum_{j=0}^{6}2^jM_{j,i}.
\]
\[
\sum_i h_i\hat p_i
=\sum_{j=0}^{6}2^j
\left[\pc(M_j\land\neg W)-\pc(M_j\land W)\right].
\]
\begin{itemize}
\item Paper Eqs. (10)--(12) use indices $1,\ldots,7$ with weights $2^j$: one shift from standard seven-bit magnitudes.
\item A common positive scale preserves top-$k$; reversing the sign does not. Eq. (13) requires a clear bit convention.
\end{itemize}
\papersource{Explicit implementation convention derived for discussion. Paper, Algorithm 3, p. 5; Eqs. (10)--(13), p. 15.}
\end{frame}

\begin{frame}{Backup: retrieval success and aggregation success differ}
\centering
\begin{tabular}{llrrr}
\toprule
Context & RULER task & Full & TOPK 2\% & BinaryPC 2\% \\
\midrule
8K & Common-word extraction & 96.30 & 75.40 & 75.30 \\
128K & Multi-key 3 & 70.00 & 59.00 & 45.00 \\
128K & Multi-value & 94.00 & 92.50 & 92.50 \\
\bottomrule
\end{tabular}\par
\medskip
First-decode-step output cosine similarity to full attention:
\medskip

\begin{tabular}{lrrrr}
\toprule
Method & 8K & 16K & 32K & 64K \\
\midrule
BinaryPC (2.0\%) & .9835 & .9811 & .9870 & .9895 \\
MagicPIG (2.2\%) & .9388 & .9651 & .9595 & .9725 \\
\bottomrule
\end{tabular}
\papersource{Paper, Tables 14 and 18, pp. 19 and 21; Table 10, p. 15. Quest 128K differs between Tables 4 and 18: 65.39 vs. 63.59.}
\end{frame}

\begin{frame}{Backup: BinaryPC is competitive, but not always the fastest sparse method}
\textbf{Single data-center GPU, 64K, batch 4:}
\medskip

\begin{tabular}{lrrr}
\toprule
Method & FlashAttention & MagicPIG & BinaryPC \\
\midrule
Throughput (tokens/s) & 87.62 & 42.05 & 148.46 \\
\bottomrule
\end{tabular}
\medskip

\textbf{Eight consumer-grade GPUs, 128K, sparse budget 2,048:}
\medskip

\begin{tabular}{lrrrr}
\toprule
Method & Full & PyramidKV & CompressKV & BinaryPC \\
\midrule
Throughput (tokens/s) & 21.31 & 28.14 & 29.01 & 27.66 \\
\bottomrule
\end{tabular}\par
\medskip
The second comparison follows official baseline implementations; FlashAttention uses StaticCache. BinaryPC retains the full KV cache.
\papersource{Paper, Tables 12--13 and Appendix B.5--B.6, PDF p. 18. Throughput comparisons are within each hardware setup.}
\end{frame}

\begin{frame}{Backup: 70B results support scale transfer with a length-dependent crossover}
\textbf{Llama-3-70B-Instruct, LongBench category scores:}
\medskip

\begin{tabular}{lrrrrrr}
\toprule
Method & S-Doc & M-Doc & Sum. & F-shot & Syn. & Code \\
\midrule
Full & 42.18 & 47.51 & 27.31 & 70.83 & 38.50 & 54.24 \\
BinaryPC & 42.06 & 47.78 & 26.98 & 70.96 & 38.25 & 55.22 \\
\bottomrule
\end{tabular}
\medskip

\textbf{Single attention layer, 70B (ms; lower is better):}
\medskip

\begin{tabular}{lrrrr}
\toprule
Method & 32K & 64K & 128K & 256K \\
\midrule
Full & .181 & .343 & .654 & 1.289 \\
BinaryPC, 2,048 tokens & .243 & .243 & .243 & .245 \\
\bottomrule
\end{tabular}\par
\medskip
The fixed-budget sparse layer is slower at 32K and faster at longer lengths.
\papersource{Paper, Table 11 and Appendix B.4, PDF p. 17. The accuracy block does not specify the same 2,048-token budget.}
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