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\title[RIS-Kernel]{RIS-Kernel}
\subtitle{Sparse attention for CPU long-context inference\\Method, results, and evidence boundaries}
\author{Paper author: Anderson R. Santos (UFU)\\[2mm]
  \small Independent paper-reading presentation}
\date{arXiv:2607.21927v1 \;|\; Submitted July 24, 2026\\
  Reading date: October 1, 2026 \;|\; Approximately 25 minutes + backup}

\begin{document}

\begin{frame}
\titlepage
\vspace{-0.35cm}
\centering
\small\href{https://arxiv.org/abs/2607.21927v1}{RIS-Kernel: A Model-Agnostic Architecture for Long-Context LLM Inference via Sparse Attention}
\end{frame}

\begin{frame}{The paper offers a CPU inference proof of concept}
\begin{block}{Core idea}
Combine local connections and random sparse views, merge selected
indices, and normalize them together without changing model weights.
\end{block}
\gap
\begin{itemize}
\item \textbf{32k:} best reported Stochastic score is 24/32; dense is 23/32.
\item \textbf{64k:} best Structural score is 42/64; no context is 33/64.
\item \textbf{Scope:} small models, four scientific documents, CPU hardware.
\end{itemize}
\readingnote{Data inconsistencies and incomplete cost accounting limit the stronger claims.}
\papersource{\src{Secs. 2.2, 4.4.1; Tables 2 and 5; PDF pp. 3--5, 9, 16--17, 20}}
\end{frame}

\begin{frame}{Three failure modes motivate the design}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.31\textwidth}
\begin{block}{Missing facts}
A sparse view can miss distant entities and their supporting context.
\end{block}
\centering\alert{Multiple views\\+ local structure}
\end{column}
\begin{column}{0.31\textwidth}
\begin{block}{Merging attention}
Separately normalized groups need a principled way to compete.
\end{block}
\centering\alert{Unified softmax\\over an index union}
\end{column}
\begin{column}{0.31\textwidth}
\begin{block}{Position extrapolation}
Selecting a useful token does not ensure usable positional features.
\end{block}
\centering\alert{Dynamic RoPE\\scaling}
\end{column}
\end{columns}
\gap\gap
The target is inference on existing models; no weight update is reported.
\papersource{\src{Introduction and Methods; PDF pp. 1--2, 14--17}}
\end{frame}

\begin{frame}{The ensemble merges connections before attention}
\centering
\begin{tikzpicture}[
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 arr/.style={-{Stealth[length=2.2mm]},thick,AcademicBlue}]
\node[box] (load) at (0,1.9) {Load model\\adjust RoPE};
\node[box] (base) at (4.25,1.9) {Local window\\+ initial anchor};
\node[box] (seeds) at (8.5,1.9) {Generate $S$ views\\streaming merge};
\node[box] (prefill) at (8.5,0.1) {Prefill with\\merged geometry};
\node[box] (decode) at (4.25,0.1) {Cached anchor\\+ sliding window};
\node[box] (pfus) at (0,0.1) {Unique indices\\KV gather + one softmax};
\draw[arr] (load)--(base); \draw[arr] (base)--(seeds);
\draw[arr] (seeds)--(prefill); \draw[arr] (prefill)--(decode);
\draw[arr] (decode)--(pfus);
\end{tikzpicture}
\gap
\begin{itemize}
\item $T$: sequence length; $S$: seed count. The paper overloads $N$.
\item Methods describe an \textbf{index union}, not $S$ answer-level votes.
\end{itemize}
\papersource{Teaching schematic based on Secs. 4.1--4.4.2 and Figs. 8--9, PDF pp. 14--17.}
\end{frame}

\begin{frame}{Structural sampling spends budget on local blocks}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.47\textwidth}
\begin{block}{Stochastic}
Uniform global neighbors per pivot; independent views improve the
chance of selecting distant content.
\end{block}
\gap
\textbf{Trade-off:} low-budget sampling can miss relevant neighborhoods.
\end{column}
\begin{column}{0.49\textwidth}
\begin{block}{Structural}
Build local cliques, then add random global edges from the remaining budget.
\end{block}
\[
B=\min(0.1T,B_{\max})
\]
\[
d_{\mathrm{eff}}=d_{\mathrm{clique}}+d_{\mathrm{global}}
\]
\end{column}
\end{columns}
\gap
Both include base geometry: a 1,024-token local window and an initial anchor.
\readingnote{A local clique preserves within-block links; it does not guarantee access to every answer.}
\papersource{\src{Secs. 4.2, 4.4.2; PDF pp. 15, 17}}
\end{frame}

\begin{frame}{Streaming removes mask copies, not quadratic storage}
\begin{block}{One seed at a time}
Sample indices $\rightarrow$ apply causality $\rightarrow$ merge into master
structures $\rightarrow$ release the temporary seed object.
\end{block}
\gap
\begin{columns}[T,onlytextwidth]
\begin{column}{0.49\textwidth}
\textbf{What it saves}
\begin{itemize}
\item Avoids holding all seed masks at once.
\item Reduces temporary memory as a function of $S$.
\end{itemize}
\end{column}
\begin{column}{0.47\textwidth}
\textbf{What remains}
\begin{itemize}
\item The master boolean mask is $O(T^2)$.
\item At 65,536 tokens: 4 GiB per full mask if one byte per entry.
\end{itemize}
\end{column}
\end{columns}
\readingnote{The stated length-independent initialization cost conflicts with the explicit quadratic matrix.}
\papersource{\src{Sec. 4.1 and Fig. 8, PDF p. 14} Memory size is a reader calculation.}
\end{frame}

\begin{frame}{PFUS puts selected tokens in one normalization domain}
\textbf{PFUS:} Pre-Fusion Unified Softmax.
\[
\mathcal I_t=\operatorname{unique}
  (\mathcal A_{\mathrm{stoch}}\cup\mathcal W_t)
\]
\[
o_t=\sum_{j\in\mathcal I_t}
 \frac{\exp(q_t^{\mathsf T}k_j/\sqrt{D_h})}
 {\sum_{\ell\in\mathcal I_t}\exp(q_t^{\mathsf T}k_\ell/\sqrt{D_h})}\,v_j
\]
\begin{itemize}
\item Cache the random anchor after the first generated token.
\item Update the local window, deduplicate, then gather the selected KV.
\item Every selected token competes using the same softmax denominator.
\end{itemize}
\readingnote{No isolated PFUS ablation is reported. Exact denominator-weighted merging of separate groups can also recover unified softmax.}
\papersource{Equation is a teaching reconstruction of Sec. 4.3 / Fig. 9, PDF pp. 15--16.
$q,k\in\mathbb R^{D_h}$; $\mathcal W_t$ is the dynamic local window.}
\end{frame}

\begin{frame}{One-percent views can produce a half-dense union}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.45\textwidth}
\[
U=1-(1-d)^S
\]
\begin{itemize}
\item Independent views, equal per-target inclusion probability $d$.
\item Probability of selection, not probability of a correct answer.
\item Shared cliques violate simple independence assumptions.
\end{itemize}
\end{column}
\begin{column}{0.49\textwidth}
\centering
\begin{tabular}{rrr}
\toprule
$d$ & $S$ & Expected $U$ \\
\midrule
1\% & 10 & 9.56\% \\
1\% & 70 & \textbf{50.52\%} \\
1\% & 100 & 63.40\% \\
5\% & 10 & 40.13\% \\
5\% & 40 & 87.15\% \\
5\% & 70 & \textbf{97.24\%} \\
\bottomrule
\end{tabular}
\end{column}
\end{columns}
\gap
\alert{Single-view density is not final attention density or end-to-end cost.}
\papersource{\src{Eq. (1), Sec. 2.2.3, PDF pp. 5--6} Table recalculated from the equation;
the paper uses $N$ for seed count here.}
\end{frame}

\begin{frame}{The stated implementation does not establish $O(T\log T)$}
If each query keeps $r(T)$ keys, ideal sparse attention costs
\[
O\!\left(T\,r(T)\,D_h\right).
\]
\begin{itemize}
\item $O(T\log T)$ requires $r(T)=O(\log T)$ at fixed head dimension.
\item Under the paper's fixed-density union model,
  $r(T)\approx T[1-(1-d)^S]$: still quadratic for fixed $d,S$.
\item A sparse mask alone does not prove that prefill skips dense arithmetic.
\item Construction, KV storage, projections, MLPs, and decoding need separate accounting.
\end{itemize}
\readingnote{The paper gives no complete scaling curve that verifies the headline asymptotic claim for this implementation.}
\papersource{Reader analysis of Secs. 3.4--3.5 and 4.1--4.3, PDF pp. 13--16.}
\end{frame}

\begin{frame}{The main benchmark is small multiple-choice QA}
\centering
\begin{tabular}{p{3.15cm}p{4.5cm}p{4.5cm}}
\toprule
 & Native-window study & Extrapolation study \\
\midrule
Model & Qwen2-1.5B-Instruct & Qwen2-1.5B-Instruct \\
Context & 32,768 tokens & 65,536 tokens \\
Questions & 32, five choices & 64, five choices \\
No-context score & 19/32 (59.38\%) & 33/64 (51.56\%) \\
Dense score & 23/32 (71.88\%) & OOM in tested setup \\
Main hardware & 16 GB desktop CPU & 128 GB Xeon CPU \\
\bottomrule
\end{tabular}
\gap
\begin{itemize}
\item Context: four cleaned biological/scientific manuscripts.
\item Choose the option with the highest log-probability; no free-text QA.
\item Float32, CPU only; some 32k configurations move to the larger server.
\end{itemize}
\papersource{\src{Secs. 2.1--2.2, 4.4.1; PDF pp. 2--5, 15--17}}
\end{frame}

\begin{frame}{At 32k, the best reported result adds one correct answer}
\centering
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\foreach \x in {0,8,16,24,32}{
 \draw[gray!20] (\x,-0.55)--(\x,3.55);
 \node[below] at (\x,-0.6){\x};}
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\node[left] at (-0.35,3.24){No context};
\node[left] at (-0.35,2.24){Dense};
\node[left] at (-0.35,1.24){Stoch. 1\%, 70--80 seeds};
\node[left] at (-0.35,0.24){Stoch. 5\%, 10 seeds};
\node[right] at (19,3.24){19/32};
\node[right] at (23,2.24){23/32};
\node[right] at (24,1.24){24/32};
\node[right] at (23,0.24){23/32};
\node[below] at (16,-1.1){Correct answers (out of 32)};
\end{tikzpicture}
\gap
\[
\text{Gap recovery}=\frac{24-19}{23-19}=125\%.
\]
\readingnote{125\% is a ratio of net accuracy gains. It does not mean recovering 125\% of document information. Dense is an empirical reference.}
\papersource{Redrawn from Table 5, PDF p. 20; Sec. 2.2.1, p. 3. Best-vs-dense gain: 3.125 percentage points.}
\end{frame}

\begin{frame}{The 32k Structural evidence is internally inconsistent}
\centering
\begin{tabular}{lrr}
\toprule
Configuration & Text / Table 5 & Figure 1 \\
\midrule
Structural 1\%, 10 seeds & 68.75\% & $\approx$65.6\% \\
Structural 1\%, 40 seeds & 71.88\% & $\approx$68.8\% \\
Structural 5\%, 10 seeds & 65.62\% & $\approx$71.9\% \\
\bottomrule
\end{tabular}
\gap\gap
\begin{itemize}
\item Figure 3 shows Structural peaks of 68.75\% at both 1\% and 2\%.
\item These conflict with the text's claim of reaching dense at those densities.
\item The headline ``75\% gap recovery with 10 seeds'' is therefore disputed within v1.
\end{itemize}
\readingnote{The reading preserves both sources; raw run records are needed to resolve the discrepancy.}
\papersource{\src{Sec. 2.2.1 / Fig. 1, p. 3; Fig. 3, p. 4; Table 5, p. 20}}
\end{frame}

\begin{frame}{At 64k, selected configurations improve on no context}
\centering
\begin{tikzpicture}[x=0.135cm,y=0.75cm,font=\small]
\foreach \x in {0,16,32,48,64}{
 \draw[gray!20] (\x,-0.55)--(\x,2.55);
 \node[below] at (\x,-0.6){\x};}
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\fill[AcademicTeal] (0,0) rectangle (42,0.5);
\node[left] at (-0.3,2.25){No context};
\node[left] at (-0.3,1.25){Stoch. 5\%, 40--60 seeds};
\node[left] at (-0.3,0.25){Struct. 1\%, 100 seeds};
\node[right] at (33,2.25){33/64};
\node[right] at (40,1.25){40/64};
\node[right] at (42,0.25){42/64};
\node[below] at (32,-1.05){Correct answers (out of 64), YaRN};
\end{tikzpicture}
\gap\gap
\begin{itemize}
\item Structural gain: $9/64=14.0625$ percentage points.
\item Stochastic gain: $7/64=10.9375$ percentage points.
\item Dense failed in this setup; dense-relative quality is unknown at 64k.
\end{itemize}
\papersource{Redrawn from Fig. 4 and Tables 2--3, PDF pp. 5, 9--10; paired results, p. 17.
42/64 is 65.625\%, rounded as 65.62\% or 65.63\% in the paper.}
\end{frame}

\begin{frame}{The two modes favor different parts of the tested grid}
\centering
\begin{tabular}{lrrrr}
\toprule
 & \multicolumn{2}{c}{Stochastic} & \multicolumn{2}{c}{Structural} \\
Density & Mean & Peak & Mean & Peak \\
\midrule
1\% & 52.13\% & 57.81\% & \textbf{56.53\%} & \textbf{65.62\%} \\
2\% & 54.97\% & 60.94\% & 56.25\% & 62.50\% \\
5\% & \textbf{58.66\%} & \textbf{62.50\%} & 55.26\% & 60.94\% \\
\bottomrule
\end{tabular}
\gap\gap
\begin{itemize}
\item Local structure helps the low-density region in this benchmark.
\item Stochastic global sampling benefits more from increasing density.
\item Increasing seeds does not guarantee monotonically improving accuracy.
\end{itemize}
\readingnote{Means summarize different grid configurations, not repeated estimates at a fixed configuration. No uncertainty intervals are reported.}
\papersource{\src{Table 2 / Sec. 2.6, PDF pp. 8--9; Fig. 5, p. 6}}
\end{frame}

\begin{frame}{YaRN beats linear scaling in the reported peak comparison}
\centering
\begin{tabular}{lrr}
\toprule
Density & Linear peak (seeds) & YaRN peak (seeds) \\
\midrule
1\% & 45.3\% (50) & 57.8\% (40) \\
2\% & 54.7\% (50) & 60.9\% (40) \\
5\% & 59.4\% (40--50) & 62.50\% (40--60) \\
\bottomrule
\end{tabular}
\gap\gap
\begin{itemize}
\item 64k is a $2\times$ extension of the model's stated 32k native window.
\item Positional scaling and sparse selection jointly affect retrieval.
\item These are separately selected peaks; seed budgets are not all matched.
\end{itemize}
\readingnote{Do not compare linear single-seed scores (15.6--23.4\%) against YaRN multi-seed peaks as a pure RoPE effect. Fig. 6 also mixes reporting conventions.}
\papersource{\src{Table 1, PDF p. 7; Secs. 2.3--2.5, pp. 6--8}}
\end{frame}

\begin{frame}{TinyLlama shows a boundary, not a universal scaling law}
\centering
\begin{tabular}{lrrr}
\toprule
Context & Native-window multiple & Questions & Correct \\
\midrule
4,096 & $2\times$ & 4 & 2 (50.0\%) \\
8,192 & $4\times$ & 8 & 1 (12.5\%) \\
16,384 & $8\times$ & 16 & 1 (6.25\%) \\
32,768 & $16\times$ & 32 & 6 (18.75\%) \\
\bottomrule
\end{tabular}
\gap
\begin{itemize}
\item TinyLlama-1.1B with YaRN; stated native window: 2,048.
\item Paper reports no accuracy change over the tested densities and seeds.
\item Adding views did not rescue these configurations.
\end{itemize}
\readingnote{Very small, changing question sets and incomplete controls prevent attribution solely to RoPE or generalization to all small models.}
\papersource{\src{Sec. 2.5, PDF pp. 7--8}}
\end{frame}

\begin{frame}{Sub-1\% density retains less net retrieval gain than claimed}
\centering
\begin{tabular}{lrrr}
\toprule
Structural setting & Best seeds & Best score & $B_{\max}$ \\
\midrule
0.3\% & 150--200 & 38/64 (59.38\%) & 197 \\
0.5\% & 150--200 & 38/64 (59.38\%) & 328 \\
0.8\% & 100 & 40/64 (62.50\%) & 524 \\
1.0\% baseline & 100 & 42/64 (65.63\%) & 655 \\
\bottomrule
\end{tabular}
\gap
\begin{columns}[T,onlytextwidth]
\begin{column}{0.46\textwidth}
\begin{block}{Absolute accuracy retained}
\centering $38/42=90.48\%$
\end{block}
\end{column}
\begin{column}{0.50\textwidth}
\begin{alertblock}{Net gain over no context retained}
\centering $(38-33)/(42-33)=55.56\%$
\end{alertblock}
\end{column}
\end{columns}
\readingnote{Lower block density with more seeds does not establish a 70\% reduction in total runtime.}
\papersource{\src{Sec. 2.7 / Table 3, PDF p. 10} Retention ratios recalculated from question counts.}
\end{frame}

\begin{frame}{Cross-document generation is qualitative and expensive}
\begin{columns}[T,onlytextwidth]
\begin{column}{0.48\textwidth}
\textbf{Different experiment}
\begin{itemize}
\item Qwen2.5-1.5B, linear RoPE.
\item Six document pairs, 22.8k--32.4k tokens.
\item Two phases change density, seeds, temperature, and repetition penalty.
\end{itemize}
\end{column}
\begin{column}{0.48\textwidth}
\textbf{Reported observations}
\begin{itemize}
\item Phase 1: 90--113 min per pair.
\item Phase 2: 16--63 min per pair.
\item One semantic error in Phase 1; none observed in Phase 2.
\item 36 GB peak across six active processes.
\end{itemize}
\end{column}
\end{columns}
\gap
\readingnote{Twelve runs with author assessment do not establish a general hallucination rate. Different output lengths and decoding parameters confound timing and quality attribution.}
\papersource{\src{Sec. 2.8 / Table 4, PDF pp. 10--11} Times converted to minutes.}
\end{frame}

\begin{frame}{The strongest reported paired test is only marginal}
\centering
\begin{tabular}{p{7.15cm}rl}
\toprule
Comparison & $p$ & Interpretation \\
\midrule
32k best Stochastic vs no context & 0.227 & Not significant \\
64k best Structural vs no context & 0.078 & Below 0.10 only \\
64k best Stochastic vs no context & 0.189 & Not significant \\
64k best Structural vs best Stochastic & 0.6875 & No detected difference \\
\bottomrule
\end{tabular}
\gap
\begin{itemize}
\item These are the paper's McNemar results, not independently reproduced tests.
\item No direct best-Stochastic-vs-dense significance result is reported.
\item Reusing questions across a grid does not create independent evidence.
\end{itemize}
\readingnote{No detected difference is not equivalence; post-selection uncertainty and multiplicity remain unresolved.}
\papersource{\src{Sec. 4.4.1, PDF pp. 16--17} Full discordant-pair counts are not given there.}
\end{frame}

\begin{frame}{A stronger evaluation needs quality and actual cost together}
\begin{enumerate}
\item \textbf{Resolve provenance:} align plots, Table 5, code snapshot,
and per-question predictions.
\item \textbf{Separate selection and testing:} larger held-out QA sets,
repeated random trials, uncertainty intervals.
\item \textbf{Measure real cost:} union density, mask construction,
prefill, decode, peak memory, end-to-end latency.
\item \textbf{Isolate mechanisms:} PFUS, cliques, local window,
cached anchors, and RoPE with matched controls.
\end{enumerate}
\gap
\alert{CPU feasibility is useful evidence; it does not establish universal GPU speedups or architecture-independent quality.}
\papersource{Reader synthesis of the evidence gaps in Secs. 2--4, PDF pp. 2--17.}
\end{frame}

\begin{frame}{Keep the engineering idea and qualify the headline claims}
\begin{block}{What the paper supports}
A runtime combination of sparse geometry, cached index selection,
unified softmax, and RoPE scaling can deliver some long-context retrieval
gains on the reported CPU benchmark.
\end{block}
\gap
\begin{itemize}
\item \textbf{Mechanism:} merge sparse views; do not confuse one-view density with total work.
\item \textbf{Evidence:} promising selected scores, small samples, disputed Structural 32k data.
\item \textbf{Boundary:} neither universal $O(T\log T)$ inference nor reliable dense superiority is established.
\end{itemize}
\papersource{Synthesis of arXiv:2607.21927v1. Full evidence locators and discrepancies are in the companion Chinese notes.}
\end{frame}

\begin{frame}{Sources and reading scope}
\textbf{Anderson R. Santos.} RIS-Kernel: A Model-Agnostic Architecture
for Long-Context LLM Inference via Sparse Attention.\\
arXiv:2607.21927v1, July 24, 2026.
\gap
\begin{itemize}
\item \href{https://arxiv.org/abs/2607.21927v1}{Versioned arXiv record}
and \href{https://arxiv.org/pdf/2607.21927v1}{20-page paper PDF}.
\item Read the author TeX, bibliography, all sections, nine figures,
five tables, and the supplementary table.
\item Paper figures are reproduced with attribution under CC BY 4.0.
Bars and arithmetic in this deck are explicitly labeled reconstructions.
\item Author's \href{https://github.com/santosardr/riskernel}{GitHub project}
is a replication entry point. Current repository content is not treated as the v1 implementation.
\end{itemize}
\readingnote{No model experiments or source-code audit were performed for this reading. Reported statistical tests are attributed to the paper.}
\end{frame}

\appendix

\begin{frame}{Backup: why naive group averaging changes softmax}
One global token has score $3$; two local tokens have scores $0,0$.
\gap
\begin{columns}[T,onlytextwidth]
\begin{column}{0.47\textwidth}
\begin{block}{One shared denominator}
\[
p_{\mathrm{global}}=\frac{e^3}{e^3+2}\approx0.909.
\]
Every token's score contributes to the same normalization.
\end{block}
\end{column}
\begin{column}{0.49\textwidth}
\begin{block}{Equal averaging of two groups}
The global token gets probability 1 within its singleton group,
then weight $1/2$ after averaging.
\[
p_{\mathrm{global}}=0.5.
\]
\end{block}
\end{column}
\end{columns}
\gap
Exact merging remains possible with group denominator weights:
\[
o=\frac{Z_G o_G+Z_L o_L}{Z_G+Z_L}.
\]
\small $Z_G,Z_L$: softmax denominators of the disjoint global and local groups.
\papersource{Teaching example, not an experiment in the paper. Motivation: Sec. 4.3, PDF pp. 15--16.}
\end{frame}

\begin{frame}{Backup: the original 32k figure exposes the conflict}
\centering
\includegraphics[width=0.94\linewidth,height=0.72\textheight,keepaspectratio]{figures/fig-01.pdf}
\papersource{Original Fig. 1, PDF p. 3, Anderson R. Santos, CC BY 4.0.
Structural 1\% at 10/40 seeds differs from Table 5 (p. 20).}
\end{frame}

\begin{frame}{Backup: further consistency checks change interpretation}
\begin{itemize}
\item \textbf{Figure 2, p. 4:} right-axis gap recovery does not correctly align
0\% with the floor and 100\% with dense. Recalculate from counts.
\gap
\item \textbf{Table 5, p. 20:} Stochastic 5\% / one seed is 57.81\%,
which cannot be an integer-correct result on a single 32-question run.
\gap
\item \textbf{Secs. 2.2.2 / 2.5:} 62.50\% is called a 64k ceiling,
but Tables 2--3 report Structural at 42/64 = 65.625\%.
\gap
\item \textbf{Sec. 2.7, p. 10:} 0.7\% and 0.9\% still improve from
150 to 200 seeds in Table 3, contrary to the saturation text.
\end{itemize}
\papersource{Reader checks against the original PDF figures, tables, and TeX. These remain unresolved in v1.}
\end{frame}

\begin{frame}{Backup: sub-1\% best scores are non-monotonic}
\centering
\begin{tabular}{rrrrr}
\toprule
Density & $B_{\max}$ & Best accuracy & Best seeds & Grid mean \\
\midrule
0.1\% & 66 & 51.56\% & 150, 200 & 48.44\% \\
0.2\% & 131 & 54.69\% & 150 & 51.95\% \\
0.3\% & 197 & 59.38\% & 150, 200 & 55.08\% \\
0.4\% & 262 & 59.38\% & 150 & 56.25\% \\
0.5\% & 328 & 59.38\% & 150, 200 & 58.20\% \\
0.6\% & 393 & 57.81\% & 100, 150 & 56.64\% \\
0.7\% & 459 & 60.94\% & 200 & 57.42\% \\
0.8\% & 524 & 62.50\% & 100 & 60.16\% \\
0.9\% & 590 & 57.81\% & 200 & 55.47\% \\
\bottomrule
\end{tabular}
\par\gap
\small Structural / Qwen2-1.5B / YaRN / 65,536 tokens.\par
\small Each density tests 50, 100, 150, 200 seeds; these are configuration means.
\papersource{Selected columns and best-seed locations from Table 3, PDF p. 10. No-context score: 51.56\%.}
\end{frame}

\end{document}