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41\section{Results}
42
43Our method performs significantly better thenthan
44the baseline on all three datasets, as
45shown in Table~\ref{tab:main}. The gap widens
46with document length: past 16k tokens the
47dense model spends most of its budget on
48pairs that contribute nothing to the answer.
49
50\begin{equation}
51  \mathcal{L}(\theta) = \sum_i \alpha_i
52    \operatorname{softmax}(q_i k_i^{\top} / \sqrt{d})
53\end{equation}

Compilemain.tex

EnginepdfLaTeX (auto)

Last build1.4 s

latexmk -pdf -interaction=nonstopmode main.tex
This is pdfTeX, Version 3.141592653-2.6-1.40.26
Latexmk: Run number 2 of rule 'pdflatex'
Output written on main.pdf (9 pages, 412218 bytes)

4 Results

Our method performs better than the baseline on all three datasets, as shown in Table 1. The gap widens with document length: past 16k tokens the dense model spends most of its budget on pairs that contribute nothing to the answer.

ℒ(θ) = Σᵢ αᵢ softmax(qᵢ kᵢᵀ / √d)(1)

Model	NarrativeQA	QuALITY	∞Bench
Dense	28.4	71.2	41.0
Sparse (ours)	31.7	74.9	45.6

Table 1: Accuracy on three long-context benchmarks.

02Ln 43, Col 28

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Sparse Attention

main.texRelated work

18Representation depth is what

19carries the gain

20\cite{hinton2015}.

22Earlier work \cite{child2019}

24Attention cost grows with

25the square of the length.

Suggested for lines 24–25

7 sources1 with no entry2 unused

Sparse Attention

Open questions · 3

Ablation on sequence length is still promisedAblations · main.texL35

Does Table 2 still need the 7B baseline?Benchmarks · main.texL57

Confirm the licence on Figure 3Discussion · main.texL64

9 sections3 open questions

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