% Compile with: python3 build_slides.py slides.en.tex % Adapted from the arxiv-paper-reader Beamer template. \documentclass[aspectratio=169,11pt]{beamer} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath,amssymb,graphicx,booktabs,array} \definecolor{AcademicBlue}{RGB}{26,57,86} \definecolor{AcademicTeal}{RGB}{0,105,112} \definecolor{PlotFull}{RGB}{75,114,177} \definecolor{PlotSliding}{RGB}{38,170,225} \definecolor{PlotBased}{RGB}{221,132,81} \definecolor{PlotMamba}{RGB}{248,237,48} \definecolor{PlotHthree}{RGB}{83,168,104} \definecolor{PlotHyena}{RGB}{197,79,83} \setbeamercolor{structure}{fg=AcademicBlue} \setbeamercolor{frametitle}{fg=AcademicBlue,bg=white} \setbeamercolor{title}{fg=AcademicBlue} \setbeamercolor{alerted text}{fg=AcademicTeal} \setbeamercolor{block title}{fg=white,bg=AcademicBlue} \setbeamercolor{block body}{fg=black,bg=AcademicBlue!5} \setbeamertemplate{navigation symbols}{} \setbeamertemplate{itemize items}[circle] \setbeamertemplate{footline}{\hfill\usebeamerfont{page number in head/foot}\insertframenumber\,/\,\inserttotalframenumber\hspace{4mm}\vspace{3mm}} \setbeamersize{text margin left=8mm,text margin right=8mm} \setbeamerfont{frametitle}{size=\Large,series=\bfseries} \setbeamerfont{title}{size=\LARGE,series=\bfseries} \setbeamerfont{block title}{size=\normalsize,series=\bfseries} \newcommand{\papersource}[1]{\par\smallskip{\scriptsize\color{black!60}#1\par}} \newcommand{\BASED}{\textsc{Based}} \newcommand{\BC}{\textsc{BaseConv}} \renewcommand{\arraystretch}{1.18} \title[BASED]{Simple linear attention language models\newline balance the recall-throughput tradeoff} \subtitle{BASED: global memory, precise local mixing, efficient execution} \author{Paper by Simran Arora, Sabri Eyuboglu, Michael Zhang,\\Aman Timalsina, Silas Alberti, Dylan Zinsley,\\James Zou, Atri Rudra, and Christopher R\'e} \date{arXiv:2402.18668v2 \enspace (7 March 2025)\\Paper discussion \enspace / \enspace 10 October 2026} \hypersetup{pdftitle={BASED: a research paper discussion},pdfauthor={Paper reading presentation}} \begin{document} \begin{frame} \titlepage \vspace{-4mm} \centering\small\href{https://arxiv.org/abs/2402.18668v2}{arxiv.org/abs/2402.18668v2}\par \end{frame} \begin{frame}{Similar perplexity can hide a large recall gap} \begin{columns}[T,onlytextwidth] \begin{column}{.48\textwidth} \begin{block}{Overall language modeling} 1.3B scale, 50B training tokens: \begin{center} \begin{tabular}{lr}\toprule Model & Pile PPL $\downarrow$\\\midrule Transformer++ & 6.28\\ Mamba & 6.28\\ \BASED & 6.30\\\bottomrule \end{tabular} \end{center} \end{block} \end{column} \begin{column}{.48\textwidth} \begin{block}{Extracting facts from the input} FDA document extraction accuracy: \begin{center} \begin{tabular}{lr}\toprule Model & Accuracy $\uparrow$\\\midrule Transformer++ & 80.47\\ Mamba & 18.51\\ \BASED & 30.40\\\bottomrule \end{tabular} \end{center} \end{block} \end{column} \end{columns} \medskip \alert{Question: how much input information can a small recurrent state retain?} \papersource{Paper, Table 1, PDF p. 8. FDA accuracy checks whether the generated text contains the answer.} \end{frame} \begin{frame}{Both state capacity and its use affect recall} \begin{columns}[c,onlytextwidth] \begin{column}{.51\textwidth} \centering\includegraphics[width=\linewidth,height=.61\textheight,keepaspectratio]{figures/fig-02-plot.pdf} \par\smallskip {\small\begin{tabular}{@{}ll@{}} \textcolor{PlotFull}{$\bullet$} Full attention & \textcolor{PlotSliding}{$\bullet$} Sliding window\\ \textcolor{PlotBased}{$\bullet$} BASED & \textcolor{PlotMamba}{$\bullet$} Mamba\\ \textcolor{PlotHthree}{$\bullet$} H3 & \textcolor{PlotHyena}{$\bullet$} Hyena \end{tabular}} \end{column} \begin{column}{.45\textwidth} \begin{itemize} \item $x$: recurrent state size in bytes. \item $y$: MQAR recall accuracy. \item Larger states usually improve recall. \item The same budget can yield different recall across architectures. \end{itemize} \medskip \alert{BASED expands the empirical frontier over the configurations tested.} \medskip\par State size is distinct from parameter count and measured runtime. \end{column} \end{columns} \papersource{Paper, Sec. 3.1 and Fig. 2, PDF pp. 3--4. Original plot cropped; legend restated.} \end{frame} \begin{frame}{MQAR isolates temporary key--value associations} \begin{block}{A small example} \centering\large \texttt{A 4\quad B 3\quad C 6\quad F 1\quad E 2}\\[3mm] \texttt{A ?\quad C ?\quad F ?\quad E ?\quad B ?}\\[3mm] \alert{Targets: 4, 6, 1, 2, 3} \end{block} \begin{itemize} \item Training: length 256; 4--64 key--value pairs. \item Evaluation: length 1,024; 4--256 key--value pairs. \item Vary state-related dimensions or window width per architecture. \item The evaluation also tests generalization to longer sequences. \end{itemize} \papersource{Paper, Sec. 3.1, PDF pp. 3--4; state accounting in Appendix E.2, pp. 36--37.} \end{frame} \begin{frame}{Reliable arbitrary recall requires growing memory} \begin{block}{State lower bound} Any causal recurrent model solving arbitrary associative recall requires \[\Omega(N)\ \text{bits of state in the worst case.}\] \end{block} \begin{enumerate} \item Alice encodes bits $x_1,\ldots,x_N$ as pairs $(j,x_j)$. \item She runs the model and sends its state to Bob. \item Bob supplies query $i$ and recovers $x_i$. \end{enumerate} \medskip A smaller state would violate the one-way Index communication lower bound. \medskip\par \alert{This applies to BASED too.} States are measured in finite bits. \papersource{Paper, Theorem 3.1, p. 4; Theorems F.10 and F.12, pp. 43--44. Index bound allows success probability $\ge 2/3$.} \end{frame} \begin{frame}{BASED combines three complementary sequence mixers} \begin{columns}[T,onlytextwidth] \begin{column}{.315\textwidth} \begin{block}{Taylor linear attention} Global access through a fixed-size association state.\par\medskip Capacity controlled by feature dimension. \end{block} \end{column} \begin{column}{.315\textwidth} \begin{block}{Sliding-window attention} Exact softmax over recent tokens.\par\medskip Precise local comparisons and alignment. \end{block} \end{column} \begin{column}{.315\textwidth} \begin{block}{Short gated convolution} Width-3 local mixing with low state cost.\par\medskip Additional quality gain in the trained hybrid. \end{block} \end{column} \end{columns} \bigskip The language models mix these layer types at roughly\par \centerline{\large 20\% linear attention / 20\% SWA / 60\% convolution.} \medskip Author hypothesis: local operations form precise associations; global state carries them across distance. \papersource{Conceptual summary, not an original figure. Paper, Sec. 4, pp. 5--6; Sec. 6, p. 8; Appendix C, p. 31.} \end{frame} \begin{frame}{Associativity turns attention into an additive memory} Using column vectors and $K(q,k)=\phi(q)^\top\phi(k)$: \[ y_i=\frac{\sum_{j\le i} K(q_i,k_j)v_j}{\sum_{j\le i}K(q_i,k_j)} =\frac{s_i^\top\phi(q_i)}{z_i^\top\phi(q_i)}. \] \begin{block}{Recurrent update} \[ s_i=s_{i-1}+\phi(k_i)v_i^\top,\qquad z_i=z_{i-1}+\phi(k_i). \] \end{block} \begin{itemize} \item $\phi(k_i)\in\mathbb R^D$, $v_i\in\mathbb R^{d_v}$, $s_i\in\mathbb R^{D\times d_v}$. \item Per head: $D(d_v+1)$ state entries; $O(Dd_v)$ work per token. \item Constant in sequence length, for fixed dimensions; normalization remains. \end{itemize} \papersource{Paper, Eqs. (2)--(3), PDF p. 5. Vector orientation standardized; $d_v$ denotes the value dimension.} \end{frame} \begin{frame}{The Taylor map expands memory without learned features} Let projected queries and keys have dimension $d'$ and define \[\bar q=q/(d')^{1/4},\qquad \bar k=k/(d')^{1/4}.\] \[ \phi(\bar q)=\left[1,\;\bar q,\;\frac{\operatorname{vec}(\bar q\bar q^\top)}{\sqrt2}\right]. \] \begin{block}{Second-order exponential approximation} \[ \phi(\bar q)^\top\phi(\bar k) =1+\frac{q^\top k}{\sqrt{d'}}+\frac{(q^\top k)^2}{2d'}. \] \end{block} \begin{itemize} \item Constant, first-order, and pairwise feature interactions. \item Polynomial expansion adds no learned weights at fixed $d'$. \item Larger $d'$ increases capacity, state traffic, and projection cost. \end{itemize} \papersource{Paper, Eq. (4), p. 5; scaling made explicit from Appendix B.1, Listing 1, pp. 20--22.} \end{frame} \begin{frame}{153, 273, and 320 describe different representations} \begin{center} \begin{tabular}{lcc}\toprule Representation & Feature dimension & $d'=16$\\\midrule Symmetry-compressed & $1+d'+d'(d'+1)/2$ & 153\\ Full outer product & $1+d'+d'^2$ & 273\\ Kernel padding & Multiple of 64 & 320\\\bottomrule \end{tabular} \end{center} \medskip \begin{itemize} \item Table 6 and Appendix E.2 use the compressed dimension. \item Algorithm 2 pads the full expansion for hardware alignment. \item Actual memory also depends on heads, layers, and numeric precision. \end{itemize} \begin{block}{Practical consequence} Use the implemented state shape when estimating GPU memory and bandwidth. \end{block} \papersource{Paper, Algorithm 2, p. 27; Table 6, p. 35; Appendix E.2, pp. 36--37.} \end{frame} \begin{frame}{Small windows preserve precise local interactions} \begin{columns}[T,onlytextwidth] \begin{column}{.49\textwidth} \[ j\in[\max(1,i-w+1),\;i] \] \begin{itemize} \item Standard causal softmax inside the window. \item State per head: $2\min(N,w)d_v$ entries. \item Global linear layers carry information beyond the local receptive field. \end{itemize} \end{column} \begin{column}{.47\textwidth} \begin{center} \begin{tabular}{lrr}\toprule Configuration & Small & Large\\\midrule Total layers & 27 & 36\\ Linear layers & 5 & 7\\ Window layers & 5 & 7\\ Conv layers & 17 & 22\\ Window size & 64 & \alert{16}\\\bottomrule \end{tabular} \end{center} \smallskip Linear layers: no position encoding.\\ Window layers: Rotary encoding. \end{column} \end{columns} \medskip Table 7's actual configurations differ from the general 64--128-window discussion. \papersource{Paper, Sec. 4.2, p. 6; Table 7, p. 75 (columns labeled 355M and 1.4B).} \end{frame} \begin{frame}{Chunking separates local causality from global history} For block $b$, feature matrices $\Phi_{Q_b},\Phi_{K_b}$, and causal mask $M_b$: \[ \underbrace{U_b}_{\text{numerator}} =\underbrace{(M_b\odot\Phi_{Q_b}\Phi_{K_b}^{\top})V_b}_{\text{within-block interactions}} +\underbrace{\Phi_{Q_b}S_{{\raggedright\arraybackslash}p{2.8cm}>{\raggedright\arraybackslash}p{4.6cm}>{\raggedright\arraybackslash}p{5.2cm}}\toprule Evaluation & Setup & Metric / purpose\\\midrule Pile & Same tokens and order; GPT-2 BPE & Overall and AR-slice PPL $\downarrow$\\ SWDE / FDA & Zero-shot field extraction & Accuracy $\uparrow$; use input facts\\ SQuAD variant & 2,984 retained rewritten prompts & F1 $\uparrow$; answer completion\\ LM Eval & Standard tasks & General language quality\\ SuperGLUE & 0, 1, 5 shots & Few-shot behavior\\\bottomrule \end{tabular} \end{center} \medskip Language models: roughly 360M and 1.3B parameters; up to 30B and 50B tokens. \medskip\par Transformer++ is the modern attention baseline; Mamba is the main recurrent baseline. \papersource{Paper, Sec. 6.1, pp. 8--9; Appendix E, pp. 36--39. Pretraining: A100; efficiency tests: H100.} \end{frame} \begin{frame}{BASED improves the AR slice at similar overall PPL} \begin{center} \begin{tabular}{llrrr}\toprule Scale / tokens & Model & Pile PPL $\downarrow$ & AR PPL $\downarrow$ & LM avg. $\uparrow$\\\midrule 360M / 10B & Transformer++ & 8.39 & 1.87 & 44.08\\ & Mamba & 8.64 & 2.21 & 43.51\\ & \BASED & 8.65 & \alert{2.07} & 43.03\\\midrule 1.3B / 50B & Transformer++ & 6.28 & 1.65 & 53.33\\ & Mamba & 6.28 & 1.74 & 53.50\\ & \BASED & 6.30 & \alert{1.71} & 53.81\\\bottomrule \end{tabular} \end{center} \medskip The AR slice targets repeated contextual bigrams that are infrequent in training. \medskip\par At 1.3B/50B, non-AR PPL is 6.82 for BASED vs. 6.78 for Mamba: gains are task-specific. \papersource{Paper, Table 1, p. 8; Table 2, p. 32; Appendix E.3, p. 37. Averages reproduced as reported.} \end{frame} \begin{frame}{Recall improves, with a substantial gap on FDA remaining} \begin{center} \begin{tabular}{lrrr}\toprule 1.3B scale / 50B tokens & SWDE Acc. & FDA Acc. & SQuAD F1\\\midrule Transformer++ & 76.50 & 80.47 & 43.47\\ Mamba & 52.75 & 18.51 & 35.92\\ \BASED & 64.45 & 30.40 & 41.62\\\midrule \BASED{} $-$ Mamba & \alert{+11.70} & \alert{+11.89} & \alert{+5.70}\\\bottomrule \end{tabular} \end{center} \medskip \begin{itemize} \item All three tasks improve over Mamba. \item FDA remains 50.07 percentage points below Transformer++. \item The unweighted mean gain here is \textbf{9.76}, not the 10.36 quoted for this setting in the prose. \end{itemize} \papersource{Paper, Table 1, p. 8. Differences and mean calculated from displayed values; accuracy points and F1 points are distinct metrics.} \end{frame} \begin{frame}{Local mixers contribute beyond a larger linear state} \begin{center} \begin{tabular}{lrrr}\toprule Variant & $d'$ & Pile PPL $\downarrow$ & AR PPL $\downarrow$\\\midrule Taylor + SWA + convolution & 16 & \alert{8.65} & \alert{2.07}\\ Without SWA & 16 & 8.91 & 2.11\\ Without convolution & 16 & 8.74 & 2.09\\ Without both local mixers & 24 & 9.49 & 2.29\\\bottomrule \end{tabular} \end{center} \medskip \begin{itemize} \item Removing either local component hurts overall perplexity. \item The two-attention hybrid without convolution is within 0.09 PPL of the full model. \item The last row also changes $d'$; it is not a pure one-variable ablation. \end{itemize} \papersource{Paper, Table 6, p. 35; about 362M parameters and 10B training tokens. Rows shown use the decay variant.} \end{frame} \begin{frame}{Increasing feature width yields diminishing PPL returns} \begin{columns}[T,onlytextwidth] \begin{column}{.49\textwidth} \begin{center} \begin{tabular}{rrrr}\toprule $d'$ & Compact $D$ & Pile PPL & AR PPL\\\midrule 8 & 45 & 8.77 & 2.18\\ 16 & 153 & 8.65 & 2.07\\ 24 & 325 & 8.58 & 2.02\\ 32 & 561 & 8.56 & 2.00\\\bottomrule \end{tabular} \end{center} \end{column} \begin{column}{.47\textwidth} \begin{itemize} \item PPL improves only 0.02 from $d'=24$ to 32. \item State width rises from 325 to 561. \item Downstream gains are not monotonic: FDA is 20.87 at 24, but 12.89 at 32. \end{itemize} \end{column} \end{columns} \medskip \begin{block}{A second control knob} Window 64 $\rightarrow$ 128: PPL 8.65 $\rightarrow$ 8.61, with larger gains on some recall tasks. \end{block} \papersource{Paper, Table 6, p. 35. Taylor map; local mixers and decay retained. PPL: lower is better.} \end{frame} \begin{frame}{Prefill gains depend on the optimized kernel} \begin{columns}[c,onlytextwidth] \begin{column}{.53\textwidth} \centering\includegraphics[width=\linewidth,height=.73\textheight,keepaspectratio]{figures/fig-04-prefill-13b.pdf} \end{column} \begin{column}{.43\textwidth} \textbf{1.3B model scale}\par \smallskip Single H100; batch 2.\\ Vertical axis: latency in ms. \medskip\par At 4K input tokens: \begin{itemize} \item About \alert{56\%} higher throughput than FlashAttention-2. \item About \alert{44\%} higher than Mamba. \end{itemize} \smallskip The unoptimized BASED implementation can be slower than attention. \end{column} \end{columns} \papersource{Paper, selected Fig. 4 panel, p. 8; Sec. 6.2, p. 9. Original panel labels the scale ``1b''; text specifies 1.3B.} \end{frame} \begin{frame}{The 24-times headline is a specific decode result} \begin{columns}[c,onlytextwidth] \begin{column}{.53\textwidth} \centering\includegraphics[width=\linewidth,height=.73\textheight,keepaspectratio]{figures/fig-04-decode-13b.pdf} \end{column} \begin{column}{.43\textwidth} \textbf{Reported comparison:} \begin{itemize} \item Single H100; 1.3B scale. \item Batch size 128. \item Generate 1,024 tokens. \item Excludes prefill; CUDA graphs. \end{itemize} \medskip \alert{$\sim$24$\times$ FlashAttention-2 throughput;}\par about \textbf{95\% of Mamba throughput}. \smallskip\par Vertical axis: latency in ms. \end{column} \end{columns} \papersource{Paper, selected Fig. 4 panel, p. 8; Sec. 6.2, p. 9. Table 1 separately labels generation length as 2,048.} \end{frame} \begin{frame}{Few-shot results support the context-use motivation} \begin{center} \begin{tabular}{lrrr}\toprule SuperGLUE, 360M scale / 10B tokens & 0-shot & 1-shot & 5-shot\\\midrule \BASED & 45.7 & 47.2 & \alert{48.0}\\ Transformer++ & 46.3 & 47.8 & \alert{48.9}\\ Mamba & 46.6 & 46.9 & 45.2\\\bottomrule \end{tabular} \end{center} \medskip \begin{itemize} \item BASED and Transformer++ improve as demonstrations increase. \item Mamba's 5-shot average drops below its 0-shot average. \item Average metrics within each task first, then average tasks. \end{itemize} \medskip This is consistent with the authors' link between recall and in-context use. \papersource{Paper, Appendix D.2 and Table 3, PDF p. 33. Reported task averages.} \end{frame} \begin{frame}{The useful principle is to co-design capacity and access} \begin{enumerate} \item \textbf{Budget memory for the task.} Fixed-state models face an information limit on arbitrary recall. \item \textbf{Separate global storage from precise local computation.} Taylor memory and local mixers complement each other. \item \textbf{Measure the implementation.} State shapes and data movement determine whether the design is fast. \end{enumerate} \bigskip \begin{block}{Remaining tradeoff} Larger state can improve recall but increases memory traffic.\par BASED still has a large FDA gap to Transformer++ at 1.3B/50B. \end{block} \papersource{Synthesis of Secs. 3--6. Language-model evidence extends to 1.3B parameters and 50B tokens in this paper.} \end{frame} \begin{frame}{Discussion: what should the next comparison control?} \begin{block}{A useful follow-up experiment} Compare memory update rules at the same actual state bytes, numeric precision, local mixers, layer count, and kernel quality. \end{block} \medskip \begin{itemize} \item Does the gain come from more capacity or a better update rule? \item Can state grow with the number of useful associations? \item Which failures are caused by interference versus local misalignment? \end{itemize} \bigskip \centering\alert{Memory capacity $+$ precise access $+$ efficient execution} \papersource{Discussion questions motivated by the paper; these are not evaluated results. Main talk ends here.} \end{frame} \appendix \begin{frame}{Backup: the depth bounds rely on a restricted model} Data-independent \BC{} uses linear operations and multiplicative gates. \[ \deg(\text{output after }L\text{ layers})\le 2^L. \] For binary tokens, $d=\log_2c$, exact matching contains \[ \operatorname{EQ}(q,k)=\prod_{a=1}^d[q_ak_a+(1-q_a)(1-k_a)]. \] \begin{itemize} \item Matching and returning a value gives a degree-$2d+1$ interaction. \item This yields a depth requirement of order $\log d=\log\log c$. \item A separate bound is $\Omega(\epsilon\log\log N)$ when $c\le N$, $\log c\le d\le2^{(\log N)^{1-\epsilon}}$, and parameters use $O(\log N)$ bits. \end{itemize} \papersource{Paper, Theorems 3.2, 3.4, pp. 4--5; Appendix F.4, pp. 44--49. Not a bound for arbitrary nonlinear recurrent architectures.} \end{frame} \begin{frame}{Backup: an upper bound uses larger internal representations} \begin{block}{Theorem F.30} With one-hot tokens and at most one matching key per query, MQAR is solvable in $O(\log\log\bar N)$ \BC{} layers, where $\bar N=\max(N,d)\ge8$. \end{block} \begin{enumerate} \item Store binary position codes with keys; cumulatively sum them. \item Let a query select the matching position code. \item Convert the code to a one-hot selector using a product tree. \item Select the associated value. \end{enumerate} \medskip Internal length and width expand to $O(\bar N\log\bar N)$ scale. \papersource{Paper, Theorem F.30 and constructive proof, PDF pp. 51--74. High-level proof explanation.} \end{frame} \begin{frame}{Backup: Taylor is efficient, but not the only good map} \begin{columns}[c,onlytextwidth] \begin{column}{.48\textwidth} \centering\includegraphics[width=\linewidth,height=.68\textheight,keepaspectratio]{figures/fig-03-memory.pdf} \end{column} \begin{column}{.48\textwidth} \centering\includegraphics[width=\linewidth,height=.68\textheight,keepaspectratio]{figures/fig-03-parameters.pdf} \end{column} \end{columns} \smallskip Taylor, PosELU, and ReLU approach the memory frontier; Taylor uses fewer learned parameters for strong recall in this setting. \papersource{Paper, Fig. 3, p. 6. 256 KV pairs; original panels separated and original legend repeated for readability.} \end{frame} \begin{frame}{Backup: DNA results extend the scope beyond English} \begin{center} \begin{tabular}{lrrrr}\toprule HG38 & Params (M) & PPL, 1K & PPL, 4K & PPL, 8K\\\midrule Transformer++ & 46.2 & 2.52 & 2.50 & 2.51\\ Mamba & 46.1 & 2.51 & 2.49 & 2.49\\ \BASED & 48.8 & 2.51 & 2.50 & 2.49\\\bottomrule \end{tabular} \end{center} \begin{itemize} \item 10B pretraining tokens; learning-rate sweeps per architecture. \item Comparable PPL across evaluated lengths. \item BASED classification: 74.6 on Enhancer Cohn, 96.8 on Non-TATA Promoters; mixed ranking across five tasks. \item Some prior published baselines use different tokenization. \end{itemize} \papersource{Paper, Appendix D.3, Tables 4--5, PDF pp. 33--34. PPL lower is better; classification accuracy in percent.} \end{frame} \begin{frame}{Backup: protocol details change what the scores mean} \begin{itemize} \item \textbf{Pile AR slice:} a repeated contextual bigram's final token; bigram occurs at most 1,250 times in training. Computed on the first 16M test tokens. \item \textbf{FDA:} 1,920-token document chunks. Count a prompt correct if generation contains the value, ignoring case. \item \textbf{SQuAD:} GPT-4 reformats questions as answer-final statements; 2,984 of 5,000 prompts retained. Table 1 reports F1. \item \textbf{Decay:} used in the 10B-token variants; absent in the 30B/50B-token main models. \end{itemize} \papersource{Paper, Appendix E.3, pp. 37--39; Appendices C and D.4, pp. 31, 34. Table 6 inconsistently labels the SQuAD metric as accuracy.} \end{frame} \begin{frame}{Backup: use task-level numbers when summaries disagree} \begin{center} \begin{tabular}{lrrrr}\toprule Setting & $\Delta$SWDE & $\Delta$FDA & $\Delta$SQuAD & Mean\\\midrule 360M / 10B & 5.49 & 5.18 & 1.01 & 3.89\\ 360M / 30B & 17.38 & 7.74 & 5.96 & \alert{10.36}\\ 1.3B / 10B & 13.32 & 11.52 & 2.26 & 9.03\\ 1.3B / 50B & 11.70 & 11.89 & 5.70 & \alert{9.76}\\\bottomrule \end{tabular} \end{center} \smallskip Differences are BASED minus Mamba, calculated from Table 1. The mean mixes accuracy and F1 points. \medskip\par The PDF associates 10.36 with 1.3B/50B; the online abstract says 6.22.\par For speed, Fig. 4 uses 1,024 generated tokens; Table 1 says 2,048. \papersource{Primary reference: Arora et al., \emph{Simple linear attention language models balance the recall-throughput tradeoff}, arXiv:2402.18668v2, 2025. \href{https://arxiv.org/abs/2402.18668v2}{Versioned paper link}. Table 1, p. 8.} \end{frame} \end{document}