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\title[Gated Slot Attention-2]{Gated Slot Attention-2}
\subtitle{Two-Sided Associative Memory Correction in Linear Attention}
\author{Research group reading presentation}
\date{arXiv:2610.02816v1; 13 November 2026}
\hypersetup{pdfauthor={Research group reading presentation on Li et al. (2026)}}
\begin{document}
\begin{frame}
\titlepage
\end{frame}

\begin{frame}{GSA2 pairs key-side and value-side correction through slots}
\begin{block}{One association, two complementary editing roles}
\[
k_t\xleftarrow{\mathrm{OJA2}}w_t\xrightarrow{\mathrm{Delta\text{-}2}}v_t
\]
\end{block}
{\small Paper authors: Ruijie Li, Shengnan Ding, Weimin Zhang, Derick Tang,
Zhanpeng Zeng, Qinsong Zeng, Ming Chen, Jiaxi Hu and Yuxuan Liang.}
\medskip
\begin{itemize}
\item Two recurrent memories share a learned slot code $w_t$.
\item Each stage has independent decay, erase and write controls.
\end{itemize}
\medskip
{\small \href{https://arxiv.org/abs/2610.02816v1}{arXiv v1, 2 October 2026}. Publication unverified as of 2026-11-13.\\
PDF header says ICLR 2027; \href{https://reyjerry.github.io/}{author page} lists arXiv; no official record found.\\
\href{https://github.com/fla-org/flash-linear-attention/tree/main/fla/models/gsa2}{Community code: FLA}. Author's complete release unverified.}
\papersource{Paper, Abstract and Sec. 1, PDF pp. 1--2. External status checked 2026-11-13.}
\end{frame}

\begin{frame}{GSA factorizes key--value memory through slots}
\[
S_t^{(1)}\in\mathbb R^{M\times D_k},\qquad S_t^{(2)}\in\mathbb R^{D_v\times M}
\]
\begin{align*}
S_t^{(1)}&=\diag(\alpha_t)S_{t-1}^{(1)}+(\mathbf1-\alpha_t)k_t^\top,\\
S_t^{(2)}&=S_{t-1}^{(2)}\diag(\alpha_t)+v_t(\mathbf1-\alpha_t)^\top,\\
o_t&=S_t^{(2)}\operatorname{softmax}(S_t^{(1)}q_t).
\end{align*}
\begin{itemize}
\item Keys map to $M$ slots; slot activations map to values.
\item Original GSA updates both memories by gated accumulation.
\item GSA2 equips each side with an explicit associative correction.
\end{itemize}
\papersource{Paper, Sec. 2.2, Eqs. (4)--(6), PDF p. 3.}
\end{frame}

\begin{frame}{Oja correction reverses the prediction direction of Delta}
\begin{columns}[T]
\begin{column}{0.48\textwidth}
\textbf{Delta: key predicts value}
\[
\mathcal L_t^\Delta(S)=\frac12\norm{v_t-Sk_t}^2
\]
\[
S_t=S_{t-1}+\beta_t(v_t-S_{t-1}k_t)k_t^\top
\]
Correction acts on the right of $S$.
\end{column}
\begin{column}{0.48\textwidth}
\textbf{Oja: value predicts key}
\[
\mathcal L_t^K(S)=\frac12\norm{k_t-S^\top v_t}^2
\]
\[
S_t=S_{t-1}+\beta_t v_t(k_t-S_{t-1}^\top v_t)^\top
\]
Correction acts on the left of $S$.
\end{column}
\end{columns}
\bigskip
\begin{block}{Transpose duality}
With $T=S^\top$, the Oja update is a Delta update with swapped roles.
GSA2 places these directions in two semantically different memories.
\end{block}
\papersource{Paper, Secs. 2.1 and 3.1, Eqs. (1)--(2), (7)--(8), PDF pp. 2--3. Duality: reading analysis.}
\end{frame}

\begin{frame}{OJA2 separates what is erased from what is written}
\[
\widetilde S_{t-1}=\diag(\alpha_t)S_{t-1}
\]
\[
\boxed{S_t=[I-v_t(b_t\odot v_t)^\top]\widetilde S_{t-1}
+v_t(c_t\odot k_t)^\top}
\]
\begin{itemize}
\item $b_t\in\mathbb R^{D_v}$ controls the value-side erase direction.
\item $c_t\in\mathbb R^{D_k}$ controls key-channel writes.
\item Setting $b_t=\beta_t\mathbf1$ and $c_t=\beta_t\mathbf1$ recovers OJA.
\end{itemize}
\begin{block}{Why decouple?}
Removing an old association and admitting new content need not share
one scalar update strength.
\end{block}
\papersource{Paper, Sec. 3.1, Eq. (10), PDF p. 4; Appendix A.2, pp. 14--15.}
\end{frame}

\begin{frame}{Stage 1 uses the shared slot code to correct keys}
\[
S_t^{(1)}\in\mathbb R^{M\times D_k},\qquad w_t\in\mathbb R^M
\]
\begin{align*}
S_t^{(1)}={}&[I-w_t(b_t^{(1)}\odot w_t)^\top]
\diag(\alpha_t^{(1)})S_{t-1}^{(1)}\\
&+w_t(c_t^{(1)}\odot k_t)^\top.
\end{align*}
\begin{itemize}
\item The associated key is predicted as $S^{(1)\top}w_t$.
\item $w_t$ plays the value-side role of the OJA2 update.
\item Erase and decay gates act in slot space; writes select key channels.
\end{itemize}
\medskip
The slot code is projected from the current input.
\papersource{Paper, Sec. 3.2, Eq. (11), PDF p. 4; Sec. 3.4, p. 6.}
\end{frame}

\begin{frame}{Stage 2 corrects values; a query then reads both memories}
\begin{align*}
S_t^{(2)}={}&S_{t-1}^{(2)}\diag(\alpha_t^{(2)})
[I-(b_t^{(2)}\odot w_t)w_t^\top]\\
&+(c_t^{(2)}\odot v_t)w_t^\top,
\qquad S_t^{(2)}\in\mathbb R^{D_v\times M}.
\end{align*}
\[
h_t=\silu(S_t^{(1)}q_t),\qquad o_t=S_t^{(2)}h_t
\]
\begin{itemize}
\item The same $w_t$ is now the addressing key of a Delta-2 memory.
\item $h_t$ is a read activation; it is different from the write code $w_t$.
\item SiLU replaces GSA's normalized competition between slots.
\end{itemize}
\papersource{Paper, Sec. 3.2, Eqs. (12)--(13), PDF pp. 4--5. Compact readout notation from the paper.}
\end{frame}

\begin{frame}{A one-hot slot illustrates the two editing roles}
\begin{block}{Teaching example: two slots, $w_t=(0,1)^\top$}
Set erase/write gates to 1 and decay to the identity.
\end{block}
\begin{center}
\begin{tabular}{lll}
\toprule
Memory & Active portion & Effect of the write\\
\midrule
$S^{(1)}$ & Second row & Replace by $k_t^\top$\\
$S^{(2)}$ & Second column & Replace by $v_t$\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Learned dense slot codes distribute edits across slot directions.
\item Total state size is $M(D_k+D_v)$ elements per head.
\item Fixed with context length; equal parameter count need not imply equal state capacity.
\end{itemize}
\papersource{Teaching example and state count derived from Eqs. (11)--(12), PDF p. 4.}
\end{frame}

\begin{frame}{The block supports recurrent and SWA hybrid backbones}
\centering
\includegraphics[width=0.98\linewidth,height=0.60\textheight,keepaspectratio]{figures/fig-01-architecture.pdf}
\par\medskip
\raggedright
$q,k,w$ are L2-normalized; output uses RMSNorm and a sigmoid gate.\\
Hybrid cell: GSA2--MLP--SWA--MLP, with a fixed 2K SWA window.
\papersource{Original Fig. 1, PDF p. 5; Sec. 3.4, p. 6. Complete architecture figure crop.}
\end{frame}

\begin{frame}{Chunkwise training absorbs edits into a triangular solve}
\begin{itemize}
\item Accumulated rank-one transitions admit a compact WY form.
\item The OJA2 stage derives new gate-aware UT factors.
\item The value stage reuses the GDN2 implementation.
\end{itemize}
\begin{block}{OJA2 chunk-boundary state}
\[
S_{\rm out}=\diag(p_C)S_{\rm in}
+(A_{\rm suffix}\odot V)^\top(U-WS_{\rm in})
\]
\end{block}
\begin{itemize}
\item $U,W$: auxiliaries from unit lower-triangular systems.
\item $W$ is not the token-level slot code $w_t$.
\item Fixed chunk length gives linear sequence scaling; recurrent state stays bounded.
\end{itemize}
\papersource{Paper, Sec. 3.3, Eqs. (14)--(15), PDF pp. 5--6; Appendix A.1--A.2, pp. 13--15.}
\end{frame}

\begin{frame}{The study trains 1.3B models on 100B tokens}
\begin{center}
\begin{tabular}{ll}
\toprule
Data / tokenizer & FineWeb-Edu; TinyLlama v1.1, 32K vocabulary\\
Training length & 4096; hybrid SWA window 2048\\
Global batch & 128 sequences, approximately 0.5M tokens\\
AdamW & $(0.9,0.95)$; peak LR $4\times10^{-4}$; weight decay 0.1\\
Schedule & Warm up 1B tokens; cosine decay to 10\% peak LR\\
Precision / GPUs & BF16; 32 NVIDIA H20 GPUs across four nodes\\
\bottomrule
\end{tabular}
\end{center}
\medskip
Starred recurrent baselines in Table 2 are taken from GDN2.\\
OJA, OJA2, GSA and GSA2 are evaluated in this work.
\papersource{Paper, Sec. 4 and Table 2, PDF pp. 6--7; Appendix A.3.1, p. 15.}
\end{frame}

\begin{frame}{Recurrent GSA2 improves both PPL and the accuracy average}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Recurrent model & Wiki. PPL $\downarrow$ & LMB. PPL $\downarrow$ & Accuracy avg. $\uparrow$\\
\midrule
GDN2 & 15.90 & 11.41 & 53.11\\
Mamba-3 MIMO & 16.17 & 11.10 & 53.31\\
OJA2 & 18.28 & 14.84 & 50.15\\
GSA & 16.52 & 11.22 & 53.28\\
GSA2 & \alert{15.69} & \alert{10.68} & \alert{54.08}\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Versus GDN2: $-0.21$ / $-0.73$ PPL and $+0.97$ accuracy points.
\item OJA2 alone is weaker; its value is in the complementary pairing.
\end{itemize}
\papersource{Paper, Table 2, PDF p. 6. Accuracy average: LAMBADA plus eight commonsense tasks (\%).}
\end{frame}

\begin{frame}{Hybrid GSA2 gains accuracy while WikiText PPL worsens}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Hybrid model & Wiki. PPL $\downarrow$ & LMB. PPL $\downarrow$ & Accuracy avg. $\uparrow$\\
\midrule
GDN2 + SWA & 16.26 & 11.93 & 52.65\\
Mamba-3 MIMO + SWA & 15.94 & 11.75 & 53.63\\
GSA + SWA & 15.98 & 11.36 & 52.67\\
GSA2 + SWA & 17.23 & \alert{10.80} & \alert{53.96}\\
\bottomrule
\end{tabular}
\end{center}
\begin{block}{A concrete trade-off}
WikiText PPL is 0.97 higher than GDN2, about 5.97\% worse.
The paper does not explain this degradation.
\end{block}
\medskip
The average gain does not mean every task improves.
\papersource{Paper, Table 2, PDF p. 6. Accuracy average uses nine reported accuracy columns.}
\end{frame}

\begin{frame}{At 2K inputs, local attention changes the retrieval ranking}
\begin{center}
\begin{tabular}{lrr}
\toprule
Model & Recurrent avg. $\uparrow$ & Hybrid avg. $\uparrow$\\
\midrule
GDN2 & 29.88 & 35.41\\
OJA & 25.95 & \textbf{37.49}\\
OJA2 & 26.24 & 37.19\\
GSA & 26.71 & 32.89\\
GSA2 & \alert{31.26} & 36.70\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Six real-world retrieval tasks; all inputs truncated to 2K.
\item Recurrent GSA2 beats GDN2 by 1.38 percentage points.
\item With a 2K SWA window, OJA/OJA2 hybrids become strongest on average.
\end{itemize}
\papersource{Paper, Table 3 and discussion, PDF p. 7. Six-task accuracy average (\%).}
\end{frame}

\begin{frame}{RULER averages favor GSA2 in both model families}
\begin{center}
\begin{tabular}{llrr}
\toprule
Family & Model & NIAH avg. $\uparrow$ & Other tasks avg. $\uparrow$\\
\midrule
Recurrent & GSA & 25.2 & 17.9\\
& GDN2 & 39.7 & 26.0\\
& GSA2 & \alert{42.1} & \alert{31.8}\\
\midrule
Hybrid & GSA & 44.7 & 33.0\\
& GDN2 & 47.7 & 28.5\\
& GSA2 & \alert{50.6} & \alert{36.2}\\
\bottomrule
\end{tabular}
\end{center}
\medskip
NIAH: 6 task variants $\times$ 4 lengths = 24 settings.\\
Other tasks: 7 tasks $\times$ 4 lengths = 28 settings, from 1K to 8K.
\papersource{Paper, Fig. 2, PDF p. 8; full Tables 6--7, pp. 16--17. Accuracy (\%).}
\end{frame}

\begin{frame}{Different RULER groups account for the average gains}
\begin{center}
\begin{tabular}{llrr}
\toprule
Family & Model & S-NIAH $\uparrow$ & MK-NIAH $\uparrow$\\
\midrule
Recurrent & GDN2 & 68.6 & 10.8\\
& GSA2 & \alert{72.8} & \alert{11.4}\\
Hybrid & GDN2 & \textbf{63.2} & 32.2\\
& GSA2 & 62.1 & \alert{39.1}\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Each subgroup averages 3 variants $\times$ 4 lengths.
\item Recurrent GSA2 still scores zero on all MK-NIAH-3 settings.
\item At 8K S-NIAH-1: recurrent GSA2 86.0\%, GDN2 92.8\%.
\end{itemize}
\papersource{Computed from paper Table 6, PDF p. 16; group means rounded to one decimal.}
\end{frame}

\begin{frame}{LongBench gains vary across tasks}
\begin{center}
\begin{tabular}{lrr}
\toprule
Model & Recurrent avg. $\uparrow$ & Hybrid avg. $\uparrow$\\
\midrule
GDN2 & 16.8 & 16.4\\
OJA2 & 13.6 & 15.9\\
GSA & 13.6 & 10.4\\
GSA2 & \alert{17.3} & \alert{17.3}\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Average of 11 task scores across QA, summaries, few-shot and code.
\item Recurrent TREC: 46.5 versus GDN2's 37.0; a large contributor.
\item Recurrent GSA2 trails GDN2 on several QA and code tasks.
\item Hybrid SAMSum improves; MultiNews and RepoBench-P decline.
\end{itemize}
\papersource{Paper, Table 4, PDF p. 8. Benchmark task scores, not a uniform accuracy metric.}
\end{frame}

\begin{frame}{Complementary rules outperform repeating one rule overall}
\begin{center}
\begin{tabular}{lrrrrr}
\toprule
Pairing & Wiki. $\downarrow$ & LMB. $\downarrow$ & Acc. $\uparrow$ & MK $\uparrow$ & LongB. $\uparrow$\\
\midrule
OJA2 + Delta-2 & \textbf{15.69} & 10.68 & \textbf{54.08} & 11.4 & \textbf{17.3}\\
Both Delta-2 & 15.92 & \textbf{10.27} & 53.03 & \textbf{13.1} & 16.8\\
Both OJA2 & 16.97 & 12.46 & 52.35 & 8.4 & 13.8\\
\bottomrule
\end{tabular}
\end{center}
\bigskip
\begin{itemize}
\item The first and second memories benefit from different correction roles.
\item Both-Delta wins LAMBADA PPL and multi-key NIAH.
\item The evidence supports an overall pairing advantage with task trade-offs.
\end{itemize}
\papersource{Paper, Table 5, PDF p. 9. All variants: 1.3B parameters, 100B tokens; Acc. and MK in \%.}
\end{frame}

\begin{frame}{Scaling, independent activation and 128 slots work best here}
\begin{center}
\begin{tabular}{lrrrr}
\toprule
Variant & Wiki. $\downarrow$ & Acc. $\uparrow$ & S-NIAH $\uparrow$ & LongB. $\uparrow$\\
\midrule
Default, 128 slots & \textbf{15.69} & \textbf{54.08} & \textbf{72.8} & \textbf{17.3}\\
No $1/\sqrt d$ scaling & 19.76 & 48.50 & 61.8 & 13.0\\
SiLU $\to$ Softmax & 16.92 & 50.66 & 55.6 & 14.0\\
64 slots & 16.55 & 53.48 & 62.6 & 16.9\\
256 slots & 16.37 & 52.87 & 61.7 & 15.3\\
\bottomrule
\end{tabular}
\end{center}
\bigskip
More slots do not automatically improve the measured balance.\\
The compact readout equation does not spell out the scaling placement.
\papersource{Paper, Table 5 and ablation discussion, PDF pp. 8--9. Acc. and S-NIAH in \%.}
\end{frame}

\begin{frame}{Training throughput stays flat with a two-stage constant cost}
\centering
\includegraphics[width=0.96\linewidth,height=0.64\textheight,keepaspectratio]{figures/fig-03-throughput.pdf}
\par\medskip
\raggedright
GSA2: 11.82 $\to$ 11.32 Kt/s ($-4.2\%$).\\
Transformer: 14.37 $\to$ 8.60 Kt/s ($-40.2\%$).
\papersource{Original Fig. 3, PDF p. 9. Hybrid 1.3B models, one H20, 16,384 tokens per training step.}
\end{frame}

\begin{frame}{The practical gain is better memory editing at an added cost}
\begin{enumerate}
\item \textbf{Mechanism:} OJA2 edits key--slot associations; Delta-2 edits slot--value associations.
\item \textbf{Evidence:} recurrent PPL and cross-task averages improve; individual tasks retain trade-offs.
\item \textbf{Cost:} at 16K, GSA2 training throughput is about 8.56\% below OJA2 and 12.73\% below GDN2.
\end{enumerate}
\begin{block}{Follow-up questions tied to the evidence}
Separate state capacity from correction direction, explain hybrid WikiText
PPL, and evaluate seed variation and inference-time costs.
\end{block}
\papersource{Paper, Secs. 3--6, PDF pp. 3--10. Throughput ratios calculated from Fig. 3 coordinates.}
\end{frame}

\begin{frame}{References and implementation status}
\begin{itemize}
\item Li et al. \emph{Gated Slot Attention-2: Two-Sided Associative Memory Correction in Linear Attention}.\\
\href{https://arxiv.org/abs/2610.02816v1}{arXiv:2610.02816v1}, 2026.
\item \href{https://reyjerry.github.io/}{First author's homepage}: lists arXiv 2026.\\
ICLR 2027 publication is not independently verified as of 2026-11-13.
\item \href{https://github.com/fla-org/flash-linear-attention}{FLA README} lists GSA2; populated
\href{https://github.com/fla-org/flash-linear-attention/blob/main/fla/layers/gsa2.py}{layer} and model implementations are public.
\item Community implementation; author-official status and complete training release unverified.
\end{itemize}
\papersource{Paper v1 promises full source upon acceptance (reproducibility statement, PDF p. 10).}
\end{frame}

\appendix
\begin{frame}{Backup: decoupling both stages gives the best overall balance}
\begin{center}
\begin{tabular}{llrrrr}
\toprule
Stage 1 & Stage 2 & Wiki. $\downarrow$ & LMB. $\downarrow$ & Acc. $\uparrow$ & LongB. $\uparrow$\\
\midrule
Coupled & Coupled & 16.22 & \textbf{10.29} & 53.25 & 17.1\\
Coupled & Decoupled & 16.01 & 10.65 & 52.46 & 14.8\\
Decoupled & Coupled & 16.28 & 11.25 & 53.37 & 16.2\\
Decoupled & Decoupled & \textbf{15.69} & 10.68 & \textbf{54.08} & \textbf{17.3}\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Independent erase/write control benefits both memory roles overall.
\item Decoupling only one side gives inconsistent gains.
\item Coupling both retains the best LAMBADA PPL of these four variants.
\end{itemize}
\papersource{Paper, Table 5, PDF p. 9. All variants: 1.3B parameters, 100B tokens. Acc. in \%.}
\end{frame}

\begin{frame}{Backup: OJA2 erase gates enter the triangular dependency}
For a generic OJA2 state $S\in\mathbb R^{D_v\times D_k}$:
\[
P_{r,:}=p_r^\top,\qquad p_r=\alpha_1\odot\cdots\odot\alpha_r
\]
\[
L=\operatorname{lower}\left([(B\odot V)\odot P](V\oslash P)^\top\right),
\quad T=(I+L)^{-1}
\]
\[
W=T[P\odot(B\odot V)],\qquad U=T(C_{\rm w}\odot K)
\]
\begin{itemize}
\item $B$: erase-gate rows; $C_{\rm w}$: write-gate rows.
\item Erase affects $L,T,W$; write gates act directly on $U$.
\item Strictly positive decay supports the divisions; triangular solve uses FP32.
\end{itemize}
\papersource{Paper, Appendix A.2, Eq. (26), PDF p. 15. $T$ renames the paper's auxiliary $M$ matrix.}
\end{frame}

\begin{frame}{Backup: chunk outputs use effective key-side residuals}
\[
R=U-WS_{\rm in},\qquad R\in\mathbb R^{C\times D_k}
\]
\[
S_{\rm out}=\diag(p_C)S_{\rm in}
+(A_{\rm suffix}\odot V)^\top R
\]
\[
O=P\odot\left[QS_{\rm in}^\top+
\operatorname{Tril}(QR^\top)(V\oslash P)\right]
\]
\begin{itemize}
\item Suffix decay applies after each write; its last row is all ones.
\item $\operatorname{Tril}$ includes the diagonal, so queries see the current write.
\item Within-chunk computation is dominated by matrix multiplications.
\end{itemize}
\papersource{Paper, Appendix A.1--A.2, Eqs. (22), (26), PDF pp. 14--15. $R$ introduced for readability.}
\end{frame}

\begin{frame}{Backup: preserve the metric and table identities}
\begin{itemize}
\item Table 2 accuracy average contains nine columns: LAMBADA plus eight commonsense benchmarks.
\item Table 5's caption says LAMBADA plus nine tasks; this does not match the displayed columns.
\item Default real-world retrieval is 31.26 in Table 3 and 31.51 in Table 5; the paper does not reconcile the difference.
\item LongBench averages task-specific scores; it is not one uniform accuracy measure.
\end{itemize}
\medskip
Compare rows within their stated protocols and keep these values separate.
\papersource{Paper, Tables 2--5, PDF pp. 6--9; benchmark descriptions, Appendix A.3.2, pp. 15--16.}
\end{frame}

\begin{frame}{Backup: throughput measures complete optimization steps}
\begin{itemize}
\item One NVIDIA H20, BF16, approximately 1.30B parameters.
\item Fixed 16,384 tokens: 2K$\times$8, 4K$\times$4, 8K$\times$2, 16K$\times$1.
\item Forward, fused cross-entropy, backward, gradient clipping and fused AdamW; no gradient accumulation.
\item Random token IDs generated on GPU; excludes input pipeline costs.
\item 20 warm-up and 50 measured iterations per configuration.
\item Three physical GPUs; report the median of three run-level means.
\end{itemize}
\medskip
Bounded-state decoding is an architectural property; this experiment measures training.
\papersource{Paper, Appendix A.3.3, PDF p. 16; Fig. 3, p. 9. Units: thousand tokens per second.}
\end{frame}
\end{document}