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\newcommand{\papersource}[1]{\par\smallskip{\scriptsize\color{gray}#1\par}}
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\newcommand{\gdn}{Gated DeltaNet}
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\title[MoM]{MoM: Linear Sequence Modeling\\with Mixture-of-Memories}
\subtitle{Routing tokens into persistent recurrent states}
\author{Paper by Jusen Du, Weigao Sun, Disen Lan, Jiaxi Hu, and Yu Cheng}
\date{arXiv:2502.13685v4 \quad | \quad Revised November 18, 2025\\Independent reading presentation \quad | \quad September 11, 2026}
\begin{document}

\begin{frame}
\titlepage
\vspace{-3mm}
\begin{center}\alert{Expand memory through selective updates; retain linear sequence processing.}\end{center}
\papersource{Primary materials: the 18-page v4 PDF, matching author TeX, and original figures. Main talk: about 25 minutes; backup follows slide 22.}
\end{frame}

\begin{frame}{Fixed states trade historical detail for efficiency}
\begin{columns}[T]
\column{0.47\textwidth}
\begin{block}{Transformer}
Stores a key and value for each past token.\\[2mm]
Historical storage and attention work grow with context length.
\end{block}
\column{0.49\textwidth}
\begin{block}{Linear recurrent model}
Compresses history into a fixed state.\\[2mm]
Later writes can interfere with information already stored there.
\end{block}
\end{columns}
\medskip
\[
\mat M_t=\mat M_{t-1}+\mat k_t^\top\mat v_t,
\qquad \mat o_t=\mat q_t\mat M_t
\]
\alert{MoM asks which state a token should update, as well as how to update it.}
\papersource{Paper, Secs. 1--3.1, PDF pp. 1--3; Eq. (2). The displayed rule is the simplest illustrative update.}
\end{frame}

\begin{frame}{A router selects states; a shared state sees every token}
\begin{columns}[c]
\column{0.43\textwidth}
\centering\fig{fig-01-architecture.pdf}{1}{0.79}
\column{0.53\textwidth}
\begin{itemize}
\item Each routed memory has its own KV projections and recurrent state.
\item Only selected states update; all others remain unchanged.
\item The query projection is shared.
\item An extra shared memory provides a path through the full causal history.
\end{itemize}
\medskip
\begin{block}{Main configuration}
4 routed memories, top-2 activation,\\plus 1 shared memory.\\Update rule: \gdn.
\end{block}
\end{columns}
\papersource{Original Fig. 1, PDF p. 3; Secs. 3.2 and 4.1, PDF pp. 3--6.}
\end{frame}

\begin{frame}{Top-$k$ routing chooses where to write and read}
\[
\mathrm{scores}_t=\mathrm{TopK}\!\left(\mathrm{softmax}(\mat x_t\mat W_g)\right),
\qquad
\mat g_t=\frac{\mathrm{scores}_t}{\sum\mathrm{scores}_t}
\]
\begin{itemize}
\item $\mat x_t\in\mathbb R^d$: current token representation; $\mat W_g\in\mathbb R^{d\times M}$: learned router.
\item Keep the selected indices $S_t$, with $|S_t|=k$.
\item Weights sum to one over the selected routed memories.
\end{itemize}
\begin{block}{Teaching example: $M=4$, $k=2$}
Softmax scores $(0.50,0.30,0.15,0.05)$ select memories 1 and 2.\\
Their mixing weights are $(0.625,0.375)$.
\end{block}
The paper uses these weights for \alert{mixing}; Eq. (6) does not weight the write by $g_t^{(m)}$.
\papersource{Paper, Sec. 3.2.1, Eqs. (3)--(4), PDF p. 4. Example constructed for this presentation.}
\end{frame}

\begin{frame}{Unselected memories skip the entire state update}
\[
\mat k_t^m=\mat x_t\mat W_k^m,\qquad
\mat v_t^m=\mat x_t\mat W_v^m
\]
\[
\mat M_t^m=
\begin{cases}
F_m(\mat M_{t-1}^m,\mat x_t),&m\in S_t,\\
\mat M_{t-1}^m,&m\notin S_t.
\end{cases}
\]
\begin{itemize}
\item The generic $F_m$ can use additive, gated, or delta-style updates.
\item The main experiments instantiate $F_m$ with \gdn.
\item A memory receiving tokens 1, 5, and 9 evolves on that subsequence: tokens 2--4 do not decay or overwrite its state.
\end{itemize}
\papersource{Paper, Sec. 3.2.2, Eqs. (5)--(6), Table 1, PDF p. 4. Piecewise form makes the prose rule explicit.}
\end{frame}

\begin{frame}{Read a mixture without collapsing the stored states}
\[
\widetilde{\mat M}_t=\sum_{m\in S_t}g_t^{(m)}\mat M_t^m,
\qquad
\mat o_t=\mat q_t\widetilde{\mat M}_t
\]
\begin{itemize}
\item Mixing is a temporary readout; the individual states persist.
\item The same query can read each selected state separately:
\end{itemize}
\[
\mat q_t\!\left(\sum_m g_t^{(m)}\mat M_t^m\right)
=\sum_m g_t^{(m)}(\mat q_t\mat M_t^m).
\]
\begin{block}{Shared path}
Fig. 1 adds an always-active shared-memory readout to the routed mixture. It covers the full causal history, but remains a compressed state.
\end{block}
\papersource{Paper, Eqs. (7)--(8), PDF p. 4; shared memory, p. 5; readout equivalence, Sec. 3.3, p. 5.}
\end{frame}

\begin{frame}{Stable grouping makes routed recurrence a varlen operation}
\centering\fig{fig-02-varlen.pdf}{0.98}{0.39}
\medskip
\begin{enumerate}
\item Group by \textbf{sample and memory}, preserving time order within each group.
\item Concatenate groups with segment boundaries; run independent causal kernels.
\item Scatter outputs to original positions and combine with routing weights.
\end{enumerate}
\medskip
\alert{Top-$k$ creates $k$ routed copies of each token; segment boundaries prevent state leakage.}
\papersource{Original Fig. 2 and Sec. 3.3, PDF pp. 5--6. Figure shows top-1 and omits QKV projections; main experiments use top-2.}
\end{frame}

\begin{frame}{Linear in context length does not mean free memory expansion}
\begin{center}
\begin{tabular}{p{0.43\linewidth}p{0.45\linewidth}}
\toprule
Quantity & Simplified dependence \\
\midrule
Training work vs. sequence length $T$ & $O(T)$ for fixed $M,k,d$ \\
Core state operations & $O\!\left(T(k+1)d^2\right)$ \\
Router score computation & $O(TdM)$, plus selection and packing \\
Persistent recurrent state & $O\!\left((M+1)d^2\right)$ \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Single-step decoding is constant in \emph{past context length}; prefill still processes the prompt.
\item Inactive states still occupy memory.
\item Fixed activation ratio $k/M$ means more active computation as $M$ grows.
\end{itemize}
\papersource{Reading analysis of Secs. 3.2--3.3, PDF pp. 3--6. Single-state dimension convention; not a full-model FLOPs estimate.}
\end{frame}

\begin{frame}{The size labels specify configurations, not equal budgets}
\begin{center}
\begin{tabular}{lrr}
\toprule
 & ``380M'' & ``1.3B'' \\
\midrule
Layers / hidden size & 24 / 1024 & 24 / 2048 \\
Training tokens & 15B & 100B \\
Batch tokens & 0.5M & 2M \\
Pretraining context & 2K & 2K \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item SlimPajama data; Mistral tokenizer; AdamW, learning rate $3\times10^{-4}$.
\item Sparse KV projections add parameters. Main-table models are not exactly parameter matched.
\item Several 1.3B baselines use public checkpoints marked $\dagger$; authors report matched training configurations.
\end{itemize}
\papersource{Paper, Sec. 4.1, PDF p. 6; Appendix C, p. 15. Exact 400M activated-parameter comparison appears in Table 9.}
\end{frame}

\begin{frame}{MoM narrows the recall gap at both reported scales}
\begin{center}
\begin{tabular}{lrr}
\toprule
Model & 380M / 15B & 1.3B / 100B \\
\midrule
Transformer++ & 31.70 & 37.31$^\dagger$ \\
\gdn & 24.78 & 32.30 \\
\textbf{MoM} & \textbf{28.16} & \textbf{36.04} \\
\midrule
MoM minus \gdn & $+3.38$ & $+3.74$ \\
MoM minus Transformer++ & $-3.54$ & $-1.27$ \\
\bottomrule
\end{tabular}
\end{center}
\begin{block}{Scope of this result}
Mean over FDA, SWDE, SQuAD, NQ, TriviaQA, and DROP.\\
\textbf{All inputs are truncated to at most 2K tokens.} Higher is better.
\end{block}
The paper does not fully specify each task's scoring metric; differences are reported in score points.
\papersource{Paper, Table 2, PDF p. 7. Differences calculated from published means. No confidence intervals reported.}
\end{frame}

\begin{frame}{The remaining gap depends strongly on the recall task}
\begin{center}
\begin{tabular}{lrrr}
\toprule
1.3B / 100B tokens & MoM & Transformer++$^\dagger$ & Difference \\
\midrule
FDA & 41.14 & 44.32 & $-3.18$ \\
SWDE & 34.30 & 32.43 & $+1.87$ \\
SQuAD & 37.08 & 42.59 & $-5.51$ \\
NQ & 24.11 & 24.49 & $-0.38$ \\
TriviaQA & 58.59 & 58.47 & $+0.12$ \\
DROP & 21.03 & 21.56 & $-0.53$ \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item MoM beats the listed linear models on all six tasks at both scales.
\item At 380M, FDA remains 22.98 vs. 46.14 for Transformer++.
\item Excluding FDA, the 380M means become 29.20 vs. 28.81.
\end{itemize}
\papersource{Paper, Table 2, PDF p. 7. All six-task comparisons use the same maximum input length of 2K.}
\end{frame}

\begin{frame}{Recall gains survive matching activated parameters}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Model & Activated params & Recall $\uparrow$ & Common $\uparrow$ \\
\midrule
\gdn & 400M & 24.78 & 41.44 \\
MoM & 400M & \textbf{26.51} & \textbf{41.50} \\
\midrule
Difference & & $+1.73$ & $+0.06$ \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Reduce MoM's MLP hidden ratio to 2; otherwise follow the main training setup.
\item All six recall scores improve in this comparison.
\item The common-sense mean changes very little; two individual tasks decline.
\end{itemize}
\begin{block}{What this control establishes}
The recall benefit is not explained solely by more activated parameters. Total parameters, total state, FLOPs, and wall time are not jointly matched.
\end{block}
\papersource{Paper, Appendix G.1, PDF pp. 16--17; Table 9, p. 17. Recall differences: points; common-sense accuracy: percentage points.}
\end{frame}

\begin{frame}{Routed memories beat a single expanded active state}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Architecture & Listed Params & Recall $\uparrow$ & Common $\uparrow$ \\
\midrule
GLA expanded & 425M & 22.87 & 38.90 \\
GLA MoM & 395M & \textbf{23.53} & \textbf{39.99} \\
\midrule
Gated DeltaNet expanded & 550M & 26.32 & 41.32 \\
Gated DeltaNet MoM & 444M & \textbf{28.16} & \textbf{41.97} \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Expand the baseline value dimension to match \textbf{activated state capacity}.
\item Benefits appear with both GLA and Gated DeltaNet updates.
\item MoM still retains additional inactive states; this is not equal total state storage.
\end{itemize}
\papersource{Paper, Table 4 and Sec. 4.2.3, PDF pp. 7--8; Appendix G.2, p. 17. ``Params'' retained from the table; Appendix G discusses activated parameters.}
\end{frame}

\begin{frame}{LongBench gains concentrate in few-shot tasks and code}
\begin{center}
\begin{tabular}{lrrrrr}
\toprule
Model & Summary & Few-shot & Synthetic & Code & Avg.* \\
\midrule
GSA$^\dagger$ & \textbf{7.75} & 20.29 & 1.92 & 42.83 & 14.61 \\
Gated DeltaNet & 7.14 & 18.00 & 2.10 & 41.52 & 13.98 \\
MoM & 6.89 & \textbf{21.26} & \textbf{2.63} & \textbf{47.79} & \textbf{15.64} \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Code improves by 6.27 points over Gated DeltaNet; Transformer++ is not included.
\item It is not best on summary, single-doc QA, multi-doc QA, or synthetic tasks across the full table.
\end{itemize}
\begin{block}{Aggregation needs clarification}
Table 10 reports MoM Zh-Avg 17.33, En-Avg 15.71, but Avg. 15.64. These cannot be a simple partition-weighted average on the same basis.
\end{block}
\papersource{Paper, Tables 3 and 10, PDF pp. 7 and 18. *Author-reported overall average; weights are not reconstructible. Input limits and model scale are not separately specified here.}
\end{frame}

\begin{frame}{Long-history decoding benefits; the shortest point does not}
\centering\fig{fig-03-efficiency.pdf}{0.85}{0.65}
\begin{itemize}
\item Generate 1K tokens: MoM remains roughly flat over 32K--512K history.
\item Transformer++ is faster at 32K, then grows; 512K is marked OOM.
\end{itemize}
\papersource{Original Fig. 3, PDF p. 8. Bars: seconds (left); lines: GB (right). Exact inference batch, precision, and prefill timing are not fully reported. OOM markers are not measured values.}
\end{frame}

\begin{frame}{Perplexity extrapolates well beyond the training length}
\centering\fig{fig-04-extrapolation.pdf}{0.78}{0.59}
\begin{itemize}
\item Train at 2K on SlimPajama; evaluate 2K--32K contexts on FineWeb.
\item MoM has the lowest plotted PPL. This does not establish exact long-range retrieval or compare all long-context Transformer adaptations.
\end{itemize}
\papersource{Original Fig. 4 and Sec. 4.2.5, PDF p. 8. Lower PPL is better. Transformer++ leaves the displayed range.}
\end{frame}

\begin{frame}{A shared state helps; the best balance weight is task dependent}
\begin{columns}[T]
\column{0.52\textwidth}
\textbf{Auxiliary loss scale}
\begin{center}
\begin{tabular}{lrr}
\toprule
Weight & Recall & Common \\
\midrule
$10^{-2}$ & 27.59 & \textbf{42.10} \\
$5\times10^{-3}$ & 26.55 & 41.71 \\
$10^{-3}$ & \textbf{28.16} & 41.97 \\
0 & 27.23 & 41.58 \\
\bottomrule
\end{tabular}
\end{center}
\column{0.44\textwidth}
\textbf{Shared memory}
\begin{center}
\begin{tabular}{lrr}
\toprule
 & Recall & Common \\
\midrule
With & 28.16 & 41.97 \\
Without & 26.06 & 40.38 \\
\bottomrule
\end{tabular}
\end{center}
\alert{Shared path: +2.10 recall points.}
\end{columns}
\medskip
\begin{itemize}
\item Routing heatmaps show much better load balance with the auxiliary loss.
\item Better balance does not guarantee higher recall for every loss weight.
\item Removing shared memory also removes capacity and computation.
\end{itemize}
\papersource{Paper, Table 6, PDF p. 10; Figs. 5 and 9, pp. 9 and 18. 380M configuration, 15B training tokens; higher scores are better.}
\end{frame}

\begin{frame}{Memory scaling helps through eight states in the main plot}
\centering\fig{fig-06-scaling.png}{0.76}{0.55}
\begin{itemize}
\item At activation ratio 0.5, more memories also mean more active updates.
\item The 1-memory point is a special starting baseline.
\item Appendix Fig. 8 shows a recall decline from 8 to 16 at 50\% activation.
\end{itemize}
\papersource{Original Fig. 6, PDF p. 10; Fig. 8, p. 17. The 4-memory scores (27.20 / 41.75) differ from the main model (28.16 / 41.97); the paper does not fully explain this configuration difference.}
\end{frame}

\begin{frame}{Common-sense gains are modest against the strongest baseline}
\begin{center}
\begin{tabular}{lrrr}
\toprule
1.3B / 100B tokens & Wiki PPL $\downarrow$ & Lambada PPL $\downarrow$ & Common $\uparrow$ \\
\midrule
Transformer++$^\dagger$ & 17.61 & 19.29 & 49.93 \\
GSA$^\dagger$ & 16.69 & 16.02 & 50.89 \\
Gated DeltaNet & 17.14 & 18.80 & 49.58 \\
MoM & \textbf{16.64} & \textbf{14.83} & \textbf{50.97} \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Mean accuracy is 1.39 percentage points above Gated DeltaNet, but only 0.08 above GSA.
\item Individual task leaders differ; no uncertainty estimates are reported.
\item Six-task mean: ARC-e/c, HellaSwag, LAMBADA, PIQA, WinoGrande. PPL is excluded from this mean.
\end{itemize}
\papersource{Paper, Appendix D, Table 7, PDF p. 15. Zero-shot via lm-evaluation-harness; ARC-c and HellaSwag use length-normalized accuracy scoring.}
\end{frame}

\begin{frame}{Three global-attention layers unlock further recall gains}
\begin{center}
\alert{24 layers = 3 repeats of [7 MoM layers + 1 Transformer layer]}
\medskip
\begin{tabular}{lrr}
\toprule
Model & Recall $\uparrow$ & Common $\uparrow$ \\
\midrule
Transformer++ & 31.70 & 41.35 \\
MoM & 28.16 & 41.97 \\
MoM Hybrid & \textbf{37.80} & \textbf{42.38} \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Hybrid recall: +9.64 points over pure MoM, +6.10 over Transformer++.
\item FDA and SWDE account for much of the gain; not every task improves.
\end{itemize}
\begin{block}{The complexity claim changes}
Global-attention layers retain growing KV caches. The full hybrid does not inherit pure MoM's constant-history-state guarantee.
\end{block}
\papersource{Paper, Appendix F, Table 8, PDF p. 16. Baseline rows match the small-scale main experiment; full hybrid compute and parameter budgets are not separately listed.}
\end{frame}

\begin{frame}{The evidence supports useful separation, not lossless memory}
\begin{enumerate}
\item \textbf{Mechanism:} unselected states avoid the current write; interference within a state and routing mistakes remain possible.
\medskip
\item \textbf{Budgets:} activated parameters, active state capacity, total state, and runtime are different controls.
\medskip
\item \textbf{Reliability:} no multi-seed error estimates; some common-sense margins are very small.
\medskip
\item \textbf{Reporting:} LongBench aggregation, scaling configuration differences, and inference details need clarification before reproduction.
\end{enumerate}
\papersource{Reading assessment based on Sec. 4 and Appendices C--I, PDF pp. 6--10 and 15--18. No training or evaluation was rerun for this presentation.}
\end{frame}

\begin{frame}{Selective persistent state is a useful design axis}
\begin{block}{Take-home message}
MoM routes tokens into independently updated recurrent states, improving recall while preserving linear sequence processing for a fixed architecture.
\end{block}
\begin{itemize}
\item Strongest result: recall gains remain after matching activated parameters.
\item Main trade-off: more stored states, routing overhead, and extra active work.
\item Practical complement: a few attention layers can add substantial recall.
\end{itemize}
\medskip
\textbf{Primary reference}\par
Jusen Du, Weigao Sun, Disen Lan, Jiaxi Hu, and Yu Cheng.\par
\emph{MoM: Linear Sequence Modeling with Mixture-of-Memories}.\par
\href{https://arxiv.org/abs/2502.13685v4}{arXiv:2502.13685v4}, November 18, 2025.
\papersource{Prepared from the matching PDF, author TeX, and original figures. Equations and examples marked as teaching explanations are this reading's reconstructions. Backup slides follow.}
\end{frame}

% Backup material
\begin{frame}{Backup: token preferences suggest possible specialization}
\begin{center}
\begin{tabular}{cll}
\toprule
Memory & Observed token types & Proposed function \\
\midrule
1 & Basic nouns / verbs / prepositions & Basic semantics / causal logic \\
2 & Proper nouns / scientific terms & Specialized knowledge \\
3 & Technical terms / adjectives & Detailed memory \\
4 & Questions / incomplete nouns & Fragmented or open information \\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Qualitative observation of an intermediate layer.
\item Token-selection procedures and cross-seed stability are not established.
\item A functional claim would require targeted state intervention or controlled routing experiments.
\end{itemize}
\papersource{Paper, Sec. 4.2.6 and Table 5, PDF pp. 8--9. Proposed functions are author interpretations, not causally demonstrated modules.}
\end{frame}

\begin{frame}{Backup: auxiliary loss spreads routing across the memories}
\centering\fig{fig-05-balance-aux.pdf}{1}{0.53}
\begin{itemize}
\item Columns: 24 layers. Rows: four routed memories.
\item Roughly 300k ARC-easy tokens; many shares are near 0.25.
\item Near-balanced shares still vary: the figure includes values from 0.12 to 0.37.
\end{itemize}
\papersource{Original Fig. 5, PDF p. 9; Sec. 4.2.6, p. 8. Columns sum to about 1, suggesting shares of routing assignments rather than per-token selection probabilities. The denominator is not explicitly defined.}
\end{frame}

\begin{frame}{Backup: without auxiliary loss, some states are nearly unused}
\centering\fig{fig-09-balance-no-aux.pdf}{1}{0.53}
\begin{itemize}
\item Layer 2 shares: 0.00, 0.50, 0.05, 0.45.
\item Color scale reaches 0.50 here, versus 0.40 in Fig. 5; compare numbers.
\item The main text labels both heatmaps ``with'' loss; this figure's caption explicitly says \textbf{without}.
\end{itemize}
\papersource{Original Fig. 9, PDF p. 18, and Sec. 4.2.6, p. 8. Unbalanced usage can reduce effective capacity, but the heatmap alone is not a downstream causal test.}
\end{frame}

\begin{frame}{Backup: the training-loss advantage is a single reported run}
\centering\fig{fig-07-training-loss.png}{0.78}{0.58}
\begin{itemize}
\item 380M configuration, 15B training tokens, random seed 42.
\item Lower training loss supports this optimization trajectory; the plot is not a throughput measurement or a multi-seed confidence interval.
\end{itemize}
\papersource{Original Fig. 7, Appendix E, PDF pp. 15--16. The horizontal scale reaches about 30k, consistent with 15B / 0.5M batch tokens; the original axis has no explicit unit title.}
\end{frame}

\begin{frame}{Backup: recall is not monotonic through sixteen memories}
\centering\fig{fig-08-scaling-full.png}{0.94}{0.58}
\begin{itemize}
\item Red: 25\% activation; blue: 50\%; open circle: one-memory start.
\item The blue recall curve drops from 8 to 16 memories; the common-sense curve rises. Every setting includes an additional shared memory.
\end{itemize}
\papersource{Original Fig. 8, Appendix H, PDF p. 17. The legend's $n$ denotes memory count. Points without numeric labels are not treated as exact tabulated results.}
\end{frame}
\end{document}