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  \hspace{8mm}{\scriptsize\color{gray}Memory for Large Language Models\;|\;2607.25380v1}
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\title[Memory for LLMs]{Memory for Large Language Models}
\subtitle{Storage, writing, and retrieval as architectural choices}
\author{Paper authors: Sining Zhoubian, Dan Zhang,\\Evgeny Kharlamov, and Jie Tang}
\date{Reading presentation\;\textbullet\;4 October 2026\\
\href{https://arxiv.org/abs/2607.25380v1}{arXiv:2607.25380v1 (28 July 2026)}}

\begin{document}

\begin{frame}
  \titlepage
  \vspace{-6mm}
  \begin{center}
    \color{AcademicTeal}\textbf{Memory quality depends on what is stored, how it changes,\\and whether it can still be recovered.}
  \end{center}
\end{frame}

\begin{frame}{The survey connects mechanisms that share a problem}
  \begin{block}{The same old fact can survive in different places}
    A token KV entry, a compressed state, writable parameters,\\or an independently indexed record.
  \end{block}
  \gap
  \begin{itemize}
    \item \textbf{Scope:} model architecture and inference dynamics.
    \item \textbf{Contribution:} a taxonomy, update-rule vocabulary, and evaluation agenda.
    \item \textbf{Evidence:} synthesis of prior work; no new controlled leaderboard.
  \end{itemize}
  \papersource{Paper, Secs. I--II, PDF pp. 1--6. Agent orchestration and prompt-level memory are outside the main scope.}
\end{frame}

\begin{frame}{Three axes answer three different questions}
  \renewcommand{\arraystretch}{1.18}
  \begin{tabular}{@{}P{.23\linewidth}P{.33\linewidth}P{.38\linewidth}@{}}
    \toprule
    \textbf{Axis} & \textbf{Question} & \textbf{Distinction}\\
    \midrule
    Representation & Storage and access interface & Implicit / explicit\\
    Update dynamics & Timing of updates & Offline / online\\
    Persistence & Effective time horizon & Short-term / long-term\\
    \bottomrule
  \end{tabular}
  \par\vspace{3mm}
  \begin{exampleblock}{Two crucial separations}
    Online updates need not use gradients.\\
    Long-horizon influence need not imply cross-session recall.
  \end{exampleblock}
  \papersource{Paper, Sec. II-A--C, PDF pp. 2--5.}
\end{frame}

\begin{frame}{In this taxonomy, KV tensors are still implicit memory}
  \par
  {\small
  \renewcommand{\arraystretch}{1.25}
  \begin{tabular}{@{}P{.34\linewidth}lll@{}}
    \toprule
    \textbf{Mechanism} & \textbf{Form} & \textbf{Update} & \textbf{Horizon}\\
    \midrule
    Transformer KV cache & Implicit & Online & Short\\
    Mamba / Gated DeltaNet & Implicit & Online & Long\\
    Titans / TTT-E2E & Explicit & Online & Long\\
    kNN-LM / Engram & Explicit & Offline & Long\\
    Sparse MoE & Explicit & Offline & Long\\
    \bottomrule
  \end{tabular}}
  \par\vspace{3mm}
  \begin{itemize}
    \item KV access is fixed by attention's forward computation.
    \item MoE changes the selected experts at inference, not their weights.
    \item Classify a specified \alert{memory component}, not just a model name.
  \end{itemize}
  \papersource{Selected and reformatted from Table I, PDF p. 4; definition in Sec. II-A, pp. 2--3.}
\end{frame}

\begin{frame}{Update timing alone does not explain memory behavior}
  \par
  {\small
  \renewcommand{\arraystretch}{1.28}
  \begin{tabular}{@{}P{.30\linewidth}P{.32\linewidth}P{.32\linewidth}@{}}
    \toprule
    \textbf{Rule family} & \textbf{Action} & \textbf{Main failure mode}\\
    \midrule
    Optimization-based & Fit writable parameters & Drift; objective mismatch\\
    State transition & Recur, project, or filter & Compression; interference\\
    Signal-gated & Decide whether to write/read & Miscalibration; delayed value\\
    Admission / eviction / consolidation & Retain, delete, or rewrite & Irreversible information loss\\
    Objective-induced / structural & Shape memory through training or design & Rigidity at inference\\
    \bottomrule
  \end{tabular}}
  \par\vspace{3mm}
  \alert{These families overlap:} HAM combines recurrent updates and gated KV admission.
  \papersource{Reorganized from Table II, PDF p. 5; risks elaborated in Sec. VI-C, p. 17.}
\end{frame}

\begin{frame}{Implicit memory either retains items or compresses history}
  \centering
  \includegraphics[width=.98\linewidth,height=.65\textheight,keepaspectratio]{figures/fig-03-implicit.pdf}
  \gap
  \raggedright
  \textbf{Read left to right:} token access, selection policies, recurrent states.
  \papersource{Original Fig. 3, PDF p. 7. Conceptual diagram, not an empirical comparison.}
\end{frame}

\begin{frame}{Attention has separate storage and access costs}
  \[
    y_t=V_t^\top\operatorname{softmax}\!\left(\frac{K_tq_t}{\sqrt{d_k}}\right)
  \]
  \begin{center}
    $K_t\in\R^{t\times d_k}$,\quad $V_t\in\R^{t\times d_v}$,\quad $q_t\in\R^{d_k}$.
  \end{center}
  \begin{itemize}
    \item \textbf{KV storage:} $\Theta(t(d_k+d_v))$ per layer/head.
    \item \textbf{Full-sequence attention work:} quadratic in sequence length.
    \item Compressing entries, reading fewer entries, and evicting entries change different costs.
  \end{itemize}
  \gap
  MLA: representation\quad MoBA/NSA: access\quad StreamingLLM: retention
  \papersource{Teaching formula; paper, Sec. III-A--B, pp. 6--8; KV scaling in Sec. V-B(a), p. 16. Fixed dimensions for scaling.}
\end{frame}

\begin{frame}{A delta write corrects the current association}
  \[
    M_t=M_{t-1}+\eta_t\underbrace{(v_t-M_{t-1}k_t)}_{\text{prediction residual}}k_t^\top
  \]
  \begin{center}
    $M_t\in\R^{d_v\times d_k}$,\quad $k_t\in\R^{d_k}$,\quad $v_t\in\R^{d_v}$.
  \end{center}
  \begin{exampleblock}{For a unit-norm key}
    $M_tk_t=(1-\eta_t)M_{t-1}k_t+\eta_tv_t$.\\
    With $\eta_t=1$, the new value replaces the old prediction along this key.
  \end{exampleblock}
  Other, non-orthogonal keys can still be affected: \alert{state interference}.
  \papersource{Teaching derivation, not a full Gated DeltaNet variant. Motivation: Sec. III-C, PDF pp. 8--9.}
\end{frame}

\begin{frame}{Recurrent memory improves through editing and allocation}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{.48\textwidth}
      \begin{block}{Change the write}
        \begin{itemize}
          \item Input-dependent decay: GLA, RWKV, Mamba.
          \item Erase/write control: GDN-2, RWKV-7, KDA.
          \item Calibrated updates: projection and Kalman-style filtering.
        \end{itemize}
      \end{block}
    \end{column}
    \begin{column}{.48\textwidth}
      \begin{exampleblock}{Change the capacity}
        \begin{itemize}
          \item Multiple routed states: MoM.
          \item Hierarchical states: Log-Linear Attention.
          \item Cached state snapshots: Memory Caching.
        \end{itemize}
      \end{exampleblock}
    \end{column}
  \end{columns}
  \gap
  \alert{Long streams do not imply unlimited exact recall.}
  \papersource{Paper, Sec. III-C--D, PDF pp. 8--9; Memory Caching in Sec. V-B(a), p. 16.}
\end{frame}

\begin{frame}{Explicit memory assigns a storage role to a component}
  \centering
  \includegraphics[width=.98\linewidth,height=.58\textheight,keepaspectratio]{figures/fig-04-explicit.pdf}
  \gap
  \raggedright
  \begin{itemize}
    \item A writable module can be parametric or slot-based.
    \item A lookup store can remain fixed throughout inference.
  \end{itemize}
  \papersource{Original Fig. 4, PDF p. 10; Sec. IV. The taxonomy concerns interfaces, not whether storage contains tensors.}
\end{frame}

\begin{frame}{Online writing separates a memory state from the backbone}
  \[
    \phi_{t+1}=\phi_t-\eta_t\nabla_{\phi_t}\mathcal L_{\mathrm{write}}(\phi_t;x_t)
  \]
  \begin{itemize}
    \item $\phi_t$: designated memory parameters; $\mathcal L_{\mathrm{write}}$: write objective.
    \item Titans / TTT-E2E: optimization-based writing. GDWM adds write control.
    \item In-Place TTT reuses an FFN matrix; MEMORYLLM instead rewrites latent slots through forward updates.
  \end{itemize}
  \begin{exampleblock}{The key design question}
    Which input is worth writing, and how much should it change memory?
  \end{exampleblock}
  \papersource{Generic teaching rule; Sec. IV-A, PDF pp. 10--11. Momentum, decay, and causal read/write order are model-specific.}
\end{frame}

\begin{frame}{One gradient step can be exactly a recurrent update}
  \[
    \mathcal L(M)=\tfrac12\|Mk_t-v_t\|_2^2
  \]
  \[
    \nabla_M\mathcal L=(Mk_t-v_t)k_t^\top
  \]
  \[
    M_t=M_{t-1}+\eta_t(v_t-M_{t-1}k_t)k_t^\top
  \]
  \begin{block}{Implication for the taxonomy}
    ``Optimization'' and ``state transition'' can describe the same operation.\\
    Inspect the write interface and lifecycle, not the method's name alone.
  \end{block}
  \papersource{Teaching derivation for linear memory and a squared loss. Paper discusses the TTT--linear-attention boundary in Sec. IV-A(c), p. 11.}
\end{frame}

\begin{frame}{Lookup selects a record; MoE selects a transformation}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{.46\textwidth}
      \begin{block}{Lookup memory}
        kNN-LM: context--target records.\par\gap
        Engram: structured hash lookup.\par\gap
        PlugLM / ExplicitLM: editable or interpretable banks.
      \end{block}
    \end{column}
    \begin{column}{.51\textwidth}
      \begin{exampleblock}{Conditional parameter memory}
        \[
          y=\sum_{i\in\mathcal S(h)}g_i(h)\operatorname{Expert}_i(h)
        \]
        $\mathcal S(h)$: selected experts.\par
        $g_i(h)$: routing weights.\par\gap
        Mixtral example: select 2 of 8 experts per layer.
      \end{exampleblock}
    \end{column}
  \end{columns}
  \gap
  Sparse activation reduces active work; total storage and data movement still matter.
  \papersource{Paper, Sec. IV-B--C, pp. 11--13; original Eq. (1), p. 12. MoE-as-memory is the survey's interpretation.}
\end{frame}

\begin{frame}{Update frequency and information lifetime are different}
  \centering
  \begin{tikzpicture}[x=.72cm,y=.74cm]
    \draw[-{Latex},gray] (0,0)--(12,0) node[right]{\small time};
    \node[anchor=east] at (0,1){\small Fast};
    \node[anchor=east] at (0,2){\small Medium};
    \node[anchor=east] at (0,3){\small Slow};
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    \foreach \i in {2,5,8,11} {\fill[AcademicBlue] (\i,2) circle(3pt);}
    \foreach \i in {2,10} {\fill[WarmOrange] (\i,3) circle(3pt);}
  \end{tikzpicture}
  \raggedright
  \gap
  \begin{itemize}
    \item Nested schedules distribute plasticity across parameter subsets.
    \item Control \textbf{frequency, magnitude, and scope} of each update.
    \item Saving, resetting, and consolidating state determine its lifecycle.
  \end{itemize}
  \papersource{Teaching schematic, not the paper's schedule. Sec. IV-D--E, PDF pp. 13--14.}
\end{frame}

\begin{frame}{Adaptive hybrids gate different resources}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{.48\textwidth}
      \begin{block}{AMOR: when to compute}
        Recurrent backbone produces a prediction.\par\gap
        High normalized output entropy triggers attention refinement.
      \end{block}
    \end{column}
    \begin{column}{.48\textwidth}
      \begin{exampleblock}{HAM: what to retain}
        Recurrent memory processes every token.\par\gap
        Hard-to-predict tokens enter a sparse KV cache.
      \end{exampleblock}
    \end{column}
  \end{columns}
  \gap
  \begin{itemize}
    \item Fixed hybrids allocate layers, heads, or channels in advance.
    \item Adaptive controllers allocate work or storage by input.
    \item A low-surprise event today may be essential to a future query.
  \end{itemize}
  \papersource{Paper, Sec. V-A(b), PDF p. 15; delayed relevance in Sec. VI-C, p. 17.}
\end{frame}

\begin{frame}{System optimizations act at different memory layers}
  \par
  {\small
  \renewcommand{\arraystretch}{1.4}
  \begin{tabular}{@{}P{.29\linewidth}P{.31\linewidth}P{.34\linewidth}@{}}
    \toprule
    \textbf{Technique} & \textbf{Changes} & \textbf{Interpretation}\\
    \midrule
    KV quantization / low rank & Entry representation & Fidelity vs. bytes\\
    PagedAttention & Physical allocation & Fragmentation and reuse\\
    Windows / sparse global links & Accessible positions & Recency and global anchors\\
    Memory Caching & Recurrent snapshots & Extra levels of state capacity\\
    Bottlenecked Transformers & Periodic cache processing & Working-memory consolidation\\
    \bottomrule
  \end{tabular}}
  \par\vspace{3mm}
  \alert{Better allocation is not itself a new retention capability.}
  \papersource{Paper, Sec. V-B, PDF p. 16. Reformatted comparison.}
\end{frame}

\begin{frame}{Memory evaluation needs more than a context length}
  \renewcommand{\arraystretch}{1.35}
  \begin{tabular}{@{}P{.27\linewidth}P{.67\linewidth}@{}}
    \toprule
    \textbf{Dimension} & \textbf{Diagnostic question}\\
    \midrule
    Recall fidelity & Can the target fact be recovered among distractors?\\
    Integration & Can distant evidence support a structured answer?\\
    Persistence & Does the fact survive delay, updates, and boundaries?\\
    Interference & Do later writes corrupt older associations?\\
    Efficiency & What storage, latency, and write cost buy that accuracy?\\
    \bottomrule
  \end{tabular}
  \par\vspace{3mm}
  NIAH / RULER probe retrieval; broader long-context tasks also involve reasoning.
  \papersource{Paper, Sec. V-C, PDF pp. 16--17; Sec. VI-F, p. 18. No unified empirical metric is established here.}
\end{frame}

\begin{frame}{A fair protocol controls both interference and budget}
  \begin{center}
    \begin{tikzpicture}[node distance=4mm,box/.style={draw=AcademicBlue,rounded corners,align=center,minimum height=10mm,font=\small},>=Latex]
      \node[box] (w) {Write facts};
      \node[box,right=of w] (i) {Inject distractors\\and corrections};
      \node[box,right=of i] (b) {Delay / boundary};
      \node[box,right=of b] (q) {Query facts};
      \draw[->] (w)--(i);\draw[->] (i)--(b);\draw[->] (b)--(q);
    \end{tikzpicture}
  \end{center}
  \gap
  \begin{itemize}
    \item Vary fact count, key similarity, delay, and reset policy.
    \item Compare token KV, fixed states, hybrids, and disabled-write controls.
    \item Include TTT updates, retrieval storage, optimizer state, and routing costs.
  \end{itemize}
  \begin{exampleblock}{Report curves, not only a best score}
    Recall $A(\Delta,I,B)$ over delay $\Delta$, interference $I$, and budget $B$.
  \end{exampleblock}
  \papersource{Presenter-proposed protocol, motivated by Sec. V-C and Sec. VI-F, pp. 16--18. Not an experiment in the paper.}
\end{frame}

\begin{frame}{The taxonomy is useful, but its boundaries need care}
  \begin{enumerate}
    \item \textbf{Interfaces form a spectrum.} KV retrieval, activation banks, writable matrices, and experts differ in autonomy.
    \gap
    \item \textbf{Classification levels can differ.} Next-Latent Prediction is an offline training intervention; recurrent state updates are online operations.
    \gap
    \item \textbf{Long-term is a coarse label.} State retention, useful influence, and exact cross-session recall need separate tests.
  \end{enumerate}
  \papersource{Critical reading of Sec. II, pp. 2--6; Sec. III-C(g), p. 9; Sec. IV-A--C, pp. 10--13.}
\end{frame}

\begin{frame}{The open problem is reliable allocation over time}
  \begin{columns}[T,onlytextwidth]
    \begin{column}{.48\textwidth}
      \begin{block}{Mechanisms}
        \begin{itemize}
          \item Measure capacity, fidelity, and interference together.
          \item Accumulate knowledge without destructive drift.
          \item Diagnose and correct unreliable write signals.
        \end{itemize}
      \end{block}
    \end{column}
    \begin{column}{.48\textwidth}
      \begin{exampleblock}{Deployment and evaluation}
        \begin{itemize}
          \item Adapt storage and compute to the input.
          \item Match access patterns to hardware memory tiers.
          \item Standardize controlled retention and cost tests.
        \end{itemize}
      \end{exampleblock}
    \end{column}
  \end{columns}
  \papersource{Paper, Sec. VI-A--F, PDF pp. 17--18. Research agenda, not demonstrated solutions.}
\end{frame}

\begin{frame}{Read a memory architecture through four concrete objects}
  \begin{center}
    {\large\color{AcademicBlue}Storage\quad$\cdot$\quad Read path\quad$\cdot$\quad Write path\quad$\cdot$\quad Reset boundary}
  \end{center}
  \gap
  \begin{enumerate}
    \item The three axes locate the mechanism.
    \item The update rule explains its behavior and failure modes.
    \item Recall--interference--cost curves test whether it is useful.
  \end{enumerate}
  \begin{exampleblock}{Discussion question}
    If a compressed state predicts an item well now, should we still cache it for a future exact query?
  \end{exampleblock}
  \papersource{Synthesis of the survey. Zhoubian, Zhang, Kharlamov, and Tang, \emph{Memory for Large Language Models},\\
  \href{https://arxiv.org/abs/2607.25380v1}{arXiv:2607.25380v1}. Main talk ends here; remaining slides are backup.}
\end{frame}

\appendix

\begin{frame}{Backup: state editing has several independent directions}
  \par
  {\small
  \renewcommand{\arraystretch}{1.35}
  \begin{tabular}{@{}P{.30\linewidth}P{.64\linewidth}@{}}
    \toprule
    \textbf{Direction} & \textbf{Examples reviewed in the paper}\\
    \midrule
    Structured dynamics & Mamba-3: richer discretization, complex states, MIMO\\
    Separate erase and write & Gated DeltaNet-2; RWKV-7 uses richer vector controls\\
    Channel-wise transition & KDA: diagonal decay with low-rank state updates\\
    Compose transformations & DeltaProduct: multiple Householder updates\\
    Closed-loop correction & Comba: scalar-plus-low-rank transitions and feedback\\
    Calibrate the write & Kaczmarz projection; Kalman-style state estimation\\
    \bottomrule
  \end{tabular}}
  \papersource{Paper, Sec. III-C, PDF pp. 8--9. Mechanism descriptions, not a ranking of these methods.}
\end{frame}

\begin{frame}{Backup: a write can disturb other keys}
  Let $r_t=v_t-M_{t-1}k_t$. For another query $q$,
  \[
    (M_t-M_{t-1})q=\eta_t r_t(k_t^\top q).
  \]
  \begin{itemize}
    \item Orthogonal keys do not interfere in this one-step linear model.
    \item Correlated keys couple the corrected association to other reads.
    \item Larger state dimension helps only if representations and writes use it effectively.
  \end{itemize}
  \gap
  For scalar decay, $s_t=\lambda s_{t-1}+u_t$, a past input contributes $\lambda^r u_{t-r}$ after $r$ steps.
  \papersource{Teaching derivations; linear delta update, and scalar $0<\lambda<1$. Motivated by Sec. III-C--D, pp. 8--9.}
\end{frame}

\begin{frame}{Backup: similar names can hide different memory substrates}
  \par
  {\small
  \renewcommand{\arraystretch}{1.35}
  \begin{tabular}{@{}P{.30\linewidth}P{.64\linewidth}@{}}
    \toprule
    \textbf{Method} & \textbf{Distinction that matters}\\
    \midrule
    MEMORYLLM (2024) & Online, forward-updated latent memory pool\\
    MemoryLLM, FFN (2026) & Offline-trained, context-free token-level FFN lookup\\
    LM2 & Dedicated slots; classified offline in Table I\\
    In-Place TTT & A standard FFN matrix receives special online write semantics\\
    LongMem / Memorizing Transformers & Indexed activation stores: a boundary class in this survey\\
    \bottomrule
  \end{tabular}}
  \par\vspace{3mm}
  Always identify \alert{which object changes} when calling a mechanism online.
  \papersource{Paper, Table I, p. 4; Sec. IV-A--B, PDF pp. 10--12.}
\end{frame}

\begin{frame}{Backup: hybrids also differ in how they are obtained}
  \begin{itemize}
    \item \textbf{LightTransfer / Priming:} replace selected attention layers and adapt or align the replacements.
    \gap
    \item \textbf{Hydra:} combine state-space computation, sparse attention, expert routing, and distinct memory roles.
    \gap
    \item \textbf{Expansion Span:} allocate attention span to retrieved tokens beyond the ordinary finite window.
    \gap
    \item \textbf{Nested updates:} combine token-level states with parameter components updated at different frequencies.
  \end{itemize}
  \papersource{Paper, Sec. V-A(a,d,e), PDF pp. 14--15. These are complementary design choices.}
\end{frame}

\begin{frame}{Backup: map a benchmark to the capability it probes}
  \par
  {\small
  \renewcommand{\arraystretch}{1.4}
  \begin{tabular}{@{}P{.30\linewidth}P{.64\linewidth}@{}}
    \toprule
    \textbf{Evaluation family} & \textbf{Interpretation}\\
    \midrule
    NIAH / RULER & Retrieval and degradation with position or context length\\
    LongBench / L-Eval / $\infty$Bench & Broad long-context use; separate task categories\\
    SCROLLS / NarrativeQA & Integrating distributed evidence and reasoning\\
    Continual-update tests & Retention after new writes; update consistency\\
    Resource sweeps & Quality at fixed storage, compute, or latency\\
    \bottomrule
  \end{tabular}}
  \par\vspace{3mm}
  Perplexity measures average prediction quality; precise recall asks a different question.
  \papersource{Paper, Sec. V-C, pp. 16--17; $\infty$Bench also in Sec. III-A, p. 7 and Fig. 2. No common scoring protocol is provided.}
\end{frame}

\end{document}