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\title[Continual memorization]{Continual Learning Mechanisms Compose for Long-Horizon Memorization}
\subtitle{A 25-minute research discussion + backup slides}
\author{Paper: Z. Zhang, A. Zhang, D. Khashabi, T. Shu}
\date{arXiv:2609.06986v1 \quad | \quad Reading: 2026-09-16}
\begin{document}
\begin{frame}\titlepage\end{frame}
\begin{frame}{Can parameters remember 100 sequential tasks?}
\begin{itemize}
\item Learn new query--answer associations through sequential SFT.
\item Retain earlier associations without storing old raw examples.
\item Answer without a task identifier at inference.
\end{itemize}\begin{block}{Central hypothesis}Mechanisms that preserve different evidence can work better together.\end{block}
\papersource{Secs. 1, 3.1; PDF pp. 1--4. Memorization evaluation, not held-out generalization.}
\end{frame}
\begin{frame}{Separate what to preserve from where updates live}
\begin{tabular}{lll}\toprule
Dimension & Mechanism & Preservation signal\\\midrule
Data anchor & Generative replay & Generated earlier sequences\\
Function anchor & Self-distillation (SD) & Teacher outputs on current data\\
Weight anchor & SI / online EWC & Important LoRA coordinates\\
Allocation & Shared / merged LoRA & Reuse / commit and restart\\\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item The contribution is systematic composition and evaluation.
\item These ingredients build on existing continual-learning methods.
\end{itemize}
\papersource{Sec. 3, PDF pp. 4--6; related work, pp. 3--4.}
\end{frame}
\begin{frame}{A task boundary determines which state survives}
\begin{enumerate}
\item Freeze the previous model; generate temporary replay data.
\item Fit current data with active retention losses.
\item Consolidate parameter importance before resetting coordinates.
\item Commit the update if using merged LoRA; initialize a fresh adapter.
\item Discard temporary replay samples and release the teacher.
\end{enumerate}
\medskip
All old-knowledge anchors are inactive on the first task.

\papersource{Appendix B.7, Algorithm 3, PDF pp. 31--32. Teaching summary of the procedure.}
\end{frame}
\begin{frame}{Replay changes the balance of the fitting loss}
For the full SI + SD + Replay composition at $t>1$:
\[
\mathcal L_{\mathrm{impl}}^t=(1-w)\mathcal L_{\mathrm{SFT}}^t+w\mathcal L_D^t
+\lambda_F\mathcal L_F^t+\lambda_{\mathrm{SI}}\mathcal R_{\mathrm{SI}}^t.
\]
\begin{itemize}
\item $w$ is a loss weight; without replay the fitting term is ordinary SFT.
\item SFT covers both query and answer tokens; padding and replay seed are masked.
\item SD and replay use the previous model, refreshed after each task.
\end{itemize}
\papersource{Appendix B.1--B.2, PDF pp. 18--21. This is the implementation-level objective.}
\end{frame}
\begin{frame}{The data anchor generates inputs and soft targets}
\begin{itemize}
\item Prompt the previous model with one task-agnostic replay token.
\item Attempt 300 sequences; discard empty outputs; keep only for this task.
\item Pair every current minibatch with one replay minibatch.
\end{itemize}\[
\mathcal L_D^t=\frac{\tau_D^2}{\sum a_{m,\ell}}
\sum_{m,\ell} a_{m,\ell}\,\mathrm{KL}(q^D_{m,\ell}\Vert p^D_{m,\ell}).
\]
Teacher $q^D$ and student $p^D$ see the same generated prefix.
\par\medskip
Generation: $\tau_G=1.5$, top-$p=0.9$. Distillation: $\tau_D=2$.

\papersource{Appendix B.3, PDF pp. 21--23. Full-vocabulary forward KL, not hard pseudo-label CE.}
\end{frame}
\begin{frame}{SD constrains a different input distribution}
\[
\mathcal L_F^t=\tau_F^2\,\operatorname{mean}_{\text{valid current tokens}}
\mathrm{KL}(q^F\Vert p^F),\qquad \tau_F=5.
\]
\begin{itemize}
\item Data anchor: distillation on generated replay sequences.
\item Function anchor: distillation on current-task sequences.
\item Both can share a frozen teacher; their support differs.
\item A teacher constraint can also resist useful new learning.
\end{itemize}
\papersource{Appendix B.4, PDF p. 24. Last bullet is an interpretation of the tradeoff.}
\end{frame}
\begin{frame}{SI estimates importance along the optimization path}
\[
\omega_{t,i}=-\sum_k g_{t,k,i}\Delta\vartheta_{t,k,i},\qquad
\Omega_{t,i}=\Omega_{t-1,i}+\frac{\max(0,\omega_{t,i})}{\Delta_{t,i}^{2}+\xi}.
\]
\[
\mathcal R_{\mathrm{SI}}^{t+1}=\sum_i\Omega_{t,i}
(\vartheta_i-\vartheta_{t,i}^{\star})^2.
\]
\begin{itemize}
\item $i$: a scalar LoRA coordinate; $g$: fitting-loss gradient.
\item $\Delta_{t,i}$: net task displacement; $\xi=0.1$ stabilizes the ratio.
\item One accumulated importance tensor and the latest reference are retained.
\end{itemize}
\papersource{Appendix B.5.1, PDF pp. 25--26. O-LoRA uses a different SI gradient source.}
\end{frame}
\begin{frame}{Merged LoRA expands cumulative update capacity}
\[
\begin{aligned}
\text{Shared:}\quad W_t&=W_0+\rho B_tA_t,\\
\text{Merged:}\quad W_t&=W_{t-1}+\rho B_tA_t.
\end{aligned}
\]
$A_t\in\mathbb R^{r\times d_{\rm in}}$, $B_t\in\mathbb R^{d_{\rm out}\times r}$, $\rho=\alpha/r$.
\begin{itemize}
\item Shared: cumulative residual rank is at most $r$.
\item Merged: sum of committed updates can reach rank $\min(tr,d_{\rm in},d_{\rm out})$.
\item New $B=0$ preserves the merged function at initialization.
\item Both rules reset the optimizer at every task boundary.
\end{itemize}
\papersource{Sec. 3.3; Appendix B.6.1--B.6.2, PDF pp. 28--29. Rank is not noninterference.}
\end{frame}
\begin{frame}{A reset can invalidate the meaning of an old penalty}
\begin{itemize}
\item SI/EWC importance is attached to named entries in LoRA factors.
\item Merged LoRA replaces those factors, but reuses old references and importance by position.
\item The new coordinate can represent a different functional direction.
\end{itemize}\[
H_{\rm new}\approx J^\top H_{\rm old}J
\]
A compatible local coordinate transform generally introduces off-diagonal terms.
\par\medskip
The implementation does not perform this transformation.

\papersource{Appendix B.5.4, PDF pp. 27--28. A structural risk, not a proven universal penalty.}
\end{frame}
\begin{frame}{Three datasets isolate different kinds of association}
\begin{tabular}{lcl}\toprule
Dataset & Tasks $\times$ items & Construction\\\midrule
Symbol-QA & $100\times100$ & Random 6-character keys / 4-character values\\
LLM-QA & $100\times100$ & Fictional entities across 100 topics\\
Real-QA & $100\times50$ & Ten filtered public QA sources\\\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Evaluation reuses training questions, with no task ID.
\item LLM-QA fiction is prompted, not externally verified.
\item Real-QA removes items answered in any of five base-model samples; this does not prove zero prior knowledge.
\end{itemize}
\papersource{Sec. 4.2; Appendix C, PDF pp. 33--35.}
\end{frame}
\begin{frame}{Measure acquisition separately from retention}
$M_{i,j}$: accuracy on task $j$ after learning through task $i$.
\[
\mathrm{Final}=\frac1T\sum_{j=1}^{T}M_{T,j},\qquad
\mathrm{Diag}=\frac1T\sum_{j=1}^{T}M_{j,j}.
\]
\[
\mathrm{Forget}=\frac1{T-1}\sum_{j=1}^{T-1}
\left(\max_{j\le i\le T}M_{i,j}-M_{T,j}\right).
\]
\begin{itemize}
\item Higher Final / Diag is better; lower Forget is better.
\item Forget uses peak observed performance and excludes the last task.
\item It is not generally equal to $100-\mathrm{Final}$.
\end{itemize}
\papersource{Sec. 4.1, Eqs. (7)--(8), PDF pp. 6--7.}
\end{frame}
\begin{frame}{The main comparison controls 16 mechanism combinations}
\begin{itemize}
\item Backbone: Qwen3-4B-Base; LoRA rank 32, alpha 64.
\item 10 epochs/task; batch 8; AdamW learning rate $5\times10^{-4}$.
\item SI, SD, Replay, Merge on/off: $2^4=16$ combinations.
\item Merge off means shared LoRA; naive is shared LoRA without anchors.
\item 21 methods/dataset in the full evaluation; three training seeds per method.
\end{itemize}
\papersource{Table 3, PDF p. 32; Sec. 5, pp. 8--9. The naive baseline is not full-parameter SFT.}
\end{frame}
\begin{frame}{Task-level halving allocates longer horizons selectively}
\begin{tabular}{lrrrr}\toprule
Horizon (tasks) & 10 & 20 & 50 & 100\\
Configurations reaching horizon & 90 & 45 & 23 & 10\\\bottomrule
\end{tabular}
\[
C=90(10)+45(10)+23(30)+10(50)=2540.
\]
\begin{itemize}
\item Promoted configurations continue from saved state.
\item 71.8\% fewer configuration-task training units than exhaustive search.
\item Search and final evaluation use different task orders.
\item 10-task vs. final rank correlations: 0.93 / 0.95 / 0.90 (17 comparable compositions).
\end{itemize}
\papersource{Sec. 4.3; Appendix D, PDF pp. 35--38. Cost is not a measured GPU-time reduction.}
\end{frame}
\begin{frame}{Compositions greatly improve final retention}
\centering
\begin{tabular}{lrrr}\toprule
Final retention (\%) & Symbol & LLM & Real\\\midrule
Naive & 1.0 & 1.4 & 1.3\\
Replay & 4.2 & 7.5 & 12.5\\
Replay + Merge & 16.6 & 32.4 & 48.2\\
SI + Replay + Merge & 15.7 & 41.2 & \textbf{54.8}\\
SD + Replay + Merge & \textbf{23.2} & 33.0 & 39.0\\
All anchors + Merge & 18.5 & \textbf{41.8} & 44.3\\\bottomrule
\end{tabular}
\par\medskip
Three-seed means; bold identifies each dataset's best main-factorial mean.
\par
Full stack: 34.9\% average; ranks 2 / 1 / 3 within the 16 combinations.

\papersource{Fig. 3, PDF p. 9; Tables 7--10, pp. 39--41. Rankings are not pairwise significance tests.}
\end{frame}
\begin{frame}{Cross-dataset robustness differs from winning everywhere}
\begin{itemize}
\item The full stack is uniquely top-3 on all datasets in the main factorial.
\item It is not the highest-retention recipe on Symbol-QA or Real-QA.
\item Its 34.9\% average is not the maximum cross-dataset average: SI + Replay + Merge averages about 37.2\%.
\item Real-QA O-LoRA alone reaches 13.9\%, above Replay at 12.5\%.
\end{itemize}\begin{block}{Read the scope carefully}The strongest-single and top-3 claims refer to the main comparison; extra task-growing methods change some ranks.\end{block}
\papersource{Sec. 5.1; Tables 7--10, PDF pp. 39--41. Average 37.2\% calculated from table means.}
\end{frame}
\begin{frame}{Replay and Merge are the dominant average effects}
\centering
\begin{tabular}{lrrr}\toprule
Effect (percentage points) & Symbol & LLM & Real\\\midrule
Replay & +9.5 & +18.5 & +19.3\\
Merge & +5.9 & +14.9 & +20.5\\
SI & +0.3 & +5.8 & +6.3\\
SD & +5.7 & +5.0 & +3.7\\
Replay $\times$ Merge & +3.6 & +9.4 & +11.7\\\bottomrule
\end{tabular}
\par\medskip
Main effects average an on/off contrast across the other factors.
\par
Replay $\times$ Merge is positive with $p<10^{-4}$ on all datasets.

\papersource{Table 1, PDF p. 10; Tables 11--13, pp. 42--43. 48 observations/dataset, error df 32.}
\end{frame}
\begin{frame}{A fixed slice makes the synergy tangible}
Without SI or SD, gains over naive fine-tuning are:
\medskip
\begin{tabular}{lrrr}\toprule
Gain (percentage points) & Symbol & LLM & Real\\\midrule
Replay alone + Merge alone & 3.9 & 7.7 & 13.9\\
Replay and Merge together & 15.6 & 31.0 & 46.9\\\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item The pair exceeds the sum of its standalone gains.
\item These conditional contrasts differ from the factorial interaction numbers.
\item SD $\times$ Replay is negative on LLM/Real; extra anchors are not always beneficial.
\end{itemize}
\papersource{Sec. 5.3, PDF pp. 10--11; Fig. 3 and Table 1.}
\end{frame}
\begin{frame}{Composition extends the timescale of forgetting}
\centering\includegraphics[width=\linewidth,height=.58\textheight,keepaspectratio]{figures/survival.pdf}
\par
Half-life, in tasks: naive 1/1/2; full stack 19/32/32.
\par
Dataset-specific best: 19/32/44. All curves still decay.

\papersource{Fig. 1, PDF p. 2; Sec. 5.2, p. 10. Log y-axis; bands are min--max across 3 seeds.}
\end{frame}
\begin{frame}{More retained task state does not consistently help}
Matched replacement of merged LoRA in the TSH-selected composition:
\medskip
\begin{tabular}{lrrr}\toprule
Change in Final (points) & Symbol & LLM & Real\\\midrule
O-LoRA & $-3.3$ & $+1.0$ & $+1.6$\\
Sequential OSRM & $-0.8$ & $-11.5$ & $-11.6$\\\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item O-LoRA retains task adapters; OSRM retains past feature means.
\item Both grow with task count; neither consistently improves retention.
\item Compared anchors: full stack on Symbol; SI + Replay on LLM/Real.
\end{itemize}
\papersource{Appendix E.6, Table 14, PDF p. 45. OSRM here is a sequential adaptation.}
\end{frame}
\begin{frame}{Better memorization does not preserve general capability}
\centering\includegraphics[width=\linewidth,height=.57\textheight,keepaspectratio]{figures/capability.pdf}
\par
Base four-benchmark mean: 69.4\%.
\par
After LLM / Real: Merge 13.0 / 13.4\%; O-LoRA 26.8 / 28.8\%.

\papersource{Fig. 6, PDF p. 46; Appendix E.9, pp. 46--47. Matched TSH anchors, not always the full stack.}
\end{frame}
\begin{frame}{The evidence supports delay, not durable general memory}
\begin{itemize}
\item Training-question recall does not establish paraphrase generalization.
\item One backbone and scale; three seeds do not measure broad task-order robustness.
\item Fixed-budget replay may fail to cover older associations.
\item The study does not isolate the causal reason for every interaction.
\item General capability remains substantially below the base model.
\end{itemize}
\papersource{Sec. 6, PDF p. 11; Appendix E.9. Coverage concern is reader analysis.}
\end{frame}
\begin{frame}{Three takeaways for a continual-learning system}
\begin{enumerate}
\item \textbf{Compose complementary signals.} Replay + Merge is the strongest common core here.
\item \textbf{Check compatibility.} A parameter reset can change what an importance penalty means.
\item \textbf{Evaluate multiple goals.} Retention, paraphrase recall, general capability, and cost can disagree.
\end{enumerate}
\medskip
Follow-up: test coordinate-compatible penalties and compute-matched replay across models and task orders.

\papersource{Takeaways synthesize the paper. The proposed follow-up is not an experiment reported by the authors.}
\end{frame}
\begin{frame}{Reference and reading scope}
\textbf{Continual Learning Mechanisms Compose for Long-Horizon Memorization}
\par\medskip
Zheyuan Zhang, Alvin Zhang, Daniel Khashabi, Tianmin Shu.
\par
Johns Hopkins University, 2026.
\par\medskip
\url{https://arxiv.org/abs/2609.06986v1}
\par
\url{https://compose-cl.github.io/}
\par\medskip
This presentation is an independent reading prepared on 2026-09-16.
Based on the matching author TeX source and 47-page PDF, including Appendices A--E. Experiments were not reproduced.

\papersource{Figures are reused from the author source. Selected tables are reformatted from the paper.}
\end{frame}
\appendix
\begin{frame}{Backup: uncertainty matters for small differences}
\centering
\begin{tabular}{lrrr}\toprule
Final (mean $\pm$ seed SD, \%) & Symbol & LLM & Real\\\midrule
Replay + Merge & $16.6\pm5.8$ & $32.4\pm8.9$ & $48.2\pm2.8$\\
SI + Replay + Merge & $15.7\pm3.3$ & $41.2\pm9.5$ & $54.8\pm10.4$\\
SD + Replay + Merge & $23.2\pm4.2$ & $33.0\pm1.8$ & $39.0\pm1.9$\\
All anchors + Merge & $18.5\pm2.8$ & $41.8\pm1.4$ & $44.3\pm8.7$\\\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Three seeds; standard deviations are not confidence intervals.
\item TSH selection and report-order winners can differ.
\item About 28-fold is based on less-rounded values; do not divide rounded 34.9 by rounded 1.2 and expect exact agreement.
\end{itemize}
\papersource{Tables 8--10, PDF pp. 40--41; Appendix E.10, p. 47.}
\end{frame}
\begin{frame}{Backup: read retention matrices down each column}
\centering\includegraphics[width=\linewidth,height=.60\textheight,keepaspectratio]{figures/matrices-symbol.pdf}\par\medskip Symbol-QA only. The bright band widens with Replay + Merge.\par Adding SI to SD + Replay + Merge lowers Final from 23.2 to 18.5\%.

\papersource{Fig. 5, PDF p. 44, cropped to Symbol-QA with the original color scale. Median seed.}
\end{frame}
\begin{frame}{Backup: implementation details that affect reproduction}
\begin{itemize}
\item LoRA targets q/k/v/o and gate/up/down projections; dropout 0.05.
\item Replay weights: 0.75 / 0.5 / 0.75 on Symbol / LLM / Real.
\item SD weight 1, temperature 5; SI weight 1, damping 0.1.
\item Online EWC: weight 1000, decay 1, Fisher rescaled to first-task mean.
\item O-LoRA: entrywise overlap penalty weight 0.5; factor norm disabled.
\item Sequential OSRM uses up to 64 samples/task for mean features, including padding.
\end{itemize}
\papersource{Appendix B.8, Table 3, PDF p. 32.}
\end{frame}
\begin{frame}{Backup: textual caveats should not become firm conclusions}
\begin{itemize}
\item E.7 describes standalone online EWC as involving a fold, although its defined allocation is shared LoRA.
\item E.7 says all other Diag scores are 96--100\%; Table 9 includes 89.2\% for online EWC and 95.3\% for SI.
\item The temperature control gives only three seeds and does not clearly name the tested dataset/composition in that paragraph.
\item Use the explicit per-configuration tables; treat stronger causal and variance claims cautiously.
\end{itemize}
\papersource{Appendix E.7--E.8, PDF pp. 45--46; Table 9, p. 41. Reader-identified inconsistencies.}
\end{frame}
\end{document}