% Original presentation based on the arxiv-paper-reader Beamer template. % Build: python3 build_slides.py slides.en.tex \documentclass[aspectratio=169,11pt]{beamer} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern} \usepackage{amsmath,amssymb,graphicx,booktabs} \definecolor{AcademicBlue}{RGB}{26,57,86} \definecolor{AcademicTeal}{RGB}{0,105,112} \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} \newcommand{\papersource}[1]{\par\smallskip{\scriptsize\color{gray}#1\par}} \newcommand{\R}{\mathbb{R}} \newcommand{\W}{\mathbf{W}} \newcommand{\x}{\mathbf{x}} \newcommand{\y}{\mathbf{y}} \newcommand{\kvec}{\mathbf{k}} \newcommand{\q}{\mathbf{q}} \newcommand{\vv}{\mathbf{v}} \title[SRWM]{A Modern Self-Referential Weight Matrix\\That Learns to Modify Itself} \subtitle{Learning a program that changes its own update controller} \author{Paper by Kazuki Irie, Imanol Schlag,\\ R\'obert Csord\'as, and J\"urgen Schmidhuber} \date{ICML 2022 \quad$\vert$\quad arXiv:2202.05780v2\\ Research discussion prepared 16 October 2026} \begin{document} \begin{frame} \titlepage \vspace{-3mm} \begin{center} \small A shared initial matrix becomes a task-dependent computation. \end{center} \end{frame} \begin{frame}{Can the update controller adapt with experience?} \begin{block}{The research question} Learn a matrix that changes both its predictions and the parameters that generate its next weight update. \end{block} \medskip \centering \begin{tabular}{lll} \toprule Model & Runtime state & Update controller \\ \midrule Fixed-weight RNN & Hidden activations & Fixed parameters \\ DeltaNet & Fast weight matrix & Fixed slow network \\ SRWM & Its own weight matrix & Self-modifying parameters \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item The algebraic update rule is fixed; its generated instructions adapt. \item Outer products replace the explicit weight addressing of early SRWMs. \end{itemize} \papersource{Paper, Secs. 1--3 and 6, PDF pp. 1--3, 8.} \end{frame} \begin{frame}{DeltaNet separates the programmer from the memory} \begin{align*} (\kvec_t,\vv_t,\q_t,\beta_t)&=\W_{\mathrm{slow}}\x_t\\ \bar{\vv}_t&=\W_{t-1}\phi(\kvec_t)\\ \W_t&=\W_{t-1}+\sigma(\beta_t)(\vv_t-\bar{\vv}_t)\phi(\kvec_t)^\top\\ \y_t&=\W_t\phi(\q_t) \end{align*} \begin{itemize} \item $\W_{\mathrm{slow}}$ generates the key, target value, query, and gate. \item The fast matrix $\W_t$ stores associations; it usually starts at zero. \item $\phi$ normalizes addresses; $\sigma(\beta_t)$ controls the write. \end{itemize} \begin{block}{The remaining fixed component} The network that decides how to update the fast matrix stays fixed. \end{block} \papersource{Paper, Sec. 2, Eqs. (1)--(4), PDF p. 2.} \end{frame} \begin{frame}{SRWM closes the loop through the same matrix} \begin{columns}[c,onlytextwidth] \begin{column}{0.47\textwidth} \centering \includegraphics[width=\linewidth,height=0.62\textheight,keepaspectratio] {figures/fig-01-srwm.pdf} \end{column} \begin{column}{0.50\textwidth} \begin{enumerate} \item Produce the output and update instructions. \medskip \item Read current and target contents from the same matrix. \medskip \item Write a delta correction back to every output block. \end{enumerate} \medskip The key, query, and gate generators are themselves modified. \end{column} \end{columns} \papersource{Original Fig. 1; Sec. 3, PDF pp. 2--3.} \end{frame} \begin{frame}{Four equations define a self-modifying layer} \[ \W_{t-1}\in\R^{m\times d_{\mathrm{in}}}, \qquad m=d_{\mathrm{out}}+2d_{\mathrm{in}}+1 \] \begin{align*} (\y_t,\kvec_t,\q_t,\beta_t)&=\W_{t-1}\phi(\x_t) &&\text{generate}\\ \bar{\vv}_t&=\W_{t-1}\phi(\kvec_t) &&\text{read old}\\ \vv_t&=\W_{t-1}\phi(\q_t) &&\text{read target}\\ \W_t&=\W_{t-1}+\sigma(\beta_t)(\vv_t-\bar{\vv}_t)\phi(\kvec_t)^\top &&\text{write} \end{align*} \begin{itemize} \item $\kvec_t,\q_t\in\R^{d_{\mathrm{in}}}$; both values lie in $\R^m$. \item The target includes the output and the update-control blocks. \item $\y_t$ uses the \alert{pre-update} matrix; DeltaNet reads after updating. \end{itemize} \papersource{Paper, Eqs. (5)--(8), PDF p. 3. Input activation differs by task; see slide 7.} \end{frame} \begin{frame}{A delta write moves one association toward another} For this step, set $k=\phi(\kvec_t)$, $q=\phi(\q_t)$, $\eta=\sigma(\beta_t)$, and $W=\W_{t-1}$. \[ W_t=W+\eta(Wq-Wk)k^\top \] Reading back the same address gives \[ \boxed{W_tk=(1-\eta\|k\|^2)Wk+\eta\|k\|^2Wq.} \] \begin{itemize} \item The effective interpolation rate depends on the key concentration. \item Another address $z$ changes in proportion to its overlap $k^\top z$. \end{itemize} \begin{block}{A one-row teaching example} With $w=[1,3]$, $k=e_1$, $q=e_2$, and $\eta=0.5$, the update gives $w'=[2,3]$. \end{block} \papersource{Presentation derivation from Eq. (8), PDF p. 3. One-hot addresses illustrate the limiting case of concentrated softmax.} \end{frame} \begin{frame}{The practical layer uses four gates and multiple heads} For each row block $s\in\{y,k,q,\beta\}$: \[ \W_t^s=\W_{t-1}^s+\sigma(\beta_{s,t}) \bigl[\W_{t-1}^s\phi(\q_t)-\W_{t-1}^s\phi(\kvec_t)\bigr] \phi(\kvec_t)^\top . \] \begin{itemize} \item Four gates give $d_{\mathrm{out}}+2d_{\mathrm{in}}+4$ output rows. \item Split inputs into $H$ heads and run independent SRWM updates. \item Per-head key projections have shape $(H,d,d)$, versus a dense $(Hd,Hd)$ slow projection in DeltaNet. \end{itemize} \medskip \begin{tabular}{lll} \toprule Experiment & Input to first projection & Key/query addresses \\ \midrule Supervised & $\x_t$ & Softmax \\ Reinforcement learning & $\operatorname{softmax}(\x_t)$ & Softmax \\ \bottomrule \end{tabular} \papersource{Paper, Appendix A, Eqs. (9)--(11), PDF p. 13; Appendix B.2, PDF p. 14.} \end{frame} \begin{frame}{Gradient descent learns the starting program} \begin{columns}[t,onlytextwidth] \begin{column}{0.48\textwidth} \begin{block}{Outer training} \begin{itemize} \item Unroll the task and its weight updates. \item Backpropagate task losses to $\W_0$. \item Also train the vision and feedforward modules. \end{itemize} \end{block} \end{column} \begin{column}{0.48\textwidth} \begin{block}{Runtime adaptation} \begin{itemize} \item Start each new episode from $\W_0$. \item Generate keys, queries, and gates from experience. \item Apply the learned delta updates in the forward pass. \end{itemize} \end{block} \end{column} \end{columns} \medskip \[ \W_0 \xrightarrow{\text{input 1}} \W_1 \xrightarrow{\text{input 2}} \W_2 \xrightarrow{\text{input stream}} \W_T \] \begin{itemize} \item Within the SRWM layer, $\W_0$ is the gradient-trained parameter. \item CNNs and surrounding Transformer blocks remain ordinary modules. \end{itemize} \papersource{Paper, Secs. 3--4, PDF pp. 3--6; Appendix B.2, PDF p. 14.} \end{frame} \begin{frame}{Two label protocols test different adaptation behavior} \begin{columns}[t,onlytextwidth] \begin{column}{0.48\textwidth} \textbf{Synchronous labels} \medskip \includegraphics[width=\linewidth,height=0.27\textheight,keepaspectratio] {figures/fig-02-synchronous.pdf} \begin{itemize} \item Read $NK$ image/label pairs. \item Predict only the final query. \item Standard $N$-way $K$-shot learning. \end{itemize} \end{column} \begin{column}{0.48\textwidth} \textbf{Delayed labels} \medskip \includegraphics[width=\linewidth,height=0.27\textheight,keepaspectratio] {figures/fig-03-delayed.pdf} \begin{itemize} \item Read image $t$ and label $t-1$. \item Predict at every step. \item Switch datasets during one input stream. \end{itemize} \end{column} \end{columns} \medskip Labels are reassigned within each few-shot episode. \papersource{Original Figs. 2--3, PDF p. 3; Secs. 4.1--4.2, PDF pp. 3--5.} \end{frame} \begin{frame}{Standard few-shot performance is close to DeltaNet} \centering \begin{tabular}{lrrr} \toprule & Omniglot & \multicolumn{2}{c}{Mini-ImageNet} \\ Model & 1-shot & 1-shot & 5-shot \\ \midrule SNAIL$^*$ & $99.1\pm0.2$ & $45.1$ & $55.2$ \\ DeltaNet & $97.2\pm0.0$ & $47.0\pm0.1$ & $62.7\pm0.1$ \\ SRWM & $97.4\pm0.0$ & $47.0\pm0.2$ & $61.4\pm0.1$ \\ \midrule HyperTransformer$^*$ & $96.2$ & $53.8$ & $67.1$ \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item 5-way classification accuracy (\%); higher is better. \item Mini-ImageNet uses Conv-4-32 for these rows. \item SRWM matches 1-shot DeltaNet; it is 1.3 pp lower in 5-shot. \item Self-modification works, but task-specific methods can score higher. \end{itemize} \papersource{Paper, Table 1, PDF p. 4. $^*$Results cited by the paper. Own-model CIs use 5 sets of 16K episodes, not training-seed variance (App. B.3, p. 14).} \end{frame} \begin{frame}{Both models recover after a dataset switch} \begin{columns}[t,onlytextwidth] \begin{column}{0.49\textwidth} \centering \textbf{Omniglot $\rightarrow$ Mini-ImageNet} \medskip \includegraphics[width=\linewidth,height=0.53\textheight,keepaspectratio] {figures/fig-06-om-first.pdf} \end{column} \begin{column}{0.49\textwidth} \centering \textbf{Mini-ImageNet $\rightarrow$ Omniglot} \medskip \includegraphics[width=\linewidth,height=0.53\textheight,keepaspectratio] {figures/fig-07-im-first.pdf} \end{column} \end{columns} \medskip Blue: SRWM. Orange: DeltaNet. Accuracy drops at the task switch and rises as new label feedback arrives. \papersource{Original Figs. 6--7, PDF p. 15. Horizontal axis: input step; vertical axis: mean test accuracy (\%). Switch marked at step 74 in the paper.} \end{frame} \begin{frame}{Mini-ImageNet gains persist in either task order} \centering \begin{tabular}{llrrr} \toprule Task order & Evaluated segment & DeltaNet & SRWM & Change \\ \midrule Omniglot first & Omniglot & 92.2 & 92.3 & $+0.1$ pp \\ & Mini-ImageNet & 50.4 & 53.3 & $+2.9$ pp \\ \midrule Mini-ImageNet first & Mini-ImageNet & 50.7 & 53.5 & $+2.8$ pp \\ & Omniglot & 92.2 & 92.9 & $+0.7$ pp \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item Delayed-label 5-way classification; up to 15 examples per class. \item After Omniglot, Mini-ImageNet's 10th-instance accuracy improves from 54.8\% to 58.0\%. \item First-instance accuracy is almost unchanged: 20.8\% vs.\ 20.9\%. \end{itemize} \begin{block}{Interpretation} The improvement appears mainly after feedback has been received. \end{block} \papersource{Paper, Table 2, PDF p. 5; Table 7, PDF p. 16. Values in the table are segment-level accuracy (\%).} \end{frame} \begin{frame}{Multi-task RL shares an initial program across games} \begin{columns}[c,onlytextwidth] \begin{column}{0.40\textwidth} \includegraphics[width=\linewidth,height=0.52\textheight,keepaspectratio] {figures/fig-05-multitask.pdf} \end{column} \begin{column}{0.57\textwidth} \begin{itemize} \item Six ProcGen \textbf{easy} environments; 300M total steps. \item IMPALA, 48 actors, shared 15-layer residual vision model. \item DeltaNet/SRWM: two layers, width 128. \item Backpropagate 50 steps; retain state until the episode ends. \end{itemize} \end{column} \end{columns} \medskip \begin{block}{Generalization protocol} 200 training levels per game. Three fixed test sets of 200 levels. Three independent training runs produce nine run/test-set measurements. \end{block} \papersource{Original Fig. 5; Sec. 4.3, PDF pp. 5--7. Games: Bigfish, Fruitbot, Maze, Leaper, Plunder, Starpilot.} \end{frame} \begin{frame}{Self-modification helps the multi-task RL agent} \centering \begin{tabular}{lrrr} \toprule Model & Parameters & Train & Test \\ \midrule Feedforward & 626K & 22.5 (2.6) & 16.4 (1.6) \\ LSTM & 1.2M & 28.3 (1.4) & 15.7 (1.6) \\ Fake SR & 959K & 27.0 (1.8) & 15.3 (1.9) \\ DeltaNet & 1.05M & 35.0 (1.6) & 18.6 (1.7) \\ SRWM & 968K & 34.6 (1.8) & \textbf{20.0 (1.8)} \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item Normalized aggregate score $\times100$, mean (SD); higher is better. \item Fake SR removes self-modification: the test gap is \alert{4.7 points}. \item The test gap to DeltaNet is smaller: \alert{1.4 points}. \item Reported variability is substantial; no significance test is provided. \end{itemize} \papersource{Paper, Table 3, PDF p. 7. Three training runs; nine test measurements. These are score units, not accuracy percentages.} \end{frame} \begin{frame}{Bigfish reveals a benefit specific to joint training} \centering \begin{tabular}{llrr} \toprule Game & Training & Fake SR & SRWM \\ \midrule Bigfish & Six games & 4.7 (2.4) & 9.0 (2.0) \\ & Expert & 15.8 (1.7) & 14.2 (2.0) \\ \midrule Starpilot & Six games & 49.6 (2.1) & 54.6 (2.4) \\ & Expert & 52.9 (1.2) & 57.3 (1.6) \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item Raw \textbf{test} returns, mean (SD). \item Experts receive 50M steps; joint agents receive about 50M per game. \item On Bigfish, SRWM reduces the loss from training jointly. \item It still falls short of the single-game expert. \end{itemize} \papersource{Paper, Table 4, PDF p. 7. Starpilot also benefits in the expert setting.} \end{frame} \begin{frame}{Truncating gradients must not erase the adaptive state} \centering \begin{tabular}{lrr} \toprule State policy & Train score & Test score \\ \midrule Retain until episode boundary & 34.6 (1.8) & 20.0 (1.8) \\ Reset every 50 steps & 28.5 (1.2) & 16.1 (2.2) \\ No self-modification (Fake SR) & 27.0 (1.8) & 15.3 (1.9) \\ \bottomrule \end{tabular} \medskip \begin{block}{Two different operations} \textbf{Detach:} retain the current weights, truncate the gradient history.\\[2mm] \textbf{Reset:} discard the accumulated weight changes. \end{block} \begin{itemize} \item The standard model uses a 50-step gradient horizon. \item The reset ablation changes both training and evaluation. \end{itemize} \papersource{Paper, Sec. 4.3, PDF p. 7; Table 9, PDF p. 17. Normalized aggregate score $\times100$, mean (SD).} \end{frame} \begin{frame}{The memory experiment adds SRWM to a DeltaNet} \begin{block}{SR-DeltaNet is a different architecture} Replace DeltaNet's slow projection with an SRWM, while retaining its separate fast weight memory. \end{block} \begin{itemize} \item Four partially observable ProcGen \textbf{memory} environments. \item 800M steps; 500 training levels; 100-step backpropagation. \item Scores use the ProcGen \textbf{hard} normalization constants. \end{itemize} \medskip \centering \begin{tabular}{lrr} \toprule & DeltaNet & SR-DeltaNet \\ \midrule Train & 51.8 (2.6) & 59.0 (2.1) \\ Test & 38.0 (4.1) & 38.5 (3.2) \\ \bottomrule \end{tabular} \medskip Better training fit; the test improvement is only 0.5 score points. \papersource{Paper, Appendix C.1, Table 8, PDF pp. 16--17. Normalized score $\times100$, mean (SD). Authors describe this as preliminary.} \end{frame} \begin{frame}{A matrix state has capacity and a practical cost} \begin{columns}[t,onlytextwidth] \begin{column}{0.45\textwidth} \textbf{State and computation} \begin{itemize} \item A width-$d$ head carries $O(d^2)$ changing weights. \item Matrix-vector products and a rank-one write per step. \item Linear in sequence length at fixed width. \item Implemented with custom CUDA kernels. \end{itemize} \end{column} \begin{column}{0.52\textwidth} \textbf{RL throughput on one P100} \medskip \begin{tabular}{lr} \toprule Model & Steps/s \\ \midrule FF / LSTM & $\sim3500$ \\ DeltaNet & $\sim2300$ \\ SRWM & $\sim1700$ \\ \bottomrule \end{tabular} \medskip Actor/learner state copying adds overhead. \end{column} \end{columns} \smallskip \begin{block}{Workload matters} On 1-shot Omniglot with Conv-4 and batch 128, LSTM, DeltaNet, and SRWM all process about 8000 images/s on one P100. \end{block} \papersource{Paper, Sec. 5, PDF pp. 7--8. Complexity interpretation follows the layer equations.} \end{frame} \begin{frame}{The evidence establishes useful runtime adaptation} \begin{itemize} \item \textbf{Learnability:} competitive few-shot behavior can emerge from a single self-referential matrix. \medskip \item \textbf{Adaptation:} feedback helps after task switches; persistent self-modification improves multi-task RL. \medskip \item \textbf{Optimization:} some runs learn label-allocation shortcuts instead of effective feedback use. \medskip \item \textbf{Scope:} direct tests of recursive self-improvement and long-run objective preservation remain open. \end{itemize} \medskip \begin{block}{A useful next experiment} Ablate the $k$, $q$, and gate-generating updates separately, then test repeated task switches and returns to earlier tasks. \end{block} \papersource{Paper, Secs. 4--6, PDF pp. 5--9; Appendix B.5, p. 16. The proposed next experiment is presentation analysis.} \end{frame} \begin{frame}{Three ideas to take away} \begin{enumerate} \item \textbf{Let the controller change.}\\[1mm] The same matrix computes outputs and generates its own updates. \medskip \item \textbf{Use associations as a programming interface.}\\[1mm] Keys, queries, and gates turn a delta rule into a learned task-dependent modification. \medskip \item \textbf{Evaluate the complete adaptive process.}\\[1mm] Task order, state persistence, training success, and runtime cost all affect the value of self-modification. \end{enumerate} \papersource{Synthesis of Secs. 3--6 and Appendices A--C.} \end{frame} \begin{frame}{Paper and reusable materials} \textbf{Kazuki Irie, Imanol Schlag, R\'obert Csord\'as, J\"urgen Schmidhuber}\\ A Modern Self-Referential Weight Matrix That Learns to Modify Itself.\\ ICML 2022. arXiv:2202.05780v2, revised 17 June 2022. \medskip \begin{itemize} \item Paper: \href{https://arxiv.org/abs/2202.05780v2} {arxiv.org/abs/2202.05780v2} \item Author implementation: \href{https://github.com/IDSIA/modern-srwm}{github.com/IDSIA/modern-srwm} \item Companion notes: \texttt{reading-notes.zh.md} \item Editable presentation: \texttt{slides.en.tex} \end{itemize} \medskip Figures are reproduced from the authors' source files. Tables select reported values; original page and table numbers appear on the relevant slides. \medskip \alert{Backup slides:} FC100, LSTM, training dynamics, game-level results, and reproduction details. \end{frame} \appendix \begin{frame}{Backup: v2 substantially revises the FC100 result} \centering \begin{tabular}{llr} \toprule Model & Vision encoder & Accuracy (\%) \\ \midrule ProtoNet Cosine$^*$ & Res-12-512 & $40.9\pm0.6$ \\ ProtoNet Cosine Scaled$^*$ & Res-12-512 & $51.0\pm0.6$ \\ TADAM$^*$ & Res-12-512 & $56.1\pm0.4$ \\ \midrule DeltaNet & Conv-4-32 & $43.2\pm0.1$ \\ SRWM & Conv-4-32 & $44.5\pm0.1$ \\ SRWM & Res-12-256 & $46.3\pm0.1$ \\ \bottomrule \end{tabular} \medskip \begin{block}{Use the corrected 5-way 5-shot result} An earlier preprint reported 57.1\% for SRWM / Conv-4-32. Version 2 corrects a meta-test shuffling bug and reports 44.5\%. \end{block} \papersource{Paper, Appendix B.4 and footnote 4, PDF p. 14; Table 5, p. 15. $^*$Results cited by the paper.} \end{frame} \begin{frame}{Backup: fixed-weight LSTMs can also learn the task} \centering \begin{tabular}{lrr} \toprule Mini-ImageNet LSTM & 600K training steps & 1.2M training steps \\ \midrule 1-shot & $<38\%$ & $46.6\pm0.1\%$ \\ 5-shot & $<55\%$ & $59.0\pm0.1\%$ \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item One 1024-unit layer: 7.5M parameters; batch size 16. \item Some configurations or seeds remain at chance accuracy. \item The reported best SRWM / DeltaNet models use 600K steps, with 3.6M / 5.5M parameters respectively. \item Task-episode confidence intervals do not measure training reliability. \end{itemize} \papersource{Paper, Appendix B.2--B.4, PDF pp. 14--15; Table 6, p. 15. Mini-ImageNet backends are Conv-4-32.} \end{frame} \begin{frame}{Backup: a training run may learn the wrong shortcut} \begin{columns}[t,onlytextwidth] \begin{column}{0.49\textwidth} \centering \textbf{Unsuccessful training} \medskip \includegraphics[width=\linewidth,height=0.49\textheight,keepaspectratio] {figures/fig-08-training-failure.pdf} \end{column} \begin{column}{0.49\textwidth} \centering \textbf{Successful training} \medskip \includegraphics[width=\linewidth,height=0.49\textheight,keepaspectratio] {figures/fig-09-training-success.pdf} \end{column} \end{columns} \begin{itemize} \item Curves measure the 1st, 2nd, 3rd, 5th, and 10th class occurrences. \item Success means later occurrences benefit strongly from label feedback. \item Batch size 32 was important in the reported delayed-label setup. \end{itemize} \papersource{Original Figs. 8--9, Appendix B.5, PDF p. 16. Axes: training steps / 100; Omniglot training accuracy (\%).} \end{frame} \begin{frame}{Backup: SRWM does not win on every easy game} \centering \begin{tabular}{lrrr} \toprule Raw test return & Feedforward & DeltaNet & SRWM \\ \midrule Bigfish & 4.3 & 7.8 & 9.0 \\ Fruitbot & 25.6 & 24.5 & 25.5 \\ Leaper & 3.4 & 3.3 & 3.4 \\ Maze & 1.4 & 1.7 & 1.8 \\ Plunder & 3.2 & 3.3 & 3.0 \\ Starpilot & 53.0 & 53.9 & 54.6 \\ \bottomrule \end{tabular} \medskip \par Gains vary by game; raw score scales differ across environments. \medskip \begin{block}{A source-table discrepancy} Table 9 swaps the True/Fake SR entries in its aggregate \emph{training} row relative to Table 3. The presentation uses Table 3 for that row. \end{block} \papersource{Paper, Table 9, PDF p. 17; Table 3, p. 7. Selected means shown; original table also reports SDs.} \end{frame} \begin{frame}{Backup: memory gains are uneven across environments} \centering \begin{tabular}{lrr} \toprule Raw test return & DeltaNet & SR-DeltaNet \\ \midrule Dodgeball & 6.4 (0.3) & 6.2 (0.6) \\ Heist & 0.8 (0.2) & 1.1 (0.3) \\ Maze & 3.3 (0.6) & 3.3 (0.4) \\ Miner & 29.2 (1.1) & 29.4 (0.7) \\ \bottomrule \end{tabular} \medskip \begin{itemize} \item SR-DeltaNet has a self-modifying programmer and a separate memory. \item Test improvement is concentrated in Heist. \item The aggregate test change is 38.0 to 38.5; training changes from 51.8 to 59.0. \end{itemize} \papersource{Paper, Tables 8 and 10, PDF pp. 17--18. Raw returns are mean (SD); aggregate scores use hard-distribution normalization.} \end{frame} \begin{frame}{Backup: reproduction depends on task-specific details} \begin{itemize} \item \textbf{Input activation:} no $\phi(\x_t)$ in supervised runs; softmax in RL. Normalize key/query addresses in both. \medskip \item \textbf{Initialization:} optimize a learned $\W_0$. An all-zero SRWM is a fixed point of Eqs. (5)--(8). \medskip \item \textbf{Capacity:} equal width and head count do not imply equal parameter counts for SRWM and DeltaNet. \medskip \item \textbf{Vision detail:} Sec. 4.1 says 64 channels for Omniglot, whereas Appendix B.2 describes Conv-4 with 32 channels. \end{itemize} \medskip These details affect a faithful comparison and should be resolved when implementing a reproduction. \papersource{Paper, Eqs. (5)--(8), p. 3; Sec. 4.1, p. 4; Appendices A--B.2, pp. 13--14. The zero-initialization observation is a direct equation-level deduction.} \end{frame} \end{document}