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% Source: Value Residual Learning, arXiv:2410.17897v5.
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\title[Value Residual Learning]{Value Residual Learning}
\subtitle{First-layer values as a path through deep Transformers}
\author[Reading presentation]{Paper by Zhanchao Zhou, Tianyi Wu, Zhiyun Jiang,\\Fares Obeid, and Zhenzhong Lan}
\hypersetup{pdfauthor={Research reading presentation},pdftitle={Value Residual Learning -- arXiv 2410.17897v5}}
\date{arXiv:2410.17897v5 \quad | \quad Revised 8 June 2025\\[2mm]\small Research reading presentation \quad | \quad 11 September 2026}
\begin{document}

% 1: 0.5 min
\begin{frame}
\titlepage
\vspace{-5mm}
\begin{center}\small
Mix first-layer values for quality; share them for a smaller KV cache.
\end{center}
\end{frame}

% 2: 1 min
\begin{frame}{A residual path may not make early information usable}
\begin{block}{The research question}
Can deep layers retrieve initial token content without directly mixing it into the hidden stream?
\end{block}
\begin{itemize}
\item Hidden states increasingly integrate context; local content can become difficult to recover.
\item \alert{ResFormer}: mix first-layer and current-layer values before attention.
\item \alert{SVFormer}: use first-layer values in every layer; keep layer-specific queries and keys.
\end{itemize}
\papersource{Paper, Sec. 1, PDF pp. 1--2. The information-dilution mechanism is the authors' hypothesis.}
\end{frame}

% 3: 1 min
\begin{frame}{The extra path enters attention through its values}
\begin{columns}[T,onlytextwidth]
\column{.30\textwidth}\centering
\textbf{Transformer}\\[1mm]
\includegraphics[width=.75\linewidth,height=4.5cm,keepaspectratio]{figures/fig01a-transformer.pdf}\\
\small $\U_n=\A_n\V_n$
\column{.34\textwidth}\centering
\textbf{ResFormer}\\[1mm]
\includegraphics[width=.75\linewidth,height=4.5cm,keepaspectratio]{figures/fig01d-resformer.pdf}\\
\small $\U_n=\A_n\widetilde\V_n$
\column{.30\textwidth}\centering
\textbf{SVFormer}\\[1mm]
\includegraphics[width=.75\linewidth,height=4.5cm,keepaspectratio]{figures/fig01e-svformer.pdf}\\
\small $\U_n=\A_n\V_1$
\end{columns}
\papersource{Original panels from Fig. 1, PDF p. 2; simplified diagrams omit MLPs, normalization, and ordinary hidden residuals.}
\end{frame}

% 4: 1.5 min
\begin{frame}{Current attention selects from both sources of content}
\[
\V_1=\Hh_0\W_1^{\V},\qquad
\V_n=\Hh_{n-1}\W_n^{\V}\quad(n\ge2)
\]
\begin{block}{ResFormer: mixing and attention}
\[
\begin{aligned}
\widetilde\V_n=\lambda_{n,1}\V_1+\lambda_{n,2}\V_n,
\qquad\U_n&=\A_n\widetilde\V_n\\
&=\lambda_{n,1}\A_n\V_1+\lambda_{n,2}\A_n\V_n
\end{aligned}
\]
\end{block}
\begin{itemize}
\item $\A_n$: current-layer attention, $l\!\times\!l$; values: $l\!\times\!d$ in the paper's simplified notation.
\item Mix values once, then call attention once. Keep ordinary hidden residuals.
\item $\V_1$ is input-dependent token content, not a fixed memory table.
\end{itemize}
\papersource{Paper, Eq. (5), Secs. 3.1--3.2, PDF p. 3; mixed value renamed as tilde-V. Normalization and heads are suppressed.}
\end{frame}

% 5: 1 min
\begin{frame}{The connection coefficients define a family of models}
\centering
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{lll}
\toprule
Variant & First-layer branch & Current-layer branch\\
\midrule
Identity & fixed $0.5$ & fixed $0.5$\\
Learnable & initialized $0.5$ & initialized $0.5$\\
Constant example & fixed $2$ & fixed $1$\\
Sparse & active in selected layers & configuration-dependent\\
SVFormer & fixed $1$ & removed for $n\ge2$\\
\bottomrule
\end{tabular}
\vspace{3mm}
\begin{itemize}
\item Dense-ResFormer mixes values from multiple earlier layers.
\item Plus couples first-layer branch coefficients across depth.
\item Ordinary Learnable coefficients are not specified as convex weights.
\end{itemize}
\papersource{Paper, Secs. 3.2--3.3, PDF pp. 3--4. Plus details and ambiguities are in the backup slides.}
\end{frame}

% 6: 1.5 min
\begin{frame}{SVFormer saves value storage; every layer still stores keys}
\[
C_{\rm base}=2NBl d_{kv},\qquad C_{\rm SV}=(N+1)Bl d_{kv}
\]
\[
\frac{C_{\rm SV}}{C_{\rm base}}=\frac{N+1}{2N}
\]
\begin{columns}[T,onlytextwidth]
\column{.48\textwidth}
\begin{block}{8 layers}
56.25\% of baseline KV storage\\
\alert{43.75\% saved}
\end{block}
\column{.48\textwidth}
\begin{block}{24 layers}
52.08\% of baseline KV storage\\
\alert{47.92\% saved}
\end{block}
\end{columns}
\begin{itemize}
\item $B$: batch; $l$: cached tokens; $d_{kv}$: per-layer KV width; $N$: depth.
\item Equal K/V widths and fixed model dimensions; element counts omit metadata.
\item ResFormer retains layer-specific V. Cache savings do not imply equal latency savings.
\end{itemize}
\papersource{Derivation from Sec. 3.3, PDF pp. 3--4. These counts are not measured memory or throughput results.}
\end{frame}

% 7: 1 min
\begin{frame}{The main evidence comes from controlled pretraining}
\begin{columns}[T,onlytextwidth]
\column{.52\textwidth}
\textbf{Main protocol}
\begin{itemize}
\item 82M--468M Llama-like models
\item About 20B SlimPajama tokens
\item Length 2,048; about 2M tokens/step
\item 10,000 steps; AdamW; peak LR $6\!\times\!10^{-4}$
\item Pre-norm, SwiGLU, RoPE; FP16
\end{itemize}
\column{.44\textwidth}
\textbf{What is measured?}
\begin{itemize}
\item Seven-domain average validation loss $\downarrow$
\item Zero-shot task accuracy $\uparrow$
\item WikiText/LAMBADA PPL $\downarrow$
\item Ablations and representation diagnostics
\end{itemize}
\end{columns}
\vspace{2mm}
\alert{Reproduction caveat:} warmup is 1,200 steps in Sec. 4.1 but 120 in Table 14. Repeated-run uncertainty is not reported.
\papersource{Paper, Sec. 4.1, PDF pp. 4--5; Tables 12--14, pp. 15--16. Larger-scale protocol is separate.}
\end{frame}

% 8: 1.5 min
\begin{frame}{ResFormer reaches a given loss with fewer resources}
\begin{columns}[T,onlytextwidth]
\column{.49\textwidth}\centering
\fig{fig02a-model-scaling}{1}
\textbf{16.11\% fewer parameters}\\
\small 82M--468M; 20B tokens
\column{.49\textwidth}\centering
\fig{fig02b-data-scaling}{1}
\textbf{20.3\% fewer training tokens}\\
\small 468M; evaluated every 2B tokens
\end{columns}
\vspace{2mm}
Separate equal-loss estimates; the two reductions were not tested jointly.
\papersource{Original Fig. 2 left/middle and Sec. 4.2, PDF pp. 4--5. Fit uncertainty is not reported.}
\end{frame}

% 9: 1 min
\begin{frame}{A 1.6B run extends the evidence under a different protocol}
\begin{columns}[c,onlytextwidth]
\column{.59\textwidth}\centering
\fig{fig02c-large-scaling}{1}
\column{.38\textwidth}
\begin{itemize}
\item About 200B internal pretraining tokens
\item Sequence length 8,192
\item Learning rate $1.5\!\times\!10^{-4}$
\item About 3,584 H800 GPU hours per run
\end{itemize}
\alert{Scope:} lower validation loss here; no final 1.6B downstream table in v5.
\end{columns}
\papersource{Original Fig. 2 right; Secs. 4.1--4.2, PDF pp. 4--5. Commented-out source tables are excluded.}
\end{frame}

% 10: 1 min
\begin{frame}{Mean accuracy improves, but no variant wins every metric}
\centering
\renewcommand{\arraystretch}{1.18}
\begin{tabular}{lrrr}
\toprule
468M / 20B tokens & Wiki PPL $\downarrow$ & LAMBADA PPL $\downarrow$ & Mean ACC $\uparrow$\\
\midrule
Transformer & 24.8 & 33.4 & 40.6\%\\
NeuTRENO & 24.3 & 36.3 & 41.4\%\\
DenseFormer & 24.0 & \textbf{28.0} & 40.8\%\\
Identity ResFormer & 23.8 & 32.9 & 41.3\%\\
Learnable ResFormer & 23.7 & 32.5 & \textbf{42.3\%}\\
Learnable ResFormer Plus & \textbf{23.2} & 31.4 & 42.0\%\\
\bottomrule
\end{tabular}
\vspace{3mm}
\begin{itemize}
\item Learnable: \alert{+1.7 percentage points} in the reported eight-task mean.
\item Plus has the best WikiText PPL; DenseFormer has the best LAMBADA PPL.
\end{itemize}
\papersource{Selected columns from Table 2, PDF p. 4. Mean ACC excludes the two PPL columns; error bars are not provided.}
\end{frame}

% 11: 1 min
\begin{frame}{Simple mixing works; learned weights are not automatically best}
\begin{columns}[T,onlytextwidth]
\column{.56\textwidth}
\centering\renewcommand{\arraystretch}{1.12}
\begin{tabular}{lr}
\toprule
8-layer, 82M model & Loss $\downarrow$\\
\midrule
Transformer & 2.739\\
DenseFormer & 2.722\\
NeuTRENO & 2.720\\
Identity ResFormer & 2.712\\
Learnable ResFormer & 2.705\\
Constant: $2\V_1+\V_n$ & 2.700\\
Sparse: $5\V_1+\V_n$, layers 6--8 & 2.687\\
Learnable ResFormer Plus & \textbf{2.681}\\
\bottomrule
\end{tabular}
\column{.40\textwidth}
\begin{itemize}
\item NeuTRENO adds a value difference after attention.
\item DenseFormer mixes hidden states across depth.
\item Fixed mixing helps; manual search can improve it further.
\end{itemize}
\alert{Caveat:} manual settings were searched; tuning budgets are unmatched.
\end{columns}
\papersource{Table 3 and Sec. 4.2, PDF p. 5; baseline definitions in Sec. 3.1, p. 3. Full variant table is in the Chinese notes.}
\end{frame}

% 12: 1.5 min
\begin{frame}{First-layer values help the last few layers most}
\begin{columns}[T,onlytextwidth]
\column{.49\textwidth}\centering
\fig{fig05a-source}{1}\\
\textbf{Source:} $\V_1$ is most useful.
\column{.49\textwidth}\centering
\fig{fig05b-destination}{1}\\
\textbf{Destination:} late layers.
\end{columns}
\vspace{2mm}
\begin{itemize}
\item Best in this 8-layer model: layer 7 alone, or layers 6--8 together.
\item Layer choices depend on architecture and initialization.
\end{itemize}
\papersource{Original Fig. 5 and Sec. 4.4, PDF p. 6. Lower validation loss is better.}
\end{frame}

% 13: 1.5 min
\begin{frame}{The location and mapping of the shortcut both matter}
\begin{columns}[T,onlytextwidth]
\column{.44\textwidth}
\textbf{Where to add a residual?}\\[2mm]
\begin{tabular}{lr}
\toprule
Position & Loss $\downarrow$\\
\midrule
None & 2.739\\
Query & 2.742\\
Key & 2.746\\
Attention matrix & 2.757\\
Value & \textbf{2.712}\\
\bottomrule
\end{tabular}
\column{.52\textwidth}
\textbf{How to map $\V_1$ to the output?}\\[2mm]
\begin{tabular}{lr}
\toprule
Mapping & Loss $\downarrow$\\
\midrule
None & 2.739\\
Identity mapping & 3.137\\
Recomputed cross-layer attention & 2.729\\
Current attention & \textbf{2.712}\\
\bottomrule
\end{tabular}
\end{columns}
\vspace{4mm}
\alert{Interpretation:} use the current semantic selection pattern to read early content. Recomputing cross-layer attention also costs more computation.
\papersource{Tables 6--7, PDF p. 7; explanation in Sec. 4.4, p. 8. Left: fixed 0.5/0.5 mixing.}
\end{frame}

% 14: 1 min
\begin{frame}{Extra hidden residuals expose an initialization trade-off}
\centering
\renewcommand{\arraystretch}{1.22}
\begin{tabular}{lcr}
\toprule
Extra shortcut & Coefficient initialization & Loss $\downarrow$\\
\midrule
None & --- & 2.7389\\
Value, from $\V_1$ & $0.5/0.5$ & \textbf{2.705}\\
Hidden, from $\Hh_0$ & $0.5/0.5$ & 2.781\\
Value, from $\V_1$ & $0/1$ & 2.730\\
Hidden, from $\Hh_0$ & $0/1$ & 2.722\\
\bottomrule
\end{tabular}
\vspace{3mm}
\begin{itemize}
\item All shortcut coefficients in this table are learnable.
\item Large initial hidden mixing hurts, but hidden wins at $0/1$ initialization.
\item The best tested value setting wins; universal superiority is not established.
\end{itemize}
\papersource{Table 4, PDF p. 7. The adjacent prose mixes H0/H1; this slide follows the table and stated experiment.}
\end{frame}

% 15: 1 min
\begin{frame}{Simple learning-rate changes do not reproduce the gain}
\begin{columns}[c,onlytextwidth]
\column{.59\textwidth}\centering
\fig{fig04b-lr}{1}
\column{.38\textwidth}
\begin{itemize}
\item Both models are best near LR 0.003 in this sweep.
\item Identity ResFormer remains better at the tested rates.
\item Doubling LR for the first layer or only $\W_1^{\V}$ does not close the gap.
\end{itemize}
\alert{Boundary:} this rules out simple explanations, not all optimization effects.
\end{columns}
\papersource{Original Fig. 4 right; Sec. 4.3, PDF pp. 5--6. This is a dedicated LR ablation, not the default protocol.}
\end{frame}

% 16: 1 min
\begin{frame}{Value similarities support a residual-learning interpretation}
\begin{columns}[T,onlytextwidth]
\column{.49\textwidth}\centering
\fig{fig08a-first-value-similarity}{1}\\
\small Similarity to first-layer values
\column{.49\textwidth}\centering
\fig{fig08b-token-similarity}{1}\\
\small Similarity between tokens within a layer
\end{columns}
\vspace{2mm}
\begin{itemize}
\item Mixed values retain early content; raw values can learn a correction.
\item Similarity does not directly measure information or residual magnitude.
\end{itemize}
\papersource{Original Fig. 8, PDF p. 8. The authors interpret the raw value branch as learning a correction.}
\end{frame}

% 17: 1 min
\begin{frame}{Attention matters more; representation variance spreads out}
\begin{columns}[T,onlytextwidth]
\column{.49\textwidth}\centering
\fig{fig09a-module-removal}{1}\\
\small Remove modules; retain layer 1.
\column{.49\textwidth}\centering
\fig{fig09b-pca}{1}\\
\small PCA dimension at 99\% variance.
\end{columns}
\vspace{2mm}
\begin{itemize}
\item ResFormer becomes more sensitive to attention removal.
\item More PCA components do not prove higher task-relevant information.
\end{itemize}
\papersource{Original Fig. 9 and Sec. 4.5, PDF p. 8. These are post-training diagnostics.}
\end{frame}

% 18: 1.5 min
\begin{frame}{SVFormer trades quality differently at short and long lengths}
\centering
\renewcommand{\arraystretch}{1.28}
\begin{tabular}{lrr}
\toprule
Method & Training length 2,048 & Training length 64,000\\
\midrule
Transformer, full KV & \textbf{2.739} & 2.753\\
CLA2, about half KV & 2.776 & 2.793\\
GQA2, half KV & 2.748 & 2.773\\
SVFormer, about half KV & 2.774 & \textbf{2.7485}\\
\bottomrule
\end{tabular}
\vspace{3mm}
\begin{itemize}
\item All entries are validation loss $\downarrow$ under the reported budget.
\item SVFormer: $+0.035$ vs. baseline at 2,048; $-0.0045$ at 64,000.
\item Training length changes across columns; this is not a context-extrapolation or retrieval test.
\end{itemize}
\papersource{Table 8 left, PDF p. 9. CLA2 shares K/V every two layers; GQA2 halves KV heads. No error bars; cache sizes are approximate.}
\end{frame}

% 19: 1 min
\begin{frame}{SVFormer can combine with grouped-query attention}
\begin{columns}[c,onlytextwidth]
\column{.52\textwidth}
\centering\renewcommand{\arraystretch}{1.3}
\begin{tabular}{lr}
\toprule
Length 64,000 & Loss $\downarrow$\\
\midrule
Transformer, full KV & 2.753\\
GQA8 & 2.807\\
CLA2 + GQA4 & 2.815\\
SVFormer + GQA4 & \textbf{2.741}\\
\bottomrule
\end{tabular}
\column{.44\textwidth}
\textbf{About one-eighth KV storage}
\[
\frac{C_{\mathrm{SV+GQA}g}}{C_{\rm MHA}}
=\frac{N+1}{2Ng}
\]
\begin{itemize}
\item $g$: KV-head reduction factor.
\item At $N=8, g=4$: 14.06\% remains, not exactly 12.5\%.
\item Formula assumes fixed depth and widths.
\end{itemize}
\end{columns}
\papersource{Table 8 right, PDF p. 9. Cache formula is our derivation; per-row measured bytes and throughput are not reported.}
\end{frame}

% 20: 1.5 min
\begin{frame}{The loss crossover is much later at 32k and 64k}
\begin{columns}[T,onlytextwidth]
\column{.53\textwidth}\centering
\fig{fig10a-length}{1}
\column{.43\textwidth}\centering
\fig{fig10b-crossover}{1}
\end{columns}
\vspace{1mm}
\begin{itemize}
\item Left: $L_{\rm SV}-L_{\rm base}$; negative favors SVFormer; about 2M tokens/step.
\item \alert{64k crossover is extrapolated} from the last 1,000 points.
\item Smaller learning rates also help; a universal eventual crossover is unproven.
\end{itemize}
\papersource{Original Fig. 10, Table 9 and Sec. 4.6, PDF p. 9. The paper's exponential-trend claim has limited support.}
\end{frame}

% 21: 1 min
\begin{frame}{Attention sinks weaken, with a caveat in the entropy text}
\begin{columns}[T,onlytextwidth]
\column{.49\textwidth}\centering
\fig{fig13a-entropy}{1}\\
\small Token-importance entropy across depth
\column{.49\textwidth}\centering
\fig{fig13b-first-token-importance}{1}\\
\small Attention importance of the first token
\end{columns}
\vspace{1mm}
\begin{itemize}
\item ResFormer/SVFormer show less first-token concentration here.
\item Entropy $-\sum_i p_i\log p_i$: \alert{higher means less concentrated}.
\end{itemize}
\papersource{Original Fig. 13(a,b), Appendix A.1, PDF p. 12. We correct the appendix prose, which reverses the entropy direction.}
\end{frame}

% 22: 1 min
\begin{frame}{The evidence is useful, but the mechanism is not settled}
\begin{itemize}
\item \textbf{Robust core:} several architectural controls support value mixing under current attention.
\item \textbf{Scale:} most ablations are small; the 1.6B study uses internal data.
\item \textbf{Optimization:} learned coefficients can lose to manually tuned settings; Plus details are incomplete.
\item \textbf{Measurement:} no repeated-run uncertainty or end-to-end inference benchmark is reported.
\item \textbf{Mechanism:} similarity, PCA, and sink reduction are supporting observations, not a complete causal proof.
\end{itemize}
\vspace{2mm}
\alert{Replication priorities:} resolve warmup/batch settings, match tuning budgets, and test the long-run SVFormer crossover.
\papersource{Paper, Secs. 4.2--4.6 and Limitations, PDF pp. 5--9; Appendix A.3, pp. 15--16. Assessment by this reading.}
\end{frame}

% 23: 1 min
\begin{frame}{Take away a design principle and a conditional trade-off}
\begin{enumerate}
\item \textbf{Separate selection from content.} Deep attention can read first-layer values using its current Q/K relationships.
\item \textbf{Mixing improves the reported quality frontier.} The location, depth, and strength of the shortcut matter.
\item \textbf{Full sharing reduces storage.} SVFormer's quality depends on training length, budget, and learning rate.
\end{enumerate}
\vspace{4mm}
\textbf{Discussion:} Does first-layer content access explain the gains after matching optimization and tuning budgets?
\vspace{3mm}
\papersource{Zhanchao Zhou, Tianyi Wu, Zhiyun Jiang, Fares Obeid, Zhenzhong Lan. Value Residual Learning.}
\papersource{\href{https://arxiv.org/abs/2410.17897v5}{arXiv:2410.17897v5}, revised 8 June 2025. Source PDF and author TeX were both read.}
\end{frame}

\appendix

% 24: backup
\begin{frame}{Backup: Plus couples first-layer coefficients across depth}
\[
\lambda_{n,1}=\lambda_{\rm scale}
\frac{e^{\lambda'_{n,1}}}{\sum_{j=1}^{N}e^{\lambda'_{j,1}}},
\qquad\lambda_{\rm scale}\text{ initialized to }N
\]
\[
\lambda_{n,2}\text{ initialized to }0.5,
\qquad\sum_{n=1}^{N}\lambda_{n,1}=\lambda_{\rm scale}
\]
\begin{itemize}
\item Equal initial logits would give $\lambda_{n,1}=1$, not 0.5.
\item The paper does not specify the logits' initialization clearly.
\item It is unclear whether this is only initialization or a constraint throughout training.
\item The motivation for stronger later-layer connections does not specify a monotone initialization.
\end{itemize}
\papersource{Paper, Sec. 3.2, PDF p. 3. Sum and equal-logit implication are our algebraic deductions.}
\end{frame}

% 25: backup
\begin{frame}{Backup: value shortcuts compensate for missing hidden paths}
\centering
\renewcommand{\arraystretch}{1.24}
\begin{tabular}{lcrr}
\toprule
Hidden residual starts at & Added source & No value skip & With value skip\\
\midrule
$\Hh_0$ (default) & $\V_1$ & 2.739 & 2.712\\
$\Hh_0$ (default) & $\V_2$ & 2.739 & 2.738\\
$\Hh_1$ & $\V_2$ & 2.780 & 2.780\\
$\Hh_2$ & $\V_2$ & 2.820 & 2.787\\
$\Hh_2$ & $\V_3$ & 2.820 & 2.833\\
$\Hh_3$ & $\V_3$ & 3.057 & 2.883\\
\bottomrule
\end{tabular}
\vspace{3mm}
\begin{itemize}
\item Loss $\downarrow$. Earlier hidden residuals are removed to change information access.
\item $\V_2$ and $\V_3$ can help when the corresponding hidden paths are missing.
\end{itemize}
\papersource{Table 5 and Sec. 4.4, PDF p. 7. This is a changed-architecture control, not the default model.}
\end{frame}

% 26: backup
\begin{frame}{Backup: SVFormer depends on learning rate and model size}
\begin{columns}[c,onlytextwidth]
\column{.55\textwidth}
\small\renewcommand{\arraystretch}{1.25}
\begin{tabular}{lrrr}
\toprule
Model & LR & Warmup & $\Delta L$\\
\midrule
Llama & $10^{-4}$ & 120 & $-0.033$\\
Llama & $3\!\times\!10^{-4}$ & 120 & $+0.021$\\
Llama & $6\!\times\!10^{-4}$ & 120 & $+0.035$\\
Llama & $6\!\times\!10^{-4}$ & 1,200 & $+0.036$\\
GPT2 & $6\!\times\!10^{-4}$ & 120 & $+0.029$\\
\bottomrule
\end{tabular}
\vspace{3mm}
\normalsize $\Delta L=L_{\rm SV}-L_{\rm base}$; negative is better.
\column{.42\textwidth}\centering
\fig{fig11-sv-scaling}{1}\\
\small Reported equal-loss cost:\\
\textbf{12.2\% more parameters}.
\end{columns}
\papersource{Table 9 and original Fig. 11, PDF p. 9. Parameter compensation and fixed-architecture KV savings are separate comparisons.}
\end{frame}

% 27: backup
\begin{frame}{Backup: shallow mixing is more sensitive to scaling}
\begin{columns}[T,onlytextwidth]
\column{.48\textwidth}
\textbf{Sparse constant coefficients}\\[2mm]
\begin{tabular}{crr}
\toprule
$\lambda$ & Layers 2--4 & Layers 5--7\\
\midrule
1 & 2.724 & 2.698\\
2 & 2.728 & 2.688\\
5 & 2.732 & 2.682\\
\bottomrule
\end{tabular}
\column{.48\textwidth}
\textbf{Post-mixing norm rescaling}\\[2mm]
\begin{tabular}{lrr}
\toprule
Layers & No & Yes\\
\midrule
All & 2.712 & 2.701\\
2--4 & 2.734 & 2.727\\
6--8 & 2.702 & 2.701\\
\bottomrule
\end{tabular}
\end{columns}
\vspace{4mm}
\begin{itemize}
\item Validation loss $\downarrow$; stronger first-layer mixing helps the later group.
\item Left follows Table 10's layers 5--7; the prose says 6--8. Do not silently merge them.
\item Norm rescaling helps shallow/all-layer variants more; normalization axes are unspecified.
\end{itemize}
\papersource{Tables 10--11 and Appendix A.1, PDF p. 14. Baseline loss: 2.739.}
\end{frame}

% 28: backup
\begin{frame}{Backup: resolve these details before exact reproduction}
\begin{itemize}
\item \textbf{Warmup:} Sec. 4.1 gives 1,200 steps; Table 14 gives 120.
\item \textbf{Batch arithmetic:} at length 2,048, Table 13 lists per-GPU batch 32, 8 GPUs, accumulation 32, but total batch 1,024.
\item \textbf{Coefficient heatmap:} Fig. 6 right is captioned 468M, while text and displayed depth indicate 8 layers.
\item \textbf{Entropy indexing:} for row-normalized $A_{ij}$, summing over $j$ is constant; incoming token importance normally sums over query rows.
\item \textbf{Coverage:} source/PDF read; no training reproduction. Original figures and build helper accompany this deck.
\end{itemize}
\papersource{PDF pp. 4, 6, 12, 15--16. Numerical discrepancies also appear in the author TeX; they are not text-extraction artifacts.}
\end{frame}
\end{document}