% Research discussion prepared from arXiv:2605.10938v2.
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\title[ELF]{ELF: Embedded Language Flows}
\subtitle{Continuous denoising, shared final-step decoding}
\author{Paper: Keya Hu, Linlu Qiu, Yiyang Lu, Hanhong Zhao,\\Tianhong Li, Yoon Kim, Jacob Andreas, Kaiming He\\[3mm]\small MIT \quad | \quad Independent paper discussion}
\date{arXiv:2605.10938v2 \quad June 26, 2026\\Reading: October 14, 2026}

\begin{document}

\begin{frame}
\titlepage
\vspace{-4mm}
\begin{center}\small Keep the trajectory continuous; recover tokens with the same network at the end.\end{center}
\end{frame}

\begin{frame}{Does discrete output require token prediction at every step?}
\begin{block}{Research question}
Is the gap between continuous and discrete language diffusion inherent, or partly a design problem?
\end{block}
\medskip
\begin{tabular}{P{0.27\linewidth}P{0.64\linewidth}}
\toprule
Design family & Interface to discrete text \\
\midrule
Discrete diffusion & Denoise directly in token space. \\
Many continuous DLMs & Predict tokens during intermediate training steps. \\
Latent diffusion LMs & Use a separate latent-to-text decoder. \\
\textbf{ELF} & \textbf{Continuous flow; a shared final decoding mode.} \\
\bottomrule
\end{tabular}\par
\papersource{Paper, Secs. 1--2, PDF pp. 1--3; App. A, Table 2, pp. 17--18. Families contain exceptions.}
\end{frame}

\begin{frame}{One network handles both continuous and discrete recovery}
\centering
\fig{fig-03-pipeline}{3.5cm}
\begin{itemize}
\item Train: encode text, corrupt embeddings, select denoise or decode mode.
\item Generate: update the whole embedding sequence, then decode once.
\item Frozen T5-small supplies 512-dimensional contextual training targets.
\end{itemize}
\papersource{Paper, Fig. 3, PDF p. 3; Sec. 4, p. 6. Original figure.}
\end{frame}

\begin{frame}{Flow Matching connects noise to clean embeddings}
\[
\z_t=t\x+(1-t)\eps,\qquad t\in[0,1]
\]
\[
\vv=\frac{d\z_t}{dt}=\x-\eps
\]
\begin{columns}[T]
\begin{column}{0.48\linewidth}
\begin{block}{State}
$\x,\z_t,\eps\in\mathbb{R}^{L\times d}$\\
OWT: $L=1024$, $d=512$.\\
$t=0$: noise; $t=1$: data.
\end{block}
\end{column}
\begin{column}{0.48\linewidth}
\begin{block}{Parameterization}
The network predicts $\x_\theta$.\\[1mm]
$\displaystyle \vv_\theta=\frac{\x_\theta-\z_t}{1-t}$\\[1mm]
Velocity is computed from that prediction.
\end{block}
\end{column}
\end{columns}
\papersource{Paper, Sec. 3.1, PDF p. 4. Training uses scaled Gaussian noise; details in backup.}
\end{frame}

\begin{frame}{Predict clean data, but train with a velocity loss}
\[
\mathcal L_{\mathrm{MSE}}
=\EE\|\vv_\theta-\vv\|^2
=\EE\frac{\|\x_\theta-\x\|^2}{(1-t)^2}
\]
\begin{itemize}
\item The objective is a time-weighted clean-embedding error.
\item Clean prediction aligns the denoising and decoding tasks.
\item In controlled ablations, $\x$-prediction is stable from 512 to 1024 dimensions; $\vv$-prediction degrades at higher dimensions.
\end{itemize}
\begin{block}{State, bottleneck, and backbone}
The flow state is 512-dimensional per token. A 128-dimensional input bottleneck feeds a 768-dimensional ELF-B backbone.
\end{block}
\papersource{Paper, Eq. (1), p. 4; Fig. 11, p. 26; Table 7, p. 30.}
\end{frame}

\begin{frame}{Final-step decoding is a second mode of the same network}
\[
\mathcal L_{\mathrm{CE}}
=\EE\bigl[\operatorname{CrossEnt}(W\x_\theta(\tilde{\z},1,\mathrm{decode}),\mathbf{s})\bigr]
\]
\medskip
\begin{tabular}{P{0.20\linewidth}P{0.33\linewidth}P{0.34\linewidth}}
\toprule
 & Denoise: 80\% & Decode: 20\% \\
\midrule
Corruption & One $t$ per sequence & One corruption level per token \\
Time condition & Sampled $t<1$ & Fixed $t=1$ \\
Objective & Velocity regression & Token cross-entropy \\
\bottomrule
\end{tabular}\par
\medskip
\begin{itemize}
\item Corrupted decoder inputs teach recovery from imperfect embeddings.
\item At inference: decode-mode forward pass, unembedding, then argmax.
\end{itemize}
\papersource{Paper, Eq. (2), p. 4; App. C.1, pp. 21--23; Alg. 5, p. 24.}
\end{frame}

\begin{frame}{Self-conditioning supplies guidance without an external prompt}
\begin{itemize}
\item Feed the previous clean prediction back alongside the noisy state.
\item Training: 50\% predicted condition, 50\% zero; stop its gradient.
\item Inference: reuse the previous step's prediction.
\end{itemize}
\[
\vv_{\mathrm{cfg}}(\z_t\mid\mathbf c)
=\omega\vv(\z_t\mid\mathbf c)+(1-\omega)\vv(\z_t\mid\varnothing)
\]
\begin{block}{ELF learns self-conditioning CFG during training}
The network takes the desired scale as input and predicts the guided field directly: one denoising forward pass per inference step.
\end{block}
\papersource{Paper, Sec. 3.3, pp. 5--6; Eq. (5), p. 23. External-input CFG is different: it uses two predictions.}
\end{frame}

\begin{frame}{Sampling updates the entire sequence before decoding}
\[
\z_{t+\Delta t}=\z_t+\Delta t\frac{\hat\x-\z_t}{1-t}
\]
\begin{enumerate}
\item Start from Gaussian embeddings and a zero self-condition.
\item Follow a logit-normal time grid, with more resolution near noise.
\item Use deterministic ODE updates or stochastic noise re-injection.
\item At $t=1$, switch modes and recover all tokens.
\end{enumerate}
\medskip
\alert{$N$ denoising steps still require a final decoding forward pass.}
\papersource{Paper, Algs. 2, 5--6, pp. 5, 24. The ``SDE'' sampler is an SDE-inspired approximation.}
\end{frame}

\begin{frame}{Evaluation measures fluency proxies and diversity together}
\begin{tabular}{P{0.23\linewidth}P{0.32\linewidth}P{0.32\linewidth}}
\toprule
Task & Data / length & Metric \\
\midrule
Unconditional & OWT; 1024 tokens;\newline 1,000 generated samples & GPT-2 Large PPL $\downarrow$;\newline unigram entropy \\
Translation & WMT14 De-En;\newline 64 source + 64 target & BLEU $\uparrow$ \\
Summarization & XSum; 1024 source\newline + 64 target & ROUGE-1/2/L $\uparrow$ \\
\bottomrule
\end{tabular}\par
\medskip
\begin{block}{What Gen. PPL means}
Another LM scores generated text. It is not ELF's held-out likelihood. Repetitive text can score well, so entropy must remain visible.
\end{block}
\papersource{Paper, Sec. 4, PDF p. 6; degeneration example in Table 5, p. 21.}
\end{frame}

\begin{frame}{Guidance trades diversity for lower generative perplexity}
\begin{columns}[c]
\begin{column}{0.54\linewidth}\fig{fig-04-cfg}{4.8cm}\end{column}
\begin{column}{0.43\linewidth}
\begin{itemize}
\item Horizontal: entropy; vertical: Gen. PPL.
\item Stronger guidance moves down and left.
\item Compare frontiers, not isolated PPL minima.
\end{itemize}
\medskip
64-step ODE, ELF-B:\\
$\omega=1$: $65.30 / 5.40$\\
$\omega=3$: $26.62 / 5.15$\\
\smallskip
\small Values: PPL / entropy.
\end{column}
\end{columns}
\papersource{Paper, Fig. 4, p. 7; exact values from Table 10, p. 32. Original figure.}
\end{frame}

\begin{frame}{Contextual embeddings help; shared decoding stays competitive}
\begin{columns}[T]
\begin{column}{0.49\linewidth}
\fig{fig-05-design-a}{3.8cm}
\par\smallskip
\small Frozen pretrained contextual representations give the best frontier among tested embeddings.
\end{column}
\begin{column}{0.49\linewidth}
\fig{fig-05-design-b}{3.8cm}
\par\smallskip
\small Sharing weights retains a similar frontier while removing a separate decoder stage.
\end{column}
\end{columns}
\papersource{Paper, Fig. 5a--b, PDF p. 7; Sec. 4.1, pp. 7--8. Complete original panels, cropped.}
\end{frame}

\begin{frame}{Stochastic sampling is especially useful with few steps}
\begin{columns}[c]
\begin{column}{0.55\linewidth}\fig{fig-05-design-c}{4.7cm}\end{column}
\begin{column}{0.42\linewidth}
\begin{itemize}
\item Same SC CFG scale: 1.
\item Re-inject noise, move slightly toward the noisy regime, then denoise.
\item Lower PPL at small step budgets; entropy also changes.
\end{itemize}
\medskip
Error correction is the authors' proposed explanation.
\end{column}
\end{columns}
\papersource{Paper, Fig. 5c, p. 7; Alg. 6, p. 24. Original panel, cropped.}
\end{frame}

\begin{frame}{Larger models improve the quality--diversity frontier}
\begin{columns}[c]
\begin{column}{0.53\linewidth}\fig{fig-06-scaling}{4.8cm}\end{column}
\begin{column}{0.44\linewidth}
ELF-B / M / L:\\
105M / 342M / 652M parameters.\\[3mm]
\textbf{A matched-entropy comparison:}\\
64-step SDE, entropy $5.28$:
\begin{itemize}
\item B, CFG 0.5: PPL 36.77.
\item L, CFG 3.0: PPL 23.31.
\end{itemize}
\smallskip
Training: 5 / 4 / 3 OWT epochs.
\end{column}
\end{columns}
\papersource{Paper, Fig. 6, p. 8; Tables 6 and 10, pp. 30, 32. Original figure.}
\end{frame}

\begin{frame}{Undistilled ELF reaches Gen. PPL 24 with 32 steps}
\begin{columns}[c]
\begin{column}{0.50\linewidth}\fig{fig-07-system-a}{4.6cm}\end{column}
\begin{column}{0.47\linewidth}
\centering
\begin{tabular}{rrr}
\toprule
Steps & PPL & Entropy \\
\midrule
8 & 67.32 & 5.14 \\
16 & 33.66 & 5.16 \\
32 & 24.08 & 5.15 \\
\bottomrule
\end{tabular}\par
\medskip
\raggedright
32-step SE: $\pm0.16$ PPL, $\pm0.002$ entropy over six evaluation seeds.\\[2mm]
ELF: 105M; baselines: about 170M. SC CFG=3; tuned SDE noise scale.
\end{column}
\end{columns}
\papersource{Paper, Fig. 7a, p. 8; means from Table 9, p. 31. Figure labels and table use different reporting detail.}
\end{frame}

\begin{frame}{The training-token advantage has a specific accounting scope}
\begin{columns}[c]
\begin{column}{0.49\linewidth}\fig{fig-07-system-c}{4.6cm}\end{column}
\begin{column}{0.48\linewidth}
\begin{itemize}
\item ELF: $5\times9.04$B = \textbf{45.2B} effective tokens.
\item Undistilled baselines: \textbf{524.3B}, about $11.6\times$ as many.
\item Counts exclude the T5 encoder's prior pretraining.
\item Tokens do not account for every extra forward pass or teacher rollout.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Fig. 7c, p. 8; Table 8, p. 31. Cost interpretation based on the stated counting formula.}
\end{frame}

\begin{frame}{ELF leads the reported translation and summarization systems}
\centering
\begin{tabular}{lrrrr}
\toprule
Model & De-En BLEU & XSum R1 & R2 & R-L \\
\midrule
AR (99M) & 25.2 & 30.5 & 10.2 & 24.4 \\
MDLM (99M) & 18.4 & 33.4 & 11.6 & 25.8 \\
Duo (170M+35M) & 21.3 & 31.4 & 10.1 & 25.0 \\
E2D2 (99M) & 24.8 & 28.4 & 8.3 & 22.0 \\
\textbf{ELF (105M+35M)} & \textbf{26.4} & \textbf{36.0} & \textbf{12.2} & \textbf{27.8} \\
\bottomrule
\end{tabular}\par
\medskip
\begin{itemize}
\item ELF: 64-step ODE, SC CFG=1, input-condition CFG=2.
\item Input guidance uses conditional and unconditional predictions.
\item Mixed literature / reproduced baselines; tokenizers and schedules differ.
\end{itemize}
\papersource{Selected rows of Table 1, p. 9; protocol: Table 11, p. 32. All scores higher is better; full table in notes.}
\end{frame}

\begin{frame}{Distillation makes one student step match a teacher interval}
Teacher: multiple steps from $\z_t$ to $\z_r$. Student: one Euler update.
\[
\z_r=\z_t+(r-t)\frac{\tilde\x-\z_t}{1-t}
\quad\Longrightarrow\quad
\tilde\x=\z_t+\frac{1-t}{r-t}(\z_r-\z_t)
\]
\[
\mathcal L_{\mathrm{distill}}=\EE\|\x_\theta(\z_t,t)-\tilde\x\|^2
\]
\begin{itemize}
\item Fixed 64-step teacher throughout; retain the decoding CE objective.
\item Student curriculum: $16\to8\to4\to2\to1$ steps, one epoch per round.
\item Each new student starts from the preceding student's weights.
\end{itemize}
\papersource{Paper, App. B, Eqs. (3)--(4), p. 19; Table 3, p. 20. First student initialized from the teacher.}
\end{frame}

\begin{frame}{ELF+PD improves few-step PPL, with a diversity trade-off}
\centering
\begin{tabular}{rrrrr}
\toprule
 & \multicolumn{2}{c}{FMLM} & \multicolumn{2}{c}{ELF+PD} \\
Steps & PPL $\downarrow$ & Entropy & PPL $\downarrow$ & Entropy \\
\midrule
1 & 168.30 & 5.17 & \textbf{136.10} & 5.26 \\
2 & 133.29 & 5.25 & \textbf{68.25} & 5.24 \\
4 & 111.31 & 5.26 & \textbf{34.33} & 5.16 \\
8 & 86.50 & 5.36 & \textbf{23.18} & 5.07 \\
16 & 63.63 & 5.29 & \textbf{22.12} & 5.06 \\
32 & 45.09 & 5.25 & \textbf{21.32} & 5.04 \\
\bottomrule
\end{tabular}\par
\medskip
All rows use the final-round student. Task training rises to about 90B tokens.\\
At 8 steps, lower PPL also comes with lower entropy.
\papersource{Paper, Table 4 and Fig. 9, p. 20. Additional distilled baselines in backup.}
\end{frame}

\begin{frame}{One-step generation remains substantially harder}
\begin{columns}[c]
\begin{column}{0.53\linewidth}\fig{fig-09-distillation-c}{4.6cm}\end{column}
\begin{column}{0.44\linewidth}
\begin{itemize}
\item CFG-swept frontiers are close for 8--32 steps.
\item Fewer than 8 steps lose quality.
\end{itemize}
\begin{block}{A revealing failure case}
Round 2, one step:\\
PPL = 1.7; entropy = 0.64.\\[1mm]
An excellent PPL can reflect collapse.
\end{block}
\end{column}
\end{columns}
\papersource{Paper, Fig. 9c, p. 20 (only entropy above 5 shown); Table 5, p. 21. Original panel.}
\end{frame}

\begin{frame}{The paper's own examples reveal semantic errors}
\begin{tabular}{P{0.18\linewidth}P{0.34\linewidth}P{0.35\linewidth}}
\toprule
Example & Intended content & Generated error \\
\midrule
Translation & Representatives in 26 US states & Turns states into countries \\
XSum & Calf-muscle injury; return expected in August & Changes the injury to a bone problem \\
8-step PD & A passage about education & Repeats loosely connected claims despite PPL 19.22 \\
\bottomrule
\end{tabular}\par
\medskip
\begin{block}{Reading assessment}
Reported metric gains coexist with factual and semantic failures. PPL, entropy, BLEU, and ROUGE do not fully measure fidelity.
\end{block}
\papersource{Paper, App. F.3, pp. 34--37; F.4, pp. 38--39. Examples paraphrased; assessment is ours.}
\end{frame}

\begin{frame}{ELF makes a strong case for continuous language generation}
\begin{enumerate}
\item \textbf{Interface:} continuous denoising and final token recovery can share one network.
\medskip
\item \textbf{Mechanism:} clean-data prediction, self-conditioning CFG, and stochastic sampling work well together.
\medskip
\item \textbf{Evidence:} strong quality--diversity--step trade-offs on OWT; gains on translation and summarization.
\medskip
\item \textbf{Next test:} include encoder/teacher compute, measure end-to-end latency, and evaluate semantic fidelity at few steps.
\end{enumerate}
\papersource{Synthesis of Secs. 3--4 and Apps. B--F. Evaluated model scale: 105M--652M; conditional targets: 64 tokens.}
\end{frame}

\begin{frame}{Primary source and discussion guide}
\textbf{Keya Hu, Linlu Qiu, Yiyang Lu, Hanhong Zhao, Tianhong Li,}\\
\textbf{Yoon Kim, Jacob Andreas, and Kaiming He.}\\[2mm]
\emph{ELF: Embedded Language Flows}. MIT, arXiv:2605.10938v2.\\
Revised June 26, 2026.\\[3mm]
\href{https://arxiv.org/abs/2605.10938v2}{arxiv.org/abs/2605.10938v2}\\
\href{https://github.com/lillian039/ELF}{github.com/lillian039/ELF}\\[4mm]
\begin{itemize}
\item Main discussion: approximately 25 minutes.
\item Following slides: equations, implementation settings, and comparison details.
\end{itemize}
\papersource{Original figures are reproduced from the authors' arXiv v2 source (CC BY 4.0). Tables are selected/reformatted.}
\end{frame}

\appendix

\begin{frame}{Backup: training-time guidance changes the regression target}
\begin{align*}
\vv_{\mathrm{target}}
&=\x-\eps+\left(1-\frac1\omega\right)(\vv_c^{\mathrm{cfg}}-\vv_0^{\mathrm{cfg}}),\\
\mathcal L&=\|\vv_\theta^{\mathrm{cfg}}-\operatorname{stopgrad}(\vv_{\mathrm{target}})\|^2.
\end{align*}
\begin{itemize}
\item $c$: self-conditioning prediction; $0$: null self-conditioning.
\item Both fields come from clean-embedding predictions via $(\x_\theta-\z_t)/(1-t)$.
\item Without self-conditioning, regress to $\x-\eps$ instead.
\item Sample $\omega\in[0.5,5]$; supply it as a control input.
\item At $\omega=1$, the target correction disappears.
\end{itemize}
\papersource{Paper, Eq. (5), p. 23; Alg. 3, p. 22. Training uses extra predictions; inference uses one guided prediction.}
\end{frame}

\begin{frame}{Backup: model and corruption settings}
\begin{columns}[T]
\begin{column}{0.48\linewidth}
\begin{block}{ELF-B}
12 layers; hidden size 768; 12 heads.\\
512-dimensional T5-small embeddings.\\
128-dimensional input bottleneck.\\
4 time + 4 CFG + 4 mode tokens.
\end{block}
\begin{block}{OWT optimization}
Muon, LR 0.002, batch 512.\\
5 epochs; EMA 0.9999.\\
No weight decay; constant LR after warmup.
\end{block}
\end{column}
\begin{column}{0.48\linewidth}
\begin{block}{Denoising branch}
$t=\sigma(u)$, $u\sim\mathcal N(-1.5,0.8^2)$.\\
One $t$ per sequence. Noise scale 2.
\end{block}
\begin{block}{Decoding branch}
$p_i=\sigma(u_i)$, $u_i\sim\mathcal N(0.8,0.8^2)$.\\
One $p_i$ per token; time input stays 1.\\
Noise scale 5 on OWT, 1 for conditional tasks.
\end{block}
\end{column}
\end{columns}
\papersource{Paper, App. C.1, pp. 21--23; Tables 6--7, p. 30.}
\end{frame}

\begin{frame}{Backup: clean prediction is robust at higher dimensions}
\centering
\fig{fig-11-targets}{3.9cm}
\begin{itemize}
\item Controlled setup: frozen encoder/decoder, adaLN-Zero, 64-step ODE.
\item Red regions: entropy below 5 or PPL above 300.
\item $\vv$-prediction is competitive at 512 dimensions, weaker at 768/1024.
\end{itemize}
\papersource{Paper, App. D.1, pp. 25--26; Fig. 11, p. 26. Original figure.}
\end{frame}

\begin{frame}{Backup: several implementation choices matter}
\begin{tabular}{P{0.26\linewidth}P{0.62\linewidth}}
\toprule
Choice & Observation in the paper \\
\midrule
Bottleneck: 32/128/512 & 32 often sacrifices entropy; 512 has worse PPL; 128 balances both. \\
Denoising probability & 0.8 gives the best tested frontier. \\
Conditioning & In-context tokens slightly improve quality; 148M $\to$ 105M parameters. \\
Optimizer & Tuned Muon improves over tuned AdamW, especially with SDE sampling. \\
Time grid / noise & Logit-normal helps few-step sampling; noise scale changes the frontier. \\
\bottomrule
\end{tabular}\par
\papersource{Paper, App. D.2--D.6, Figs. 12--16, pp. 26--29.}
\end{frame}

\begin{frame}{Backup: the stochastic update uses the original state}
\[
\alpha=1-\gamma\Delta t,\qquad
t_{\mathrm{back}}=\alpha t,\qquad
\z_{\mathrm{back}}=\alpha\z_t+(1-\alpha)\eps'
\]
\[
\hat\x=\mathrm{net}_\theta(\z_{\mathrm{back}},t_{\mathrm{back}},\mathrm{denoise})
\]
\[
\vv=\frac{\hat\x-\z_t}{1-t},\qquad
\z_{t+\Delta t}=\z_t+\Delta t\,\vv
\]
\begin{itemize}
\item Perturb the evaluation point; update from the original $\z_t,t$.
\item $\gamma=0$ recovers the ODE update.
\item This is the paper's practical SDE-inspired rule, not an exact SDE solver.
\end{itemize}
\papersource{Paper, Alg. 6, p. 24; App. C.2, pp. 24--25. Self-conditioning omitted here as in Alg. 6.}
\end{frame}

\begin{frame}{Backup: distilled systems across all reported step budgets}
\centering
\small
\begin{tabular}{rllll}
\toprule
Steps & MDLM+SDTT & Duo+DCD & FMLM & ELF+PD \\
\midrule
1 & 1260.60 / 5.26 & 5743.90 / 6.02 & 168.30 / 5.17 & 136.10 / 5.26 \\
2 & 877.22 / 5.34 & 891.16 / 5.41 & 133.29 / 5.25 & 68.25 / 5.24 \\
4 & 339.73 / 5.38 & 250.86 / 5.37 & 111.31 / 5.26 & 34.33 / 5.16 \\
8 & 112.66 / 5.41 & 118.21 / 5.41 & 86.50 / 5.36 & 23.18 / 5.07 \\
16 & 57.74 / 5.39 & 78.74 / 5.43 & 63.63 / 5.29 & 22.12 / 5.06 \\
32 & 40.41 / 5.34 & 63.98 / 5.40 & 45.09 / 5.25 & 21.32 / 5.04 \\
\bottomrule
\end{tabular}\par
\medskip
\normalsize
Each cell: Gen. PPL / entropy.\\[2mm]
ELF+PD settings:\\
1--8 steps: $\gamma=1.5$, SC CFG=2.5.\\
16--32 steps: $\gamma=2.0$, SC CFG=2.0.
\papersource{Paper, Table 4, p. 20; App. B.2, p. 19. Values from final-round student.}
\end{frame}

\begin{frame}{Backup: conditional protocols qualify the comparison}
\begin{itemize}
\item ELF keeps source embeddings clean and prepends them to targets; drop the source condition with 10\% probability during training.
\item Table 1 includes a 35M encoder for ELF and Duo.
\item WMT14 mostly uses literature results; XSum mostly uses reproduced baselines.
\item Reproduced MDLM uses two 32-token blocks; E2D2 uses 8-token blocks; Duo uses 1,000 sampling steps.
\item Fig. 17's XSum axis says ROUGE-1 near 27.8, whereas Table 1 reports R1=36.0 and R-L=27.8. Use Table 1 for numeric metric identity.
\end{itemize}
\papersource{Paper, Table 1, p. 9; App. C.1, p. 23; Fig. 17, p. 28; Table 11, p. 32. Last point is a reading observation.}
\end{frame}

\end{document}