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\newcommand{\vh}{\mathcal V_h}
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\title[zip2zip]{zip2zip: Inference-Time Adaptive Tokenization via Online Compression}
\subtitle{Research group discussion \enspace$\cdot$\enspace 25-minute main talk}
\author{Paper by Saibo Geng, Nathan Ranchin, Yunzhen Yao,\\Maxime Peyrard, Chris Wendler, Michael Gastpar, Robert West}
\date{arXiv:2506.01084v2 \enspace$\cdot$\enspace Reading: 12 November 2026}
\begin{document}

\begin{frame}
\titlepage
\end{frame}

\begin{frame}{Online tokens save steps, with a quality cost}
\begin{block}{Central idea}
Build context-specific tokens during inference, compute their vectors from base tokens, and generate them directly.
\end{block}
\begin{itemize}
\item Tokenizer tests: roughly \alert{13--41\% fewer tokens}; strongest gains in code and math.
\item H100 inference throughput improves; GSM8K accuracy drops sharply.
\item Published at \href{https://papers.nips.cc/paper_files/paper/2025/hash/def682d57535b9e778508b4b1a911034-Abstract-Conference.html}{NeurIPS 2025, main conference}.
\item \href{https://github.com/epfl-dlab/zip2zip}{Official implementation} and \href{https://github.com/epfl-dlab/zip2zip-compression}{compression library} are publicly available.
\end{itemize}
\papersource{Paper v2, Tables 3, 5, 9, PDF pp. 8--9, 19. Publication/code checked 2026-11-12.}
\end{frame}

\begin{frame}{Fixed vocabularies repeatedly pay for the same fragment}
\begin{block}{Problem}
A domain-specific phrase may require several base tokens every time it appears, even within one context.
\end{block}
\begin{itemize}
\item Larger static vocabularies still cannot cover every local distribution.
\item Domain-specific vocabulary expansion requires an adaptation stage.
\item Input compression alone leaves output decoding steps unchanged.
\end{itemize}
\medskip
\alert{zip2zip adapts the active vocabulary in the current session.}\\
The base tokenizer remains in place; an online compression layer sits above it.
\papersource{Paper, Secs. 1 and 4, PDF pp. 1--3, 9--10.}
\end{frame}

\begin{frame}{Context and dictionary evolve together}
\centering
\includegraphics[width=0.98\linewidth,height=0.62\textheight,keepaspectratio]{figures/fig-01-online.pdf}
\medskip
\raggedright
Blue: base tokens. Green: hypertokens. Pink: special tokens.\\
Read each row as a decoding step, then follow the codebook on the right.
\papersource{Original Fig. 1, PDF p. 2. Illustration permits longer entries; main experiments cap merge size at $M=3$.}
\end{frame}

\begin{frame}{One hypertoken replaces several predictions}
\begin{columns}[T]
\begin{column}{0.49\textwidth}
\begin{block}{Dictionary entries in Fig. 1}
\[
\begin{aligned}
1&\mapsto\texttt{to}\\
2&\mapsto\texttt{be}\\
7&\mapsto(1,2)\\
11&\mapsto(7,3)
\end{aligned}
\]
Thus $7$ means \texttt{to be};\\
$11$ means \texttt{to be or}.
\end{block}
\end{column}
\begin{column}{0.47\textwidth}
\begin{itemize}
\item Start each session with $\vh=\varnothing$.
\item LZW grows a dictionary from the token stream; later occurrences reuse entries.
\item A single model step can emit multiple base tokens.
\item $M$ limits constituent base-token count, including nested merges.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 2.1, PDF p. 3; Fig. 1, PDF p. 2.}
\end{frame}

\begin{frame}{A shared encoder gives unseen hypertokens a vector}
\begin{columns}[c]
\begin{column}{0.40\textwidth}
\centering
\includegraphics[width=\linewidth,height=0.55\textheight,keepaspectratio]{figures/fig-02a-embedding.pdf}
\end{column}
\begin{column}{0.57\textwidth}
\[
h=f_\phi(y_{1:M})\in\mathbb R^d
\]
\begin{itemize}
\item Look up constituent base embeddings: $M\times d$ values.
\item Pad shorter compositions; map them to one $d$-dimensional vector.
\item Main configuration: a two-layer Transformer encoder, $M=3$.
\item Base-token lookup stays available.
\end{itemize}
\end{column}
\end{columns}
\papersource{Original Fig. 2(a), cropped; Secs. 2.2 and 3.1, PDF pp. 3--4, 6--7.}
\end{frame}

\begin{frame}{The output head must also admit new tokens}
\[
p(v\mid z_{\le t})=
\frac{\exp(s_t^\top u_v)}{\sum_{w\in\vb\cup\vh(t)}\exp(s_t^\top u_w)}
\]
\begin{itemize}
\item $s_t\in\mathbb R^d$: Transformer hidden state.
\item $u_v$: static output vector for a base token; dynamically computed vector for a hypertoken.
\item Tied input/output weights permit a shared hyper-encoder; untied weights require separate mappings.
\item Keep input dictionary, output candidates, and decoder consistent.
\end{itemize}
\papersource{Teaching expansion of the joint-softmax mechanism; paper, Secs. 2.2--2.3, Fig. 3, PDF pp. 3--5.}
\end{frame}

\begin{frame}{Train the model on the representation it will generate}
\[
z=\mathcal C(y),\qquad
\min_{\theta,\phi}\;\mathbb E_{y\sim\mathcal D}
\left[-\log\pi_{\theta,\phi}(\mathcal C(y))\right]
\]
\begin{itemize}
\item $\mathcal C$: lossless online compression of base-token sequences.
\item Compress documents independently before training.
\item Teacher forcing predicts the next base token or hypertoken in $z$.
\item Adapt the backbone with LoRA and train the dynamic embedding modules.
\end{itemize}
\begin{block}{Training/inference interface}
Training precomputes a sequence codebook. The paper does not fully specify per-position masking of dictionary entries created in the future.
\end{block}
\papersource{Paper, Eq. (2), Sec. 2.4, PDF p. 5; Sec. 3.1, PDF pp. 6--7. Interface observation is reading analysis.}
\end{frame}

\begin{frame}{Reconstruction preserves the token composition}
\[
\mathcal L=\mathcal L_{\rm CLM}
+\lambda\,\mathbb E_{y_{1:M}}
\left[\Delta\bigl(y_{1:M},f_\psi(f_\phi(y_{1:M}))\bigr)\right]
\]
\begin{columns}[c]
\begin{column}{0.47\textwidth}
\begin{itemize}
\item $f_\psi$ reconstructs constituent base tokens.
\item $\Delta$: reconstruction cross-entropy; $\lambda=0.1$.
\item Exact text decompression uses the symbolic codebook.
\end{itemize}
\end{column}
\begin{column}{0.48\textwidth}
\includegraphics[width=\linewidth,height=0.40\textheight,keepaspectratio]{figures/fig-02c-reconstruction.pdf}
\end{column}
\end{columns}
\papersource{Paper, Eq. (3), PDF p. 5; original Fig. 2(c), cropped, PDF p. 4.}
\end{frame}

\begin{frame}{Caching avoids repeated work; the dictionary still grows}
\begin{enumerate}
\item Compress the prompt and initialize its dictionary.
\item Compute vectors for new entries; cache them by composition.
\item Run the Transformer on the compressed sequence.
\item Sample over base and current hyper-vocabulary; update and repeat.
\end{enumerate}
\medskip
\begin{itemize}
\item Embeddings are context-independent; hidden states are context-dependent.
\item Dictionary and embedding cache grow with context length.
\item More output candidates also increase projection and memory costs.
\item Implementation uses caching, Triton kernels, and a Rust tokenizer.
\end{itemize}
\papersource{Paper, Secs. 2.3 and 3.6, PDF pp. 4--5, 9; App. F, PDF pp. 20--21.}
\end{frame}

\begin{frame}{Lossless compression preserves total sequence entropy}
For a bijection $g$ onto its image, define transported distributions:
\[
P_Z(z)=P_X(g^{-1}(z)),\qquad
p_\gamma(z)=p_\theta(g^{-1}(z)).
\]
Then, by changing the summation variable,
\[
H(P_Z)=H(P_X),\qquad
H(P_Z,p_\gamma)=H(P_X,p_\theta).
\]
\begin{block}{Interpretation}
An equivalent model distribution exists in compressed space. The trained finite model must still learn to approximate it.
\end{block}
This concerns total sequence entropy; normalization per token changes.
\papersource{Paper, Sec. 2.6, PDF p. 6; proof in App. G, PDF pp. 20--21.}
\end{frame}

\begin{frame}{Separate adaptation from compression with three variants}
\begin{center}
\begin{tabular}{lll}
\toprule
Variant & Representation & Updated components\\
\midrule
Base & Original tokens & None\\
Cont. pretrain & Original tokens & LoRA\\
zip2zip & Compressed tokens & LoRA + hyper-modules\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Reported model families: Phi-3.5-4B and Phi-3-14B (table labels).
\item Main setting: $M=3$, two-layer hyper-encoder, $\lambda=0.1$.
\item Data mix: code 25\%; math, chat, web 20\% each; multilingual 15\%.
\item Training cost/configuration reports conflict across sections; details in backup.
\end{itemize}
\papersource{Paper, Sec. 3.1, PDF pp. 6--7; Apps. I--J, PDF pp. 22--24.}
\end{frame}

\begin{frame}{Structured domains show the largest tokenizer gains}
\begin{center}
\begin{tabular}{llrrr}
\toprule
Tokenizer & Domain & Base $\eta$ & +zip2zip $\eta$ & Fewer tokens\\
\midrule
Llama-3 & Code & 4.1 & 6.3 & 34.9\%\\
Llama-3 & Math & 2.7 & 4.0 & 32.5\%\\
Llama-3 & Chat & 5.1 & 6.4 & 20.3\%\\
Llama-3 & Multilingual & 3.8 & 4.7 & 19.1\%\\
Llama-3 & Web & 4.6 & 5.4 & 14.8\%\\
Gemma-3 & Code & 3.3 & 5.6 & 41.1\%\\
\bottomrule
\end{tabular}
\end{center}
\[
\eta=\frac{\text{UTF-8 bytes}}{\text{tokens}}\;\uparrow,
\qquad \text{token reduction}=1-\frac{\eta_{\rm base}}{\eta_{\rm z2z}}
\]
These are tokenizer tests, including vocabularies up to 256K.
\papersource{Paper, Table 2, PDF p. 8; Table 9, PDF p. 19. Reductions here computed from rounded Table 2 values.}
\end{frame}

\begin{frame}{Byte-level perplexity rises on every reported corpus}
\begin{center}
\begin{tabular}{llrrrr}
\toprule
Model & Method & Wiki & Pile & mC4 & dC4\\
\midrule
4B & Cont. pretrain & 1.59 & 1.81 & 1.88 & 1.74\\
 & zip2zip & 1.69 & 1.95 & 2.00 & 1.82\\
\midrule
14B & Cont. pretrain & 1.47 & 1.79 & 1.86 & 1.68\\
 & zip2zip & 1.56 & 1.90 & 1.96 & 1.75\\
\bottomrule
\end{tabular}
\end{center}
\[
\mathrm{BytePPL}=\exp\!\left[-\frac{\log Q(x)}{B}\right]
=\mathrm{PPL}^{1/\eta}\qquad\downarrow
\]
$B$: UTF-8 byte count; $Q(x)$: autoregressive sequence likelihood.\\
1024 model-token contexts imply different amounts of original text.
\papersource{Paper, Sec. 3.4 and Table 3, PDF p. 8.}
\end{frame}

\begin{frame}{GSM8K reveals a major quality cost}
\begin{columns}[T]
\begin{column}{0.48\textwidth}
\begin{center}
\begin{tabular}{lrr}
\toprule
GSM8K accuracy $\uparrow$ & 4B & 14B\\
\midrule
Base & .82 & .84\\
Cont. pretrain & .40 & .52\\
zip2zip & .15 & .25\\
\bottomrule
\end{tabular}
\end{center}
\begin{block}{Extra drop vs. matched adaptation}
4B: 25 percentage points.\\
14B: 27 percentage points.
\end{block}
\end{column}
\begin{column}{0.48\textwidth}
\begin{itemize}
\item Other two-shot benchmarks remain much closer to continued pretraining.
\item 4B PIQA: .82 vs. .82; WinoGrande: .75 vs. .75.
\item 14B HellaSwag: .68 vs. .66; PIQA: .85 vs. .87.
\item Token-boundary sensitivity is an author hypothesis for the math failure.
\end{itemize}
\end{column}
\end{columns}
\papersource{Paper, Sec. 3.5, Table 3, PDF p. 8. Bootstrap standard deviations reported as approximately .02.}
\end{frame}

\begin{frame}{Translation quality also depends on the language pair}
\begin{center}
\begin{tabular}{llrrrr}
\toprule
Model & Method & Fr BLEU & De BLEU & Ro BLEU & Ro TER\\
\midrule
4B & Cont. pretrain & 36.5 & 42.3 & 16.7 & 79.7\\
 & zip2zip & 34.1 & 39.7 & 14.3 & 93.5\\
14B & Cont. pretrain & 38.9 & 48.4 & 21.8 & 68.3\\
 & zip2zip & 36.4 & 44.8 & 19.5 & 72.9\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item WMT14 En--Fr; WMT16 En--De and En--Ro; average over both directions.
\item BLEU $\uparrow$ measures overlap; TER $\downarrow$ measures editing needed.
\item 4B En--Ro TER worsens by 13.8 points: degradation is not uniformly small.
\end{itemize}
\papersource{Paper, Table 4, PDF p. 9; Table 11 bootstrap TER: $79.7\pm2.3$ vs. $93.5\pm2.5$, PDF p. 22.}
\end{frame}

\begin{frame}{H100 throughput improves; M1 prefill can become slower}
\begin{center}
\begin{tabular}{llrr}
\toprule
Hardware / model & Input + output & Prefill: Base$\to$z2z & Decode: Base$\to$z2z\\
\midrule
H100 / 4B & 512+256 & 1347.2$\to$2722.1 & 54.4$\to$79.8\\
H100 / 14B & 1024+256 & 2328.6$\to$3657.0 & 45.1$\to$66.8\\
M1 / 4B & 256+256 & 165.0$\to$145.5 & 7.3$\to$7.9\\
M1 / 4B & 1024+256 & 200.9$\to$189.6 & 7.1$\to$7.4\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Values are reported tokens/s, split by inference phase.
\item Baselines: HuggingFace Transformers on H100; MLX on M1.
\item Token accounting for hypertokens versus expanded base tokens is not fully detailed in Table 5.
\end{itemize}
\papersource{Paper, Sec. 3.6, Table 5, PDF p. 9. Absolute values retained; some printed relative percentages differ.}
\end{frame}

\begin{frame}{Three efficiency metrics need different denominators}
\begin{columns}[T]
\begin{column}{0.48\textwidth}
\begin{block}{Same text, different token counts}
\[
\rho=\frac{N_{\rm comp}}{N_{\rm orig}}
=\frac{\eta_0}{\eta_1}
\]
A 50\% gain in bytes/token means\\
$1-1/1.5=33.3\%$ fewer tokens.
\end{block}
\end{column}
\begin{column}{0.48\textwidth}
\begin{block}{Same work, different processing times}
\[
\frac{T_1}{T_0}=\frac{R_0}{R_1}
\]
45.1$\to$66.8 tokens/s means\\
48.1\% more throughput, but\\
32.5\% less time for equal work.
\end{block}
\end{column}
\end{columns}
\medskip
Equal original-text workload and complete pipeline timing are needed to turn phase throughput into an end-to-end latency claim.
\papersource{Teaching calculations using the metric definitions and Table 5; PDF pp. 7--9. $R$: throughput; $T$: time.}
\end{frame}

\begin{frame}{Merge size 3 is a useful compromise}
\begin{center}
\begin{tabular}{crrr}
\toprule
Maximum merge size $M$ & Wiki Byte-PPL $\downarrow$ & Pile $\downarrow$ & Retained tokens $\rho$ $\downarrow$\\
\midrule
1 & 1.62 & 1.70 & 100.00\%\\
2 & 1.96 & 2.21 & 75.30\%\\
3 & 1.72 & 1.84 & 71.21\%\\
4 & 1.71 & 1.84 & 68.93\%\\
5 & 1.72 & 1.84 & 68.41\%\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item $M=2$ has the worst quality among compressed settings.
\item Moving from $M=3$ to 5 saves only another 2.8\% of original tokens.
\item PPL: 1024-token contexts; compression: 2048-token contexts.
\end{itemize}
\papersource{Paper, App. B, Table 6, PDF p. 17; training-loss trends in Fig. 5, PDF p. 18. Separate ablation run.}
\end{frame}

\begin{frame}{Learned composition matters more than encoder depth}
\begin{center}
\begin{tabular}{lrrrr}
\toprule
Hyper-encoder & Wiki & Pile & mC4 & dC4\\
\midrule
Averaging & 1.81 & 1.97 & 2.29 & 2.08\\
One attention layer & 1.73 & 1.86 & 2.16 & 2.01\\
One Transformer layer & 1.71 & 1.83 & 2.13 & 1.99\\
Two Transformer layers & 1.72 & 1.84 & 2.15 & 2.00\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item All values: byte-level perplexity $\downarrow$, 1024-token contexts.
\item Trainable composition improves substantially over averaging.
\item The one-layer Transformer is slightly better on all four columns; the table does not show a two-layer advantage.
\end{itemize}
\papersource{Paper, App. C, Table 7, PDF p. 18; training-loss curves in Fig. 6, PDF p. 19.}
\end{frame}

\begin{frame}{A complete interface for dynamic token prediction}
\begin{enumerate}
\item \textbf{Build}: online dictionary compression creates context-specific units.
\item \textbf{Represent}: shared hyper-encoders produce vectors for unseen compositions.
\item \textbf{Predict}: compressed CLM and a joint output head generate those units directly.
\end{enumerate}
\medskip
\begin{block}{Practical judgment}
Compression is substantial, especially for structured text. Quality loss on numerical reasoning and some translation settings is a central cost.
\end{block}
Only about 25\% of hypertokens are reused during generation. Selective retention and codebook prefilling are proposed directions, not evaluated solutions.
\papersource{Paper, Secs. 5--6, PDF p. 10; quantitative evidence in Tables 2--5 and 9.}
\end{frame}

\begin{frame}{References and discussion materials}
\begin{itemize}
\item Geng et al. \emph{zip2zip: Inference-Time Adaptive Tokenization via Online Compression}. \href{https://arxiv.org/abs/2506.01084v2}{arXiv:2506.01084v2}, 24 October 2025.
\item \href{https://papers.nips.cc/paper_files/paper/2025/hash/def682d57535b9e778508b4b1a911034-Abstract-Conference.html}{NeurIPS 2025 official proceedings}, volume 38, main conference. DOI: 10.52202/085713-5077.
\item \href{https://github.com/epfl-dlab/zip2zip}{epfl-dlab/zip2zip}: official model and tokenizer implementation.
\item \href{https://github.com/epfl-dlab/zip2zip-compression}{epfl-dlab/zip2zip-compression}: official compression component.
\end{itemize}
\medskip
This deck discusses the arXiv v2 paper. External publication and code status were checked on 12 November 2026.
\papersource{Companion Chinese notes: reading-notes.zh.md. Original figures are distributed with this deck.}
\end{frame}

\appendix
\begin{frame}{Backup: multilingual drift has two sources}
\begin{center}
\begin{tabular}{llrrr}
\toprule
Task & Language & Base & Cont. pretrain & zip2zip\\
\midrule
HellaSwag & Spanish & .66 & .57 & .55\\
HellaSwag & Arabic & .44 & .27 & .27\\
Winograd & Chinese & .74 & .61 & .64\\
TruthfulQA-2 & Chinese & .41 & .46 & .43\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Phi-3.5-4B; accuracy $\uparrow$; selected rows from five-language evaluation.
\item zip2zip is usually close to continued pretraining on these tasks.
\item This does not imply complete preservation of the original model's multilingual performance.
\end{itemize}
\papersource{Paper, App. H.2, Table 12, PDF p. 22. Missing task-language combinations in the original are NA.}
\end{frame}

\begin{frame}{Backup: training budgets conflict across sections}
\begin{center}
\begin{tabular}{lll}
\toprule
Item & Main text / one report & Appendix / other report\\
\midrule
4B / 14B GPU-hours & About 10 / up to 40 & 14.0 / 63.0 (Table 13)\\
Tokens & 0.1B training tokens & 1B compressed-token dataset\\
LoRA rank / alpha & 32 / 32 (I.1) & 16 / 16 (I.2)\\
Hardware & 4$\times$A100 (I.4) & H100 (I.5, Table 13)\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item I.1 also lists $32768$ tokens/step and $10000$ steps: about 0.328B processed tokens if used together.
\item Dataset size and consumed tokens can differ; experiments are not explicitly reconciled.
\item Treat the abstract's 10 GPU-hours as a headline claim, not every model's measured cost.
\end{itemize}
\papersource{Paper, Sec. 3.1, PDF p. 7; Apps. I--J and Table 13, PDF pp. 22--24.}
\end{frame}

\begin{frame}{Backup: hypertoken fraction and token savings differ}
\begin{center}
\begin{tabular}{lrrr}
\toprule
Example & Code & Biomedical & French\\
\midrule
Original tokens & 344 & 322 & 399\\
Compressed tokens & 265 & 270 & 367\\
Hypertoken count & 44 & 35 & 26\\
Hypertoken fraction & 16.6\% & 13.0\% & 7.1\%\\
Token reduction & 23.0\% & 16.1\% & 8.0\%\\
\bottomrule
\end{tabular}
\end{center}
\begin{itemize}
\item Fraction: hypertoken count / compressed sequence length.
\item Reduction: 1 $-$ compressed length / original length.
\item Sec. 3.2's larger example ratios are not reconciled with Table 8.
\end{itemize}
\papersource{Paper, Table 8, PDF p. 19; reductions computed from its counts. Sec. 3.2 and Fig. 4, PDF p. 7.}
\end{frame}

\begin{frame}{Backup: compression must offset module overhead}
\[
\frac{\Gamma_{\rm z2z}}{\Gamma}\approx\rho(1+\alpha),
\qquad \alpha\approx\frac{lM}{L}
\]
\begin{itemize}
\item $\rho$: retained token fraction; $l$: hyper-encoder layers; $L$: backbone layers; $M$: maximum merge size.
\item Teaching example: $\rho=.7$, $\alpha=.1$ gives $.77$ of baseline FLOPs.
\item Appendix E prints $12d_{\rm model}\ll n$ while neglecting quadratic attention cost; the stated condition needs clarification.
\item A trainable-parameter count alone also misses frozen-backbone forward work under LoRA.
\end{itemize}
\medskip
\alert{Measure pipeline time to resolve the competing costs.}
\papersource{Paper, App. E, PDF pp. 19--20; caveat on the printed approximation is reading analysis.}
\end{frame}

\begin{frame}{Backup: reindexing proves entropy invariance}
\[
\begin{aligned}
H(P_Z,p_\gamma)
&=-\sum_{z\in g(\mathcal X^*)}P_X(g^{-1}(z))\log p_\theta(g^{-1}(z))\\
&=-\sum_{x\in\mathcal X^*}P_X(x)\log p_\theta(x)
=H(P_X,p_\theta).
\end{aligned}
\]
\begin{itemize}
\item Bijection onto the image is the key condition for reindexing the sum.
\item The statement preserves sequence likelihood and total cross-entropy.
\item It does not establish that the chosen finite Transformer/LoRA family realizes every transported model.
\item Auxiliary reconstruction and symbolic decompression have different roles.
\end{itemize}
\papersource{Paper, Sec. 2.6 and App. G, PDF pp. 6, 20--21; model-family interpretation is reading analysis.}
\end{frame}

\end{document}