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\title[VarRate]{VarRate}
\subtitle{Training-Free Variable-Rate KV Cache Compression\\for Long-Context LLMs}
\author{Paper authors: Shahrzad Esmat, Dhawal Shah, Ali Jannesari\\Iowa State University}
\date{arXiv:2607.15498v1 --- July 16, 2026\\Reading presentation --- September 24, 2026}

\begin{document}

\begin{frame}
\titlepage
\vspace{-3mm}
\begin{center}\alert{Spend more rank on salient tokens; retain a representation of every token.}\end{center}
\papersource{Independent paper discussion, not an author presentation. Main talk: 22 frames; 8 backup frames.}
\end{frame}

\begin{frame}{What happens when an importance score is wrong?}
\centering
\includegraphics[width=\linewidth,height=0.61\textheight,keepaspectratio]{figures/fig-01-concept.pdf}
\begin{block}{The question}
Can a cheap attention score guide \emph{fidelity} while preserving future access to every token?
\end{block}
\papersource{Paper, Secs. 1--2; Fig. 1, PDF p. 2. Original schematic; bar heights are not experimental data.}
\end{frame}

\begin{frame}{One layer: represent, allocate, then reconstruct}
\centering
\includegraphics[width=\linewidth,height=0.67\textheight,keepaspectratio]{figures/fig-02-pipeline.pdf}
\medskip
\alert{The flat ablation shares the representation and basis. Only rank allocation changes.}
\papersource{Paper, Sec. 3, Fig. 2, PDF p. 4; Algorithm 1, p. 5. Original method schematic.}
\end{frame}

\begin{frame}{Encode residuals in a joint pre-RoPE space}
\[
 z_t=[\tilde{k}_t;v_t]\in\mathbb R^D,\qquad D=2Gd_h
\]
\begin{itemize}
\item Undo RoPE on keys; concatenate all $G$ KV heads and values.
\item Keep strided anchors and the last $w$ tokens exactly.
\item For every other token, subtract its nearest-anchor mean:
\end{itemize}
\[
 \bar z_t=\frac1c\sum_{a\in\mathcal N_c(t)}z_a,\qquad e_t=z_t-\bar z_t.
\]
\alert{Nearest means Euclidean distance in the joint KV space, not token position.}
\papersource{Paper, Sec. 3.1, Eqs. (1)--(2), PDF p. 3. $d_h$: head width; $c$: number of anchors.}
\end{frame}

\begin{frame}{Training-free still requires a calibrated basis}
\begin{columns}[T]
\column{0.53\textwidth}
\begin{block}{Once per model}
Gather residuals on six unlabeled LongBench contexts. Use the top-$R$ right singular vectors per layer.
\end{block}
\[
V=[\mathbf v_1;\ldots;\mathbf v_R]\in\mathbb R^{R\times D}
\]
\column{0.43\textwidth}
\begin{itemize}
\item No gradients or fine-tuning.
\item Default $R=1024$.
\item Llama basis: about 134 MB in half precision, all layers.
\item Shared basis excluded from the per-sequence cache budget.
\end{itemize}
\end{columns}
\medskip
\alert{Deployment memory must still include the model-side basis.}
\papersource{Paper, Secs. 3.1 and 4.1, PDF pp. 3, 5; calibration cross-check: App. A.8, Table 10, p. 13.}
\end{frame}

\begin{frame}{The signal is cheap, but still query-dependent}
\[
s_t=\frac{1}{|\mathcal W|H}\sum_{q\in\mathcal W}\sum_{h=1}^{H}\alpha^h_{q,t}
\]
\begin{itemize}
\item Average attention over the last $w_{\rm obs}$ queries and all query heads.
\item Apply a length-5 moving average, then min--max normalization.
\item With the question in the prompt tail, this can identify relevant content.
\item Under document reuse, the question is absent when the cache is compressed.
\end{itemize}
\begin{block}{Design choice}
Use the same imperfect signal to coarsen low-scoring tokens instead of deleting their entire KV entries.
\end{block}
\papersource{Paper, Sec. 3.2, Eq. (4), PDF p. 4. Signal inherited from SnapKV.}
\end{frame}

\begin{frame}{Water-filling redistributes a fixed coefficient budget}
$L$: prompt length; $\kappa$: retained fraction; $\E,\C$: exact/coded sets.
\[
B=D(\kappa L-|\E|),\qquad
r_t=\operatorname{clip}(r_{\min}+\lambda\hat s_t,r_{\min},R)
\]
\[
\sum_{t\in\C}r_t=B,\qquad |\C|r_{\min}\le B\le |\C|R.
\]
\begin{itemize}
\item Start at the floor; assign extra rank in proportion to salience.
\item Cap tokens at $R$ and redistribute the remaining budget.
\end{itemize}
\begin{block}{Teaching example: $B=20$, floor $2$, cap $8$}
Scores $(0,\frac13,\frac23,1)$ give ranks $(2,4,6,8)$ with $\lambda=6$.\\
Uniform allocation would use $(5,5,5,5)$.
\end{block}
\papersource{Paper, Eqs. (3), (5), PDF pp. 3--4. Feasibility inequality and toy example: reader derivation.}
\end{frame}

\begin{frame}{Nested reconstruction gives a local error guarantee}
\[
\mathbf c_t=Ve_t,\qquad
\hat z_t=\bar z_t+\sum_{j\le r_t}c_{t,j}\mathbf v_j
\]
\begin{itemize}
\item Retain only the leading $r_t$ coefficients; split back into K and V.
\item Reapply each token's RoPE to its reconstructed key.
\item Orthogonal directions: extra rank cannot increase the same token's squared reconstruction error.
\end{itemize}
\begin{block}{What this does not establish}
No guarantee of monotone task accuracy or globally optimal attention distortion. Discarded coefficients are still lost.
\end{block}
\papersource{Paper, Sec. 3.3, Eq. (6), PDF p. 4. Guarantee boundary: reader interpretation.}
\end{frame}

\begin{frame}{Keep the evaluation protocols separate}
\begin{itemize}
\item Main: Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct; 16 LongBench tasks, official metrics, greedy decoding.
\item Default: $\kappa=.20$, $r_{\min}=16$, $R=1024$, $\Delta=16$, $c=4$, $w=w_{\rm obs}=64$.
\item Main setup states 200 examples/task; paired comparisons over 16 tasks with 20,000 bootstrap resamples.
\item Reuse: compress without the question; passage / MuSiQue / Qasper. Standard three-task ablations use GovReport instead.
\end{itemize}
\begin{block}{Budget and fairness}
KIVI-2 is near 20\%; KIVI-4 is 31\%. KVzip receives the same 64-token tail pin as VarRate.
\end{block}
\papersource{Paper, Secs. 4.1--4.3, PDF pp. 5--7. AVG-16 averages heterogeneous task scores.}
\end{frame}

\begin{frame}{At 20\%, the strongest result is the flat ablation}
\centering
\begin{tabular}{lrr}
\toprule
Method & Llama AVG-16 & Qwen AVG-16\\
\midrule
Full & 46.01 & 48.79\\
\alert{VarRate} & \alert{45.69} & \alert{48.00}\\
flat & 43.47 & 30.50\\
SnapKV & 45.79 & 46.25\\
PyramidKV & 46.02 & 44.90\\
KIVI-2 & 44.82 & 46.82\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Relative to Full: $-0.32$ / $-0.79$ score points.
\item Relative to flat: $+2.22$ / $+17.50$ at matched storage.
\end{itemize}
\papersource{Selected rows from paper Table 1, PDF p. 6. Higher is better. KIVI-2 uses about 19\%, not exactly 20\%.}
\end{frame}

\begin{frame}{A nominal lead is not always statistically supported}
\centering
\begin{tabular}{lcc}
\toprule
VarRate minus baseline & Llama 95\% CI & Qwen 95\% CI\\
\midrule
flat & $[+0.72,+4.05]$ & $[+10.77,+24.69]$\\
SnapKV & $[-1.18,+0.93]$ & $[+0.49,+3.59]$\\
KIVI-2 & $[-0.73,+2.76]$ & $[-0.30,+3.11]$\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Flat is significantly worse on both models.
\item Selection-family wins are significant mainly on Qwen.
\item Neither model establishes a win over KIVI-2.
\end{itemize}
\alert{An interval crossing zero is a non-significant difference, not proof of equivalence.}
\papersource{Paper, App. A.13, selected rows from Table 15, PDF p. 16; paired bootstrap over 16 tasks.}
\end{frame}

\begin{frame}{Reuse hurts selection more in the tested protocol}
\centering
\begin{tabular}{lrr}
\toprule
Query-agnostic, three-task mean & Llama & Qwen\\
\midrule
Full control & 59.91 & 58.21\\
\alert{VarRate} & \alert{56.21} & \alert{51.79}\\
SnapKV & 45.75 & 41.35\\
Ada-KV & 47.48 & 40.28\\
KVzip, identical tail pin & 55.34 & 56.42\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item From query-aware to reuse: VarRate loses 3.53 / 5.50 points.
\item SnapKV loses 12.96 / 14.66; Full barely changes.
\item KVzip is stronger on Qwen reuse.
\end{itemize}
\papersource{Paper, Sec. 4.3; Table 2, PDF p. 7. Tasks: passage / MuSiQue / Qasper. Scenario drops are not gaps to Full.}
\end{frame}

\begin{frame}{The powered KVzip comparison favors a careful claim}
\centering
\begin{tabular}{lrc}
\toprule
VarRate $-$ KVzip & Delta & 95\% CI\\
\midrule
Llama, query-aware & $-0.55$ & $[-2.00,+0.91]$\\
Llama, query-agnostic & $+0.95$ & $[-1.48,+3.42]$\\
Qwen, query-aware & $-0.04$ & $[-1.67,+1.62]$\\
Qwen, query-agnostic & $-5.06$ & $[-7.57,-2.58]$\\
Pooled, all four cells & $-1.18$ & $[-2.20,-0.16]$\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item About 600 paired examples/cell, 2,400 pooled.
\item No significant difference in three cells; KVzip leads in the fourth and in the pooled comparison.
\end{itemize}
\papersource{Paper, App. A.16, Table 18, PDF p. 17. Different aggregation from the main-text four-cell mean gap of 0.77.}
\end{frame}

\begin{frame}{About $8\times$ lower added cost is not $8\times$ faster}
\begin{columns}[c]
\column{0.53\textwidth}
\includegraphics[width=\linewidth,height=0.65\textheight,keepaspectratio]{figures/fig-04-cost-frontier.pdf}
\column{0.44\textwidth}
\begin{itemize}
\item Added prefill: VarRate $+44.0\%$, KVzip $+372.2\%$.
\item Added-cost ratio: $372.2/44.0\approx8.46$.
\item Including base prefill: $4.722/1.44\approx3.28$.
\end{itemize}
\medskip
\alert{VarRate is about 1.9 points below KVzip on the plotted reuse mean.}
\end{columns}
\papersource{Paper, Fig. 4 and Table 3, PDF p. 7. Cost: Llama, A100, 16K; accuracy: two-model reuse mean. Ratios: reader calculation.}
\end{frame}

\begin{frame}{The current accuracy path reconstructs full K/V}
\begin{block}{Compressed representation versus runtime memory}
The reported 20.2\% cache representation is not a demonstrated 5$\times$ reduction in end-to-end peak GPU memory.
\end{block}
\begin{itemize}
\item Decode: 37.4 tok/s for VarRate versus 37.5 for Full.
\item A fused kernel is still needed to consume compressed states efficiently.
\item End-to-end retrieval: 1.256 s $\to$ 1.781 s ($+41.8\%$).
\item End-to-end GovReport: 13.59 s $\to$ 13.95 s ($+2.6\%$, reported within noise).
\end{itemize}
\papersource{Paper, Sec. 4.4, Table 3, PDF p. 7; App. A.14, Table 16, p. 16. Wall-clock: Llama, A100, n=18.}
\end{frame}

\begin{frame}{Both content scoring and graded allocation matter}
\centering
\begin{tabular}{lrr}
\toprule
Llama, 20\% budget & Passage & GovReport\\
\midrule
flat & 87.5 & 30.1\\
Random score + water-filling & 93.0 & 29.6\\
Salience + binary split & 99.5 & 29.0\\
\alert{Salience + water-filling} & \alert{99.5} & \alert{30.4}\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Real salience adds retrieval quality beyond random allocation.
\item A binary split matches retrieval, but loses distributed summary information.
\item Controls on Qwen also penalize scores assigned to the wrong tokens.
\end{itemize}
\papersource{Paper, Table 4, PDF p. 7; content controls in Table 19, p. 18. Scores higher are better.}
\end{frame}

\begin{frame}{The explicit rank floor is slack in observed runs}
\begin{columns}[c]
\column{0.57\textwidth}
\includegraphics[width=\linewidth,height=0.61\textheight,keepaspectratio]{figures/fig-07-rank-position.pdf}
\column{0.40\textwidth}
\begin{itemize}
\item Removing the floor changes each tested task by less than one point.
\item Logged floor occupancy is reported as 0.0\% for both settings.
\item The tail receives much more rank; content alignment adds value beyond position.
\end{itemize}
\end{columns}
\medskip
\alert{Preserving a representation is the design; the explicit floor is not an established active cause of the gains.}
\papersource{Paper, App. A.19, Table 21, PDF p. 18; Fig. 7, p. 19. Means by position do not prove a per-token minimum.}
\end{frame}

\begin{frame}{Quantization is a strong alternative and a complement}
\centering
\begin{tabular}{lrrrr}
\toprule
Llama, coefficient coding & Passage & MuSiQue & GovReport & Storage\\
\midrule
VarRate fp16 & 99.5 & 32.0 & 30.4 & $\sim20\%$\\
VarRate + 3-bit & 99.5 & 31.3 & 30.4 & $\sim9\%$\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item The exact anchors and metadata limit how far coefficient quantization reduces storage.
\item KIVI-2 is stronger on Llama GovReport: 35.2 versus 30.4.
\item Near-parity to fp16 VarRate does not mean parity to Full or to KIVI.
\end{itemize}
\papersource{Paper, Apps. A.3--A.4, Tables 6--7, PDF pp. 10--11. Three-task evidence; runtime caveat still applies.}
\end{frame}

\begin{frame}{The advantage does not grow indefinitely as budgets shrink}
\centering
\begin{tabular}{lrrr}
\toprule
Qwen passage retrieval, query-aware & Keep 8\% & Keep 10\% & Keep 12\%\\
\midrule
SnapKV & 99.5 & 99.5 & 99.5\\
VarRate & 29.6 & 98.8 & 99.5\\
flat & 27.8 & 37.3 & 46.0\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item At 8\%, VarRate approaches flat's retrieval score on Qwen.
\item Selection can still retain some useful tokens exactly.
\item Wider anchor stride helps tight budgets, but loses on the 20\% full suite.
\end{itemize}
\papersource{Paper, App. A.20, selected results from Table 22, PDF p. 20; stride: Table 14, p. 15.}
\end{frame}

\begin{frame}{Long-context retrieval is promising, with a narrow scope}
\begin{columns}[c]
\column{0.50\textwidth}
\includegraphics[width=\linewidth,height=0.62\textheight,keepaspectratio]{figures/fig-08-long-context.pdf}
\column{0.47\textwidth}
\begin{itemize}
\item Fixed needle set; 75 examples per cell; 20\% budget.
\item At 64K: VarRate 92\%, SnapKV 48\%.
\item Both reach 100\% at 128K; the rebound is unexplained.
\item The 128K full-reconstruction run needs two GPUs.
\end{itemize}
\end{columns}
\papersource{Paper, App. A.21, Fig. 8 and Table 24, PDF pp. 19--20. Llama, query-agnostic NIAH, not a broad 128K benchmark.}
\end{frame}

\begin{frame}{The evidence supports allocation, with deployment work left}
\begin{itemize}
\item \textbf{Strongest evidence:} adaptive versus uniform rank under a shared codec and budget.
\item \textbf{Workload boundary:} reuse benefits differ from known-query, very-low-budget behavior.
\item \textbf{System boundary:} offline basis, quadratic anchor search, and full K/V reconstruction remain costs.
\item \textbf{Comparison boundary:} no universal win over quantization or KVzip; no direct trained-codec comparison.
\end{itemize}
\begin{block}{Reader's next experiment}
Measure a fused variable-rank implementation on real multi-query reuse: peak memory, time to first token, throughput, and quality together.
\end{block}
\papersource{Synthesis of Secs. 3--4; Apps. A.5, A.19--A.21. Proposed experiment is reader analysis, not a reported result.}
\end{frame}

\begin{frame}{Three takeaways for the discussion}
\begin{enumerate}
\item A cheap score can control how much information survives, not only which token survives.
\item The cleanest win is over uniform allocation; competing methods remain strong in their own regimes.
\item Storage quality, actual memory savings, and latency must be evaluated separately.
\end{enumerate}
\medskip
\textbf{Primary source}\par
Esmat, Shah, and Jannesari. \emph{VarRate: Training-Free Variable-Rate KV Cache Compression for Long-Context LLMs}.\\
\href{https://arxiv.org/abs/2607.15498v1}{arXiv:2607.15498v1}, July 16, 2026.
\papersource{Read: author TeX, original figures, final 20-page PDF, Secs. 1--5 and Apps. A.1--A.21. Experiments not independently rerun.}
\end{frame}

\appendix
\begin{frame}{Backup: three cross-checks support a limited generalization}
\begin{block}{Language modeling: WikiText-2}
VarRate PPL 6.95 versus flat 7.26 at identical realized storage. Lower is better; detailed setup is incompletely specified.
\end{block}
\begin{block}{Third family: Mistral-7B}
At a 15\% budget, passage retrieval is 73.6 for VarRate, 29.1 for flat, and 75.6 for Full. This is a three-task cross-check.
\end{block}
\begin{block}{Calibration choice}
Three independently built bases vary by at most 1.8 points on the tested Llama tasks. This is not an arbitrary-domain guarantee.
\end{block}
\papersource{Paper, App. A.1, PDF p. 10; Apps. A.7--A.8, Tables 9--10, p. 13.}
\end{frame}

\begin{frame}{Backup: the Palu gap also includes representation design}
\centering
\includegraphics[width=\linewidth,height=0.61\textheight,keepaspectratio]{figures/fig-03-palu-sweep.pdf}
\begin{itemize}
\item Flat already beats Palu: residual/anchor coding contributes to the gap.
\item Palu footprint 20.41\% versus VarRate 20.22\% at the tightest point.
\item The reported Palu kernel does not support these GQA shapes.
\end{itemize}
\papersource{Paper, Fig. 3, PDF p. 6; App. A.6, Table 8 and implementation discussion, pp. 11--12.}
\end{frame}

\begin{frame}{Backup: summary gains survive a small budget sweep}
\centering
\begin{tabular}{lrrr}
\toprule
Llama GovReport & Keep 15\% & Keep 20\% & Keep 25\%\\
\midrule
Best selection score in Table 5 & 27.8 & 28.8 & 29.5\\
VarRate & 28.6 & 30.4 & 32.2\\
Difference & $+0.8$ & $+1.6$ & $+2.7$\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Selection set: SnapKV, PyramidKV, Ada-KV.
\item Reported significance at 20\% and 25\%; retrieval and multi-hop QA are not significantly separated.
\item This is a specific summarization task, not a win over quantization.
\end{itemize}
\papersource{Paper, App. A.2, Table 5, PDF p. 10. Best-selection rows and differences computed from the table.}
\end{frame}

\begin{frame}{Backup: anchor stride changes the exactness--rank tradeoff}
\centering
\begin{tabular}{lrr}
\toprule
Llama protocol & Stride 16 & Stride 64\\
\midrule
10\%, query-agnostic, 3 tasks & 29.92 & 48.88\\
20\%, query-agnostic, 3 tasks & 56.21 & 57.34\\
20\%, AVG-16 & 45.69 & 44.98\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Fewer exact anchors free more coefficients for coded tokens.
\item Full-suite losses concentrate in few-shot and code tasks.
\item Default remains 16; the wider setting is an ablation.
\end{itemize}
\papersource{Paper, App. A.12, Table 14, PDF p. 15. App. A.12's 256-example rerun wording differs from the main n=200 setup.}
\end{frame}

\begin{frame}{Backup: implementation dominates much of the measured tax}
\begin{columns}[T]
\column{0.48\textwidth}
\textbf{Share of compression time}
\begin{itemize}
\item Anchor search: 32.5\%.
\item PCA projection: 21.8\%.
\item Reconstruction: 19.9\%.
\item Water-filling: 6.4\%.
\end{itemize}
\column{0.48\textwidth}
\textbf{Separate optimized run}
\begin{itemize}
\item Reference overhead: $+41.7\%$.
\item GPU-cached basis: $+40.3\%$.
\item Additional bf16 compute: $+25.1\%$; max score change 0.07.
\end{itemize}
\end{columns}
\medskip
\begin{block}{Reimplementation detail}
Keep anchor distances numerically stable; the tested bf16 distance shortcut failed. Preserve salience precision when comparing allocations.
\end{block}
\papersource{Paper, App. A.11, Tables 12--13, PDF p. 15. FLOPs share is not a measured latency lower bound.}
\end{frame}

\begin{frame}{Backup: content alignment survives a stronger control}
\centering
\begin{tabular}{lrrr}
\toprule
Qwen, 20\% budget & Passage & GovReport & MuSiQue\\
\midrule
flat & 75.0 & 29.6 & 8.5\\
Mass + water-filling & 99.5 & 31.3 & 28.7\\
Shuffled mass & 64.7 & 27.4 & 7.5\\
Position-only & 89.0 & 26.5 & 7.7\\
Fisher + water-filling & 100.0 & 30.8 & 27.9\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Shuffling preserves the score multiset but destroys token alignment.
\item Position alone does not recover multi-hop QA; it does exceed flat on retrieval.
\item The second-order Fisher heuristic is reported statistically tied with mass.
\end{itemize}
\papersource{Paper, Apps. A.17--A.18, Tables 19--20, PDF p. 18. Later controls use a separately calibrated basis.}
\end{frame}

\begin{frame}{Backup: RULER broadens tasks, not the tested length range}
\centering
\begin{tabular}{lr}
\toprule
Llama, RULER at 16K & Score\\
\midrule
Full & 90.0\\
SnapKV, 20\% & 81.7\\
VarRate, 20\% & 82.5\\
\bottomrule
\end{tabular}
\medskip
\begin{itemize}
\item Only 40 examples; VarRate--SnapKV difference is within noise.
\item Both compressors lose about eight points to Full.
\item No RULER results beyond 16K are reported here.
\item The paper's 128K evidence comes from controlled NIAH retrieval.
\end{itemize}
\papersource{Paper, App. A.15, Table 17, PDF p. 16. Uncertainty widths omitted here because their precise type is not clearly defined.}
\end{frame}

\begin{frame}{Backup: details that matter when reusing this v1}
\begin{itemize}
\item KVzip: task-averaged and example-pooled gaps differ; pooled analysis favors KVzip by 1.18 points.
\item Fig. 6 labels Qwen flat retrieval as 87.5; Table 19 gives 75.0. This deck uses the table.
\item Table 19's broad caption overstates the negative controls: position-only beats flat on Qwen retrieval.
\item The paper discloses a fixed cross-model table-aggregation bug. Raw result files were not independently audited for this reading.
\end{itemize}
\medskip
\alert{Read quantitative tables, statistical units, and implementation limits together.}
\papersource{Paper, App. A.9, PDF p. 12; Fig. 6 and Tables 18--19, pp. 17--18. Source: arXiv:2607.15498v1 only.}
\end{frame}

\end{document}