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\title[DepthWeave-KV]{DepthWeave-KV}
\subtitle{Token-Adaptive Cross-Layer Residual Factorization\\for Long-Context KV Cache Compression}
\author{Independent paper-reading presentation}
\date{arXiv:2607.06523v1 --- 20 September 2026}
\begin{document}
\begin{frame}\titlepage
\papersource{Paper authors: Anna C\'ordoba, Adam Puente Tercero, Nerea Angulo Hijo, Mar Linares Tercero,\\Julia Barrientos, Ainhoa Miranda, Jes\'us Olivera. Submitted 7 July 2026.}
\end{frame}
\begin{frame}{Share common structure; preserve important deviations}
\begin{block}{Core proposal}
Shared low-rank KV bases across neighboring layers, plus token-specific residual capacity controlled by attention-output error.
\end{block}
\begin{itemize}
\item Reported: $8.3\times$ KV reduction; average score 62.9 vs. 63.8 for full KV.
\item Reported decode throughput: 72.8 vs. 42.1 token/s.
\item Evidence boundary: model and hardware are unspecified; results are not independently reproduced.
\end{itemize}
\papersource{Paper, Secs. 3--4, pp. 3--5; Table 1. All results are author-reported.}
\end{frame}
\begin{frame}{Uniform compression can lose late-useful evidence}
\begin{itemize}
\item Long contexts make repeated KV reads and cache residency expensive.
\item An entity or instruction boundary may matter much later in generation.
\item Neighboring layers can share structure while retaining different details.
\item Design goal: spend fidelity across both depth and tokens.
\end{itemize}
\papersource{Paper, Sec. 1, pp. 1--2. Motivation, not a measured layer-redundancy result.}
\end{frame}
\begin{frame}{The proposal combines three compression decisions}
\centering
\begin{tabular}{lll}\toprule
Decision & Representative comparison & Proposed choice\\\midrule
Which tokens? & Eviction / retention & Keep compressed tokens\\
Which representation? & Layer sharing / low rank & Shared bases + residuals\\
How much fidelity? & Fixed allocation & Token routing + feedback\\\bottomrule
\end{tabular}
\vspace{5mm}
\begin{block}{Closest conceptual comparison}
MiniCache and KVSharer exploit depth redundancy. Here, layers share a subspace while retaining token-local coefficients and corrections.
\end{block}
\papersource{Paper, Sec. 2, pp. 2--3. Comparison roles as described by this paper.}
\end{frame}
\begin{frame}{Overview: residual capacity follows token importance}
\centering
\includegraphics[width=0.97\linewidth,height=0.67\textheight,keepaspectratio]{figures/overview.png}

\papersource{Paper, Fig. 1, p. 2; original source image. Conceptual diagram, not experimental evidence.}
\end{frame}
\begin{frame}{Factorization separates shared and local information}
\[
\widehat X^Z_{\ell,h,t}=A^Z_{\ell,h,t}B^Z_{m,h}+g^Z_{\ell,h,t}R^Z_{\ell,h,t},\quad Z\in\{K,V\}.
\]
\begin{itemize}
\item $B\in\mathbb R^{r_b\times d}$: shared across tokens and layers in window $\mathcal W_m$.
\item $A\in\mathbb R^{1\times r_b}$: coefficients specific to layer, head and token.
\item $R\in\mathbb R^{1\times d}$: residual reconstruction; $g\in[0,1]$: gate.
\item $\ell,h,t$: layer, head, token; $d$: head dimension; $r_b$: basis rank.
\end{itemize}
\papersource{Paper, Eq. (1), p. 3. K and V are handled separately.}
\end{frame}
\begin{frame}{Quantization reduces storage, but updates need detail}
\begin{itemize}
\item Initialize per-window, per-head bases with a randomized sketch after prefill.
\item Update bases with an exponential moving average during generation.
\item Store coefficients in 8-bit blocks; residuals in 4-bit groups.
\item Not specified: basis rank, window size, overlap resolution, quantization groups.
\item Open implementation question: how do old coefficients stay valid after basis changes?
\end{itemize}
\papersource{Paper, Sec. 3, p. 3. Last two points: missing details identified in this reading.}
\end{frame}
\begin{frame}{Routing uses salience and recent output error}
\[
\rho_{m,h,t}=\rho_{\min}+(\rho_{\max}-\rho_{\min})
\mathbf 1[\sigma(u^\top\phi_{m,h,t})>\tau_m].
\]
\begin{itemize}
\item $\phi$: accumulated attention, maximum spike, boundary indicators, probe error.
\item $u$: learned router weights; $\tau_m$: adaptive memory-budget threshold.
\item Lower $\tau_m$ promotes more tokens to higher residual capacity.
\item Equation: two levels. Prose: ``three levels, but lists 0, 2, 4 and 8.
\end{itemize}
\papersource{Paper, Eq. (2) and Sec. 3, p. 3. The multi-level mapping is not fully defined.}
\end{frame}
\begin{frame}{Output probes target behavior after aggregation}
\[
e_{\ell,h}=\frac{\|O_{\ell,h}-\widehat O_{\ell,h}\|_2}{\|O_{\ell,h}\|_2+\epsilon},
\]
\[
O=\operatorname{Attn}(Q,K,V),\qquad
\widehat O=\operatorname{Attn}(Q,\widehat K,\widehat V).
\]
\begin{itemize}
\item Every $p$ decode steps, sample heads and recent queries.
\item High error: lower the threshold; persistently low error: raise it.
\item This is a relative, dimensionless output error, not a task-correctness guarantee.
\end{itemize}
\papersource{Paper, Eq. (3), p. 4. O notation introduced here only to shorten the original equation.}
\end{frame}
\begin{frame}{Feedback needs a recoverable high-fidelity reference}
\begin{itemize}
\item The paper temporarily materializes a higher-fidelity reference cache.
\item It does not explain how previously discarded information is recovered.
\item Promoting an old token needs residual information, not just a larger rank label.
\item Probe interval, tolerances, peak memory and token-level error attribution are unspecified.
\end{itemize}
\papersource{Paper, Sec. 3, pp. 3--4; implementation questions from this reading.}
\end{frame}
\begin{frame}{Frozen LLM weights do not make the method training-free}
\begin{block}{Offline}
Residual gates and router parameters are trained once on unlabeled long-context text with a frozen teacher-cache objective.
\end{block}
\begin{block}{Deployment}
No task-specific calibration; online basis and threshold adaptation. Base-model weights remain unchanged.
\end{block}
Training data, loss details, optimization and transfer across models are not reported.
\papersource{Paper, Sec. 3, p. 4. This distinction qualifies the abstract\textquotesingle s calibration-free claim.}
\end{frame}
\begin{frame}{Fusion aims to avoid writing reconstructed KV back}
\centering
\includegraphics[width=0.96\linewidth,height=0.70\textheight,keepaspectratio]{figures/architecture.png}

\papersource{Paper, Fig. 2, p. 4; original image. Basis lookup, residual dequantization and attention are fused.}
\end{frame}
\begin{frame}{Evaluation reports a configuration, not a full frontier}
\begin{itemize}
\item Default: 64K prefill, greedy decoding, 512 generated tokens.
\item LongBench / L-Eval; QA, summarization and Needle retrieval.
\item Compressed baselines target quality with at least $4\times$ KV reduction; actual budgets differ.
\item Model, GPU, batch size, subset weights, sample counts and run variance are missing.
\item Needle protocol says 16K--128K averaging; the main table caption says 64K.
\end{itemize}
\papersource{Paper, Sec. 4, pp. 4--5; Table 1. Preserve the Needle length ambiguity.}
\end{frame}
\begin{frame}{Reported quality remains below full KV}
\centering
\begin{tabular}{lrrr}\toprule
Method & Avg. score (\%) & Needle (\%) & KV reduction\\\midrule
Full KV & 63.8 & 98.7 & $1.0\times$\\
MiniCache & 59.8 & 89.4 & $6.4\times$\\
ChunkKV & 60.7 & 91.2 & $6.0\times$\\
TailorKV & 61.4 & 92.6 & $6.5\times$\\
DepthWeave-KV & 62.9 & 96.1 & $8.3\times$\\\bottomrule
\end{tabular}
\vspace{4mm}
\begin{itemize}
\item Full-KV gaps: $-0.9$ average-score points; $-2.6$ Needle points.
\item TailorKV gains: $+1.5$ and $+3.5$ points, respectively.
\item $8.3\times$ leaves about 12.05\% of the original KV memory, not total VRAM.
\end{itemize}
\papersource{Table 1, p. 5; selected rows re-typeset from same-version TeX because PDF tables overlap.}
\end{frame}
\begin{frame}{Reported speedup depends on unspecified hardware}
\centering
\begin{tabular}{lrrrr}\toprule
Method & token/s $\uparrow$ & TTFT s $\downarrow$ & PPL $\Delta\downarrow$ & Error $\downarrow$\\\midrule
Full KV & 42.1 & 6.84 & 0.00 & 0.000\\
MiniCache & 63.2 & 5.48 & 0.24 & 0.061\\
TailorKV & 65.0 & 5.36 & 0.18 & 0.049\\
DepthWeave-KV & 72.8 & 4.89 & 0.09 & 0.027\\\bottomrule
\end{tabular}
\vspace{4mm}
\begin{itemize}
\item Calculated: +72.9\% throughput vs. full KV; +12.0\% vs. TailorKV.
\item TTFT decreases by 1.95 s vs. full KV; no timing breakdown is given.
\item At the reported precision, 0.09 is exactly half of 0.18.
\end{itemize}
\papersource{Table 1 and Sec. 4, p. 5. Prose says ``less than half; table values do not support that wording.}
\end{frame}
\begin{frame}{Task-family evidence is limited to aggregate gaps}
\begin{block}{Retrieval / extractive group}
Qasper, HotpotQA, MultiFieldQA-en, TriviaQA and Needle: gap to full KV is 1.4 points for DepthWeave-KV, 5.6 for MiniCache, 3.2 for TailorKV.
\end{block}
\begin{block}{Summarization group}
GovReport and QMSum: DepthWeave-KV improves over TailorKV by 0.8 points and ChunkKV by 1.7 points.
\end{block}
No task-level absolute scores or uncertainty estimates are supplied.
\papersource{Paper, Sec. 4, ``Breakdown by task family, p. 5. These are prose aggregates.}
\end{frame}
\begin{frame}{Residuals and routing preserve retrieval in Table 2}
\centering
\begin{tabular}{lrrr}\toprule
Variant & Avg. score & Needle (\%) & KV reduction\\\midrule
Complete & 62.9 & 96.1 & $8.3\times$\\
No cross-depth sharing & 61.5 & 93.2 & $5.9\times$\\
No token router & 61.2 & 92.4 & $7.9\times$\\
No online tracking & 61.7 & 93.5 & $8.5\times$\\
No residual gates & 61.0 & 91.8 & $8.4\times$\\
Shared bases only & 58.9 & 87.6 & $10.2\times$\\\bottomrule
\end{tabular}\par
\vspace{4mm}
Thresholds may be retuned: these are not strictly equal-budget ablations.

\papersource{Table 2, p. 5, re-typeset from TeX. Sec. 5, pp. 5--6. Both score columns: higher is better.}
\end{frame}
\begin{frame}{The fused kernel mainly changes systems performance}
\centering
\begin{tabular}{lrrrr}\toprule
Variant & Needle (\%) & KV $\times$ & token/s & TTFT s\\\midrule
Complete & 96.1 & 8.3 & 72.8 & 4.89\\
No fused CUDA & 95.9 & 8.3 & 61.9 & 5.58\\
No online tracking & 93.5 & 8.5 & 73.4 & 4.84\\
Shared bases only & 87.6 & 10.2 & 76.4 & 4.62\\\bottomrule
\end{tabular}
\vspace{4mm}
\begin{itemize}
\item Removing fusion lowers throughput by 15.0\%; adding it raises throughput by 17.6\% (different denominator).
\item The complete method is not the fastest or smallest ablation.
\item Probe overhead is not isolated when compression also changes.
\end{itemize}
\papersource{Table 2, p. 5; Sec. 5, p. 6. Percentage calculations made for this reading.}
\end{frame}
\begin{frame}{Conflicting ablation reports should remain visible}
\centering
\begin{tabular}{lll}\toprule
Case & Sec. 4 prose & Table 2\\\midrule
No router: score / Needle & 61.1 / 91.8 & 61.2 / 92.4\\
No probes: Needle & 89.9 (``further'') & 93.5\\
Direct layer sharing & $6.9\times$, error .052 & No matching row\\\bottomrule
\end{tabular}
\vspace{5mm}
\begin{itemize}
\item The 89.9 value may describe a cumulative ablation, but this is not explicit.
\item This presentation uses Table 2 for systematic component comparisons.
\item PDF p. 5 tables overlap and extend beyond columns; TeX enables recovery of the entries.
\end{itemize}
\papersource{Paper, Sec. 4 and Table 2, p. 5. Do not merge or average conflicting results.}
\end{frame}
\begin{frame}{Reproduction requires more than the conceptual equations}
\begin{itemize}
\item Define residual decoding, depth-window overlap and historical coefficient updates.
\item Explain high-fidelity probes and recovery of promoted residuals.
\item Release model / hardware / training details and exact cache layouts.
\item Measure matched-budget curves, per-task variance and length-by-depth retrieval.
\item Check all metadata and temporary caches in peak memory accounting.
\end{itemize}
\papersource{Reading analysis based on omissions in Secs. 3--5. These are proposed checks, not completed experiments.}
\end{frame}
\begin{frame}{Source artifacts also warrant independent verification}
\begin{itemize}
\item PDF p. 1 retains an ICML 2024 proceedings footer; arXiv v1 is dated July 2026.
\item The source contains a ``Fixed synthetic byline comment.
\item Unrelated bibliography entries appear alongside cache papers; the source uses \texttt{\textbackslash nocite\{*\}}.
\item These are observable document anomalies, not proof of misconduct.
\item No runnable CUDA implementation appears in the downloaded source bundle.
\end{itemize}
\papersource{Paper p. 1, references pp. 6--9, main.tex and downloaded source manifest. External provenance not established.}
\end{frame}
\begin{frame}{Useful design idea; performance claims need validation}
\begin{enumerate}
\item Share depth-local structure while preserving token-specific deviations.
\item Combine behavior-aware feedback with compression-aware execution.
\item Treat the reported $8.3\times$ / 72.8 token/s as conditional, unreproduced results.
\end{enumerate}
\begin{block}{Authors\textquotesingle\ future directions}
Non-contiguous layer groups, risk-aware routing, batching, prefix reuse and disaggregated serving. Not evaluated in this version.
\end{block}
\papersource{Paper, Secs. 6--7, p. 6; limitations from this reading. Designed for a 20--30 minute discussion.}
\end{frame}
\begin{frame}{Source and reading scope}
\textbf{Anna C\'ordoba et al.}\\
DepthWeave-KV: Token-Adaptive Cross-Layer Residual Factorization for Long-Context KV Cache Compression.\\[3mm]
\url{https://arxiv.org/abs/2607.06523v1}\\[4mm]
Read: complete main.tex + body.tex, PDF pp. 1--9, all three equations, two figures and two tables. No appendix in the retrieved version.\\[3mm]
Tables re-typeset from the same-version TeX; original PNG figures retained. No independent model runs or external-reference audit.

\papersource{Retrieved 20 September 2026. Chinese companion notes contain full baseline and ablation tables.}
\end{frame}
\end{document}