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\title[FusedKV]{FusedKV: Reconstructing KV Caches\\with Cross-Layer Fusion}
\subtitle{Paper discussion: quality, memory, and inference trade-offs}
\author{Reading presentation of work by Hongzhan Lin et al.}
\date{arXiv:2512.03870v3 (19 February 2026)\\Reading: 20 September 2026}
\begin{document}
\begin{frame}\titlepage\end{frame}
\begin{frame}{Half the cache can improve language modeling}
\begin{itemize}
\item Upper layers reconstruct K/V from early and middle layers.
\item At 1.5B: WikiText PPL 13.67 $\rightarrow$ 13.33; mean task accuracy 54.55 $\rightarrow$ 55.82.
\item Cache capacity falls by 50\%; decoding latency does not always improve.
\item Long-context quality remains below the full-cache baseline.
\end{itemize}
\papersource{Tables 1--2, 16; PDF pp.5, 7, 23. About 25 minutes + backup.}
\end{frame}
\begin{frame}{Capacity and bandwidth are different bottlenecks}
\[\text{KV elements}=2LSH_{kv}D\]\begin{itemize}
\item $L$: layers; $S$: sequence length; $H_{kv}$: KV heads; $D$: head dimension.
\item Multiply by batch size and bytes per element for payload memory.
\item GQA shares within layers; CLA and YOCO share across layers.
\item Research question: should keys and values use the same source layer?
\end{itemize}
\papersource{Sec.1--2; Table 1, PDF pp.2--5.}
\end{frame}
\begin{frame}{Learned fusion suggests asymmetric source roles}
\begin{center}\includegraphics[width=.95\linewidth,height=.62\textheight,keepaspectratio]{figures/dense_kv.pdf}\end{center}\small Left: key weights. Right: value weights. Columns: source layers; rows: upper layers. Signed coefficients are not probabilities.
\papersource{Fig.2, PDF p.2. Exploratory 16-layer, 1B model; zero-based plot indices.}
\end{frame}
\begin{frame}{Only the lower half stores independent caches}
\begin{center}\includegraphics[width=.95\linewidth,height=.78\textheight,keepaspectratio]{figures/main1.pdf}\end{center}
\papersource{Fig.3, PDF p.4. Queries and upper-layer computation remain layer-specific.}
\end{frame}
\begin{frame}{FusedKV learns two-source, channel-wise fusion}
\[\begin{aligned}
K^i&=a_{i,1}\odot K^1+a_{i,n}\odot K^n,\\
V^i&=b_{i,1}\odot V^1+b_{i,n}\odot V^n,\qquad i>n=L/2.
\end{aligned}\]\begin{itemize}
\item $K^i,V^i\in\mathbb R^{S\times d}$ in the paper's simplified notation.
\item Learned vectors broadcast over tokens; each target layer has its own weights.
\item Weights need not be positive or sum to one.
\item Train the architecture end to end; no frozen-teacher KV reconstruction loss is specified.
\end{itemize}
\papersource{Sec.2.1--2.3, Eqs.(1), (4)--(5), PDF pp.3--4.}
\end{frame}
\begin{frame}{Lite separates the key source from the value source}
\[K^i=K^n,\qquad V^i=V^1,\qquad i>n.\]\begin{itemize}
\item No two-source fusion: read one key cache and one value cache.
\item For 16 layers, layers 1--8 store caches; layers 9--16 reuse $K^8,V^1$.
\item Shared K/V does not imply identical attention: upper-layer queries still differ.
\item This is an architecture trained for sharing; arbitrary pretrained checkpoint conversion is not established.
\end{itemize}
\papersource{Sec.2.3, Eq.(6), Fig.3, PDF p.4.}
\end{frame}
\begin{frame}{Post-RoPE fusion needs paired key weights}
\[
(R_mq)^T W(R_tk)=q^TR_m^TWR_tk.
\]
\[w_{2j}=w_{2j+1}=c_j\quad\Longrightarrow\quad W=c_jI
\quad\Longrightarrow\quad c_jq^TR_{t-m}k.\]\begin{itemize}
\item Tie both coordinates in each RoPE rotation pair.
\item Unequal weights introduce absolute-position terms involving $m+t$.
\item Linear sums preserve the property if every source meets the constraint.
\item Assume compatible position/frequency conventions across sources.
\end{itemize}
\papersource{Sec.2.4, Eqs.(7)--(8), PDF pp.4--5; A.4, pp.16--17. Matrix form is a teaching derivation.}
\end{frame}
\begin{frame}{Half the storage can require 50\% more cache I/O}
\begin{center}\begin{tabular}{lcc}\toprule
Method & Cache capacity & Cache I/O\\\midrule
Vanilla & 1.0 & 1.0\\
YOCO / Lite & 0.5 & 1.0\\
FusedKV & 0.5 & 1.5\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item All ratios hold KV head count and precision fixed.
\item Fuse on demand; retaining all reconstructed upper caches defeats the capacity saving.
\item Table 1 counts attention computation only, excluding FFNs.
\end{itemize}
\papersource{Table 1, PDF p.5. Ratios derived from the reported element counts.}
\end{frame}
\begin{frame}{Prefill improves while kernel throughput falls}
\begin{center}\includegraphics[width=.95\linewidth,height=.62\textheight,keepaspectratio]{figures/kernel_comparison_TTFT.pdf}\end{center}\small Left: throughput, higher is better. Right: TTFT, lower is better. FusedKV kernel throughput is 28.4\% lower on average; TTFT is about halved at $S\geq8$k.
\papersource{Sec.2.5, Fig.4, PDF pp.5--6; normalized to MHA.}
\end{frame}
\begin{frame}{Decode cost depends on the inference regime}
\begin{center}\includegraphics[width=.95\linewidth,height=.62\textheight,keepaspectratio]{figures/tpot.pdf}\end{center}\small Left: memory-bound TPOT is about $1.5\times$ for FusedKV. Right: $H_q=128,H_{kv}=2$; overhead is hidden. Lite stays close to baseline.
\papersource{Sec.2.5, Fig.5, PDF p.6. Lower TPOT is better; ratios use the respective baselines.}
\end{frame}
\begin{frame}{Evaluation spans four model sizes}
\begin{center}\begin{tabular}{lrrr}\toprule
Parameters & Layers & Heads & Training tokens\\\midrule
332M & 12 & 16 & 200B\\
650M & 16 & 16 & 200B\\
1.5B & 24 & 16 & 400B\\
4B & 36 & 32 & 800B\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Qwen3-style decoder; FineWeb-Edu; 8192 context; vocabulary 128,000.
\item 500M-token validation split; WikiText perplexity.
\item Seven five-shot task accuracies, averaged; no multi-seed uncertainty reported.
\end{itemize}
\papersource{Sec.3.1/3.3; Tables 4,6; PDF pp.6--8,14--15.}
\end{frame}
\begin{frame}{At 1.5B, both variants improve mean accuracy}
\begin{center}\begin{tabular}{lrrrr}\toprule
Method & Cache & Valid loss & WikiText & Avg. acc.\\\midrule
Vanilla & 1 & 2.241 & 13.67 & 54.55\\
CLA & 1/2 & 2.258 & 14.19 & 53.91\\
YOCO & 1/2 & 2.244 & 13.65 & 54.19\\
GQA & 1/2 & 2.245 & 13.74 & 54.58\\
Lite & 1/2 & 2.225 & 13.45 & 55.30\\
FusedKV & 1/2 & 2.221 & 13.33 & 55.82\\\bottomrule
\end{tabular}\end{center}\small FusedKV: +1.27 percentage points in average accuracy; 2.49\% relative reduction in WikiText PPL. Valid loss is not perplexity.
\papersource{Table 2, PDF p.7. GQA uses two Q heads per KV head by default.}
\end{frame}
\begin{frame}{Smaller models show mixed downstream results}
\begin{center}\begin{tabular}{llrr}\toprule
Size & Method & WikiText $\downarrow$ & Avg. acc. $\uparrow$\\\midrule
332M & Vanilla & 22.85 & 43.33\\
 & Lite & 22.78 & 43.19\\
 & FusedKV & 22.35 & 43.59\\
650M & Vanilla & 18.47 & 48.08\\
 & Lite & 18.55 & 48.51\\
 & FusedKV & 18.09 & 47.45\\\bottomrule
\end{tabular}\end{center}\small Lower language-model loss does not guarantee higher task accuracy. The prose reverses the small-model winners; these are the table values.
\papersource{Table 2 and Sec.3.2, PDF pp.7--8.}
\end{frame}
\begin{frame}{Larger scale and longer training retain gains}
\begin{center}\begin{tabular}{lrrr}\toprule
4B model & Valid loss & WikiText & Avg. acc.\\\midrule
Vanilla & 2.002 & 9.18 & 59.07\\
FusedKV & 1.978 & 8.94 & 60.01\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Scaling experiments cover 332M--4B, with different token budgets.
\item 1.5B training continues from 400B to 600B tokens at LR $3\times10^{-5}$.
\item Reported learning curves retain an advantage in the extended run.
\item Evidence for persistence over the tested range; not a proof of asymptotic scaling.
\end{itemize}
\papersource{Table 3, Fig.7; A.5, Figs.11--12; PDF pp.8,17--19.}
\end{frame}
\begin{frame}{The direction of asymmetry matters}
\begin{center}\includegraphics[width=.95\linewidth,height=.62\textheight,keepaspectratio]{figures/ablation.pdf}\end{center}\small Reversed sharing uses $K^1,V^8$; the proposed Lite uses $K^8,V^1$. Learnable channel weights improve WikiText over fixed Lite.
\papersource{Fig.8, PDF p.9. 650M model, 200B tokens. No LAMBADA panel is shown.}
\end{frame}
\begin{frame}{Source-layer choice supports a qualified conclusion}
\begin{center}\begin{tabular}{rrrrr}\toprule
K source & V source & Valid loss & WikiText & Avg. acc.\\\midrule
8 & 1 & 2.473 & 18.55 & 48.51\\
8 & 5 & 2.489 & 18.62 & 48.22\\
8 & 8 & 2.498 & 19.21 & 47.18\\
5 & 1 & 2.473 & 18.40 & 48.39\\
3 & 1 & 2.479 & 18.60 & 48.00\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Earlier values help at fixed key source.
\item Middle-layer keys give the best mean accuracy among tested choices; layer 5 wins WikiText.
\item Larger shallow-layer gradient norms are suggestive, not causal proof of better learning.
\end{itemize}
\papersource{Table 17, PDF p.23; A.8, p.24; gradient analysis: Sec.4/Fig.9, pp.9--10.}
\end{frame}
\begin{frame}{GQA and MLA compose, with residual trade-offs}
\begin{center}\begin{tabular}{lrrr}\toprule
650M method & Cache vs. MHA & WikiText & Avg. acc.\\\midrule
GQA & 1/2 & 19.05 & 47.04\\
GQA + FusedKV & 1/4 & 18.48 & 47.15\\
MLA & 1/2 & 21.03 & 45.03\\
MLA + FusedKV & 1/4 & 20.08 & 44.79\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item GQA TPOT: 0.512 $\rightarrow$ 0.741 relative to MHA; slower than GQA alone.
\item MLA fuses compressed latent KV and positional keys.
\item MLA jointly compresses K/V; Lite is not directly transferable.
\end{itemize}
\papersource{A.6.1--2, Tables 8,11, PDF pp.18--21. Separate appendix experiments.}
\end{frame}
\begin{frame}{MoE and hybrid SWA do not improve every metric}
\begin{itemize}
\item MoE: 8 experts, top-2, 100B tokens; WikiText 19.62 (Vanilla) $\rightarrow$ 19.50 (FusedKV).
\item Vanilla MoE training loss 2.513 is lower than Lite 2.524, despite the prose claim.
\item Hybrid SWA: window 512; three window layers per full-attention layer.
\item FusedKV +WF: cache 29.7\% $\rightarrow$ 12.9\% of full-attention reference; mean accuracy 47.84 $\rightarrow$ 48.88.
\item But WikiText worsens 24.04 $\rightarrow$ 29.63; source selection must respect attention type.
\end{itemize}
\papersource{A.6.3--4, Tables 12--13, PDF pp.21--22.}
\end{frame}
\begin{frame}{Four-bit KV quantization is the stronger combination}
\begin{center}\begin{tabular}{lrr}\toprule
1.5B FusedKV setting & WikiText & Avg. acc.\\\midrule
FP16 & 13.33 & 55.82\\
4-bit KV (KIVI) & 13.39 & 55.63\\
2-bit KV (KIVI) & 15.49 & 50.73\\
50\% weight pruning (Wanda) & 20.63 & 48.56\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item 4-bit adds a 4-fold payload reduction relative to FusedKV FP16.
\item Combined ideal payload: 1/8 of full-cache FP16 Vanilla, excluding quantization metadata.
\item Wanda storage reduction concerns model weights, not KV capacity.
\end{itemize}
\papersource{A.6.5, Tables 14--15, PDF pp.22--23.}
\end{frame}
\begin{frame}{128k quality is better than YOCO, below Vanilla}
\begin{center}\begin{tabular}{lrr}\toprule
Model & RULER average & Difference vs. Vanilla\\\midrule
Vanilla & 49.11 & ---\\
YOCO & 17.32 & $-31.79$\\
Lite & 42.31 & $-6.80$\\
FusedKV & 42.00 & $-7.11$\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Additional training: 50B tokens at 32k, then 25B tokens at 128k.
\item RoPE bases: 50,000 then 500,000; not zero-shot extrapolation.
\item Subtask losses can be much larger: multikey\_2 is 63.0 $\rightarrow$ 4.0 for FusedKV.
\end{itemize}
\papersource{A.7, Table 16, PDF p.23. Higher scores are better.}
\end{frame}
\begin{frame}{The contribution is a useful design trade-off}
\begin{itemize}
\item K and V need not share the same source layer.
\item Two-source fusion can halve cache capacity and improve language modeling.
\item Lite avoids fusion I/O; full FusedKV is sensitive to arithmetic intensity.
\item Long-context retrieval and some downstream metrics still regress.
\item Reader assessment: choose using task quality, memory, TTFT, and TPOT together.
\end{itemize}
\papersource{Evidence synthesis: Secs.2--4 and A.6--A.8. No independent reproduction performed.}
\end{frame}
\begin{frame}{References and evidence scope}
\textbf{Primary source}\\
Hongzhan Lin et al.\\
\emph{Reconstructing KV Caches with Cross-Layer Fusion for Enhanced Transformers}.\\
arXiv:2512.03870v3, 19 February 2026.\\
\url{https://arxiv.org/abs/2512.03870v3}
\medskip
\begin{itemize}
\item Read author TeX, referenced tables, and the 24-page PDF, including Appendix A.1--A.8.
\item Author code link: \url{https://github.com/LivingFutureLab/FusedKV}
\item Tables in this deck are selected transcriptions; figures are author originals.
\item The following slides are backup material.
\end{itemize}
\papersource{Paper metadata and source bundle retrieved 20 September 2026.}
\end{frame}
\begin{frame}{Backup: initialization changes the result}
\begin{center}\begin{tabular}{lrrr}\toprule
650M / 200B tokens & Valid loss & WikiText & Avg. acc.\\\midrule
Equivalent initialization & 2.475 & 18.06 & 48.69\\
Normal initialization & 2.478 & 18.33 & 48.18\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Iterative fusion carries an auxiliary cache through upper layers.
\item Equivalent initialization expands the recurrence into two-source coefficients, then trains them independently.
\item Table 5's iterative row conflicts with related main-table values; do not silently repair it.
\item Independent cache reconstruction does not remove the hidden-state dependency between layers.
\end{itemize}
\papersource{A.3, Table 5, PDF pp.14--16.}
\end{frame}
\begin{frame}{Backup: MLA timing is simulated, not deployed}
\begin{center}\begin{tabular}{llrr}\toprule
Heads & Metric (ms) & MLA & MLA + FusedKV\\\midrule
16 & TTFT & 8010.93 & 4014.26\\
16 & TPOT & 23.58 & 29.39\\
48 & TTFT & 22147.56 & 11084.81\\
48 & TPOT & 59.64 & 59.64\\\bottomrule
\end{tabular}\end{center}\begin{itemize}
\item Input/output length: 128k/2k.
\item These are InferSim estimates; the appendix does not report an integrated vLLM/SGLang benchmark.
\item The 48-head compute-bound scenario uses the H20 compute-to-memory ratio.
\item Do not transfer these numbers to arbitrary hardware or serving workloads.
\end{itemize}
\papersource{A.6.1, Tables 9--10, PDF pp.19--20.}
\end{frame}
\begin{frame}{Backup: prefill skipping has a specific scope}
\begin{itemize}
\item Teaching interpretation: only the final prompt position is needed for first-token output.
\item Lower layers build the stored history; upper layers consume those caches.
\item Earlier upper-layer hidden states no longer need to generate stored upper-layer KV.
\item The final position still traverses upper-layer queries, attention, and FFNs.
\item This does not eliminate all upper-layer work during full-token loss training or arbitrary sequence-output requests.
\end{itemize}
\papersource{Interpretation of Sec.2.5 and Table 1, PDF pp.5--6; not an independently benchmarked implementation.}
\end{frame}
\end{document}