LIME: Link-based User-item Interaction Modeling with Decoupled XOR Attention for Efficient Test Time Scaling

Yang Liu; Yunjiang Jiang; Ayush Agarwal; Yihan Wu; Haoran Liu; Bi Xue

cs.IROct 21, 2025

LIME: Link-based User-item Interaction Modeling with Decoupled XOR Attention for Efficient Test Time Scaling

Authors: Yang Liu, Yunjiang Jiang, Ayush Agarwal, Yihan Wu, Haoran Liu, Bi Xue

Organizations: Meta

Abstract

Scaling large recommendation systems requires advancing three major frontiers: processing longer user histories, expanding candidate sets, and increasing model capacity. While promising, transformers' computational cost scales quadratically with the user sequence length and linearly with the number of candidates. This trade-off makes it prohibitively expensive to expand candidate sets or increase sequence length at inference, despite the significant performance improvements. We introduce \textbf{LIME}, a novel architecture that resolves this trade-off. Through two key innovations, LIME fundamentally reduces computational complexity. First, low-rank ``link embeddings" enable pre-computation of attention weights by decoupling user and candidate interactions, making the inference cost nearly independent of candidate set size. Second, a linear attention mechanism, \textbf{LIME-XOR}, reduces the complexity with respect to user sequence length from quadratic ( $O(N^2)$ ) to linear ( $O(N)$ ). Experiments on public and industrial datasets show LIME achieves near-parity with state-of-the-art transformers but with a 10 $\times$ inference speedup on large candidate sets or long sequence lengths. When tested on a major recommendation platform, LIME improved user engagement while maintaining minimal inference costs with respect to candidate set size and user history length, establishing a new paradigm for efficient and expressive recommendation systems.

Figures & tables

Panel of Figure 1 — Figure 1 : Overall latency analysis across different model parameters. This figure illustrates the inference latency vs number of candidates, user history length, and QK dimension of MHA, HSTU, LIME-MHA, and LIME-XOR. LIME-MHA consistently achieves the lowest and most stable latency across all three metrics.

Figure 2 : Architecture of TTSN (left), LIME-MHA (middle), and MHA (right). With a lightweight cross module using precomputed attention weights in a decoupled attention framework, LIME-MHA achieves MHA-level expressiveness with similar latency to TTSN.

Figure 3 : Architecture of HSTU Transformer (left) and LIME-XOR Decoupled Transformer (right) with a visual comparison of our proposed XOR attention mask against the standard HSTU causal self-attention mask.

Figure 4 : LIME Inference as part of the entire recommendation system

Model	gAUC	AUC	Log loss
VISTA (32 seeds)	$0.569079\pm 0.000465$	$0.646075\pm 0.000224$	$0.192632\pm 0.000106$
TTSN	$0.570523\pm 0.000328$	$0.645368\pm 0.000216$	$0.192685\pm 0.000227$
DIN	$\mathbf{0.571175\pm 0.000489}$	$0.647357\pm 0.000420$	$0.192587\pm 0.000458$
HSTU	$0.570691\pm 0.000500$	$\mathbf{0.647669\pm 0.000238}$	$0.192597\pm 0.000170$
LIME-XOR (32 links)	$0.570567\pm 0.000152$	$0.646799\pm 0.000239$	$\mathbf{0.192545\pm 0.000111}$

Table 1 : Five-seed Taobao-Ad results (mean

\pm

standard deviation). Lower log loss is better.

Table 2 : Offline, online, and public dataset experimental results.

Candidate-side basis	gAUC	AUC	Log loss	QK cacheable
Learned global links	$0.570567\pm 0.000152$	$\mathbf{0.646799\pm 0.000239}$	$\mathbf{0.192545\pm 0.000111}$	Yes
Frozen random links	$0.570323\pm 0.000255$	$0.644434\pm 0.000268$	$0.192834\pm 0.000243$	Yes
Fixed item centroids	$\mathbf{0.571714\pm 0.000337}$	$0.644832\pm 0.000288$	$0.192608\pm 0.000111$	Yes
Personalized-link keys	$0.569040\pm 0.000789$	$0.643578\pm 0.000553$	$0.192915\pm 0.000265$	No

Table 3 : Controlled five-seed Taobao-Ad link/key ablation with 32 links (mean

\pm

standard deviation). Lower log loss is better.

Table 4 : Ablation Study and comparison to linear sparse attention variants on KuaiRand-1K dataset.

Panel of Figure 5 — Figure 5 : Left: cumulative singular value of self/cross attention matrices in a pretrained transformer model. Right: cumulative singular value of the raw/personalized link embeddings.

Links	Jensen–Shannon divergence	Cosine similarity
1	0.122	0.837
4	0.072	0.902
32	0.055	0.915
128	0.050	0.923

Table 5 : Similarity between factorized LIME-MHA and direct MHA attention distributions.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description
$U$	User
$N(U)$	Number of items in user $U$ ’s interaction history
$M(U)$	Number of candidate items for user $U$
$E_{j}$	Embedding representation of item $j$
$E=\{E_{j}\}_{j=1}^{N(U)}$	Sequence of user history embeddings, $E\in\mathbb{R}^{N(U)\times d}$
$E^{C}$	User context features (e.g., location, device type)

Appendix

Table 6 : Notation Table

Axis	Transformers (HSTU)	SIM/TWIN	Two-Tower	LIME (Ours)
User-Item Interaction	Deep	Medium	Limited late interaction	Deep
Latency	High	Medium	Low	Low
Complexity	$O(MN+N^{2})$	$O(MN)$	$O(N)$	$O(M\ell+N\ell)$
Pre-computation	Minimal	Minimal	Item Emb	QK Attention Weights

Appendix

Table 7 : Comparison of Ranking Model Architectures where

N

is the user history length,

M

is the number of candidates to rank, and

L\ll N

is the LIME-compressed history size.

Parameter	KuaiRand	TaoBao Ad	Industrial
Num. of Interactions	$12\times 10^{6}$	$25\times 10^{6}$	$100\times 10^{9}$
Learning Rate	$1\times 10^{-4}$	$1\times 10^{-3}$	$4\times 10^{-4}$
Batch Size	1024	8192	1024
Number of Heads	4	4	4
Epochs	2	10	1
Embedding Dimension	32	32	256

Appendix

Table 8 : Model Hyperparameters for KuaiRand, TaoBao Ad, and Industrial datasets

Panel of Figure 6 — Figure 6 : Top: Cross-attention as a low-rank product. Bottom: Self-attention as two low-rank cross-attentions. UIH stands for user interaction history.

Table 9 : Latency (in seconds) comparison for different models under varying conditions. The columns correspond to the models: LIME-MHA, MHA Skyline, HSTU Skyline, and LIME-XOR. All numerical values are truncated to two decimal places.

Candidates	Uncached global	BF16 lookup	Weighted sum	BF16 total	Int8 lookup+dequant	Int8 total	Personalized keys
100	0.198	0.037	0.119	0.157	0.068	0.194	0.193
1,000	0.202	0.037	0.124	0.146	0.068	0.192	0.205
10,000	0.191	0.038	0.117	0.162	0.070	0.186	0.196
100,000	0.313	0.092	0.222	0.301	0.207	0.414	0.321

Appendix

Table 10 : P50 candidate-side latency in milliseconds for 32 links. Cached totals include lookup and weighted aggregation.

Table 11 : Performance across varying sequence lengths (1k, 2k, 4k) and link counts (32, 64, 128, 256). Each cell reports metric value and relative change from the baseline (1k, 32 links).

Links	User encoding (ms)	Uncached global (ms)	BF16 cached total (ms)	Int8 cached total (ms)	Int8 cache (GB)
8	0.330	0.187	0.143	0.186	3.2
16	0.347	0.193	0.154	0.182	6.4
32	0.340	0.191	0.162	0.186	12.8
64	0.349	0.195	0.151	0.186	25.6
128	0.476	0.212	0.157	0.197	51.2

Appendix

Table 12 : P50 latency at 10k candidates and estimated int8 cache size for 100M items and four heads.

Number of Layers	VC NE % Improvement	WT AUC % Improvement
3	0%	0%
6	-0.25%	+0.12%
9	-0.34%	+0.18%
12	-0.38%	+0.19%

Appendix

Table 13 : VC NE and WT AUC for increasing model depth on fixed 1k sequence length with 32 links.

Variant	256/128	64/128	256/32	64/32	Complexity
HSTU Skyline	$0.7444$	$0.7300$	$0.7425$	$\mathbf{0.7296}$	$\begin{aligned} O(N^{2}+NM)\end{aligned}$
Linear Trans.	$0.7423$	$0.7292$	$0.7404$	$0.7278$	$\,O(NM)$
Longformer	$0.7443$	$0.7300$	$0.7425$	$0.7292$	$\,O(NM)$
Linformer (LREA)	$0.7408$	$0.7289$	$0.7406$	$0.7275$	$\,O(NM)$
LIME-XOR	$0.7448$	$0.7301$	$\mathbf{0.7427}$	$0.7295$	$\begin{aligned} O(N\ell+M\ell)\end{aligned}$
LIME-XOR+Win.	$\mathbf{0.7453}$	$\mathbf{0.7305}$	$0.7425$	$0.7292$	$\begin{aligned} O(N\ell+M\ell)\end{aligned}$

Appendix

Figure 7 : AUC Comparison of Sparse Attention Variants with columns reporting on a particular Sequence Length/QK Dimension (e.g. 256/32 means 256 sequence length, 32 QK-dimension).

Panel of Figure 8 — Figure 8 : Latency comparison of linear attention to LIME-XOR and HSTU.

Cold-Start User Threshold	LIME-XOR	HSTU
$N(U)\leq 4$	0.7022	0.7016
$N(U)\leq 8$	0.7179	0.7173
$N(U)\leq 16$	0.7284	0.7273
$N(U)\leq 32$	0.7369	0.7356

Appendix

Table 14 : LIME-XOR vs HSTU Performance (AUC) on the cold-start user cohort in KuaiRand-1k

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