User embeddings are central components of modern recommendation, personalization, and behavioral modeling systems. Though these embeddings can compactly encode rich behavioral information, they are inherently dense and opaque, limiting interpretability. To address this gap, we argue that user embeddings can be understood as sparse superpositions of interpretable behavioral modes. This structure is directly predicted by generative models of user behavior for linear embeddings and extends approximately to deep-learning representations by the superposition hypothesis. Superimposed modes can naturally be recovered by sparse dictionary learning methods, such as sparse autoencoders (SAEs), and recovered modes can be automatically named and queried in natural language. We validate mode recovery against known ground truth on synthetic data, where SAEs recover modes better than classical sparse baselines, including on transformer-encoded embeddings. We then apply the method to classical and transformer-based user embeddings from two real-world datasets. We also show how the corresponding natural-language labels enable zero-shot audience retrieval and characterization over embeddings never trained on text. The framework is post-hoc and model-agnostic, requiring no modification to the upstream embedding system.
Figures & tables
Figure 1: Mode recovery vs. embedding dimension m (mean ± 1 std over 5 random projections). Left: median per-feature Pearson r with best-matching ground-truth mode. Center: mean per-user cosine similarity between projected codes and ground-truth weight vector. Right: fraction of modes recovered at decoder–centroid cosine similarity ≥0.7 . The vertical line marks m=75 , the ground-truth mode count.
Task type
Method
FVU ↓
Lift
AUROC
AUROC scored
Coverage
Category
SAE (ours)
0.075
1.93 ×
0.705
0.678
0.735
FastICA
0.083
1.86 ×
0.695
0.660
0.770
K-Means encoding
0.388
1.85 ×
0.680
0.663
0.614
Text-embedding baseline
—
1.39 ×
0.633
0.633
1.000
Life-event
SAE (ours)
0.075
5.30 ×
0.715
0.741
0.876
FastICA
0.083
4.75 ×
0.713
0.717
0.932
Table 1: Open e-commerce zero-shot NL audience retrieval, metrics averaged per task block (6 category tasks and 2 life-event tasks, see Appendix C.2 ). AUROC scored restricts AUROC to users with nonzero scores. Text baseline is the matched-input category-pooled variant (Section 5 ). Text baseline has no FVU.
Encoder
Method
FVU ↓
Lift
AUROC
AUROC scored
Coverage
SASRec
SAE (ours)
0.041
2.53
0.692
0.687
0.977
K-Means encoding
0.136
2.16
0.678
0.663
0.811
BERT4Rec
SAE (ours)
0.032
2.38
0.690
0.688
0.984
K-Means encoding
0.108
2.41
0.697
0.676
0.848
—
Text-embedding baseline
—
1.64
0.701
0.701
1.000
Table 2: MovieLens zero-shot NL audience retrieval, averaged over 2 SAE-training seeds × 32 non-compositional queries (query list in Appendix E.2 ). FVU is from a single SAE seed per encoder. Text baseline is encoder-independent. Bold: SAE significantly better than K-Means encoding ( p<0.05 , cross-seed paired Wilcoxon, see Appendix D ).
K-Means encoding top-5 for Jurassic Park
SAE (ours) top-5 for Jurassic Park
5/5 paraphrase a comedy concept
5 distinct concepts
comedy
Late-1990s indie/quirky dramedies
thriller
1990s B-movie action-thriller
comedy
Early-2000s indie/quirky comedy
action
Low-quality 1990s action blockbuster
comedy
Low-budget 1990s B-movie comedy
comedy
1990s low-quality mainstream comedy
comedy
1990s low-quality mainstream comedy
sequel
1980s-90s action-comedy sequel
comedy
LGBT romantic comedy and drama
sci-fi
1990s B-grade sci-fi action
Figure 2: Top-5 features describing the Jurassic Park audience (a sci-fi action franchise) under K-Means encoding and SAE on SASRec, ranked by lift at a 10% top-activator threshold. All five K-Means features paraphrase a mainstream-comedy concept, while the SAE top-5 span five distinct themes. Small-caps tags are our one-word summaries of the LLM-assigned feature names.
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Items
Interactions per item
Top 1%
Top 10%
Singletons
Synthetic
778,639
7.5
50.9%
79.7%
62.3%
Open e-commerce (ASIN)
939,082
2.0
19.1%
45.8%
75.6%
MovieLens 1M
3,706
270
8.7%
44.4%
3.1%
Appendix
Table 3: Item popularity in the synthetic data and both real datasets: share of interactions carried by the most popular 1% and 10% of items, and the fraction of items that appear exactly once.
Figure 3: Item popularity and user activity for the synthetic data and both real datasets. (a) Share of interactions carried by the most popular items, with dots at the top 1% and 10% of items (cf. Table 3 ). (b) Interactions per user divided by each dataset’s median. Synthetic histories are bounded at about 100 interactions by the generation budget, which truncates the upper tail.
ID
Behavioral mode
Domain
Technology & Gaming
1
Tech Enthusiast
Tech/Electronics
2
Mobile Gamer
Gaming
3
PC Gamer
Gaming/Hardware
4
Smart Home Builder
IoT/Automation
5
Audiophile
Audio
Appendix
Table 4: Complete taxonomy of the 75 synthetic behavioral modes used as ground truth for the synthetic experiments of Section 4 . Each behavioral mode was generated with a name, description, product categories, and example products (not shown for compactness); only the name and domain grouping are displayed here.
ID
Behavioral mode
Domain
Lifestyle & Hobbies
46
Book Lover
Books/Literature
47
Board Game Enthusiast
Gaming/Tabletop
48
Puzzle Solver
Puzzles/Games
49
Craft Enthusiast
Crafts/DIY
50
Knitter/Crocheter
Yarn/Crafts
Appendix
Table 5: Complete taxonomy of the 75 synthetic behavioral modes used as ground truth (continued).
Method
Code–GT alignment
Median per-feature r
Modes recovered (cos ≥0.7 )
Oracle (linear ceiling)
0.78
—
—
SAE
0.58
0.28
0.97
SAE (merged)
0.54
0.54
0.95
FastICA
0.53
0.62
0.59
K-Means encoding
0.45
0.30
0.52
PCA
0.25
0.17
0.00
Appendix
Table 6: Mode recovery on mean-pooled SASRec embeddings ( d=256 ) of the synthetic data, all methods at matched L0 . LDA is fit to raw user–item counts and has no decoder directions.
K′
Users
Oracle
SAE
Best classical
SAE / oracle
15
4,591
0.943
0.695
0.667
0.737
20
8,394
0.931
0.683
0.598
0.734
25
13,245
0.918
0.679
0.643
0.740
30
19,880
0.897
0.651
0.631
0.725
40
36,737
0.871
0.642
0.623
0.737
50
58,248
0.838
0.619
0.617
0.739
Appendix
Table 7: Sensitivity to the number of modes K′ on the d=256 transformer embeddings. Code–GT alignment for the oracle, the SAE, and the best of PCA, FastICA, and K-Means encoding at each K′ .
Dataset
Method
FVU ↓
Lift
AUROC
Coverage
Open e-commerce
PCA
0.388
1.28 ×
0.579
0.797
ICA
0.083
1.86 ×
0.695
0.770
MovieLens (SASRec)
PCA
0.189
1.65
0.576
0.815
ICA
0.343
1.99
0.610
0.910
MovieLens (BERT4Rec)
PCA
0.200
1.60
0.592
0.904
ICA
0.357
2.08
0.580
0.833
Appendix
Table 8: Additional baselines on both datasets. Metrics averaged across tasks. SAE significantly exceeds every classical baseline on Lift at matched L0 (cross-seed Wilcoxon, Appendix D ); ICA is SAE’s closest competitor on AUROC (tied on life-event AUROC, SAE wins elsewhere) and achieves higher Coverage by construction (denser activations). NMF is excluded as it requires non-negative preprocessing that doesn’t naturally arise in either embedding space and underperforms classical baselines at all m (Section 4 ).
Task type
Task name
npos
Base rate
Category retrieval
Musician
345
8.4%
Baby products
839
20.5%
Board gamer
1421
34.8%
Coffee enthusiast
1482
36.3%
Gardener
1539
37.7%
Pet owner
2196
53.8%
Appendix
Table 9: Open e-commerce task definitions. npos is the number of users satisfying the positive definition out of the evaluated user set for each task block (4085 users with at least one post-2021 window for category retrieval; 4373 users with a 2021 survey response for life-event retrieval).
Table 10: Consolidated paired Wilcoxon one-sided p -values. Default alternative H1: SAE > baseline on the named metric. Bold indicates p<0.05 in the SAE-wins direction ; reverse-direction losses are reported unbolded for clarity. MovieLens retrieval columns report per-encoder and Stouffer-combined p ; Open e-commerce and audience-characterization sections are single-dataset (e-commerce) or Stouffer-combined across MovieLens encoders (audience). Stouffer across encoders assumes independence; here the two encoders share users and queries, so combined p -values should be read as descriptive summaries rather than independence-based combinations (per-encoder columns are the primary quantity). Note on pairing: Open e-commerce and MovieLens SAE-vs-K-Means rows are cross-seed (Open e-commerce: 5 seeds × task; MovieLens: 2 SAE-training seeds × 32 queries). MovieLens rows vs. PCA/ICA/text are single-seed paired across 32 queries. † For top-5 redundancy (median pairwise cosine among the top-5 features), smaller is more diverse; alternative hypothesis is H1: K-Means redundancy > SAE redundancy. ‡ For tests where the named comparison wins in the reverse direction, the reported p is the reverse-direction one-sided value (equal to 1−pprimary ) rather than the alternative-hypothesis p .
λ
mean L0
cdec
% eligible
n eligible
recon. MSE
5.70×10−3
68.7
0.095
24.5%
251
0.060
3.62×10−3
65.9
0.080
24.6%
252
0.044
1.98×10−3
82.8
0.081
37.1%
380
0.026
1.46×10−3
102.3
0.083
43.6%
446
0.021
8.30×10−4
147.7
0.086
38.0%
389
0.014
Appendix
Table 11: Width-and-sparsity sweep on MovieLens SASRec embeddings at dhidden=1024 . Selected operating point (bold) sits at the cdec elbow with the highest eligible-feature count. “Eligible” counts features with 30–500 activating users.
Epochs
mean L0
cdec
n eligible
n too-rare
recon. MSE
125
101.0
0.054
653
0
0.091
250
80.2
0.059
572
125
0.052
500
74.3
0.076
498
165
0.033
Appendix
Table 12: Training-length sensitivity at dhidden=1024 , λ=1.98×10−3 on SASRec embeddings. Selected training length (bold) balances feature count against within-theme redundancy. Metrics at 250 epochs differ slightly from the corresponding row in Table 11 because the two tables report independent training runs; seed-level variation on MovieLens SAE training can reach ∼10% on L0 and reconstruction MSE at a fixed operating point (see seed-variance discussion in the supplementary notes).
Query
Title patterns (representative)
Genre
n+
Broad audiences (21 queries)
Fans of Quentin Tarantino films
Pulp Fiction, Reservoir Dogs, Jackie Brown, Kill Bill, Four Rooms
—
517
Fans of Steven Spielberg adventure and sci-fi films
Raiders of the Lost Ark, Indiana Jones, Jurassic Park, E.T., Close Encounters, …(9 total)
—
3099
Fans of classic Disney animated films
Lion King, Little Mermaid, Beauty and the Beast, Aladdin, Snow White, …(21 total)
—
1682
Viewers of dark, psychological thrillers
Silence of the Lambs, Se7en, Fight Club, American Psycho, Memento, …(13 total)
—
1748
Fans of romantic comedies from the 1990s
Pretty Woman, Sleepless in Seattle, You’ve Got Mail, Notting Hill, Four Weddings, …(10 total)
Romance/Comedy
1237
Appendix
Table 13: Natural-language audience queries on MovieLens 1M with title-pattern and genre-constraint ground-truth definitions. n+ is the resulting number of positive users out of 6040.
Encoder
Threshold
Δ Lift
Δ AUROC
Δ AUROC scored
Coverage (SAE / K-Means)
SASRec
0.0
+6.3%
−0.016
−0.004
0.973 / 0.818
0.5
+10.8%
+0.000
+0.011
0.976 / 0.817
0.6
+11.2%
+0.009
+0.018
0.975 / 0.808
0.7
+7.4%
+0.019
+0.019
0.983 / 0.795
BERT4Rec
0.0
−5.8%
−0.019
+0.003
0.971 / 0.847
0.5
−4.2%
−0.016
+0.006
0.973 / 0.846
Appendix
Table 14: Sensitivity of MovieLens retrieval to the auto-interpretation confidence threshold (operating point 0.6). SAE minus K-Means encoding: Lift as a percentage of the K-Means value, AUROC and AUROC scored as absolute differences, and coverage as the raw SAE / K-Means pair. Computed over 3 SAE seeds per encoder, a different seed set from Table 2 , so the 0.6 row differs slightly from it.
Sparse retrieval underpins modern search systems, from web search to retrieval-augmented generation. Existing work has introduced Learned Sparse Retrieval (LSR) to push beyond exact lexical matching toward richer semantics. Yet LSR has so far remained tied to encoder-style bidirectional architectures, and its extension to multimodal settings still relies heavily on auxiliary cross-modal modules. To address these limitations, we introduce UEmbed (Unified Embedding), a decoder-only multimodal embedding model that produces both sparse lexical and dense representations in one causal forward pass. UEmbed appends N learnable special tokens to the input and partitions the vocabulary into N disjoint subsets. Each token's causal hidden state predicts sparse weights over its assigned subset, and the N subsets are concatenated into the full sparse vector. Trained on public data, we release UEmbed at 2B, 4B, and 9B scales. UEmbed-9B reaches 71.8 (dense) and 71.0 (sparse) on MMEB-v2, outperforming multimodal embedding models trained on publicly available data (e.g., RzenEmbed). On BEIR, UEmbed also remains competitive with strong dense and sparse baselines. Furthermore, we demonstrate the practical utility of UEmbed across three dimensions: effectiveness, efficiency, and agentic applications. Overall, UEmbed offers a new paradigm: it unifies dense and sparse embeddings in one model, while further extending sparse retrieval to unify text and multimodal inputs.
Tingyu Song, Mingxin Li, Yanzhao Zhang +5
CASIA · University of Chinese Academy of Sciences · Alibaba Group +1
Personalized systems rely on user representations to connect behavioral history with downstream recommendation applications. Existing methods typically employ either supervised latent user embeddings, which are effective for retrieval but difficult to interpret, or textual user profiles, which are interpretable but challenging to optimize for downstream utility due to lack of direct supervision. To bridge this gap, we present BLUE, a reinforcement learning framework that unifies these two forms of user representation by aligning language-based user profiles with embedding-based recommendation objectives. Given a user interaction history, BLUE leverages a profiler Large Language Model (LLM) to generate textual profiles, while an embedding model provides reward signals. This encourages the resulting textual representations to move closer to positive items and farther from negative ones in the embedding space. We further introduce a text-space supervision signal based on next-item prediction, ensuring the learned profiles remain both semantically meaningful and highly effective for downstream retrieval. Experiments on Amazon Reviews 2023 and Google Local Reviews in zero-shot sequential recommendation settings demonstrate that BLUE consistently outperforms strong baselines under both frozen and trainable embedding conditions. Notably, BLUE achieves clear gains in cross-domain transfer, highlighting the strong generalization ability of the learned user profiles. Furthermore, these generated profiles provide superior personalized context for question answering compared to raw user histories or alternative profile optimization methods. Overall, these results show that BLUE provides an effective way to unify interpretable textual profiling with discriminative latent embeddings for personalization.
Zhaoxuan Tan, Xiang Zhai, Yan Zhu +2
University of Notre Dame · 2Google · * This work was done while Zhaoxuan was a student researcher at Google.
Industrial-scale user representation learning requires balancing robust universality with acute task-sensitivity. However, existing paradigms primarily yield static, task-agnostic embeddings that struggle to reconcile the divergent requirements of downstream scenarios within unified vector spaces. Furthermore, heterogeneous multi-source data introduces inherent noise and modality conflicts, degrading representation. We propose Query-as-Anchor, a framework shifting user modeling from static encoding to dynamic, query-aware synthesis. To empower Large Language Models (LLMs) with deep user understanding, we first construct UserU, an industrial-scale pre-training dataset that aligns multi-modal behavioral sequences with user understanding semantics, and our Q-Anchor Embedding architecture integrates hierarchical coarse-to-fine encoders into dual-tower LLMs via joint contrastive-autoregressive optimization for query-aware user representation. To bridge the gap between general pre-training and specialized business logic, we further introduce Cluster-based Soft Prompt Tuning to enforce discriminative latent structures, effectively aligning model attention with scenario-specific modalities. For deployment, anchoring queries at sequence termini enables KV-cache-accelerated inference with negligible incremental latency. Evaluations on 10 Alipay industrial benchmarks show consistent SOTA performance, strong scalability, and efficient deployment. Large-scale online A/B testing in Alipay's production system across two real-world scenarios further validates its practical effectiveness. Our code is prepared for public release and will be available at: https://github.com/JhCircle/Q-Anchor.
Jiahao Yuan, Yike Xu, Jinyong Wen +9
Ant Group · East China Normal University · Zhejiang University