UNISON: A Unified Framework for Learning from Scored Bags

Ofek Kirshenboim; Or Shkuri; Shani Finkelshtein; Yoram Louzoun

cs.LGOct 11, 2026

UNISON: A Unified Framework for Learning from Scored Bags

Authors: Ofek Kirshenboim, Or Shkuri, Shani Finkelshtein, Yoram Louzoun

Organizations: Department of Mathematics, Bar-Ilan University, Israel

Abstract

We introduce UNISON, a unified framework that bridges multiple instance learning and recommendation systems by treating both as instances of learning from scored bag collections of (item, score) pairs. Unlike traditional approaches that address bag-level classification and personalized recommendation as separate problems, UNISON decomposes learning into three interconnected stages: (1) learning universal item representations, (2) modeling bag-specific preference patterns through lightweight personalized parameters, and (3) inferring bag-level characteristics from learned preferences. We justify the architectural choice of linear bag-specific scoring through a first-order analysis: when item embeddings are sufficiently smooth in the score, a linear function approximates the score up to a Taylor remainder controlled by the curvature of the underlying preference function. For cold-start scenarios, we show that the cold-bag fitting problem reduces to ridge-less linear regression with a closed-form solution, and provide convergence guarantees for the iterative variant. Empirically, UNISON matches or outperforms state-of-the-art approaches across diverse domains: entertainment (books, movies), immunology (T cell receptor (TCR) based classification), and microbiome, offering superior computational efficiency and interpretability. A controlled synthetic experiment further confirms that the bag-specific parameters ( $w_j, b_j$ ) recover the latent factors that drive item scores even when the projection $φ$ has no access to the original scoring mechanism (AUC > 0.998). UNISON is available at https://github.com/louzounlab/UNISON.

Figures & tables

Panel of Figure 1 — Figure 1: UNISON operates in three stages (Left plot): (Stage 1) Raw items from a bag (e.g., books) are processed by domain-specific encoders to produce latent representations $z_{i}$ . (Stage 2) Items are partitioned into a support set (known scores) and a query set (unobserved scores). An MLP, shared across bags, projects items into a low-dimensional space. For each bag, linear parameters $(w_{j},b_{j})$ are optimized at inference time to predict the known support set scores. These parameters are then used to predict scores for the query set. (Stage 3) $(w_{j},b_{j})$ are treated as functional embeddings, serving as input to a final MLP that predicts bag-level characteristics (e.g., user demographics). Comprehensive performance analysis and ablation studies (Right plot). (A) Conceptual Workflow Example: Raw items are transformed into latent embeddings, which are then used to optimize user-specific weights $(w_{j},b_{j})$ based on the support set. These functional embeddings enable dual-task inference: predicting ratings for unobserved items (query set) and classifying bag-level traits (e.g., gender) without auxiliary metadata. (B) Predicted vs. ground-truth scores for 10 representative cold-start users, demonstrating the model’s ability to recover individual preference patterns. (C) Comparison of performance with (brown) and without (blue) the shared MLP projection. The left bars represent the Spearman correlation (Stage 2), and the right bars represent the AUC for bag-level classification (Stage 3). (D) Impact of support set size on performance. The green curve (left y-axis) tracks Stage 2 Spearman correlation. The orange curve (right y-axis) tracks Stage 3 AUC. (E) Histogram of items per user across the dataset. (F) Distribution of individual Spearman correlation coefficients across all users. (G) Stage 2 Spearman correlation (left triplet) and Stage 3 AUC (right triplet) comparison of three optimization regimes: sequential (Stage 2 then Stage 3), joint (Stage 2 and 3 simultaneously), and joint training followed by Stage 3 fine-tuning.

Panel of Figure 2 — Figure 2: Left -plot - Training/Test definitions and recommendation benchmarks on Book-Crossing and MovieLen-1M. (A) Training/Test definitions: Users and books are partitioned into warm (red) and cold (blue) sets. Training is conducted exclusively on the WU-WI quadrant, while inference is evaluated on WU-CI, CU-WI, and CU-CI scenarios. Each user is associated with a support set (observed ratings, always consisting of warm items) and a query set for evaluation. (B) Mean Absolute Error (MAE $\downarrow$ ) across cold-start scenarios for MovieLen and Book-Crossing datasets. Each group shows three methods: MeLU (orange), ColdNAS (green), and UNISON (blue). (C) Spearman Correlation (SCC $\uparrow$ ) across cold-start scenarios for MovieLen and Book-Crossing datasets. The right hand plot is similar to Figure 1, but for MovieLens (A) Predicted vs. ground-truth scores for 10 representative cold-start users, (B) Stage 2 Ablation, (C) Support Set Sensitivity (D) Bag Statistics.

Figure 3: Effect of support set size on UNISON performance across three domains: TCR (left), and Microbiome (right). For MovieLens and TCR, we report both SCC (green) and AUC (orange). For Microbiome, we compare Stage 2 (solid, light) vs Stage 3 (dashed, dark) AUC across three datasets (M1-M3). Error bars show standard error across 5 random seeds.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Empirical verification of Lipschitz property. Each blue point represents distances before ( $x$ -axis) and after ( $y$ -axis) projection $\phi$ for an item pair. The orange dashed line ( $y=0.014x$ ) bounds nearly all pairs, confirming $L\approx 0.014$ . The red line ( $y=0.003x$ ) shows average scaling. All points remain well below the diagonal ( $y=x$ , black), validating the boundedness and contractive assumptions in Theorem 1.

Dataset	Bags	Items	Ratings	Sparsity
MovieLens	6,040	3,706	1,000,209	95.53%
BookCrossing	278,858	271,379	1,149,780	99.99%
Vaccine TCR	125	24,386	125,000	58.98%
Emerson TCR	600	82,565,945	600,000	99.98%
Microbiome 1	445	448	27,037	86.44%
Microbiome 2	344	175	11,627	80.69%

Appendix

Table 1: Dataset statistics.

Dataset	Bag	Item	Range
MovieLens	Age, Zip	Genre, Dir.	$1\sim 5$
Book-Crossing	Age	Auth., Pub.	$1\sim 10$
Vaccine TCR	Response	Vgene, cdr3	$1.1e^{-5}\sim 0.17$
Emerson TCR	CMV	Vgene, cdr3	$1e^{-5}\sim 0.001$
Microbiome 1	Gastric	Sequence	$-1\sim 4.95$
Microbiome 2	Parkinson	Sequence	$-1\sim 3.97$

Appendix

Table 2: Detailed content attributes and rating ranges for each dataset.

Hyperparam	MovieLens	Book-Crossing	TCR	Microbiome
Stage 2
Enc Dim ( $d$ )	3584	3584	75	8
Latent Dim ( $d^{\prime}$ )	48	48	64	8
MLP Arch.	1536-768-384-192-96	1536-768-384-192-96	64-48	32-16-8
MLP Dropout	0.15	0.15	0.03	0.07
Stage 3

Appendix

Table 3: Hyperparameters across all stages.

Dataset	Method	WU-CI	CU-WI	CU-CI
		MAE $\downarrow$	MAE $\downarrow$	MAE $\downarrow$
Movie Lens	MeLU	0.9275	0.7854	0.9235
	ColdNAS	0.8996	0.7896	0.8836
	UNISON	0.8937	0.7579	0.8551
Book Crossing	MeLU	1.4468	1.3924	1.4302
	ColdNAS	3.5052	3.3487	3.4908

Appendix

Table 4: Stage 2 performance comparison of recommendation methods across cold scenarios (MAE).

Dataset	Method	WU-CI	CU-WI	CU-CI
		MAE $\downarrow$	MAE $\downarrow$	MAE $\downarrow$
Movie Lens	BPR	0.8639	0.8746	0.8563
	NGCF	0.8406	0.8522	0.8357
	LightGCN	0.8242	0.8410	0.8294
	MetaHIN	0.7967	0.8066	0.7993
	MeLU	0.9196	0.8104	0.9091

Appendix

Table 5: Stage 2 performance comparison of recommendation methods across cold scenarios (MAE).

Dataset	Method	WU-CI	CU-WI	CU-CI
		SCC $\uparrow$	SCC $\uparrow$	SCC $\uparrow$
Movie Lens	MeLU (original enc.)	0.300	0.476	0.291
	MeLU (Qwen3)	$-$ 0.103	0.080	$-$ 0.036
	MeLU (Qwen3 + PCA)	0.299	0.299	0.286
	UNISON (Qwen3)	0.261	0.377	0.323
Book Crossing	MeLU (original enc.)	0.224	0.185	0.111

Appendix

Table 6: Stage 2 performance comparison under different embedding configurations (Spearman correlation).

Scenario	MeLU	UNISON (Opt. CU-CI)	UNISON (Opt. WU-CI)	UNISON (Opt. CU-WI)
WU-CI	0.301	0.260	0.311	0.248
CU-WI	0.476	0.377	0.366	0.441
CU-CI	0.291	0.323	0.318	0.320

Appendix

Table 7: Spearman correlation (SCC

\uparrow

) on MovieLens under different UNISON optimization targets.

Scenario	MeLU	UNISON (Opt. CU-CI)	UNISON (Opt. WU-CI)	UNISON (Opt. CU-WI)
WU-CI	0.301	0.260	0.311	0.248
CU-WI	0.476	0.377	0.366	0.441
CU-CI	0.291	0.323	0.318	0.320

Appendix

Table 8: Spearman correlation (SCC

\uparrow

) on MovieLens under different UNISON optimization targets.

Configuration	AUC S2 $\uparrow$	AUC S3 $\uparrow$
Microbiome #1
Full UNISON (with MLP)	0.905	0.722
w/o MLP ( $\phi$ )	0.610	0.582
Microbiome #2
Full UNISON (with MLP)	0.885	0.627
w/o MLP ( $\phi$ )	0.642	0.545

Appendix

Table 9: Ablation study results for Microbiome datasets. The results demonstrate the impact of the MLP projection

\phi

on performance across Stage 2 (S2) and Stage 3 (S3).

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