Towards Multi-Table Learning: A Novel Paradigm for Complementarity Quantification and Integration
Authors: Junyu Zhang
Lizhong Ding
MinghongZhang
Ye Yuan
Xingcan Li
Pengqi Li
Tihang Xi
Guoren Wang
Changsheng Li
Venue: NeurIPS 2025 spotlight ()
Keywords: Multi-table learning
Complementary information
Primary area: deep_learning

Abstract: Multi-table data integrate various entities and attributes, with potential interconnections between them. However, existing tabular learning methods often struggle to describe and leverage the underlying complementarity across distinct tables. To address this limitation, we propose the first unified paradigm for multi-table learning that systematically quantifies and integrates complementary information across tables. Specifically, we introduce a metric called complementarity strength (CS), which captures inter-table complementarity by incorporating relevance, similarity, and informativeness. For the first time, we systematically formulate the paradigm towards multi-table learning by establishing formal definitions of tasks and loss functions. Correspondingly, we present a network for multi-table learning that combines Adaptive Table encoder and Cross table Attention mechanism (ATCA-Net), achieving the simultaneous integration of complementary information from distinct tables. Extensive experiments show that ATCA-Net effectively leverages complementary information and that the CS metric accurately quantifies the richness of complementarity across multiple tables. To the best of our knowledge, this is the first work to establish theoretical and practical foundations for multi-table learning.

Towards Multi-Table Learning: A Novel Paradigm for Complementarity Quantification and Integration
Junyu Zhang
Lizhong Ding Minghong Zhang
Ye Yuan Tihang Xi Guoren Wang Changsheng Li
Xingcan Li
Pengqi Li
Beijing Institute Technology
fzhangjunyu, 1xc, pengqi.. .l, tihangxi, yuan-ye, lcs Habitit.ede cn
1 Lizhong.o wiwggouttooo.o....o.o. com, zhangmh020126.. 2tcch002222.ccoo com, wanggrbit@126. com
Abstract
Multi-table data integrate various entities and attributes, with potential interconnec- tions between them. However, existing tabular learning methods often struggle describe and leverage the underlying complementarity across distinct tables. To address this limitation, we propose the first unified paradigm for multi-table learn- ing that systematically quantifies and integrates complementary information across tables. Specifically, introduce metric called complementarity strength (CS), which captures inter-table complementarity by incorporating relevance, similarity, and informativeness. For the first time, we systematically formulate the paradigm towards multi-table learning by establishing formal definitions of tasks and loss functions. Correspondingly, we present network for multi-table learning that combines Adaptive Table encoder and Cross table Attention mechanism (ATCA- Net), achieving the simultaneous integration complementary information from distinct tables. Experiments show that ATCA-Net effectively leverages comple- mentary information and that the CS metric accurately quantifies the richness complementarity across multiple tables. To the best of our knowledge, this is the first work to establish theoretical and practical foundations for multi-table learning.
Introduction
Multiple tables often exhibit inherent connections due to the interrelated nature of the entities they describe, which can yield valuable complementary information when such associations exist [15] 36].
These data have widespread applications across various domains, such finance [19 37] healthcare
229 (26) and geography 322 (39]. However, most existing table learning methods 38 20 21 4
are limited utilizing information from single or pairwise tables to accomplish tasks such as table
completion [21 (26] or entity matching [23 28 There is notable lack of methodologies to analysis
and learn from multiple tables [88 42
Current approaches for analyzing inter-table relationships predominantly depend on similarity metrics 115 36 25 [6] 30). However, these methods face significant challenges in quantifying meaningful
complementary information between tables: (1) High similarity scores may originate from redundant tables (i.e., duplicated schemas) that provide negligible complementary value, while (2) completely unrelated tables inherently lack meaningful information complementarity. This distinction highlights the need for new metric that quantifies complementarity by effectively balancing table similarity and relevance, thereby enabling a more comprehensive evaluation for multiple tables. On the other hand, to effectively harness the complementary information across multiple tables, two critical
I Equal contribution. Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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technical barriers must be addressed. First, the inherent intra-table heterogeneity (divergent attribute semantics within tables) and inter-table heterogeneity (schema mismatch across tables) demand unified representation learning that preserves both table-specific characteristics and cross-table consistency. While modern single-table encoders [21 388 excel at isolated table processing, they fundamentally lack cross-table alignment mechanisms. Second, current cross-table information fusion techniques either rely on explicit relational graphs [8 18 17 or employ computationally intensive full-table encoding via language models [32). neither of which efficiently captures latent complementary patterns. These challenges, including the inability to effectively describe and quantify multiple tables complementarity. as well the difficulty in learning unified representation and integrating complementary information across tables, underscore the necessity for a novel multiple tables learning paradigm that specifically designed to address these limitations.
To address these challenges in learning multiple tables, we propose a comprehensive paradigm that systematically quantifies and integrates complementary information. Specifically, we propose a novel metric termed complementarity strength (CS), which balances the statistical correlations and semantic similarities to quantify the complementarity between tables. A higher CS score indicates stronger inter-table correlation with minimal redundancy, overcoming the limitation of existing methods that exclusively prioritize similarity (36, 30) while neglecting complementarity. We develop the systematic, formal definitions for multiple tables learning tasks and their corresponding loss functions, offering clear guidance for model design and training processes. Furthermore, we propose novel network for learning multiple tables, which consist of the adaptive table encoders and cross-tale tabular attention layers (ATCA-Net), effectively integrating complementary information from multiple tables. Extensive experiments demonstrate that CS effectively quantifies complementarity. while ATCA-Net efficiently integrates complementary information across tables. Our work provides both solid theoretical foundation and practical guidelines for multiple table learning. The main contributions are summarized as follows:
To the best of our knowledge, we are the first to define the complementarity strength (CS) metric, which quantifies the complementary information between multiple tables.
We present the first comprehensive, systematically formalized definitions for multi-table learning tasks and their correspondigg loss functions.
We propose the new architecture, ATCA-Net, which efficiently processes multiple tables and integrates complementary information across tables.
2
Related work
Tabular Representation Learning. Previous methods for learning tabular data mainly rely on
information from a single table [9]10] 12 13 [4]. Multi-table learning confronts substantial challenges in achieving semantic alignment and effectively extracting and integrating information across tables. These challenges encompass tackling schema heterogeneity 126 43 resolving column-
level semantic inconsistencies (2). and developing robust representations for tabular data [38] 37 35)
Techniques such as learnable cell-level semantic encoding [2]] and BERT-based embeddings 24
have facilitated column alignment, while table pretraining strategies 34 reconstruction tasks 35
and mutual information learning (38] underpin the development of table learning encoders. Despite these advancements, the extraction of complementary information across diverse tables remains an unresolved challenge. BERT-based approaches (32 have explored transforming tables into textual formats, and GNN methods [17 have enabled information exchange through foreign key linkages. In multimodal learning contexts 4T). mechanisms such as cross-altention [I] or learnable query these methods have not fully explored the
modules [27] are utilized for information information fusion in multiple tables settings.
Multiple Tables Measurements. Quantifying the strength of complementarity among multiple tables is crucial for advancing multi-table learning. research primarily focuses on similarity measurements, such as through column-level similarity evaluations ascertain whether tables share analogous schemas [36] 40 30]. Column-level similarity is typically assessed through the
overlap of column names and values R1 25) or via the matching of learned column embeddings
15. For numerical columns, comparing whether they originate from similar distributions is an optional approach 3 33). These methodologies are extensively employed in applications like table augmentation [6] and dataset discovery within data lakes [5]. However, similarity metrics fail to reflect

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the complementarity strength across tables,as identical tables, despite exhibiting maximum similarity, offer redundant information, while completely unrelated tables contribute minimally to the learning process. Consequently, the development of novel metric for quantifying the complementarity of multiple tables imperative.
Complementarity Strength
When tables exhibit relevance, they may provide complementary information that has the potential to enhance learning performance in multi-table integration. contrast, unrelated tables tend to yield fragmented information that inherently lacks synergistic capacity. Beyond relevance alone, the degree of complementarity is also influenced by two additional factors: the informativeness of each table and the similarity between them. On the one hand, richer table content contributes more complementary information. On the other hand, higher similarity implies greater redundancy-whee two tables identical, despite their strong relevance, they offer additional complementary benefit. Taken together, these analyses suggest that complementary information should be positively associated with both relevance and informativeness, but inversely associated with similarity. In this section, we formally define three key metries: relevance, similarity, and informativeness, and derive composite measure inter-table complementarity strength.
3.1 Definition of Complementarity Strength
collection defined as D := TT.,,,,,T where the k-th table is given by T* := [ & E [K], with (gespp. N2) denoting the number rows (resp. columns) in table Tg. Here, vny represents the value of the (i, j) cell in table T We denote the i-th row and j-th column of T r (u be(N) hft {ot [E(M))-
We begin by defining the column-level similarity between two tables. Each table T is encoded by a pretrained model [I5], producing a vector representation 2ÿ for each column h Given two column embeddings 2 and =/ from tables T and T', their similarity is computed as the cosine similarity:
2 | ||a
[0,
(I)
where || denotes the Euclidean (Lz) norm. A similarity score of indicates that the two columns are directionally aligned (i.e., linearly dependent), whereas score of 0 indicates complete orthogonality, implying no semantic overlap.
Table-level relevance between two tables T and T' is defined as the maximum similarity between any pair of columns across the two tables. Formally, the relevance score is computed as:
R₂ T') = maxje[Ma).
sE[N]] (Sc(z)) 2 E [0,
high relevance score indicates that least one column pair is semantically similar, suggesting possible relationship between the tables. Conversely, low score implies that all column pairs are dissimilar, and the tables are considered unrelated.
Table-level similarity between two tables is computed by identifying the optimal bipartite matching 15] that maximizes the sum of column similarities. Each column from one table can be paired with at most one column from the other table or remain unpaired. Formally, table-level similarity between two tables t and T' is defined
(T T') maxUeu
E So(2),z/) E [0, (in,
(3)
where U represents the set of all possible matchings between columns of T and T
We define the metric informativeness to quantify the richness of information within table. A table is considered more informative when its columns convey diverse and non-redundant semantics, and less
'We adopt the pretrained model [55] which is trained on large-scale corpus of 50M tables to leam generalizable column representations.
3

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informative when its columns are similar. Formally, the informativeness of a table T is computed as:
Info(T*)=>> vE[Na] (1-M--72 JEIN So(Ef
1
[0, Ne],
(4)
where Se 2 denotes the similarity between the i-th and j-th columns of T The inner summa- tion quantifies how similar each column is to the rest of the table. By subtracting this value from 1, we obtain measure the uniqueness of the column. The overall Info(T**) score aggregates these uniqueness values in all columns, reflecting the total amount of distinct information the table contains.
Based on the above defined metrics, relevance (Rt), similarity (St) and informativeness (Info), we introduce the metric of complementarity strength (CS), which quantifies how much novel and relevant information table contributes to T'. It balances relevance against redundancy, and is formally defined as:
CS, T Info(T")) a (-B((TTTT) (1- (1- S.
E [0,No).
(5)
STS,(T,,T)
In our experiments, we set both a and 7 to 1. This formulation encourages high relevance and source table informativeness while penalizing redundancy by suppressing similarity. Notably, the complementarity is asymmetric, i.c., CS(T* TT) * CS(T", For example, if all columns in T are already present Th then T contributes little new information T Conversely, since T contains information not present in T", it can still provide complementary information to T".
Given a group of tables D (T1, T ,.... TK}, }, the aggregate complementarity strength from all other tables D 7" to table 7" is computed follows:
(S,(D)T',T) -.T.r'-Ererny CS (5(T")T')
T')
0.
0.
K
N
3.2 Discussion Complementarity Strength
Table shows how the complementarity strength obtained for the same target table T varies across five distinct groups of synthesized tables. All tables are randomly sampled by columns from the blastchar dataset from the OpenML Repository, with each table containing 5 columns. The i-th group denoted as GP; (T", _ JE(3) including the target table 7 and three auxiliary tables T Fach group features different column overlap ratio between 7 and its auxiliary tables, ranging from to across groups GP: to GP5. anticipated, when the overlap zero, the auxiliary tables struggle to form meaningful associations with the target table 7 resulting in low relevance (R,) and complementarity strength (CS). Conversely, when the overlap high, the auxiliary tables become largely redundant, leading increased similarity (S,) but diminished complementarity. In cases of moderate overlap, the auxiliary tables establish some relevant associations with 7', while maintaining relatively low redundancy, thus preserving a higher level of complementarity. The metrics we propose effectively capture and reflect these patterns.
Table 1: Complementarity Strength for target table across five table groups sampled from the blastchar dataset. Each group GP, has different column-overlap ratio (0.0-1.0) between T and three auxiliary tables (,)) The metries S,, Re, Info, and CS, report the mean = standard deviation across the three auxiliary tables.
Metric
0.0 (GP1)
0.2 (GP2)
0.5 (GP₂)
0.8 (GP.)
1.0 (GPs)
(T(T (T))
2.81 + 0.17
2.96 + 0.08
3.15 + 0.13
3.15 + 0.21
3.58 + 0.34
RT( TD)
0.78 0.05
0.82 0.02
0.89 0.01
0.91 0.03
0.95 0.04
Info(I
2.10 0.34
1.87 0.11
2.13 0.50
0.31
1.90 + 0.03
(T,(1,))) To)
0.26 + 0.08
0.28 + 0.02
0.35 + 0.04
0.29
0.10 + 0.08
CS,(GP: T T
0.73
0.83
1.03
0.87
0.35

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4 Formulations of Multi-Table Learning
Traditional table learning paradigms were limited to utilizing information from single table. In contrast, multi-table learning involves the integration of information from multiple tables. When complementary information exists between these tables, multi-tabe ttble learning can leverage this complementarity to achieve performance improvements. In this section, we provide a formal definition of multi-table tasks along with the corresponding loss functions.
Let T := [Utyke[M [JENN denote a table with M rows (entities) and N columns (attributes), where the i-th row and j-th column are represented by vi and hy, respectively. In single-table learning, the objective is to minimize Σ L(f (r:), ys), where (-) is the prediction function for the single- table task, Y4 represents the ground truth, and L the loss function. In contrast, multi-table learning can leverage information from multiple tables. Let D {Te, Tr(l1), ..... TT(kk denote group of tables, where 7 is the target table and TT(1), ..... ,T.(k)) are auxiliary tables. The multi-table learning task can be formulated as:
ming (Erermal C (,),,, )ef))
(6)
where fo(-) the prediction function that integrates information from the target table T and the auxiliary tables .f.....Ty .
In equation (6). fo implicitly learns the alignment and integration of complementary information across multiple tables. Consequently, we divide multi-table learning into two stages: pretraining for cross-table alignment, followed by training for the integration of complementary information across tables. The two pretraining tasks, multi-table reconstruction and cross-table correlation prediction, focus on learning the associations between attributes and entities, respectively, effectively aligning the complementary information across tables.
Multi-table reconstruction pretraining involves recovering the corrupted cells in tables. Given the corrupted tables D (T' _e...... T...,, the learning target is to recovering the complement tables
D (T 722 ..... T J. By constructing á randomly, this task enables self-supervised training. We suppose that T (Th TT) = ( (R.)EEN for the corrupted index set O+ C R C* This learning task can be formalized
ming Σ E Easeoo C (10 (0t5 D) ./))
Cross-table correlation prediction pretraining involves prodicting the correlation between entities across different tables. For each pair of rows rf from table T and r from table T", the label y represents the correlation between these two rows. The objective is to minimize the following loss:
mino E E EieMMAJsetaa ( r/: D).
(8)
Typically, the labels v are constructed using pseudo-labeling techniques. Row sampling is performed on the vertical partition (37 of table, resulting partial row r, S r;- When the sampled rows 7; and k! is set to I; otherwise, the label is assigned a value of O. Ty originate from the same row, the label y4)
After pretraining with the tasks of multi-table reconstruction and cross-table correlation prediction, the model gains the ability to align complementary information across tables. Building on this, the model integrates complementary information from multiple tables through the process defined in Equation (6). In Section 5] we propose network architecture designed to implement this two-stage leamnngg process, facilitating effective multi-tabe table learning.
5 Architecture for Multi-table Learning
Multi-table learning involves aligning and integrating complementary information across tables; to achieve this, we introduce ATCA-Net, which combines an Adaptive Table encoder and a Cross-Table Attention mechanism. To align the complementary information, we introduce the adaptive table encoder, which enables adaptation to various table schemas. Through the multi-table pretraining strategy, project distinct tables into unified representation space and model the correlations
5

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emb.r
conciteratz
IxX
Coosstablle Attention A.
O JSEE product
(
E
emb. 1
Aa
emmh.
Adathe
Goottrax
xX
S Neightt vars
Adaptrin
emb. Tulty
pooling
(
Ep
womb. polk
Aa
Figure 1: ATCA-NNN operates in two stages: cross-table alignment stage and complementary informa- tion integration stage. In the first stage, the adaptive table encoder &g is pretrained using Equation (9) In the second stage, the cross-table attention mechanism Aw extracts complementary information between tables and the fusion module Ug integrates the complementary information for prediction.
between cross-table attributes and entities. To integrate the complementary information, propose a cross-table attention mechanism, which computes aggregation weights for auxiliary tables based on the target table's 's entities, ultimately achieving the fusion of complementary information across multiple tables.
5.1 Cross-table Alignment
We propose adaptive table encoder with BERT-based [24] cell-level representation handle various table schemas. Through multi-table reconstruction (Equation 77) and cross-table correla- tion prediction (Equation (8) pretraining, data from different tables projected into unified representation space, ensuring alignment of complementary information across tables.
Cell-level representations obtained using a pretrained BERT model [24] to promote semantic consistency across heterogeneous attributes in multiple tables. Specifically, for each categorical cell, concatenate the category value Veat with its attribute name Geas "Veat_Gcus" and feed this string into BERT to produce a cell-level embedding. For each numerical cell, we encode the attribute name anum with BERT and scale the resulting embedding by the normalized cell value obtain the cell-level embedding. Finally, to standardize dimensionality, we apply average pooling to project each cell embedding to IR.. Thus, input table T with M rows and N columns is represented To enable row-level representations, we prepend a special [CLS] column to the table; the resulting tensor has shape E R M Notably, we adopt mini-batch training, where each batch consists of an input sub-table sampled from the complete table with fixed number of rows (e.g., M 64).
tensor X E TR M x
Building upon these cell-level representations, the adaptive encoder Ea is designed encode various tables using a two-dimensional Transformer 24 that captures dependencies along both the row and column axes. The encoder stacks Transformer layers that model contextual relationships in both dimensions. For table embeddings (x,, J.M N+1 [Kij)==j=11 with Xij E TRdd we apply standard multi-head self-attention layer to the row sequence (Xi....., X((+1)) (((N++)))(((+11) to obtain contextualized row outputs (%/..... ())+))); likewise, apply the same operation to the column sequence (Xij...., XMj) to obtain column outputs (zi,...., Z)rz). The output representation of cell (i,j) is the average of the two directional outputs, Z,j = (2/, + 2 which integrates context from both rows and columns.
We introduce two multi-table pretraining strategies for the adaptive encoder Eg: multi-tabe recon- struction and cross-table correlation prediction. These strategies enable the encoder align table representations across different tables. In the multi-table reconstruction pretraining, misalignment and masking 34 corruption strategies are randomly applied various positions within the tables. Training pairs { {TT, (.),,, her are randomly generated from the multiple tables D, where T₃ E D is a original table and 7; is the corrupted version. Let T; represent the reconstructed table based on the encoded representation (T,). The corresponding loss function for Equation 7 can be rewritten as:
Lroe = Eiern (Ammn Σ Eieftmm |
r122 + Aets Σ Eestp H(T.0)).

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where ő Trum or ő T: denotes the values of numerical or categorical types, respectively. The term represents the cross-entropy loss, and T; is the ground truth of i.
In the pretraining task of cross-table correlation prediction, we randomly sample pairs of tables T and 7 from the dataset DD during each iteration E [7]. These tables then vertically partitioned into sub-tables P and pl (37. Let and F represent rows from P and pl, respectively. The goal of the cross-table correlation prediction task is to predict the correlation between rows P and Pt. The corresponding loss function for Equation (8) can be rewritten
Levr I Σ iienn ExER H (v(F,))).
where (b(F, F!) denotes the cosine similarity between the [CLS] embeddings of rows F and Fl, and y: if they correspond the same entity (otherwise yk 0). Let Ave and Acor denote the combination weights. The total pretraining loss is
Cpre
Area free
Acor Loor-
5.2 Complementary Information Integration
Let D = {T", and (T(1)_ ..... Ta(K) are auxiliary tables. The adaptive encoder &g is first pretrained across all tables in D through the objective defined in Equation (9). We subsequently introduce the multi-table fusion module Fg to integrate complementary information across tables.
",, TT(K)) (T", (
denote a collection of tables, where 7 is the target table
During the training of Fe. each iteration involves sampling row from the target table T as the query instance, while constructing contextual sub-tables (Tra(k) }KERK] by randomly selecting M. rows from each auxiliary table T=(k) to ensure computational tractability.The fusion process can be represented as
Fe pC (pa(k) (E((K).EMM.) u6 Av = (19 (pa(k) )xE(K),EEM.))
(10)
where PC E ())+ denotes the encoded embedding of the i-th entity in target table (a(() ((N++1jxe represents the s-th entity embedding of k-th auxiliary sub-table, while A., and Ug denoting the cross-table attention module and the fusion module.
Au leverages cross-table attention extract and integrate complementary information. To enable effective interaction, adaptive pooling is first employed to project the row-level representations from different tables into unified feature space. Let pk (ū ak i....., ofN,} represent encoded embedding of the i-th entity in table 7% where N₂ is the number of columns in table 1k Through adaptive pooling, the entity oft Nx is transformed into vector 2 Rd by
2 = [)E)N)) o /1++1++0 + + (W.&%)), ( where W E IRd is the learnable weights.
Through aligning the row-level information from different tables into the d-dimensional space, we are able to further extract the complementary information between the fs and auxiliary tables. Denote of the complementary information from table (a(k) to iç. It can be fomulated as follows:
(
Ma
E Nexd
The complementary information from all auxiliary tables is concatenated and fed into the fusioner ||... ct Here, the fusioner Ug is
Ug to produce the final prediction: j.a = (F," implemented as stack of standard Transformer layers. The learnable parameters & of Fg comprise the parameters of A. and the parameters @ of Ug; all parameters are optimized according the objective in Equation
Experiment
In this section, we demonstrate ATCA-Net's ability to integrate complementary information across multiple tables and show that the CS metric effectively measures inter-table complementarity. We
7

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Table 2: Statistics of datasets, organized into three groups for multiple tables setting.
Group
Name
Datapoints
Categorical
Numerical
Positive Ratio
credit-g (CG)
1,000
13
0.70
adult (AD)
48,842
12
0.24
Group 1
blastchar (BL)
7,043
16
3
0.27
1995-income (IC)
32,561
0.24
employee CEC)
1543
0.57
banking churn(BC)
28382
15
0.18
Group 2
churn modeling(CM)
10000
5
8
0.20
customer churn(CC)
64374
0.47
support (SP)
9106
14
29
0.68
Group 3
diabetes (DI)
10000
19
0.13
evaluate performance on classification tasks and report the mean over five runs. Specifically, we construct three groups of real-world multi-table datasets (as shown in Table 2) and four groups of synthesized datasets; detailed settings for the datasets are provided in Appendix A.1.
To compute the complementarity coefficient across multiple tables, we set the hyper parameters = and 7 in Equation ( We set the Ere combination weights Arec 1, and Acur in Equation ( During training stage, we randomly sample sub-tables from the original tables by selecting rows and columns, with the number of rows fixed 64 and the number of columns varying between 2 and the maximum number of columns. The sub-tables is firstly embedded by BERT, where each cell represented
768-dimensional vector, which then reduced to 192 dimensions via fully connected layer to support larger table inputs. These embeddings are subsequently processed by a shared-weight adaptive encoder. Additional experimental details and supplementary results are provided in Appendix B.
6.1 Baselines
We include the following baselines for comparison: the methods learning from single table, in- cluding Logistic Regression (LR). XGBoost (7]. Multilayer Perceptron (MLP), Saint [3], and
Transfofforerr (FT-Trans) [21]: and the method learning from multiple tables Trans Tab [37, |. To further validate the effectiveness of our approach, we extend FT-Transformer and Saint multiple tables learning settings, through single-table encoder pretraining and multiple tables fusion to further validate the effectiivneess of our approach.
6.2 Results
Performance real-world datasets We evaluate ATCA-Net's performance classification tasks across three groups of tables, with AUC scores reported in Table Most baseline methods [22] trained and tested single tables. ATCA-Net and TransTab (37) employ cross-table
21 34 7
collaborative training across grouped tables, The results demonstrate that ATCA-Net achieves state- of-the-art performance. outperforming all comparative methods. ATCA-Net (S) denotes the model variant trained and tested solely on single-table representations without any fusion or pretraining processes. ATCA-Net (M) represents the complete multi-table training pipeline with all fusion mechanisms. This set of comparisons also demonstrates the effectiveness of multi-table alignment pretraining and the integration mechanism of complementary information.
Performance on synthetic datasets To further demonstrate the effectiveness of our approach in multiple tables learning tasks, we design the variants learned on multiple tables based on SAINT (4 and FT- Transfforrrrr [21]. Specifically, we train independent encoders on each table using SAINT and FT-Transformer, followed by a fusion network incorporating the cross-table attention mechanism described in Section 5.2 Furthermore, we evaluated TransTab [37]. which employs a collaborative training mechanism related tables to facilitate transfer learning. Furthermore, we implement an AdaBoost ensemble, where base decision tree learners are trained separately on individual tables.

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Table 3: AUC performance on the real-world datsets. Except for ATCA-Net and Trans-tab trained on multiple tables, all methods are trained and tested on single table.
Group 1
Group 2
Group 3
Model
AD
BL
IC
CG
EC
BC
CM
CC
SP
DI
LR
0,851
0.801
0.869
0.720
0.805
0.768
0.734
0.736
0.830
0.827
XGBoost 7
0.912
0.821
0.925
0.726
0.786
0.817
0.837
0.792
0.851
0.832
MLP
0.904
0.832
0.892
0.643
0.769
0.776
0.692
0.782
0.773
0.754
TabPEN v2 22
0.878
0.837
0.888
0.718
0.753
0.809
0.817
0.756
0.820
0.828
FT- Trans 21
0.827
0.756
0.832
0.674
0.714
0.758
0.713
0.738
0.769
0.678
Saint 34
0.859
0.792
0.855
0.701
0.816
0.671
0.826
0.795
0.763
0.862
Trans-tab 37
0.881
0.825
0.893
0.707
0.798
0.751
0.814
0.764
0.841
0.822
ATCA-Net (S)
0
0.825
0.911
0.617
0.812
0.724
0.836
0.757
0.801
0.805
ATCA-Net (M)
0.913
0.846
0.918
0.796
0.862
0.758
0.879
0.803
0.828
0.918
Table 4: AUC performance for the same target table on the blastchar synthetic dataset, trained with five different table groups. CS denotes the complementarity strength, indicating the degree of complementarity offered by each group.
Methods
GP
GP
GP
GP 4
GP 5
CS
0.73
0.83
1.03
0.87
0.35
Saint(S)
0.653
0.653
0.653
0.653
0.653
FT-Trans(S))
0.557
0.557
0.557
0.557
0.557
TransTab(S)
0.599
0.599
0.599
0.599
0.599
ATCA-Net(S)
0.625
0.625
0.625
0.625
0.625
Adaboost(M)
0.613
0.601
0.617
0.609
0.620
Saint(M)
0.620
0.608
0.607
0.606
0.617
FT-Trans(M)
0.557
0.501
0.550
0.523
0.633
TransTab(M)
0.603
0.599
0.606
0.606
0.595
ATCA-Ne((M)
0.657
0.654
0.661
0.663
0.625
The results across five multiple tables groups are present in Table Our method consistently achieves the best performance. It worth noting that, since the evaluation conducted on the target table, the methods with single-table setting produce the same experimental results across all groups. Notably, apart from ATCA-Net, other multiple tables methods exhibited varying degrees of performance degradation compared to their single-table counterparts. This suggests that the introduction of noise makes difficult to extract complementary information, likely due to the absence of cross-table representation alignment mechanism. Our method, leveraging a two-stage framework for multiple tables representation learning and fusion, achieved the best results, with performance improving as the complementarity strength increases. We present additional experimental results on other synthetic datasets in the Appendix B.
6.3 Analysis of Complementarity Strength
3.2p. we provided an initial discussion on the performance of complementary strength. Here, we further analyze it in detail. Using the same setup as Section (.22). we constructed synthetic table datasets. The details of the synthetic dataset and the complementary strength analysis are reported in Appendix B. Figure 2 presents the performance of the proposed multi-table learning method, ATCA-Net, along with the correlation analysis of complementary strength, showing the results across four datasets. The x-axis represents the complementarity strength, and the y-axis repre- sents the AUC or ACC performance. A consistent trend is observed across all four datasets, where the performance of ATCA-NG gradually improves as the complementary strength increases. This demonstrates that the CS metric accurately measures the degree of complementarity between tables, while also validating the ability of ATCA-Net to extract and integrate complementary information from multiple tables.
In Section

---

0.90
KICA Net (MC
ATCA-bor (N)
ATCA-Net (M0
KTTA Nett 291
ATCA-Ae (S)
ATCA-Nat 15)
0.80
235
"coptmeeeaa diway Synthetic dataset on covertype
Synthetic dataset
(b) Synthetic dataset
(c) Synthetic dataset
(a)
(d)
blastchar
airline
diabetes
Figure 2: Experimental results on the four synthetic datasets demonstrate that multi-table approaches consistently outperform single-table methods across all datasets. Notably, ATCA-Net exhibits progressively enhanced performance with increasing complementary strength between tables. The corresponding table coverage metrics annotated adjacent to each point.
Conclusion
In summary, to address the limitation of existing table learning methods in capturing and utilizing the interrelationship among multiple tables, we systematically propose a novel paradigm for learning from multiple tables, which quantifies and integrates complementary information between tables. We introduce the metric complementarity strength to measure how a set of tables can contribute to target table. Furthermore, we provide formal definition for multiple table learning tasks, along with corresponding loss functions. We then present ATCA-Net, which incorporates unified representation learning stage for multiple tables and a complementary integration stage, facilitating the integration of complementarity from multiple tables. Experiments on multiple tables entity prediction tasks demonstrate the effectiveness of our approach for learning multiple tables. This work explores the learning of multiple tables from both theoretical and practical perspectives, providing significant foundation for the advancement the field.
Acknowledgments and Disclosure of Funding
This work was supported by the National Key Research and Development Program of China under Grant R022YFB2703100 the Joint Funds of the National Natural Science Foundation of China under Grant U22A2099, the National Natural Science Foundation China under Grant 62376028, the Excellent Young Scientists Fund (Overseas) of the National Natural Science Foundation of China, and the National Key Scientific Instruments and Equipment Development Project under Grant 62427808.
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A Datasets and Implement Details
Real-World Datasets In our experiments, we examine three distinct groups of datasets. As shown in 2 the first group includes four credit-related tables, encompassing data for tasks such as credit card risk prediction and adult income estimation. The second group consists of four tables focused on predicting both bank customer churn and employee attrition. The third group contains two tables centered on disease prediction, based on health indicators and lifestyle habits. In the same group of tables, there are explicit entity links, but potential associations exist due to the shared similar attributes and entities.
Synthetic Datasets
The synthetic datasets were derived from the OpenML repository, including blastchar, airline, diabetes, and covertype, with details provided in Ta Each synthetic dataset was randomly partitioned by columns into multiple groups of tables; each group contains shared target table and several auxiliary tables. Across groups, both the overlap ratio and the complementarity strength vary. The synthesis procedure is described in Appendix B.
Table 5: Statisties of synthetic datasets
Name
Datapoints
Categorical
Numerical
Positive Ratio
blastchar (BL)
7,043
16
3
0,27
diabetes (DI)
10,000
19
3
0.13
airline (AIR)
129,880
17
0.55
covertype (COV)
81,013
44
10
B
Additional Results
Synthetic dataset on airline Airline dataset has been used to construct five groups of tables by randomly sampling its columns. Each group contains tables, and each table contains N = columns. The i-th group is denoted as GP; = {T", TT,(E)
)je")) [jjj), including the target table T and three auxiliary tables 1:(()) Each group features a different column overlap ratio between T and its auxiliary tables, ranging from 0 to I across groups GP1 GPs.
Table reports the correlation between CS and the column-overlap ratio on the airline synthetic dataset, exhibiting the same trend as in Section 3.22 Using the synthetic dataset airline, we further report the performance of the same target table T across different groups, as shown in Table 7 As CS increases, the proposed ATCA-Net consistently achieves better performance, trend also illustrated in Figure 2(b).
Table The correlation between CS and the overlap rate the synthetic dataset on airline. Values reported as mean + standard deviation across the three auxiliary tables for each group.
Metric
0.0 (GP))
0.2 (GP)
0.5 (GP))
0.8 (GP))
1.0 (GP)
(((T()))T
1.70 0.10
2.03 + 0.19
2.48 0.07
3.48 + 0.24
3.82 + 0.07
Re (TU(()))
0.37 0.02
0.48 + 0.04
0.65 0.04
0.83 0.07
0.88 + 0.01
Info(rali))
1.41 + 0.28 0.28
1.97 + 0.13
2.54 0.27
3.08 0.13
2.31 0.03
CS(1,6)))
0.26 0.05
0.40 + 0.03
0.56 0.06
0.45 0.05
0.19 + 0.02
CS(GP) (T,T7)
0.78
1.19
1.67
1.35
0.56
Synthetic dataset on covertype All tables are randomly sampled by columns from the covertype datasct from the OpenML Repository, with each table containing 10 columns. The i-th group is denoted as GP; = (T (TTTT(()))) ( Jejs. including the target table 7 and three auxiliary tables 7,) Fach group features different column overlap ratio between T and its auxiliary tables, ranging from to across groups GP, to GP3- analysis of the correlation between overlap rate and CS
metrics presented in Table g The corresponding performance metrics provided in Table
13

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Table 7: AUC performance of synthetic dataset on airline
Methods
0.0 (GP)
0.2 (GP))
0.4 (GPs)
0.8 (GP4)
1.0 (GP)
CS
0.78
1.19
1.67
1.35
0.56
Tabpin (S)
0.753
0.753
0.753
0.753
0.753
FT-Trans (S)
0.691
0.691
0.691
0.691
0,691
Saint (S)
0.753
0.753
0.753
0.753
0.753
Trans (S)
0.760
0.760
0.760
0.760
0.760
ATCA-Net (S)
0.742
0.742
0.742
0.742
0.742
Adaboost (M)
0.713
0.714
0.710
0.711
0.711
TransTab (M)
0.760
0.760
0.759
0.760
0.762
ATCA-Net (M)
0.767
0.772
0.787
0.765
0.745
Table 8: The correlation between CS and the overlap rate of the synthetic dataset on covertype. Values reported as mean + standard deviation across the three auxiliary tables for each group.
Metric
0.0 (GP))
0.2 (GP2)
0.5 (GPs)
0.8 (GP1)
1.0 (GPs)
(,(T,o))) TD)
2.00 0.09
3.75 0.15
6.02 + 0.12
7.87 + 0.05
9.53 + 0.11
(T,10))) T))
0.27 0.02
0.66 0.02
0.86 + 0.04
0.92 0.02
0.98 - 0.00
Info(7
3.89 + 0.45
5.04 0.09
5.60 + 0.15
5.06 + 0.24
3.47 + 0.03
(T.()) T
0.70 0.11
1.52 0.07
1.21 + 0.08
0.55 0.02
0.08 0.03
(S,(GR, T))))
2.11
4.57
3.61
1.67
0.25
Table 9: ACC performance of covertype dataset
Methods
0.0(GIP)
0.2(GPP)
0.5(GP))
0.8(GP))
1.0(P)))
CS
2.11
4.57
3.61
1.67
0.25
TabPFN v2 (S)
72.65
72,65
72.65
72.65
72.65
FT-Trans (S)
78.39
78.39
78.39
78.39
78.39
Saint (S)
77.85
77.85
77.85
77.85
77.85
ATCA-Net(S)
78.73
78.73
78.73
78.73
78.73
Adaboost (M)
72.46
72.94
72.20
73.03
72.86
ATCA-Net (M)
80.73
82.39
83.40
79.67
78.75
C Limitations
To our knowledge, we are the first to quantify complementarity across multiple tables and to introduce an architecture that extracts and integrates Several limitations remain: (i) CS depends on column representations from large-scale pretraining, making its accuracy sensitive to representation quality; (ii) CS is defined via column-leve levell similarity and may align with task task-specific gains, motivating task-oriented measures of complementarity; and (iii) although CS correlates positively with predictive performance on real and synthetic data, the gains are modest, underscoring the need for architectures that more effectively exploit complementarity.
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Reviews:
[{"review_id": "wo9oHsT3ZI", "reviewer": "Reviewer_t6gb", "summary": "This paper introduces a novel paradigm for multi-table learning, aiming to quantify and integrate complementary information across heterogeneous tables. The authors propose a new metric, Complementarity Strength (CS), which captures how much relevant and non-redundant information an auxiliary table contributes to a target table, based on relevance, informativeness, and similarity.\n\nTo leverage such complementary information, the authors design a two-stage framework called ATCA-Net. It consists of a cross-table alignment stage (via multi-table pretraining with masked reconstruction and row correlation prediction) and a complementary information integration stage (via cross-table attention over sampled auxiliary rows).\n\nExtensive experiments on real-world and synthetic datasets show that CS correlates well with performance improvements and that ATCA-Net outperforms baselines in classification tasks when trained over multiple semantically related tables.", "questions": "1. **Generalization of pretraining**:\n   Have the authors tested whether the encoder trained on a set of tables A can transfer to a new, unseen table B from the same or different domain? Can CS still be computed in this case? A simple cross-group transfer experiment would significantly strengthen the paper's claims about generality.\n\n2. **Clarify the encoder architecture**:\n   Please specify the architecture of the adaptive table encoder in detail. Is it a 2D Transformer trained from scratch? What pretrained model is used for column/cell embedding? How are categorical and numerical fields embedded in practice?\n\n3. **Interpretability of attention**:\n   Could the authors provide attention heatmaps or illustrative examples showing which auxiliary rows/columns are attended to for a given query row? This would help establish that the model is indeed leveraging “complementary” information and not just aggregating noise.\n\n4. **Robustness to noisy tables**:\n   Have you tested performance when auxiliary tables are semantically unrelated or low-CS? Does the model degrade gracefully? This would help assess whether CS could serve as a practical filter before fusion.\n\n5. **Performance vs number of tables**:\n   Do more tables always help? Could the authors report AUC or accuracy vs number of integrated tables (e.g., 1 → 3 → 5 → 10) on one dataset to assess marginal utility?", "limitations": "The authors provide a “Limitations” section in Appendix C that candidly acknowledges several issues: the reliance on column-level embedding quality, the potential mismatch between structural complementarity and downstream usefulness, and the limited performance gain observed in some settings. These acknowledgments are appropriate and appreciated.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 4, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n\n1. **First formalization of multi-table learning as a general learning paradigm**\n  This paper is, to the best of my knowledge, the first to *explicitly define and instantiate multi-table learning* as a general-purpose learning setting—moving beyond narrow tasks like entity matching, table union, or table pretraining. It positions multi-table learning as an end-to-end supervised prediction setting where tabular inputs may come from heterogeneous, loosely related sources. This framing fills an important methodological gap in the tabular learning literature and is likely to inspire follow-up work.\n\n2. **Practical and impactful motivation**\n  Many real-world data ecosystems (e.g., enterprise data lakes, healthcare systems, multi-source knowledge tables) involve semantically related but structurally diverse tables with no explicit joins. This work is directly motivated by such settings and is one of the first to propose a scalable and general-purpose learning framework for them.\n\n3. **Solid empirical evidence and controlled validation**\n  The authors perform extensive experiments across both real-world and synthetic datasets. They include ablations (e.g., with/without pretraining or auxiliary tables), controlled table synthesis with varying degrees of overlap, and correlation analysis between CS and performance. These carefully designed studies build strong empirical support for the claims.\n\n---\n\n### **Weaknesses**\n\n1. **Lack of transparency about the encoder backbone and architecture visualization**\n  While the paper refers to an adaptive table encoder based on BERT embeddings and a 2D Transformer, the **model’s structural details are under-specified**. It remains unclear whether the encoder is trained from scratch or fine-tuned from existing models like TURL or TabBERT, and what architectural choices (e.g., number of layers, attention heads, pooling) were made.\n  Furthermore, **the paper lacks adequate architecture diagrams**. Figure 1 only shows the high-level pipeline but not the inner structure of key modules such as the encoder or fusion transformer. For a model that claims generality across diverse tables, such architectural clarity is essential for understanding and reproducibility.\n\n2. **Limited evaluation of pretraining generalization**\n  All reported pretraining is done within the same group of task-specific tables. The paper does not test whether the encoder can generalize to unseen tables or whether representations learned from one domain can transfer to another. This limits the claim of general-purpose pretraining.\n\n3. **No interpretability analysis for attention or CS usage**\n  The cross-table attention mechanism is central to ATCA-Net, but there is no visualization (e.g., attention heatmaps or examples) to show how the model chooses auxiliary information. The CS metric, while well-defined, is also not tied to any qualitative analysis showing whether high-CS tables truly lead to meaningful information fusion. This weakens the interpretability and trustworthiness of the mechanism.\n\n4. **No study of failure modes or low-quality auxiliary tables**\n  The model is tested only under curated settings where auxiliary tables are semantically relevant. It is unclear whether ATCA-Net degrades gracefully when given noisy or unrelated tables. The effectiveness of CS as a safeguard filter is not evaluated under such negative conditions.\n\n5. **Scalability reporting is partial**\n  While the fusion-stage training is benchmarked up to 223 tables, the **cost and feasibility of pretraining on hundreds of tables is not reported**. Additionally, the performance gain relative to the number of tables is not analyzed—i.e., whether more tables always help or whether performance plateaus or declines due to noise or redundancy.", "was_revised": true, "final_justification": "The authors have addressed my all concerns.", "rebuttal": "We sincerely thank the reviewer for the detailed and thoughtful feedback. We are particularly encouraged by your recognition of our contributions to formalizing the multi-table learning paradigm, motivating the framework with real-world scenarios, and validating it through controlled empirical studies. We respond to your key concerns below:\n\n---\n\n\n> ### **Q1. Generalization of pretraining**  \n> Have the authors tested whether the encoder trained on a set of tables A can transfer to a new, unseen table B from the same or different domain? Can CS still be computed in this case? A simple cross-group transfer experiment would significantly strengthen the paper's claims about generality.\n\nWe appreciate this important question. The effectiveness of computing CS scores on unseen tables fundamentally depends on the generalization capability of the column embedding model used to extract semantic representations. In our work, we adopt a pretrained column encoder from [1], which is trained on a large and diverse corpus of real-world tables. Importantly, as shown in our experiments (Table 1, Table 6, Table 7), the datasets used for evaluation (e.g., Covertype, Airline, BlastChar) are not part of the pretraining corpus of the column encoder. **This empirical evidence supports the transferability of CS: the metric remains effective even when applied to previously unseen tables from different domains, without requiring retraining.** \nWe will clarify this generalization capability in the final version. \n\n---\n\n\n> ### **Q2. Clarify the encoder architecture**  \n> Please specify the architecture of the adaptive table encoder in detail. Is it a 2D Transformer trained from scratch? What pretrained model is used for column/cell embedding? How are categorical and numerical fields embedded in practice?\n\nThank you for raising this important point. We clarify the architecture and embedding design as follows, and will include these details in the camera-ready version.\n\n**(a) What pretrained model is used for column/cell embedding? How are categorical and numerical fields embedded?**\n\nTo compute column-level embeddings for the CS score, we adopt the pretrained column encoder from [1], which was trained on a large corpus of web and enterprise tables. \nWithin **ATCA-Net**, we further incorporate **cell-level embeddings** based on a BERT model:  \n\n- For **numerical cells** $c_{\\text{num}}$, we first embed the corresponding column header $h_{\\text{cat}}$ using BERT and apply average pooling to obtain a 768-dimensional embedding $e^h_{\\text{num}}$. This is multiplied with the normalized cell value to yield the numerical cell embedding.\n- For **categorical cells** $c_{\\text{cat}}$, we concatenate the cell value and its header as `\"c_{cat} + '_' + h_{cat}\"`, and input this string into BERT. The output is pooled into a 768-d embedding.\n\nTo reduce computation, we project the 768-d cell embeddings into 192 dimensions using a learned linear transformation before passing them to the ATCA-Net encoder.\n\n**(b) Is it a 2D Transformer trained from scratch?**\n\nYes. The adaptive table encoder in ATCA-Net consists of two stacked **2D-Transformer blocks**, each composed of one **row-wise attention** and one **column-wise attention** layer. This encoder is **trained from scratch** during the multi-table training process. We also add a **row-level attention layer** after the 2D blocks to further enhance entity-level alignment across tables.\n\nWe will provide an architectural diagram and implementation details in the camera-ready version for clarity and reproducibility.\n\n\n---\n> ### **Q3. Interpretability of attention**  \n> Could the authors provide attention heatmaps or illustrative examples showing which auxiliary rows/columns are attended to for a given query row? This would help establish that the model is indeed leveraging “complementary” information and not just aggregating noise.\n\n\nWe appreciate the reviewer’s interest in the interpretability of our cross-table attention mechanism. To investigate whether ATCA-Net truly attends to complementary rather than noisy information, we conducted an additional analysis on a synthetic benchmark based on the Invistico Airline dataset, where the tables are constructed by randomly sampling columns and rows. In each trial, we randomly sample one query row from the target table and 60 rows from an auxiliary table, and analysis the cross-table attention distribution over these 60 candidates.\n\nIn more than 75% of the iterations, the highest attention weights are assigned to rows from the same semantic class (e.g., same label) as the query row. This strongly suggests that the attention mechanism is not uniformly aggregating, but rather selectively focusing on informative and semantically aligned auxiliary instances.\n\nDue to rebuttal format constraints, we are unable to include attention heatmaps here. However, we will incorporate full visualizations and case studies in the camera-ready version to further enhance the interpretability of our method.\n\n---\n\n> ### **Q4. Robustness to noisy tables**\n> Have you tested performance when auxiliary tables are semantically unrelated or low-CS? Does the model degrade gracefully? This would help assess whether CS could serve as a practical filter before fusion.\n\n\nThank you for the insightful question. ATCA-Net is designed to handle noisy or low-quality auxiliary tables gracefully. Its Transformer-based fusion module $\\mathcal{U}_\\phi$ automatically downweights auxiliary tables that lack complementary information. When auxiliary tables offer little relevance or no complementarity, the model’s predictions remain close to those made using the target table alone, demonstrating strong robustness to irrelevant tables.\n\nMoreover, the proposed $CS$ metric serves as a practical pre-fusion filter, effectively identifying and excluding low-complementarity tables. We will include a more detailed discussion of this property in the revised version.\n\n> ### **Q5. Performance vs number of tables**  \n> Do more tables always help? Could the authors report AUC or accuracy vs number of integrated tables on one dataset to assess marginal utility?\n\nThank you for the thoughtful question. We clarify that more tables do not always yield better performance. What matters is the complementarity of the tables, not their count. In our experiments, we observed diminishing returns beyond 3–4 tables, as the attention module focuses on those with the highest Complementarity Strength (CS).\n\nThus we conducted a controlled experiment using a synthetic benchmark based on the BlasterChar dataset, where we fixed the number of auxiliary tables and varied their Complementarity Strength (CS). Results show that higher CS leads to consistently better AUC. \n\n**Table: AUC Performance under Varying Complementarity Strength (CS)**\n|   |  |  |  |  | |\n|-------------------|---------:|---------:|---------:|---------:|---------:|\n| **CS**            | 0.35     | 0.73     | 0.83     | 0.87     | 1.03     |\n| **ATCA-Net (M)**  | 0.625    | 0.657| 0.654| 0.663| 0.661|\n\n\n---\nOnce again, we thank the reviewer for the insightful feedback. Your comments helped us strengthen the technical clarity, empirical robustness, and practical relevance of our work. We look forward to incorporating these improvements into the final version.\n\n[1] *Semantics-aware dataset discovery from data lakes with contextualized column-based representation learning. VLDB 2023*"}, {"review_id": "OdxAjL0Xqr", "reviewer": "Reviewer_kAtP", "summary": "This paper introduces a novel paradigm for multi-table learning, addressing the critical challenge of quantifying and integrating complementary information across heterogeneous tables. The authors propose two main contributions:\n1. ​​Complementarity Strength ​​: A metric combining relevance, similarity, and informativeness to quantify inter-table complementarity.\n2. ​​ATCA-Net​​: An architecture featuring adaptive table encoders and cross-table attention mechanisms to align and fuse complementary information.\nThe framework is validated through extensive experiments on real-world and synthetic datasets, demonstrating superior performance in classification tasks compared to single-table and baseline multi-table methods.", "questions": "The paper designs two types of losses: multi-table reconstruction loss and cross-table correlation prediction loss. Additional experiments and analyses are needed to specifically determine the roles and necessity of these two losses.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strength:\n* The paper systematically formalizes multi-table learning tasks, loss functions, and the CS metric, providing a solid theoretical foundation for future research.\n*  ATCA-Net’s dual-stage design (alignment + fusion) effectively handles schema heterogeneity and latent complementarity, outperforming existing methods.\n* Comprehensive experiments on diverse datasets demonstrate the robustness of CS and ATCA-Net, with clear performance trends tied to complementarity strength.\n\nWeakness:\n* The pretraining stage (reconstruction + correlation prediction) and cross-table attention mechanisms may incur significant computational costs for large-scale tables.\n* The CS metric relies on pretrained column embeddings, which may introduce bias or fail to capture domain-specific semantics without fine-tuning.\n* The CS metric and ATCA-Net rely on hyperparameters (e.g., α, γ in CS), but their impact on performance across diverse datasets is not thoroughly analyzed", "was_revised": true, "final_justification": "Thank you for the detailed rebuttal. The ablation results effectively demonstrate the necessity of both the reconstruction and correlation losses, as removing either leads to consistent performance drops. While my overall assessment remains unchanged, the rebuttal has addressed some concerns and improved the clarity of the work.", "rebuttal": "We sincerely thank the reviewer for the constructive and detailed feedback. We are encouraged by your recognition of our contributions to formalizing the multi-table learning paradigm, designing ATCA-Net, and introducing the CS metric. We respond to the key concerns below:\n\n> ### **Q1. Necessity of the two loss components**  \n> The paper designs two types of losses: multi-table reconstruction loss and cross-table correlation prediction loss. Additional experiments and analyses are needed to specifically determine the roles and necessity of these two losses.\n\nWe thank the reviewer for highlighting the importance of understanding the role of each loss component. \nThe two proposed loss objectives are central to enabling the encoder to embed heterogeneous tables into a unified representation space while capturing latent inter-table dependencies:\n- The **reconstruction loss** encourages the encoder to capture attribute-level semantics within each table;\n- The **correlation prediction loss** models the correlation between entities across different tables.\n\nTo validate their necessity, we conducted an ablation study across five variants of ATCA-Net:\nWe conducted an **ablation study** comparing five variants of ATCA-Net:\n- **(S)**: Trained/tested on single tables (without pretraining or fusion);\n- **(P)**: Pretrained/Trained/tested on single table;\n- **($M_{\\lambda_{\\text{cor}}=0}$)**: Trained/tested on multi tables (without correlation loss);\n- **($M_{\\lambda_{\\text{rec}}=0}$)**: Trained/tested on multi tables (without reconstruction loss);\n- **($M$)**: Full ATCA-Net with both losses.\n\nThe results (see Table below) show that **removing either loss leads to consistent performance degradation**, with most variants falling below even the single-table pretrained baseline (ATCA-Net (P)). This strongly indicates that Only their joint optimization enables effective complementarity-based fusion. \n\n\n| Model                                | AD    | BL    | IC    | CG    | EC    | BC    | CM    | CC    |\n|-------------------------------------|-------|-------|-------|-------|-------|-------|-------|-------|\n|                                     | **Group 1** → |       |       |       | **Group 2** → |       |       |       |\n|                                     | AD    | BL    | IC    | CG    | EC    | BC    | CM    | CC    |\n| **ATCA-Net (S)**                    | 0.911 | 0.825 | 0.911 | 0.617 | 0.812 | 0.724 | 0.836 | 0.757 |\n| **ATCA-Net (P)**                    | 0.905 | 0.833 | 0.915 | 0.773 | 0.762 | 0.726 | 0.837 | 0.767 |\n| **ATCA-Net ($M_{\\lambda_{\\text{cor}}=0}$)** | 0.899 | 0.828 | 0.912 | 0.742 | 0.758 | 0.721 | 0.832 | 0.760 |\n| **ATCA-Net ($M_{\\lambda_{\\text{rec}}=0}$)** | 0.894 | 0.824 | 0.908 | 0.630 | 0.754 | 0.715 | 0.829 | 0.755 |\n| **ATCA-Net ($M$)**                    | **0.913** | **0.846** | **0.918** | **0.796** | **0.862** | **0.758** | **0.879** | **0.803** |\n\n--- \n\nWe also acknowledge the reviewer’s concern regarding the hyperparameters (e.g., α, γ) in the CS metric. While the current version adopts fixed values $\\alpha=\\gamma=1$, we agree that their interpretability and effect deserve further analysis. We have addressed this point in detail in our response to Reviewer MnRt (W1), including usage guidance, empirical ranges, and score interpretation. We will incorporate this discussion into the camera-ready version.\n\nThank you again for your thoughtful feedback and for recognizing the contributions of our work. Your comments have helped us improve the paper."}, {"review_id": "AJ81bkCmbG", "reviewer": "Reviewer_MnRt", "summary": "This paper proposes a metric, Complementarity Strength (CS), and a learning strategy for multi-table setting. CS blends relevance, similarity, and informativeness to quantify how much new, non‑redundant information one table adds to another. The authors formalizes self‑supervised pretraining objectives (multi‑table reconstruction and cross‑table correlation prediction) and implements them in ATCA‑Net, which uses an adaptive 2D‑Transformer encoder plus a cross‑table attention fusion module to align and integrate auxiliary tables into a target table. Experiments on real‑world and synthetic classification tasks show that CS predicts downstream gains and that ATCA‑Net outperforms both single‑table baselines and prior multi‑table methods.", "questions": "please see weaknesses.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n- The Complementarity Strength (CS) metric is thoughtfully designed, with clear, intuitive motivation for how relevance, informativeness, and redundancy are balanced.\n- The formulation of multi‑table learning objectives is coherent and aligns well with the problem setting.\n\nWeaknesses\n- Interpretability of CS\n    - There is no guidance for choosing the two hyperparameters, $\\alpha$ and $\\gamma$. When should practitioners adjust them, and based on what criteria?\n    - The paper does not state the full range of $CS_t(T^k,T^l)$ and $CS_g(T^k,D \\ T^k)$ , nor explain how to interpret specific values (e.g., what constitutes a \"high\" vs. \"low\" score). A discussion or examples would greatly improve clarity. \n- While the two multi-table pretraining strategies, multi-table reconstruction and multi-table reconstruction, are somewhat interesting, they are incremental adaptions from previous studies. Also, the authors introducing two additional hyper-parameters with the pretraining loss (Equation 9), $\\lambda_{rec}$ and $\\lambda_{cor}$ without any ablation or sensitivity analysis makes it hard to understand their impact.\n- The experiments only cover table‑classification tasks. Evaluating on other downstream applications would better demonstrate the versatility and practical value of the approach.\n\nOverall, while the paper offers a novel perspective on quantifying and leveraging table complementarity, addressing the points above would strengthen its interpretability, completeness, and empirical validation.", "was_revised": true, "final_justification": "After considering the rebuttal and other reviews, I recommend a score of 4 (Borderline Accept) for this paper. The authors have adequately addressed my concerns regarding hyperparameter selection and provided clarification on their impact through additional discussion. While I am not directly working in the area of table learning, I acknowledge the contributions highlighted by other reviewers, particularly the novelty of the proposed metric (Complementarity Strength) and the potential of the overall framework to advance multi-table learning. Some concerns, such as broader downstream evaluations, remain partially unaddressed, but on balance, I believe the paper makes a meaningful contribution that warrants acceptance.", "rebuttal": "We would like to thank the reviewer for the careful reading and constructive suggestions. We respond to each point below.\n\n> ### **W1: Interpretability of CS**\n>  - There is no guidance for choosing the two hyperparameters, $\\alpha$ and $\\gamma$. When should practitioners adjust them, and based on what criteria?\n> - The paper does not state the full range of $CS_t(T^k,T^l)$ and $CS_g(T^k,D \\ T^k)$ , nor explain how to interpret specific values (e.g., what constitutes a \"high\" vs. \"low\" score). A discussion or examples would greatly improve clarity.\n\n\n**(a) How should α and γ be adjusted?**\n\n*Complementarity Strength (CS)* is the first metric explicitly designed to quantify how much new, non-redundant information auxiliary tables contributes to a target table. The score $CS_t(T^k,T^l)$ increases with the informativeness $\\mathrm{Info}(T^l)$ and relevance $\\mathrm{R_t}(T^k, T^l)$, and decreases with similarity $\\mathrm{S_t}(T^k, T^l)$ in a convex manner. \n\nSince $CS$ is computed based on pretrained column-level embeddings, **the numerical distributions of relevance and similarity may vary significantly across different embedding models.** To enhance the cross-task generalizability and ranking resolution of $CS$, we introduce the parameters **α** and **γ** as tunable controls:\n- **α** adjusts the overall magnitude of the CS scores；\n- **γ** controls the strength of non-linear penalization for similarity, thus shaping how rapidly $CS$ decays with increasing redundancy.\n\n**Practitioners may adjust these parameters based on two considerations:**\n- The observed range of $R_t/S_t$ produced by the pretrained embeddings;\n- The desired sensitivity to redundancy, which may vary depending on application-specific tolerance for overlapping information.\n\nIn practice, we suggest fix $\\alpha=1$ and adjust $\\gamma\\in[0.5,2]$ to adjust the sharpness of $CS$ decay. In our experiments, we adopt the pretrained embedding model from [1] and simply set **α = γ = 1**, which yields stable and discriminative $CS$ rankings across tables. \n\n**(b) What is the value range of CS and how should specific values be interpreted?** \n\nWe appreciate the reviewer’s request for clarification on the value range and interpretation of the $CS$ score.\n\n**Range of CS.** \nAs defined in Eq.(5), $\\mathrm{CS_t}(T^k, T^l)\\in [0, N_l]$，$\\mathrm{CS_g}(T^k,D \\setminus T^k) \\in \\left[0,\\sum\\nolimits_{k=1}^K N_k\\right]$, where $N_l$ denotes the number of columns in the auxiliary table $T^l$. This upper bound naturally reflects that tables with more columns can encode richer information and offer greater potential complementarity.\n\n\n**Interpretation of the $CS$ score.** \nWhile the theoretical value range of $CS_t(T^k, T^l)$ lies in $[0, N_l]$, in practice, the effective scores tend to be much lower due to the combined effects of three scaling factors: $\\mathrm{Info}(T^l) \\in [0, N_l]$, $\\mathrm{R_t}(T^k, T^l) \\in [0, 1]$, and the term $1 - \\frac{1}{N_l} \\mathrm{S_t}(T^k, T^l) \\in [0, 1]$.\n\nWhen all components are moderately valued (e.g., $\\mathrm{Info}(T^l) \\approx 0.5 N_l$, $\\mathrm{R_t}(T^k, T^l) \\approx 0.5$, $1 - \\frac{1}{N_l} \\mathrm{S_t}(T^k, T^l) \\approx 0.5$), the resulting score approximates $0.125 \\times N_l$. Based on extensive empirical observations, we therefore suggest the following interpretation:\n- **$CS_t(T^k, T^l) > 0.125 \\times N_l$**: strong complementarity;\n- **$CS_t(T^k, T^l) < 0.125 \\times N_l$**: weak or marginal complementarity.\n\nThis threshold is validated in Table 1 of the main paper, where each candidate table contains 10 columns and a score of $CS_t > 1.25$ effectively identifies complementary tables. Further confirmation is provided by the case studies reported in Tables 6 and 7 in the appendix. We will include this interpretation and threshold discussion in the camera-ready version.\n\n[1] *Semantics-aware dataset discovery from data lakes with contextualized column-based representation learning.*\n\n> ### **W2: Pretraining Strategy**  \n> While the two multi-table pretraining strategies, multi-table reconstruction and multi-table reconstruction, are somewhat interesting, they are incremental adaptations from previous studies. Also, the authors introducing two additional hyper-parameters with the pretraining loss (Equation 9), $\\lambda_{\\text{rec}}$ and $\\lambda_{\\text{cor}}$, without any ablation or sensitivity analysis makes it hard to understand their impact.\n\n\nWe thank the reviewer for raising concerns about the novelty and justification of the pretraining strategies and associated hyper-parameters.\n\nTo best of our known, this is the **first learning paradigm** that directly learns from multiple tables — introducing the **first architecture**, ATCA-Net, to integrate the complementarity. \nThe joint pretraining strategy—including multi-table reconstruction and cross-table correlation prediction—is specifically designed to support the architecture for multi-table learning, which have not been explored before. It allows the encoder to map heterogeneous tables into a unified space and model cross-table attribute and entity dependencies.\n\nTo further clarify the role of the two loss components in table alignment, we will included an ablation study in the revised version. \nWe compare five ATCA-Net variants to assess the effect of multi-table training and each loss component:\n\n- **(S)**: Trained and tested on single tables only, without any fusion or pretraining.\n- **(P)**: Pretrained on individual tables, but no cross-table fusion.\n- **($M$)**: Full multi-table model with both reconstruction and correlation objectives.\n- **($M_{\\lambda_{\\text{cor}}=0}$)**: Removes correlation loss.\n- **($M_{\\lambda_{\\text{rec}}=0}$)**: Removes reconstruction loss.\n\n**Table: Ablation Results**  \n| Model                                | AD    | BL    | IC    | CG    | EC    | BC    | CM    | CC    |\n|-------------------------------------|-------|-------|-------|-------|-------|-------|-------|-------|\n|                                     | **Group 1** → |       |       |       | **Group 2** → |       |       |       |\n|                                     | AD    | BL    | IC    | CG    | EC    | BC    | CM    | CC    |\n| **ATCA-Net (S)**                    | 0.911 | 0.825 | 0.911 | 0.617 | 0.812 | 0.724 | 0.836 | 0.757 |\n| **ATCA-Net (P)**                    | 0.905 | 0.833 | 0.915 | 0.773 | 0.762 | 0.726 | 0.837 | 0.767 |\n| **ATCA-Net ($M_{\\lambda_{cor}=0}$)** | 0.899 | 0.828 | 0.912 | 0.742 | 0.758 | 0.721 | 0.832 | 0.760 |\n| **ATCA-Net ($M_{\\lambda_{rec}=0}$)** | 0.894 | 0.824 | 0.908 | 0.630 | 0.754 | 0.715 | 0.829 | 0.755 |\n| **ATCA-Net ($M$)**                    | **0.913** | **0.846** | **0.918** | **0.796** | **0.862** | **0.758** | **0.879** | **0.803** |\n\nAs shown in the table above, removing either objective leads to a significant performance drop, and in most cases, the model underperforms even the single-table pretraining baseline ATCA-Net (P). This confirms that both losses are essential: **the representations learned from their joint training are critical for the subsequent complementarity-based fusion, and neither component can be omitted.**\n\n> ### **W3. Limited evaluation scope**:  \n> The experiments only cover table‑classification tasks. Evaluating on other downstream applications would better demonstrate the versatility and practical value of the approach.\n\nWe appreciate the reviewer’s suggestion. As the first work to define a multi-table learning paradigm—introducing the first metric (CS) to quantify complementarity and the first architecture (ATCA-Net) to integrate it—we focus on classification tasks to validate the approach. \nThese experiments demonstrate the effectiveness of both ATCA-Net and the proposed complementarity metric. We also agree that broader downstream tasks would better showcase the generality of our method. In future work, we plan to extend this paradigm to regression and table-based question answering."}]

Author rebuttal:

Meta-review: This paper makes a timely and impactful contribution by formalizing multi-table learning as a general paradigm and introducing both a principled metric (Complementarity Strength, CS) and an architecture (ATCA-Net) for quantifying and integrating complementary information across heterogeneous tables. The framing is novel and well-motivated, addressing challenges that arise naturally in enterprise, healthcare, and other multi-source data ecosystems.

The reviewers appreciated the clear methodological contribution, strong empirical validation, and practical motivation. While some initial concerns were raised about architectural details, interpretability, and the necessity of loss components, the rebuttal provided clarifications, ablations, and interpretability analyses that substantially strengthened the paper. Evaluation is currently limited to classification tasks, but the reviewers agreed this work lays important foundations for broader applications.

Overall, this is a technically solid and original paper that is expected to stimulate follow-up research in tabular learning.
Decision: Accept (spotlight)