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Hei et al. J. Mater. Inf. 2026, 6, 15 Page 7 of 22

Based on S , we apply an inter-attention mechanism to generate g-aware representations for h and h-aware
i
ij
j
i
representations for g :
[29]
j
∑
2ℎ = · (8)

=1
∑
ℎ2 = · ℎ (9)

=1
where A and A are the updated representations of h and g, respectively. They are also represented by the
h2g
g2h
j
i
i
j
vectors in the upper box of Figure 1C.
Intra-entity attention allows the model to learn implicit relationships among entities of the same type. For
example, among PROPERTY VALUE entities, relationships such as magnitude or unit consistency can help
avoid confusion between PROPERTY VALUE and PROPERTY. The calculation methods for the two
attention mechanisms are similar. For h, we have :
[29]
i
1
= Softmax( √ (ℎ , ℎ )) (10)

∑
ℎ2ℎ = · ℎ (11)

=1
where μ is the semantic correlation between h and h, σ denotes the dot product operator, d represents the
j
ij
i
embedding dimension of h, and A is the updated representation of h. For g, we have :
[29]
h2h
i
j
i
i
1
= Softmax( √ ( , )) (12)

∑
2 = · (13)

=1
where v is the semantic correlation between g and g and A is the updated representation of g. j
g2g
k
jk
j
j
Finally, for each pair of potentially confusable entities, we concatenate the six resulting vector
representations and transform the entity allocation task into a binary classification problem :
[29]
2ℎ ℎ2 ℎ2ℎ 2
ˆ = U ℎ ([ℎ ; ; ; ; ; ]) (14)

where z is the matching score between h and g and U is a learnable parameter.
ˆ
hg
i
j
ij
As for training, the objective is to minimize the following cross-entropy function :
[29]
1 ∑ ∑
L 2 = − log(ˆ ) (15)
|H||G|
ℎ∈H ∈G
where and are the sets of the two entity types, and z is the gold label indicating whether h and g are in
G
j
H
i
ij
the same tuple. During testing, each h chooses the g (j = 1, 2, ..., m) that maximizes the matching score z . If
ˆ
ij
j
i
the number of potentially confusable entity types is x (x > 2), the model matches each PROPERTY VALUE
entity with the other four kinds of entities until all PROPERTY VALUE entities are assigned to complete
tuples. During the test, the fully connected layer and activation function transform z into probabilities
ˆ
ij
indicating whether h and g form a correct match. After calculating all z values in the matching matrix, the
i
j
ij
correct matches are given by the h and g corresponding to the maximum probability in each row.
j
i