NIR: Approximate Neural Instance Retrieval for ALCIQ

N'Dah Jean Kouagou; Pritilata Saha; Caglar Demir; Axel-Cyrille Ngonga Ngomo

cs.LGNov 2, 2026

NIR: Approximate Neural Instance Retrieval for ALCIQ

Authors: N'Dah Jean Kouagou, Pritilata Saha, Caglar Demir, Axel-Cyrille Ngonga Ngomo

Organizations: Data Science Group, Heinz Nixdorf Institute, Paderborn University, Germany

Abstract

Instance retrieval is the main bottleneck of concept-learning systems based on refinement operators. We present NIR, a family of neural instance retrievers for ALCIQ that output graded membership scores from knowledge graph embeddings. We compare tokenization-based encoders (GRU, LSTM, Transformer) with a Compositional encoder that mirrors DL operators via primitive sub-networks. On eight benchmarks, all variants approximate Pellet closely on complete knowledge bases, while the Transformer model is most robust under incompleteness. The source code of our approach is at https://github.com/dice-group/owlapy.

Figures & tables

Construct	Synthax	Semantics
Top concept	$\top$	$\Delta^{\mathcal{I}}$
Bottom concept	$\bot$	$\emptyset$
Atomic concept	$C$	$\{a\in\Delta^{\mathcal{I}}:a\in C^{\mathcal{I}}\}$
Negation	$\neg C$	$\Delta^{\mathcal{I}}\backslash C^{\mathcal{I}}$
Conjunction	$C\sqcap D$	$C^{\mathcal{I}}\cap D^{\mathcal{I}}$
Disjunction	$C\sqcup D$	$C^{\mathcal{I}}\cup D^{\mathcal{I}}$

Table 1: Syntax and Semantics of

\mathcal{ALCIQ}

\xspace .

\mathcal{I}=(\Delta^{\mathcal{I}},\cdot^{\mathcal{I}})

is an interpretation.

Symbol	Meaning
$\phi(C)$	embedding of concept $C$ (composition of $\phi_{\and}$ , $\phi_{\leq}$ , $\phi_{\mathrm{inv}}$ )
$\mathbf{a}$ , $\mathbf{R}$	KGE vectors for individual $a$ and role $R$
$\rho(C)$ , $h(\cdot)$	instance set from Pellet; PMA pooling over all $\mathbf{a}$ ’s from $C$
$\phi_{\and},\phi_{\leq},\phi_{\mathrm{inv}}$	primitive maps used in $\phi(\cdot)$
$(\phi_{\and},f_{\phi_{\and}})$ , $(\phi_{\leq},f_{\phi_{\leq}})$ , $(\phi_{\mathrm{inv}},f_{\phi_{\mathrm{inv}}})$	neural modules (map and scoring head)
$f_{\phi_{\ldots}}$	scoring head of primitive $\phi_{\ldots}$ (logit for $(C,a)$ )

Table 2: Notation for the Compositional retriever (our experiments use

d{=}256

, hidden size

128

, dropout

0.1

, threshold

\gamma{=}0.5

Constructor	$\phi(\cdot)$
$\exists\,R.C$	$\phi_{\and}\!\bigl(\phi_{\leq}(0,\mathbf{R},\phi(C)),\phi_{\leq}(0,\mathbf{R},\phi(C))\bigr)$
$\forall\,R.C$	$\phi_{\leq}(0,\mathbf{R},\phi(\neg C))$
$R^{-}$	$\phi_{\mathrm{inv}}(\mathbf{R})$
$\leq n\,R.C$	$\phi_{\leq}(n,\mathbf{R},\phi(C))$
$\geq n\,R.C$ , $n\geq 1$	$\phi_{\and}\!\bigl(\phi_{\leq}(n{-}1,\mathbf{R},\phi(C)),\phi_{\leq}(n{-}1,\mathbf{R},\phi(C))\bigr)$
$\geq 0\,R.C$	$\phi(\top)$

Table 3: Recursive definition of

\phi

	Animals	Carcinogenesis	Family	Lymphography	Mutagenesis	Nctrer	Semantic Bible	Suramin
$\|N_{C}\|$	39	142	18	49	86	37	48	46
$\|N_{R}\|$	2	4	4	0	5	9	29	3
$\|N_{I}\|$	20	22372	202	148	14145	10209	724	2979
Train	2983	20877	3484	3368	10556	4231	16000	2946
Test	746	5220	872	842	2640	1058	4000	737

Table 4: Evaluation datasets.

|N_{C}|

|N_{R}|

, and

|N_{I}|

are the numbers of named concepts, named roles, and individuals, respectively.

Individual	Type	Individual	Type
animals#bat01	Bat	animals#lizard01	Lizard
animals#boy01	Boy	animals#ostrich01	Ostrich
animals#cat01	Cat	animals#penguin01	Penguin
animals#croco01	Crocodile	animals#platypus01	Platypus
animals#dog01	Dog	animals#shark01	Shark
animals#dolphin01	Dolphin	animals#snake01	Snake

Table 5: Individuals in the Animals benchmark. The prefix animals# denotes the DL-Learner namespace.

Dataset	Metric	Compositional	Transformer	GRU	LSTM	EBR
Animals	Jaccard	0.994	0.989	0.981	0.841	0.198
	$F_{1}$ -score	0.995	0.992	0.986	0.854	0.309
	$\Delta_{\text{Time}}$ (%)	-100*	-75 *	-50 *	-150*	<-1000 *
Carcinogenesis	Jaccard	0.871	0.937	0.894	0.802	–
	$F_{1}$ -score	0.917	0.952	0.933	0.871	–
	$\Delta_{\text{Time}}$ (%)	-78.2*	-5.5*	33.8 *	-5.3 *	–

Table 6: Retrieval results across all datasets. For each dataset, we report Jaccard,

F_{1}

-score, and relative

\Delta_{\text{Time}}

(%). The asterisk (*) indicates that the runtime difference between the respective model and Pellet is statistically significant (Wilcoxon signed-rank test,

p<0.05

\Delta_{\text{Time}}

100\times(T_{\text{Pellet}}-T_{\text{model}})/T_{\text{Pellet}}

; values outside

[-1000,1000]

are shown as <-1000 or >1000 . Hence, positive

\Delta_{\text{Time}}

indicates that an approach is faster than Pellet. Empty entries for EBR indicate that it did not complete within 96 hours.

Panel of Figure 1 — Figure 1: Average Jaccard scores by class expression length for different model architectures. Markers (disc, square, triangle, pentagon) indicate the actual performance for each architecture.

Panel of Figure 2 — Figure 2: Average Jaccard on complete knowledge bases for GRU and Transformer with TransE and DeCal embeddings.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Setting	Value
Optimizer	Adam, learning rate $3.5\times 10^{-4}$
LR schedule	Cosine annealing
Epochs	400 (no early stopping)
Batch size	256
Train/validation split	90% / 10%
Embedding dimension $d$	256

Appendix

Table 7: Shared training hyperparameters for all

\mathrm{NIR}

variants.

Description Logic

Description logic provides formal languages for representing ontologies and reasoning about concepts, relations, and their instances.

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Abstract

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