Organizations: Key Laboratory of High Confidence Software Technologies (PKU), Ministry of Education School of Computer Science, Peking University Beijing, China · School of Computer Science Zhejiang University Hangzhou, China · School of Cyber Science and Engineering Wuhan University Wuhan, China · School of Information Science and Technology Tibet University Lhasa, China
Real-world multimodal knowledge graphs (MMKGs) are dynamic, with new entities, relations, and multimodal knowledge emerging over time. Existing continual knowledge graph reasoning (CKGR) methods focus on structural triples and cannot fully exploit multimodal signals from new entities. Existing multimodal knowledge graph reasoning (MMKGR) methods, however, usually assume static graphs and suffer catastrophic forgetting as graphs evolve. To address this gap, we present a systematic study of continual multimodal knowledge graph reasoning (CMMKGR). We construct several continual multimodal knowledge graph benchmarks from existing MMKG datasets and propose MRCKG, a new CMMKGR model. Specifically, MRCKG employs a multimodal-structural collaborative curriculum to schedule progressive learning based on the structural connectivity of new triples to the historical graph and their multimodal compatibility. It also introduces a cross-modal knowledge preservation mechanism to mitigate forgetting through entity representation stability, relational semantic consistency, and modality anchoring. In addition, a multimodal contrastive replay scheme with a two-stage optimization strategy reinforces learned knowledge via multimodal importance sampling and representation alignment. Experiments on multiple datasets show that MRCKG preserves previously learned multimodal knowledge while substantially improving the learning of new knowledge.
Figures & tables
Figure 1. CMMKG stores knowledge in the form of triplets; however, unlike traditional knowledge graphs, its multimodal information also continuously evolves over time. Three snapshots illustrate a continually evolving multimodal knowledge graph. Entities representing political figures and the United States gain and change structural relations, portrait images, and textual descriptions over time.
Figure 2. Overall framework of MRCKG for continual multimodal knowledge graph reasoning. The MRCKG pipeline combines a scalable multimodal encoding backbone with multimodal structure-aware curriculum learning, cross-modality knowledge preservation, multimodal contrastive replay, and two-stage optimization across graph snapshots.
Dataset
Split
S0
S1
S2
S3
S4
#Ent
#Rel
#Triples
#Ent
#Rel
#Triples
#Ent
#Rel
#Triples
#Ent
#Rel
#Triples
#Ent
#Rel
#Triples
DB15K
Entity
4,494
216
50,149
8,501
253
36,735
10,504
261
12,255
11,839
273
5,207
12,842
279
2,012
Higher
1,884
136
8,616
4,266
185
14,853
6,813
206
19,806
9,895
232
29,718
12,842
279
28,290
Equal
4,332
181
19,808
7,221
204
22,783
9,459
229
22,783
11,530
256
22,778
12,842
279
11,451
MKG-W
Entity
5,250
126
21,025
9,930
150
15,891
12,270
156
5,111
13,830
166
2,651
15,000
169
1,323
Higher
1,648
67
3,717
3,891
67
6,411
5,982
100
8,550
9,166
129
12,825
15,000
169
17,095
Table 1. Dataset statistics for all 9 continual MMKG benchmarks ( T=5 snapshots). #Ent and #Rel denote cumulative entity/relation counts at each snapshot; #Triples denotes the number of triples used at each snapshot after bridge augmentation, rather than only newly introduced triples (split into Train/Valid/Test at a 3:1:1 ratio).
DB15K
MKG-W
MKG-Y
Entity
Higher
Equal
Entity
Higher
Equal
Entity
Higher
Equal
Setting
Method
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
MRR
H@10
Unimodal +FT
TransE+FT
0.1085
0.2355
0.0987
0.2271
0.0913
0.2160
0.0956
0.1909
0.1024
0.2289
0.0867
0.1919
0.1243
0.2212
0.1587
0.2962
0.1462
0.2697
DistMult+FT
0.1186
0.2092
0.1063
0.1988
0.0978
0.1880
0.1043
0.1693
0.1098
0.1995
0.0942
0.1695
0.1356
0.1961
0.1725
0.2617
0.1589
0.2382
ComplEx+FT
0.1644
0.2348
0.1512
0.2289
0.1387
0.2159
0.1425
0.1872
0.1536
0.2260
0.1308
0.1905
0.1872
0.2192
0.2316
0.2845
0.2153
0.2614
TuckER+FT
0.1618
0.2151
0.1489
0.2098
0.1354
0.1962
0.1397
0.1709
0.1503
0.2058
0.1276
0.1730
0.1835
0.2000
0.2274
0.2600
0.2108
0.2382
Table 2. Average MRR and Hits@10 comparison on all nine benchmarks. The best result in each column is shown in bold , and the second best is underlined .
Variant
MRR
H@1
H@10
BWT
Full
0.2856
0.2213
0.4102
− 0.068
w/o CMKP
0.2549
0.1988
0.3673
− 0.126
w/o MMCR
0.2683
0.2056
0.3875
− 0.095
w/o MSCL
0.2715
0.2075
0.3914
− 0.085
w/o Prog.
0.2639
0.2021
0.3749
− 0.102
w/o Visual
0.2671
0.2003
0.3931
− 0.073
Table 3. Ablation study on DB15K-Entity, including component ablation and modality ablation.
Figure 3. Analysis on DB15K-Entity. (a) Per-snapshot MRR on new vs. old triples; (b) S0 forgetting curves; (c) MRR–BWT Pareto front; (d) multi-metric radar plot. Four plots compare continual-learning behavior on DB15K-Entity: MRR for new and old triples, forgetting on the first snapshot, the MRR versus backward-transfer frontier, and a radar chart of normalized performance metrics.
Figure 4. Per-snapshot MRR bar plots of MRCKG on the three DB15K settings. Three grouped bar charts show MRR for snapshots zero through four after successive training stages under the Entity, Higher, and Equal DB15K splits.
Figure 5. (a) Error type distribution of MRCKG; (b) Hits@1 of three methods across snapshots. A donut chart partitions MRCKG predictions into forgetting, cold-start, cross-modal ambiguity, other, and correct outcomes. A grouped bar chart compares MRCKG, Structure-CL, and fine-tuning Hits at one across five snapshots.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Method
Entity
Higher
Equal
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
TransE+FT
0.1085
0.0427
0.1331
0.2355
− 0.064
0.0987
0.0350
0.1247
0.2271
− 0.067
0.0913
0.0334
0.1165
0.2160
− 0.074
DistMult+FT
0.1186
0.0751
0.1274
0.2092
− 0.057
0.1063
0.0606
0.1176
0.1988
− 0.060
0.0978
0.0576
0.1093
0.1880
− 0.066
ComplEx+FT
0.1644
0.1275
0.1798
0.2348
− 0.024
0.1512
0.1055
0.1703
0.2289
− 0.025
0.1387
0.1000
0.1578
0.2159
− 0.028
TuckER+FT
0.1618
0.1338
0.1724
0.2151
− 0.022
0.1489
0.1108
0.1634
0.2098
− 0.023
0.1354
0.1041
0.1500
0.1962
− 0.025
TransE+EWC
0.1088
0.0477
0.1301
0.2276
− 0.062
0.0994
0.0392
0.1224
0.2204
− 0.065
0.0921
0.0376
0.1145
0.2100
− 0.071
Appendix
Table 4. Full results on DB15K benchmarks (Avg MRR / H@1 / H@3 / H@10 / BWT). Best bold , second best underlined .
Method
Entity
Higher
Equal
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
TransE+FT
0.0956
0.0376
0.1138
0.1909
− 0.061
0.1024
0.0351
0.1269
0.2289
− 0.066
0.0867
0.0314
0.1074
0.1919
− 0.072
DistMult+FT
0.1043
0.0660
0.1087
0.1693
− 0.054
0.1098
0.0605
0.1191
0.1995
− 0.059
0.0942
0.0549
0.1022
0.1695
− 0.064
ComplEx+FT
0.1425
0.1105
0.1512
0.1872
− 0.023
0.1536
0.1036
0.1697
0.2260
− 0.025
0.1308
0.0933
0.1445
0.1905
− 0.027
TuckER+FT
0.1397
0.1155
0.1444
0.1709
− 0.021
0.1503
0.1081
0.1617
0.2058
− 0.023
0.1276
0.0971
0.1373
0.1730
− 0.025
TransE+EWC
0.0968
0.0424
0.1123
0.1863
− 0.059
0.1037
0.0396
0.1252
0.2234
− 0.064
0.0879
0.0355
0.1062
0.1876
− 0.069
Appendix
Table 5. Full results on MKG-W benchmarks (Avg MRR / H@1 / H@3 / H@10 / BWT). Best bold , second best underlined .
Method
Entity
Higher
Equal
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
MRR
H@1
H@3
H@10
BWT
TransE+FT
0.1243
0.0611
0.1403
0.2212
− 0.056
0.1587
0.0768
0.1811
0.2962
− 0.053
0.1462
0.0719
0.1668
0.2697
− 0.055
DistMult+FT
0.1356
0.1073
0.1340
0.1961
− 0.050
0.1725
0.1344
0.1723
0.2617
− 0.047
0.1589
0.1258
0.1587
0.2382
− 0.049
ComplEx+FT
0.1872
0.1685
0.1884
0.2192
− 0.021
0.2316
0.2084
0.2356
0.2845
− 0.020
0.2153
0.1938
0.2190
0.2614
− 0.021
TuckER+FT
0.1835
0.1651
0.1799
0.2000
− 0.019
0.2274
0.2047
0.2253
0.2600
− 0.018
0.2108
0.1897
0.2089
0.2382
− 0.019
TransE+EWC
0.1258
0.0689
0.1384
0.2158
− 0.055
0.1604
0.0865
0.1784
0.2886
− 0.051
0.1478
0.0810
0.1644
0.2628
− 0.053
Appendix
Table 6. Full results on MKG-Y benchmarks (Avg MRR / H@1 / H@3 / H@10 / BWT). Best bold , second best underlined .
Technology, Innovation, Entrepreneurship Department King Abdullah University of Science and Technology · School of Computing and Information Systems The University of Melbourne · College of Computer Science and Technology Jilin University +2