Missing modality remains a longstanding challenge in multimodal learning. Existing methods typically address this issue through modality recovery or adaptive strategies. However, they overlook models' internal cross-modal dependencies formed during multimodal training, which later impair robustness. We systematically characterize a counterintuitive deployment-time failure mode: models trained on full modalities can underperform unimodal models when one modality is missing at inference time. This pattern appears across diverse architectures, such as fusion models, CLIP-style two-tower models, and vision-language models. We show that such degradation is closely associated with learned cross-modal dependencies in the principal parameter subspaces. Multimodal training induces structured rotations of these subspaces, particularly in cross-modal interaction layers. These rotations are associated with reduced task-aligned margins and larger task-aware representation harm under missing-modality inputs. We propose Geodesic Unlearning (GU), a lightweight parameter-editing method that leverages Grassmannian subspace geometry for structured subspace correction to improve missing-modality robustness. It rotates the principal input subspace toward a unimodal reference along a geodesic path. We prove that this correction minimizes the distance to the reference within a fixed subspace-distance budget. Experiments across architectures and datasets show that GU improves performance under missing-modality inference while preserving full-modality accuracy, outperforming strong missing-modality robustness baselines. These findings support a geometric view of deployment-time missing-modality degradation and suggest localized subspace editing as a practical route for robustness correction.
Figures & tables
Figure 1: Missing-modality degradation across architectures and datasets. F1 scores are reported for TI-TI, T-T, and TI-T settings. In 26 of the 27 settings, we observe TI-TI>T-T>TI-T , revealing a recurring deployment-time missing-modality degradation pattern.
Model Family
Backbone(s)
Variants
Fusion
RoBERTa [ 33 ] + ResNet50 [ 28 ]
Concat, Gate, Cross-Attention
Fusion (strong encoders)
Qwen [ 62 ] + OpenCLIP [ 24 ]
Concat, Gate, Cross-Attention
Two-tower
OpenCLIP
Mean Pooling, Late Concat
VLM
BLIP-2 [ 31 ]
Classifier Head
Table 1: Representative model families used in our analysis. We cover distinct multimodal integration mechanisms, including explicit fusion architectures, aligned two-tower encoders, and VLMs.
Figure 2: Principal subspace rotation correlates with missing-modality degradation. (a) Within-family z-score normalization reveals a global positive association. (b) Raw within-family measurements show consistent positive associations without normalization.
Figure 3: Stage-wise distribution of task-aware representation harm. The final-error versus final-correct harm gap appears at cross-modal interaction stages and often persists near the classifier.
Dataset
Null-token
SMIL
Flex-MoE
DyMo
Interpolation
GU (Ours)
HM
57.63
56.60
47.58
48.82
58.50
60.88 (+2.38)
IU-XRay
80.00
79.21
71.02
79.19
80.14
81.41 (+1.27)
SNLI-VE
66.35
72.20
70.74
61.30
67.29
74.41 (+2.21)
Table 2: Main missing-image performance (TI-T, F1 ↑ ). Values are three-run means. Underline and bold denote the second-best and best results, and parentheses show gains over the second best.
Figure 4: Representation structure and ablation analysis. (a) On SNLI-VE, GU and layer interpolation preserve similar broad UMAP layouts. (b) On IU-XRay, target-layer selection has the largest effect on robustness recovery.
Family
#Var
TI-T
TI-TI
Δ T
Δ TI
Interp.
GU
Interp.
GU
Interp.
GU
Interp.
GU
Fusion
3
71.34
73.86
86.33
86.37
0.98
3.49
−0.13
−0.09
Fusion (str.)
3
72.34
73.06
75.16
75.95
0.96
1.69
−1.13
−0.34
CLIP
2
74.50
74.68
76.13
76.70
1.04
1.22
−1.21
−0.64
VLM
1
70.65
70.65
81.72
81.73
0.01
0.01
0.00
+0.01
Table 3: Family-level robustness–preservation trade-off on SNLI-VE. ΔT and ΔTI denote changes from the original TI model in TI-T and TI-TI, respectively.
Architecture
Method / Phase
Wall-clock (s)
Peak Mem. (GiB)
ΔT
ΔTI
Fusion CA
Post-hoc LoRA
1812.30
2.090
+6.02
-1.62
Dual CE
2592.03
13.954
+13.57
-0.94
T Reference
1849.09
5.241
–
–
GU Edit
297.19
1.744
–
–
GU (Total)
2146.28
5.241
+8.06
-0.11
CLIP MP
Post-hoc LoRA
1910.39
4.423
+1.03
-3.66
Table 4: Offline cost and robustness–preservation trade-off on SNLI-VE. Including reference training, GU uses less time and peak GPU memory than Dual CE.
Appendix figures & tables21 assets
Supplementary material from the paper’s appendix.
Appendix
Family
Dataset
Variant
TI-TI
T-T
TI-T
Δmiss
Fusion
HM
Concat
69.46±0.32
68.99±0.25
68.96±0.44
0.50±0.14
HM
Gate
67.98±0.28
67.86±0.23
67.57±0.38
0.41±0.12
HM
Cross-Attn
68.82±0.48
68.41±0.40
57.63±0.88
11.19±0.45
IX
Concat
86.41±0.22
81.94±0.18
80.70±0.38
5.71±0.18
IX
Gate
82.79±0.20
81.18±0.17
80.76±0.33
2.03±0.15
IX
Cross-Attn
84.57±0.28
80.97±0.23
80.00±0.47
4.57±0.22
Appendix
Table 5: F1 performance under three training–testing regimes. TI-T consistently underperforms T-T across model families and datasets.
Variant
Layer
Δharm
Δviol
Concat
text_proj_out
0.5187
0.6170
image_proj_out
0.0000
0.0000
fusion_mlp0_concat_input
0.5187
0.6170
fusion_mlp3_output
0.5617
0.7308
head_last_linear_input
0.5617
0.7308
Gate
text_proj_out
0.3881
0.5735
Appendix
Table 6: Layer-wise task-aware representational harm for fusion models on SNLI-VE. Harm gaps appear at cross-modal interaction stages and often persist near the classifier.
Variant
Layer
Overlap (In / Out)
Mean Angle (In / Out)
Fro. Dist.
Concat
text_proj
0.9666 / 0.9666
8.3333 / 8.3150
1.4884
image_proj
0.8368 / 0.8409
19.2640 / 18.7282
2.5745
fusion_mlp0
0.9307 / 0.9314
11.4472 / 11.3110
1.8050
fusion_mlp3
0.9578 / 0.9573
4.2398 / 4.2895
1.3692
head_last_linear
0.9991 / 1.0000
1.7072 / 0.0000
0.0511
Gate
text_proj
0.9715 / 0.9714
7.7292 / 7.7325
1.4133
Appendix
Table 7: Layer-wise parameter subspace rotation for fusion models on SNLI-VE. Projection and cross-modal interaction layers generally exhibit larger rotations than the final classifier.
Split
Hateful Memes
SNLI-VE
IU-XRay
Train
8,500
353,482
2,928
Dev
500
11,898
366
Test
1,000
11,937
366
Appendix
Table 8: Dataset split statistics used in our experiments.
Dataset
GU
SMIL Outer
SMIL Inner
Flex-MoE
DyMo
Hateful Memes
3.0×10−5
3.0×10−5
1.0×10−3
3.0×10−5
3.0×10−5
SNLI-VE
3.0×10−5
3.0×10−5
1.0×10−3
3.0×10−5
3.0×10−5
IU-XRay
3.0×10−5
3.0×10−5
1.0×10−3
3.0×10−5
3.0×10−5
Appendix
Table 9: Learning rates for missing-modality baselines. Unspecified hyperparameters follow the official codebase defaults.
Dataset
Concat
Cross-Attention
Gate
Hateful Memes
3.0×10−5
3.0×10−5
3.0×10−5
SNLI-VE
3.0×10−5
3.0×10−5
3.0×10−5
IU-XRay
3.0×10−5
3.0×10−5
3.0×10−5
Appendix
Table 10: Learning rates for basic fusion models. A single global learning rate is used for all trainable parameters.
Dataset
Variant
Text/Image
Fusion
Bottleneck/Head
Hateful Memes
Concat
2.0×10−5
3.0×10−5
3.0×10−5
Cross-Attention
2.0×10−5
2.0×10−5
3.0×10−5
Gate
1.0×10−5
2.0×10−5
2.0×10−5
SNLI-VE
Concat
2.0×10−5
3.0×10−5
3.0×10−5
Cross-Attention
1.0×10−5
1.0×10−5
1.0×10−5
Gate
2.0×10−5
3.0×10−5
3.0×10−5
Appendix
Table 11: Module-wise learning rates for fusion models with stronger encoders. Text/image denotes both text_encoder.proj and image_encoder.proj ; bottleneck/head denotes both modules.
Dataset
Variant
Text/Image
Fusion
Bottleneck/Head
Hateful Memes
Late Concat
1.0×10−5
1.0×10−5
1.0×10−5
Mean Pooling
1.0×10−5
–
1.0×10−5
SNLI-VE
Late Concat
1.0×10−5
1.0×10−5
1.0×10−5
Mean Pooling
1.0×10−5
–
1.0×10−5
IU-XRay
Late Concat
1.0×10−5
1.0×10−5
1.0×10−5
Mean Pooling
1.0×10−5
–
1.0×10−5
Appendix
Table 12: Module-wise learning rates for CLIP-style two-tower models. Text/image denotes both projection modules; bottleneck/head denotes both modules.
Dataset
Q-Former
Projection
Bottleneck
Head
Hateful Memes
5.0×10−6
5.0×10−6
2.0×10−5
2.0×10−5
SNLI-VE
1.0×10−5
3.0×10−5
3.0×10−5
3.0×10−5
IU-XRay
1.0×10−5
3.0×10−5
3.0×10−5
3.0×10−5
Appendix
Table 13: Module-wise learning rates for BLIP-2 based VLM models. Q-Former denotes both vlm_encoder.qformer_embeddings and vlm_encoder.backbone.qformer ; projection denotes both vlm_encoder.backbone.language_projection and vlm_encoder.proj .
Model Family
Variant
Target Layer
Fusion / Fusion (strong)
Concat
fusion_mlp0
Fusion / Fusion (strong)
Gate
gate_mlp0
Fusion / Fusion (strong)
Cross-Attention
attn_v_from_t_in_proj
Two-tower
Late Concat
fusion_mlp0
Two-tower
Mean Pooling
text_proj
VLM
BLIP-2 Classifier Head
qformer_crossattn0_out
Appendix
Table 14: Target layers edited by Geodesic Unlearning. We use η=0.75 and k=8 for all configurations.
Method
HM
IU-XRay
SNLI-VE
Null-token
57.63±0.88
80.00±0.47
66.35±0.38
SMIL
56.60±0.74
79.21±0.68
72.20±0.52
Flex-MoE
47.58±1.38
71.02±0.82
70.74±0.64
DyMo
48.82±0.93
79.19±0.77
61.30±0.70
Interpolation
58.50±0.91
80.14±0.49
67.29±0.61
GU (Ours)
60.88±0.73
81.41±0.63
74.41±0.77
Appendix
Table 15: Supplementary results for Table 2 . We report mean ± sample standard deviation over three independent runs. Underline and bold denote the second-best and best mean results, respectively.
Metric
Method
Fusion
Fusion (str.)
CLIP
VLM
TI-T
Interp.
71.34±0.46
72.34±0.38
74.50±0.44
70.65±0.79
GU
73.86±0.56
73.06±0.43
74.68±0.52
70.65±0.68
TI-TI
Interp.
86.33±0.18
75.16±0.37
76.13±0.38
81.72±0.30
GU
86.37±0.14
75.95±0.31
76.70±0.31
81.73±0.18
Δ T
Interp.
0.98±0.30
0.96±0.22
1.04±0.35
0.01±0.10
GU
3.49±0.26
1.69±0.20
1.22±0.33
0.01±0.04
Appendix
Table 16: Supplementary robustness–preservation results for Table 3 on SNLI-VE. Results are mean ± sample standard deviation over three independent runs.
Dataset
Comparison
10-seed paired Δ F1
GU wins
Raw p
Holm p
HM
GU − Null
+3.19±1.14
9/10
0.003906
0.011719
HM
GU − Interp.
+2.41±0.77
10/10
0.001953
0.011719
IX
GU − Null
+1.51±1.71
9/10
0.033203
0.033203
IX
GU − Interp.
+1.34±0.45
10/10
0.001953
0.011719
SV
GU − Null
+8.09±0.22
10/10
0.001953
0.011719
SV
GU − SMIL
+2.21±0.68
10/10
0.001953
0.011719
Appendix
Table 17: Ten-seed paired tests for GU against Null and the strongest competing method in Table 2 . All six comparisons remain significant after Holm correction.
Method
TI-T
CKA to orig.
Error-margin gain
Corr./regr. rate (%)
Orig. TI-T
66.35±0.38
1.000
0
0/0
Interp.
67.29±0.61
0.988±0.001
+0.06±0.01
11.8±0.6/4.5±0.2
GU (Ours)
74.41±0.77
0.991±0.001
+0.30±0.02
34.0±1.3/5.1±0.3
Appendix
Table 18: Quantitative analysis of Figure 4 (a) on SNLI-VE Fusion Cross-Attention. Both edits preserve high representation similarity, while GU yields larger task-level improvements.
Family
Variant
Target Layer
Method
TI-T
TI-TI
ΔT
ΔTI
Fusion
Concat
fusion_mlp0
Interp.
74.86±.68
86.10±.16
1.82±.48
−0.12±.10
Concat
fusion_mlp0
GU
75.11±.56
86.14±.12
2.07±.32
−0.08±.05
Gate
gate_mlp0
Interp.
71.88±.47
86.40±.18
0.18±.24
−0.13±.11
Gate
gate_mlp0
GU
72.05±.35
86.44±.12
0.35±.07
−0.09±.04
Cross-Attn
attn_v ← t_in
Interp.
67.29±.61
86.50±.24
0.94±.29
−0.14±.15
Cross-Attn
attn_v ← t_in
GU
74.41±.77
86.53±.17
8.06±.40
−0.11±.08
Appendix
Table 19: Per-variant robustness–preservation results on SNLI-VE. GU generally provides stronger recovery with comparable or better full-modality preservation than interpolation.
Method
Fusion Concat
CLIP Late Concat
CLIP Mean Pooling
Hateful Memes
Null-token
68.96±0.44/69.46±0.32
66.58±0.41/67.31±0.27
66.87±0.24/67.14±0.20
MoRA
– / –
65.64±0.28/65.39±0.83
60.45±6.17/64.98±0.87
OGM-GE
66.71±0.56/67.07±0.78
66.07±0.47/65.85±0.41
64.51±0.66/65.68±1.10
GU
69.01±0.24/69.32±0.30
67.03±0.17/67.26±0.31
66.96±0.34/67.09±0.22
GU Δ TI
−0.14
−0.05
−0.05
Appendix
Table 20: Cross-architecture comparison with MoRA and OGM-GE. GU achieves the highest mean TI-T in all nine evaluated settings. Entries report TI-T / TI-TI F1. Δ TI denotes GU’s mean TI-TI change relative to Null-token (GU minus Null-token).
Architecture
Method
TI-T
TI-TI
Fusion CA
Null-token
66.35±0.38
86.64±0.10
LoRA
72.37±0.25
85.02±0.35
Dual CE
79.92±0.23
85.70±0.22
GU
74.41±0.77
86.53±0.17
Dual CE+GU
80.09±0.30
86.51±0.19
CLIP MP
Null-token
74.15±0.18
76.62±0.06
Appendix
Table 21: Comparison with post-hoc LoRA and Dual CE on SNLI-VE. Entries report F1 as mean ± sample standard deviation over three independent runs.
Angle only
Harm only
Angle+harm
Selected layer
attn_t_from_v_out_proj
text_proj
attn_v_from_t_in_proj
TI-T
80.34±0.66
80.72±0.40
81.41±0.63
TI-TI
83.96±0.37
84.21±0.32
84.44±0.28
ΔT
+0.34
+0.72
+1.41
ΔTI
−0.61
−0.36
−0.13
Appendix
Table 22: Target-layer selection on IU-XRay Fusion Cross-Attention. Joint angle–harm selection yields the strongest recovery and preservation.
Dataset
Weight
Linear
GU (Ours)
HM
58.50±0.91/66.52±0.33
58.07±1.03/66.62±0.21
60.88±0.73/67.55±0.26
IX
80.14±0.49/82.67±0.56
79.83±0.75/82.39±0.36
81.41±0.63/84.44±0.28
SV
67.29±0.61/86.50±0.24
66.84±1.29/86.50±0.07
74.41±0.77/86.53±0.17
Appendix
Table 23: Controlled comparison of editing strategies on Fusion Cross-Attention. GU achieves the highest mean TI-T and TI-TI across all three datasets. Entries report TI-T / TI-TI F1.
Method
TI-T Acc.
TI-TI Acc.
T Refer. (T-T)
47.17±0.31
–
Shuffle-I
–
39.85±1.97
Orig. TI
38.94±1.92
50.79±0.71
Interp.
39.80±1.21
43.21±1.44
LoRA
43.52±0.60
45.01±1.72
GU (Ours)
41.07±1.79
47.40±1.19
Appendix
Table 24: A-OKVQA multiple-choice accuracy (%) over ten runs. GU provides the strongest full-modality preservation among the evaluated interventions. Bold marks the best result among Interpolation, LoRA, and GU.
Method
Eval.
HM
IU-XRay
SNLI-VE
Orig. TI
TI-TI
68.82±0.48
84.57±0.28
86.64±0.10
I Refer.
I-I
66.58±0.15
75.32±0.41
68.74±0.00
Orig. TI
TI-I
63.32±0.88
73.58±0.85
64.48±0.97
Interp.
TI-I
64.10±0.24
73.70±0.76
65.87±0.46
Interp.
TI-TI
68.30±0.28
84.39±0.36
86.01±0.15
GU (Ours)
TI-I
64.34±0.20
74.42±0.22
66.61±0.27
Appendix
Table 25: Missing-text evaluation with Fusion Cross-Attention. GU improves TI-I while largely preserving full-modality performance across all three datasets.
This paper addresses the missing-modality challenge in multi-modal learning by introducing Unsupervised Learning for Missing Modalities in Multi-Modal Learning (UL4M4), a flexible framework that imputes missing feature embeddings in a task-independent manner before supervised prediction. We propose modality-specific normalization and a novel partial-modality distance metric to enable fair clustering of incomplete observations, capturing cross-modal structures while preserving scale-invariance across varying dimensionalities and modality counts. Cluster centers from this unsupervised stage guide an iterative greedy imputation process for any missing modalities during training or inference, supporting arbitrary numbers of modalities and arbitrary missing patterns per sample. The imputation module is lightweight, uses frozen encoders, and decouples from the downstream task, allowing easy integration with any fusion/prediction architecture. Extensive experiments under diverse and highly incomplete regimes demonstrate UL4M4's robustness, achieving, to the best of our knowledge, the first consistent F1-Micro scores above 0.7 on challenging missing configurations even when more than 50% of modality slots are missing. Results are also stable across cluster sizes and significantly outperform state-of-the-art baselines. Code is available here: https://github.com/h-ismkhan/Multimodal-Learning-with-Missing-Modalities-via-Unsupervised-Learning.
Multimodal learning robust to missing modalities is essential for real-world applications. Existing methods mainly focus on inter-modality missing, where entire modalities are absent, while overlooking intra-modality degradation, where modalities are present but severely corrupted. In practice, these two types of missing often coexist, making existing approaches ineffective. To address this limitation, we propose General Incomplete Multimodal Learning (GIML), a unified framework that simultaneously handles both inter-modality missing and intra-modality degradation through dynamic quality perception. Specifically, GIML models heterogeneous missing patterns as continuous modality information degradation, enabling degradation-aware adaptive fusion. To achieve reliable quality perception, we introduce a Noise-aware Quality Estimator that learns the mapping from corrupted features to noise intensity through controlled noise injection. Furthermore, we propose a Noise-Semantic Decoupled module that separates semantic information from noise interference. This improves robustness and generalization to unseen corruption patterns. Extensive experiments across datasets with diverse modality types demonstrate the effectiveness and generality of GIML. Code is available at: https://github.com/Yu-Five/GIML.
Xiangyu Meng, Shicai Wei
University of Electronic Science and Technology of China
Multimodal systems are vulnerable to partial or complete loss of input channels at deployment, which undermines reliability in real-world settings. This paper presents ModalImmune, a training framework that enforces modality immunity by intentionally and controllably collapsing selected modality information during training so the model learns joint representations that are robust to destructive modality influence. The framework combines a spectrum-adaptive collapse regularizer, an information-gain guided controller for targeted interventions, curvature-aware gradient masking to stabilize destructive updates, and a certified Neumann-truncated hyper-gradient procedure for automatic meta-parameter adaptation. Empirical evaluation on standard multimodal benchmarks demonstrates that ModalImmune improves resilience to modality removal and corruption while retaining convergence stability and reconstruction capacity.
Rong Fu, WeiZhi Tang, Ziming Wang +6
University of Macau · Zhejiang University · Renmin University of China +3