No-Free-Graph: Learning When Multimodal Data Should Be Graphified

Zekai Chen; Kai Hu; YuXin Zeng; Xunkai Li; Xun Wu; Yinlin Zhu; Zhengyu Wu; Xu Wang

cs.LGOct 2, 2026

No-Free-Graph: Learning When Multimodal Data Should Be Graphified

Authors: Zekai Chen, Kai Hu, YuXin Zeng, Xunkai Li, Xun Wu, Yinlin Zhu, Zhengyu Wu, Xu Wang,

Organizations: Beijing Institute of Technology · Sun Yat-sen University · Shandong University

Abstract

Multimodal graph learning has recently emerged as an effective paradigm for in corporating inter-entity relationships into multimodal representations. Existing studies have made substantial progress on how to construct and optimize graphs, but rarely consider a more fundamental question: whether additional relational structures should be introduced for a given dataset and task. Through empirical studies across diverse datasets, tasks, and graph constructors, we reveal that graphification is not consistently beneficial: introducing relational structures can provide substantial improvements in some cases, while offering limited or even negative gains. This observation motivates a new perspective that graph construction should be treated as a selective decision based on its expected utility rather than a default preprocessing step. To address this issue, we propose MAG-SCOUT, a pre-construction graph assessment framework that estimates whether introducing graph structures is beneficial before generating the complete topology. MAG-SCOUT collects limited relational evidence, analyzes its potential taskspecific contribution, and estimates the expected utility of graphification together with construction cost to make a build-or-skip decision. Extensive experiments across six multimodal datasets, three downstream tasks, and diverse graph constructors demonstrate that MAG-SCOUT effectively identifies when graph structures should be introduced, saving 33.1% of task-macro graph work while retaining 96.7% of held-out positive-gain mass under the pre-registered floor.

Figures & tables

Constructor	Node classification (Acc)		Link prediction (AUC)		Cross-modal retrieval (R@5)
	Toys	Grocery	Bili Music	DY	QB	Bili Cartoon
kNN-GCN	+0.58 ±0.31	+2.25 ±0.30	-4.17 ±1.34	-3.77 ±0.61	-3.65 ±2.03	-0.08 ±2.54
MM-kNN-GCN	+0.92 ±0.36	+1.93 ±0.08	-3.89 ±1.27	-2.39 ±0.49	+0.33 ±0.82	-0.34 ±1.34
AutoG	+4.26 ±0.19	+2.92 ±0.16	-0.87 ±0.49	-3.80 ±0.62	-2.41 ±1.14	+1.56 ±0.96
AutoGraph	+7.27 ±0.60	+6.79 ±0.60	+2.02 ±0.49	-2.13 ±1.41	-3.26 ±0.70	-0.34 ±1.37
auGraph	+5.11 ±0.29	+4.97 ±0.27	+1.23 ±0.92	-2.81 ±1.08	-4.31 ±1.83	-0.30 ±1.26

Table 1: GraphGain relative to RawOnly across six multimodal benchmarks, in percentage points (

\Delta\equiv 0

). Cells report five-seed means with standard deviations. All nine constructors are included. The Average row is their unweighted mean on each dataset.

Figure 1: Overview of MAG-Scout : (1) Relational encoding on $\mathcal{P}$ yields compact sketch $\mathcal{S}_{B}$ ; (2) Tri-bottleneck reasoning ( $\mathbf{e}_{N},\mathbf{e}_{C},\mathbf{e}_{U}$ ) estimates value $\mu_{V}$ and scale $\sigma_{V}$ ; (3) Cost-aware gating uses calibrated scale $\tilde{\sigma}_{V}$ to render Build/Skip decisions.

Panel of Figure 2 — Figure 2: Macro prediction quality across five methods and three task families on the 13 parent sources. Panels report Spearman correlation, Kendall correlation, and gain MAE.

Predictor	Spearman rank correlation ( $\rho\uparrow$ )			Kendall rank correlation ( $\tau\uparrow$ )			Gain error ( $\text{MAE}\downarrow$ )
	NC	LP	CMR	NC	LP	CMR	NC	LP	CMR
MAG-Scout	0.417 ±0.05	0.383 ±0.06	0.276 ±0.06	0.362 ±0.03	0.331 ±0.03	0.253 ±0.08	1.63 ±0.17	6.83 ±0.45	3.97 ±0.29
NetInfoF	0.358 ±0.11	0.429 ±0.08	0.099 ±0.13	0.318 ±0.07	0.295 ±0.06	0.074 ±0.06	2.14 ±0.24	8.48 ±1.53	5.22 ±0.53
WDGH	0.336 ±0.12	0.414 ±0.07	0.079 ±0.12	0.294 ±0.11	0.282 ±0.06	0.068 ±0.08	2.39 ±0.22	8.74 ±1.36	4.82 ±0.79
GLEMOS-S2	0.182 ±0.08	0.342 ±0.11	0.059 ±0.08	0.155 ±0.08	0.279 ±0.08	0.046 ±0.06	2.89 ±0.28	7.94 ±0.93	5.70 ±0.72
MetaGL	0.167 ±0.09	0.298 ±0.10	0.037 ±0.12	0.132 ±0.11	0.246 ±0.10	0.027 ±0.09	3.45 ±0.59	7.54 ±1.18	4.76 ±0.67

Table 2: Pre-construction prediction quality across the 13 parent sources. Cells report task-family means with seed-level standard deviations; bold and underline indicate the best and second-best values.

Ablation Variant	Spearman $\rho$ ( $\uparrow$ )			Kendall $\tau$ ( $\uparrow$ )			Gain error (MAE $\downarrow$ )
	NC	LP	CMR	NC	LP	CMR	NC	LP	CMR
Full MAG-Scout (Reference)	0.418 ±0.058	0.379 ±0.047	0.276 ±0.071	0.361 ±0.034	0.324 ±0.041	0.238 ±0.052	1.716 ±0.112	6.748 ±0.418	3.964 ±0.346
Frozen Heuristic Sketch	0.396 ±0.041	0.351 ±0.053	0.241 ±0.036	0.342 ±0.039	0.297 ±0.046	0.209 ±0.033	1.893 ±0.168	7.164 ±0.514	4.218 ±0.431
w/o Necessity ( $\mathbf{e}_{N}$ )	0.361 ±0.064	0.341 ±0.049	0.208 ±0.043	0.312 ±0.058	0.286 ±0.051	0.174 ±0.064	2.163 ±0.246	7.514 ±0.581	4.581 ±0.374
w/o Constructability ( $\mathbf{e}_{C}$ )	0.347 ±0.057	0.328 ±0.038	0.239 ±0.082	0.301 ±0.043	0.274 ±0.067	0.206 ±0.072	2.087 ±0.138	7.628 ±0.894	4.443 ±0.476
w/o Utility ( $\mathbf{e}_{U}$ )	0.339 ±0.046	0.286 ±0.054	0.214 ±0.051	0.287 ±0.031	0.241 ±0.063	0.183 ±0.038	2.458 ±0.184	8.247 ±0.512	4.916 ±0.467

Table 3: Matched component-ablation results on the separate rebuilt source bank across node classification, link prediction, and cross-modal retrieval. Cells report means with seed-level standard deviations; bold marks the best value in each column.

Figure 4: Build/Skip comparison across five predictors: threshold trade-offs, retained-gain floors, and warm decision latency.

Figure 5: One-factor retained mass at a zero threshold, the threshold trade-off, and gain error under input perturbations.

Dimension	Pts	$t=0$ Ref.	$t=0$ Best (Spread)	Perturbation	$\Delta$ Ret.	$\Delta$ Build	Flips
Learning Rate	3	81.9	83.6 (1.7)	Rewiring	$-0.4$	$-7.1$	2/13
BCE Loss Weight	3	96.2	96.5 (0.3)	Relation Collapse	$-0.8$	$-7.1$	2/13
Relation Budget	3	87.8	88.2 (0.4)	Single-Modal Dominant	$-1.6$	$-14.3$	3/13
Utility Head Width	3	93.0	93.4 (0.4)	Relation-Bank Partition	$-0.1$	$-0.2$	0/13

Table 4: Zero-threshold sensitivity (left) and frozen-policy evidence corruption (right) on 13 parent sources. Each factor has its own reference. Best (Spread) is the grid maximum and its difference from that reference.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{D}=(\mathcal{V},\{\mathcal{X}^{(m)}\}_{m\in\mathcal{M}})$	multimodal dataset: entity set $\mathcal{V}$ (cardinality $N=\|\mathcal{V}\|$ ) with modality tensors $\mathcal{X}^{(m)}$
$\mathcal{M}$	set of observed modalities (text, visual, and auxiliary attributes)
$\mathcal{T}$ , $\mathcal{C}$	downstream task and candidate graph constructor
$\mathcal{C}(\mathcal{D})=(\mathcal{V},\mathcal{E}_{\mathcal{C}},\mathbf{A}_{\mathcal{C}})$	graph induced by constructor $\mathcal{C}$
$\mathbf{H}=\{\mathbf{h}_{i}\}_{i=1}^{N}\in\mathbb{R}^{N\times d}$	frozen multimodal entity representations ( $E_{\mathrm{mm}}$ )
$\mathbf{h}_{i}^{(m)}$	modality- $m$ representation of entity $i$

Appendix

Table 5: Notation used throughout the methodology. Dimensions are for a single source; the encoder width is

d

and the reduced projection width is

d^{\prime}\ll d

Task	Nominal	Raw coverage	Calibrated coverage	Raw width	Calibrated width	Raw / calibrated NLL
NC	80%	72.5	77.4	4.69	3.66	1.48 / 1.22
NC	90%	82.9	87.6	6.02	4.70	1.48 / 1.22
NC	95%	88.1	92.7	7.17	5.60	1.48 / 1.22
LP	80%	70.8	76.8	6.84	5.33	1.74 / 1.42
LP	90%	81.2	87.0	8.78	6.84	1.74 / 1.42
LP	95%	86.4	92.1	10.46	8.15	1.74 / 1.42

Appendix

Table 6: Source-held-out uncertainty diagnostics before and after scale calibration. Coverage is reported at each nominal interval level; width is in GraphGain percentage points.

\mathbf{z}_{ij}=\phi_{\theta}([\mathbf{h}_{i}\,\|\,\mathbf{h}_{j}\,\|\,\mathbf{h}_{i}\odot\mathbf{h}_{j}\,\|\,|\mathbf{h}_{i}-\mathbf{h}_{j}|\,\|\,\mathbf{t}\,\|\,\mathbf{c}]).

Appendix

Table 11

Benchmark	Downstream Task	Entities ( $\|\mathcal{V}\|$ )	Source Edges	Modalities	Dims (T/V)	Classes / Targets	Split (Train/Val/Test)
Toys	Node Classification	20,695	126,886	Text, Visual	768 / 768	18 categories	60% / 20% / 20%
Grocery	Node Classification	17,074	171,340	Text, Visual	768 / 768	20 categories	60% / 20% / 20%
Bili Music	Link Prediction	6,038	21,592	Text, Visual	768 / 768	Binary interaction	70% / 10% / 20%
DY	Link Prediction	8,299	35,627	Text, Visual	768 / 768	Binary interaction	70% / 10% / 20%
QB	Cross-modal Retrieval	6,121	24,145	Text, Visual	768 / 768	Query-Item Pairs	60% / 20% / 20%
Bili Cartoon	Cross-modal Retrieval	4,724	18,660	Text, Visual	768 / 768	Query-Video Pairs	60% / 20% / 20%

Appendix

Table 7: Source benchmark statistics for the six datasets. Source edges are published graph counts. Feature dimensions correspond to frozen text and visual encoders; split ratios specify the evaluation protocol, including a held-out-edge split for link prediction.

Ablation Variant	$\Delta$ Spearman $\rho$			$\Delta$ Kendall $\tau$			$\Delta$ MAE
	NC	LP	CMR	NC	LP	CMR	NC	LP	CMR
Frozen Heuristic Sketch	$-0.022$	$-0.028$	$-0.035$	$-0.019$	$-0.027$	$-0.029$	$+0.177$	$+0.416$	$+0.254$
w/o Necessity ( $\mathbf{e}_{N}$ )	$-0.057$	$-0.038$	$-0.068$	$-0.049$	$-0.038$	$-0.064$	$+0.447$	$+0.766$	$+0.617$
w/o Constructability ( $\mathbf{e}_{C}$ )	$-0.071$	$-0.051$	$-0.037$	$-0.060$	$-0.050$	$-0.032$	$+0.371$	$+0.880$	$+0.479$
w/o Utility ( $\mathbf{e}_{U}$ )	$-0.079$	$-0.093$	$-0.062$	$-0.074$	$-0.083$	$-0.055$	$+0.742$	$+1.499$	$+0.952$
Uniform Bottleneck Gates	$-0.137$	$-0.105$	$-0.085$	$-0.115$	$-0.095$	$-0.071$	$+0.625$	$+1.158$	$+0.765$

Appendix

Table 8: Component ablations on the rebuilt 11-source bank, reported as differences from Full MAG-Scout in Table 6.3 . Rank correlations are subtracted from Full. MAE differences are positive when absolute error increases. The bank has 5 node-classification, 4 link-prediction, and 2 cross-modal sources, with three model seeds.

Method	Held-out Retained Gain Mass (%)					Avoided Graph Work (%)
	90%	92.5%	95%	97.5%	99%	90%	92.5%	95%	97.5%	99%
MAG-Scout	96.7	96.7	96.7	96.8 ∗	96.8 ∗	24.2	24.2	23.6	19.6	18.4
NetInfoF	96.3	96.4	96.4	96.4 ∗	97.6 ∗	24.3	23.5	23.2	22.6	21.8
WDGH	85.4 ∗	90.5 ∗	90.5 ∗	90.5 ∗	90.5 ∗	25.0	23.8	23.5	22.3	22.3
GLEMOS-S2	60.0 ∗	60.2 ∗	60.5 ∗	60.9 ∗	64.2 ∗	34.8	32.9	30.3	28.6	24.1
MetaGL	80.2 ∗	80.2 ∗	80.2 ∗	80.4 ∗	83.5 ∗	32.6	32.6	32.6	29.7	25.9

Appendix

Table 9: Build/Skip policies at five retention floors on 13 parent sources. An asterisk ( ∗ ) marks a held-out retention below the floor named in that column.

Retained-fraction $\times$ loss-weight interaction grid (all four cells)
Configuration	Grid Points	Retained (%)	$\Delta$ ref (percentage points)
Selected setting in Figure 6.5 (a)	4	81.9 / 96.2 / 87.8 / 93.0	0
Learning Rate ( $0.001\rightarrow 0.004$ )	3	83.6	+1.7
BCE Loss Weight ( $0.0\rightarrow 1.0$ )	3	96.5	+0.3
Relation Budget ( $0.50\rightarrow 0.75$ )	3	88.2	+0.4
Utility Head Width ( $16\rightarrow 48$ )	3	93.4	+0.4

Appendix

Table 10: One-factor sensitivity at a fixed zero threshold, followed by the budget

\times

loss-weight grid. Retained mass is task-macro positive-gain mass. One-factor differences use that factor’s reference: 81.9, 96.2, 87.8, and 93.0. Interaction differences use the 90.5 grid reference.

Perturbation Family	Scope	$\Delta$ Ret.	$\Delta$ Build	Flips
Rewiring	Macro (13)	$-0.4$	$-7.1$	2/13
	Node classification (5)	$-0.7$	$-13.4$	1/5
	Link prediction (5)	$-0.3$	$-4.7$	1/5
	Cross-modal retrieval (4)	$-0.2$	$-2.2$	0/4
Relation Collapse	Macro (13)	$-0.8$	$-7.1$	2/13
	Node classification (5)	$-1.4$	$-12.1$	1/5

Appendix

Table 11: Frozen-threshold evidence corruption on 13 parent sources. The predictor and threshold are frozen before perturbation.

\Delta

Ret. is the task-macro change in retained positive-gain mass;

\Delta

Build is the build-rate change in percentage points. Macro flips count parent sources. Task rows count evaluations: the books parent contributes one node-classification evaluation and one link-prediction evaluation.

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