From Complex Histories to Simple Predictors: Predictive Dimension in Dynamic Graph Learning

Hantong Feng; Duxin Chen; Wenwu Yu

cs.LGOct 20, 2026

From Complex Histories to Simple Predictors: Predictive Dimension in Dynamic Graph Learning

Authors: Hantong Feng, Duxin Chen, Wenwu Yu

Organizations: School of Cyber Science and Engineering, Southeast University. · School of Mathematics, Southeast University. · Frontiers Science Center for Mobile Information Communication and Security.

Abstract

Existing continuous-time graph learning methods rely heavily on complex neural architectures to encode ever-expanding interaction histories. However, the future conditional distribution induced by complex histories can often be characterized by a low-dimensional predictive state manifold, implying that only a few predictive degrees of freedom are essential for future interactions. We therefore argue that continuous-time graph learning should identify low-dimensional states sufficient for future prediction rather than reconstruct the full history. To make this perspective measurable, we define and independently estimate the intrinsic predictive dimension, which quantifies the effective predictive degrees of freedom required by a given task. Specifically, we remove the history-independent marginal from the history-conditioned future distribution, decompose the resulting predictive residual operator, and estimate the minimum effective rank needed to preserve the predictive power of the full history. Experiments across datasets show that model performance saturation is largely determined by the intrinsic predictive dimension. Based on this finding, we propose PreDyG, a lightweight model whose capacity is matched to the intrinsic predictive dimension. PreDyG achieves superior predictive performance with only 0.07% of the parameters of a representative complex baseline.

Figures & tables

Figure 1: Overview of PreDyG, the encoder guided by intrinsic predictive dimension.

Figure 2: (a) History-conditioned future distributions are lower-dimensional than the independence null. (b) The estimated predictive dimension $\widehat{d}_{\mathrm{pred}}$ aligns with the held-out saturation dimension $d_{\mathrm{hold}}$ , marking the onset of capacity saturation.

Dataset	Original	Time/order	Destination	Source	Source–destination pair
Reddit	$256/256$ (100%)	$256/256$ (100%)	$1/1$ ( $<1\%$ )	$1/1$ ( $<1\%$ )	$256/256$ (100%)
SocialEvo	$32/32$ (100%)	$32/16$ (100%)	$1/1$ (3%)	$1/1$ (3%)	$16/16$ (50%)
UCI	$256/256$ (100%)	$1/1$ ( $<1\%$ )	$1/1$ ( $<1\%$ )	$1/1$ ( $<1\%$ )	$1/1$ ( $<1\%$ )
Contacts	$512/512$ (100%)	$512/512$ (100%)	$1/1$ ( $<1\%$ )	$4/1$ (1%)	$512/512$ (100%)

Table 1: Dependency interventions. Each cell reports

\widehat{d}_{\mathrm{pred}}/d_{\mathrm{hold}}

, followed by the percentage of the original predictive dimension retained.

Figure 3: (a) Test AP across ordered capacity configurations; diamonds mark $P_{0.05}$ . (b) $P_{0.05}$ versus $\widehat{d}_{\mathrm{pred}}/D_{\mathrm{amb}}$ ; the line and shading show the fitted trend and its $95\%$ confidence interval.

Panel of Figure 4 — Figure 4: The AP metrics and generalization gap on multiple datasets with the early stopping mechanism were compared: (a) Wikipedia; (b) UCI; (c) Enron.

Figure 5: Training efficiency. (a) Trainable parameter counts, with baselines grouped into five comparable scales. Validation accuracy versus time per epoch on (b) Wikipedia and (c) UCI.

Method	Wiki	Reddit	LastFM	Enron	SocialEvo	UCI	Flights	Contacts
JODIE	$96.50{\pm}.18$	$98.31{\pm}.12$	$70.85{\pm}2.11$	$84.77{\pm}.28$	$89.89{\pm}.52$	$89.43{\pm}1.06$	$95.60{\pm}1.72$	$95.31{\pm}1.36$
DyRep	$94.86{\pm}.04$	$98.22{\pm}.07$	$71.92{\pm}2.20$	$82.38{\pm}3.32$	$88.87{\pm}.31$	$65.14{\pm}2.33$	$95.29{\pm}.69$	$95.98{\pm}.15$
TGN	$98.45{\pm}.05$	$98.63{\pm}.05$	$77.07{\pm}3.99$	$86.53{\pm}1.14$	$93.57{\pm}.21$	$92.34{\pm}1.02$	$97.95{\pm}.16$	$96.89{\pm}.54$
CAWN	$98.76{\pm}.03$	$99.11{\pm}.01$	$86.99{\pm}.07$	$89.56{\pm}.13$	$84.96{\pm}.09$	$95.18{\pm}.05$	$\underline{98.51{\pm}.01}$	$90.26{\pm}.30$
GraphMixer	$97.25{\pm}.03$	$97.31{\pm}.01$	$75.61{\pm}.22$	$82.25{\pm}.16$	$93.37{\pm}.07$	$93.25{\pm}.54$	$90.99{\pm}.08$	$91.92{\pm}.03$
DyGFormer	$98.82{\pm}.02$	$99.11{\pm}.01$	$93.00{\pm}.12$	$92.47{\pm}.15$	$94.47{\pm}.01$	$95.76{\pm}.16$	$98.25{\pm}.01$	$\underline{98.29{\pm}.01}$

Table 2: Transductive average precision (%) on eight domains, reported as mean

\pm

standard deviation. Best and second-best entries are bold and underlined, respectively.

Method	tgbl-wiki	tgbl-review	tgbl-coin	tgbl-comment
CAWN	73.04 $\pm$ .60	19.30 $\pm$ .10	–	–
DyRep	$51.91{\pm}1.95$	$\underline{40.06{\pm}.59}$	$45.20{\pm}4.60$	$28.90{\pm}3.30$
DyGFormer	$77.36{\pm}.31$	$22.39{\pm}1.52$	$\underline{75.17{\pm}.38}$	$67.03{\pm}.14$
TCL	$\underline{78.11{\pm}.20}$	$16.51{\pm}1.85$	$68.66{\pm}.30$	$\underline{70.11{\pm}.83}$
TGAT	59.94 $\pm$ 1.63	19.64 $\pm$ .23	60.92 $\pm$ .57	56.20 $\pm$ 2.11
TGN	68.93 $\pm$ .53	37.48 $\pm$ .23	58.60 $\pm$ 3.70	37.90 $\pm$ 2.00

Table 3: MRR (%) on large TGB datasets. Dashes denote unavailable reported results. Best and second-best entries are bold and underlined, respectively.

Variant	Wiki	Reddit	Enron	UCI
Full PreDyG	99.30	99.34	93.18	97.01
w/o NIF	97.44	97.87	84.05	93.28
w/o modalities	98.16	98.73	90.99	95.19
w/o fusion	99.07	99.18	90.43	95.14

Table 4: The results of Component ablation experiments.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Competing data statistics. Spearman correlation of each statistic with $d_{\mathrm{hold}}$ across the eight datasets used in the capacity analysis.

Panel of Figure 7 — Figure 7: Compared to the performance of lightweight baselines, our method achieves state-of-the-art results on all datasets.

Panel of Figure 8 — Figure 8: Training time comparison for one epoch across different baselines on multiple datasets: (a) Wikipedia; (b) UCI; (c) Enron; (d) Reddit.

Dataset	$\text{Dim}_{n}$	$\text{Dim}_{e}$	# Nodes	# Edges	Information	Duration	Time Granularity
Wikipedia	-	172	9,227	157,474	Social	1 month	Unix timestamps
Reddit	-	172	10,984	672,447	Social	1 month	Unix timestamps
LastFM	-	-	1,980	1,293,103	Interaction	1 month	Unix timestamps
Enron	-	-	184	125,235	Communication	3 years	Unix timestamps
Social Evo.	-	-	59	90,879	Proximity	77 days	Unix timestamps
Contact	-	-	274	28,244	Proximity	20 days	Unix timestamps

Appendix

Table 6: The statistical information of each component of the dataset used in the experiment.

Panel of Figure 9 — Figure 9: The AP , AUC and loss metrics and generalization gap of multiple training sets with the early stopping mechanism were compared. Training curves comparison across different datasets and evaluation metrics. The first row shows Wikipedia, the second row shows UCI, the third row shows Enron, and the fourth row shows Reddit datasets. From left to right: the average precision (AP) curve, the ROC-AUC curve, and the validation loss curve during training. Each plot displays the PreDyG and other baselines over training time.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	EdgeBank	TCL	GraphMixer	DyGFormer	PhyDyG
rnd	Wikipedia	96.50 $\pm$ 0.18	94.86 $\pm$ 0.04	96.94 $\pm$ 0.06	98.45 $\pm$ 0.05	98.76 $\pm$ 0.03	90.37 $\pm$ 0.00	96.47 $\pm$ 0.14	97.25 $\pm$ 0.03	98.82 $\pm$ 0.02	99.30 $\pm$ 0.01
	Reddit	98.31 $\pm$ 0.12	98.22 $\pm$ 0.07	98.52 $\pm$ 0.02	98.63 $\pm$ 0.05	99.11 $\pm$ 0.01	94.86 $\pm$ 0.00	97.53 $\pm$ 0.02	97.31 $\pm$ 0.01	99.11 $\pm$ 0.01	99.34 $\pm$ 0.01
	Enron	84.77 $\pm$ 0.28	82.38 $\pm$ 3.32	71.12 $\pm$ 0.96	86.53 $\pm$ 1.14	89.56 $\pm$ 0.13	83.53 $\pm$ 0.00	79.70 $\pm$ 0.72	82.25 $\pm$ 0.16	92.47 $\pm$ 0.15	93.18 $\pm$ 0.19
	UCI	89.43 $\pm$ 1.06	65.14 $\pm$ 2.33	79.63 $\pm$ 0.71	92.34 $\pm$ 1.02	95.18 $\pm$ 0.05	76.20 $\pm$ 0.00	89.57 $\pm$ 1.61	93.25 $\pm$ 0.54	95.76 $\pm$ 0.16	97.01 $\pm$ 0.03
	LastFM	70.85 $\pm$ 2.11	71.92 $\pm$ 2.20	73.42 $\pm$ 0.18	77.07 $\pm$ 3.99	86.99 $\pm$ 0.07	79.29 $\pm$ 0.00	67.27 $\pm$ 2.13	75.61 $\pm$ 0.22	93.00 $\pm$ 0.10	93.97 $\pm$ 0.06
	Social Evo.	89.89 $\pm$ 0.52	88.87 $\pm$ 0.31	93.16 $\pm$ 0.20	93.57 $\pm$ 0.21	84.96 $\pm$ 0.09	74.95 $\pm$ 0.00	93.13 $\pm$ 0.17	93.37 $\pm$ 0.07	94.47 $\pm$ 0.01	94.68 $\pm$ 0.01

Appendix

Table 7: Average Precision (AP) comparison across different negative sampling strategies (rnd: random, hist: historical, ind: inductive) in transductive link prediction setting.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	EdgeBank	TCL	GraphMixer	DyGFormer	PhyDyG
rnd	Wikipedia	96.33 $\pm$ 0.05	94.37 $\pm$ 0.06	96.67 $\pm$ 0.07	98.37 $\pm$ 0.07	98.54 $\pm$ 0.04	90.78 $\pm$ 0.00	95.84 $\pm$ 0.15	96.92 $\pm$ 0.03	98.91 $\pm$ 0.02	99.30 $\pm$ 0.01
	Reddit	98.31 $\pm$ 0.06	98.17 $\pm$ 0.02	98.47 $\pm$ 0.02	98.60 $\pm$ 0.07	99.01 $\pm$ 0.01	95.37 $\pm$ 0.00	97.42 $\pm$ 0.02	97.17 $\pm$ 0.02	99.15 $\pm$ 0.01	99.31 $\pm$ 0.01
	LastFM	70.49 $\pm$ 1.70	71.16 $\pm$ 1.86	71.59 $\pm$ 0.17	78.47 $\pm$ 2.94	85.92 $\pm$ 0.09	83.77 $\pm$ 0.00	64.06 $\pm$ 1.17	73.53 $\pm$ 0.09	93.05 $\pm$ 0.10	94.10 $\pm$ 0.07
	Enron	87.96 $\pm$ 0.51	84.89 $\pm$ 3.04	68.89 $\pm$ 1.08	88.32 $\pm$ 0.95	90.45 $\pm$ 0.17	87.05 $\pm$ 0.00	75.74 $\pm$ 0.73	84.38 $\pm$ 0.24	93.33 $\pm$ 0.14	93.88 $\pm$ 0.02
	Social Evo.	92.05 $\pm$ 0.47	90.76 $\pm$ 0.22	94.76 $\pm$ 0.16	95.39 $\pm$ 0.13	87.34 $\pm$ 0.10	81.60 $\pm$ 0.00	94.84 $\pm$ 0.20	95.23 $\pm$ 0.04	96.30 $\pm$ 0.01	96.40 $\pm$ 0.01
	UCI	90.44 $\pm$ 0.45	68.77 $\pm$ 2.38	78.53 $\pm$ 0.71	92.03 $\pm$ 1.11	93.87 $\pm$ 0.11	77.30 $\pm$ 0.00	87.82 $\pm$ 1.39	91.81 $\pm$ 0.69	94.49 $\pm$ 0.29	96.22 $\pm$ 0.03

Appendix

Table 8: AUC-ROC comparison across different negative sampling strategies in transductive link prediction setting.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	PhyDyG
rnd	Wikipedia	94.82 $\pm$ 0.23	92.43 $\pm$ 0.38	96.22 $\pm$ 0.06	97.83 $\pm$ 0.07	98.24 $\pm$ 0.03	96.22 $\pm$ 0.15	96.65 $\pm$ 0.02	98.59 $\pm$ 0.03	98.96 $\pm$ 0.01
	Reddit	96.50 $\pm$ 0.16	96.09 $\pm$ 0.11	97.09 $\pm$ 0.06	97.50 $\pm$ 0.09	98.62 $\pm$ 0.01	94.09 $\pm$ 0.11	95.26 $\pm$ 0.02	98.84 $\pm$ 0.02	99.00 $\pm$ 0.01
	LastFM	81.61 $\pm$ 3.81	83.02 $\pm$ 1.44	78.63 $\pm$ 0.34	81.45 $\pm$ 4.29	89.42 $\pm$ 0.06	73.53 $\pm$ 1.67	82.11 $\pm$ 0.40	94.23 $\pm$ 0.06	95.18 $\pm$ 0.02
	Enron	80.72 $\pm$ 1.42	74.55 $\pm$ 3.93	67.05 $\pm$ 1.54	77.94 $\pm$ 1.05	86.35 $\pm$ 0.51	76.14 $\pm$ 0.82	75.88 $\pm$ 0.46	89.76 $\pm$ 0.34	89.90 $\pm$ 0.19
	Social Evo.	91.96 $\pm$ 0.49	90.04 $\pm$ 0.50	91.41 $\pm$ 0.13	90.77 $\pm$ 0.89	79.94 $\pm$ 0.20	91.55 $\pm$ 0.08	91.86 $\pm$ 0.06	93.14 $\pm$ 0.06	93.20 $\pm$ 0.08
	UCI	79.86 $\pm$ 1.46	57.48 $\pm$ 1.85	79.54 $\pm$ 0.51	88.12 $\pm$ 2.05	92.73 $\pm$ 0.07	87.36 $\pm$ 2.04	91.19 $\pm$ 0.41	94.54 $\pm$ 0.15	95.75 $\pm$ 0.09

Appendix

Table 9: Average Precision (AP) comparison across different negative sampling strategies in inductive link prediction setting.

NSS	Datasets	JODIE	DyRep	TGAT	TGN	CAWN	TCL	GraphMixer	DyGFormer	PhyDyG
rnd	Wikipedia	94.33 $\pm$ 0.28	91.49 $\pm$ 0.47	95.90 $\pm$ 0.10	97.72 $\pm$ 0.03	98.03 $\pm$ 0.03	95.57 $\pm$ 0.18	96.30 $\pm$ 0.06	98.48 $\pm$ 0.03	98.93 $\pm$ 0.01
	Reddit	96.52 $\pm$ 0.10	96.05 $\pm$ 0.11	96.98 $\pm$ 0.07	97.39 $\pm$ 0.08	98.42 $\pm$ 0.02	93.80 $\pm$ 0.03	94.97 $\pm$ 0.02	98.71 $\pm$ 0.01	98.93 $\pm$ 0.01
	LastFM	81.13 $\pm$ 3.37	82.24 $\pm$ 1.48	76.99 $\pm$ 0.26	82.61 $\pm$ 3.15	87.82 $\pm$ 0.15	70.84 $\pm$ 0.82	80.37 $\pm$ 0.21	94.08 $\pm$ 0.07	95.12 $\pm$ 0.02
	Enron	81.96 $\pm$ 1.37	76.34 $\pm$ 4.20	64.63 $\pm$ 1.72	78.83 $\pm$ 1.13	87.02 $\pm$ 0.47	72.33 $\pm$ 0.96	76.51 $\pm$ 0.71	90.69 $\pm$ 0.29	90.84 $\pm$ 0.17
	Social Evo.	93.70 $\pm$ 0.32	91.18 $\pm$ 0.52	93.41 $\pm$ 0.17	93.43 $\pm$ 0.57	84.73 $\pm$ 0.30	93.71 $\pm$ 0.17	94.09 $\pm$ 0.10	95.29 $\pm$ 0.03	95.37 $\pm$ 0.05
	UCI	78.80 $\pm$ 0.97	58.08 $\pm$ 1.79	77.64 $\pm$ 0.41	86.68 $\pm$ 2.26	90.40 $\pm$ 0.13	84.49 $\pm$ 1.84	89.30 $\pm$ 0.59	92.63 $\pm$ 0.10	94.40 $\pm$ 0.13

Appendix

Table 10: AUC-ROC comparison across different negative sampling strategies in inductive link prediction setting.

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Dynamic graph learning models how entities and their relations evolve from historical observations to predict future graph states. Existing methods do not fully address dynamic graph world modelling, which requires learning transitions from temporal context to future latent graph states. This is difficult for three reasons: nodes and relations rely on different historical evidence, structural evolution is path-dependent, and future snapshots provide sparse and realization-specific targets. We propose Dynamic Graph World Modelling (DyG-WM), the first framework to jointly predict future node and relation representations from temporal context by answering three questions: what has evolved, how it evolved, and what will evolve next. To capture what has evolved, a historical node-relation context encoder summarizes node-neighborhood trajectories and pair-specific histories. To characterize how it evolved, a node-relation path-signature encoder captures ordered structural changes. To predict what will evolve next, a dual-level joint-embedding objective predicts target-snapshot node and relation representations without reconstructing the raw graph. Experiments on 12 link-prediction and two node-classification datasets demonstrate the effectiveness of DyG-WM across both tasks.

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