CalibHyper: Chance-Corrected Relational Hypergraphs for Few-Shot Molecular Property Prediction

Linyu Li; Zhi Jin; Yuanpeng He; Dongming Jin; Huanyu Liu; Huanyao Zhang; Haoran Duan; Heng Tian

cs.LGSep 27, 2026

CalibHyper: Chance-Corrected Relational Hypergraphs for Few-Shot Molecular Property Prediction

Authors: Linyu Li, Zhi Jin, Yuanpeng He, Dongming Jin, Huanyu Liu, Huanyao Zhang, Haoran Duan, Heng Tian, +2 more

Organizations: School of Computer Science, Peking University · Key Laboratory of High Confidence Software Technologies, Peking University, Ministry of Education · School of Computer Science, Wuhan University · School of Information Science and Technology, Tibetan Language Intelligence National Key Laboratory, Tibet University

Abstract

Molecular property prediction is central to drug development and materials discovery, but experiments are costly and labeled data are scarce. Context-aware methods use auxiliary assay labels to support few-shot prediction, and recent work supervises property relations with label agreement. However, label agreement is sensitive to class marginals and does not directly capture dependence between properties. We propose CalibHyper, a chance-corrected relational hypergraph method based on the joint label distribution. CalibHyper subtracts an independence baseline from the ordered four-state label distribution and shrinks the residual according to the number of joint observations. A swap-equivariant relation head estimates these residuals, which choose the auxiliary properties for each molecule and set the sign and weight of their hyperedge messages. On thirteen datasets from five benchmarks, in both 1-shot and 10-shot settings, CalibHyper and its ablation settings achieve ROC-AUC competitive with the strongest reported results.

Figures & tables

Figure 1: Motivation. (A) Few-shot prediction with auxiliary assays. (B) Chance agreement under rare positives. (C) Binary targets merge states $01$ and $10$ . (D) Structure-dependent association in Tox21. (E) Similar estimates from unequal numbers of joint observations. B, C, and E are schematic.

Figure 2: Label statistics (Appendix H ). (a) Observed and independence agreement and (b) mean Cohen’s

\kappa

per dataset (TC: ToxCast). (c) MUV-713 and MUV-733. (d) A CEETOX increase and decrease pair. (e)

\kappa

with and without phosphorus. (f)

|\Delta\kappa|

after one

11\to 10

relabeling.

Figure 3: Architecture. (A) Context graph and encoder. (B) C4RC: chance-corrected four-state relation head. (C) MSRHA: signed messages on top- $k$ hyperedges. (D) Prediction and training.

	Tox21		SIDER		MUV		ToxCast		PCBA
Method	10-shot	1-shot	10-shot	1-shot	10-shot	1-shot	10-shot	1-shot	10-shot	1-shot
Siamese	80.40 $\pm$ 0.35	65.00 $\pm$ 1.58	71.10 $\pm$ 4.32	51.43 $\pm$ 3.31	59.96 $\pm$ 5.13	50.00 $\pm$ 0.17	–	–	–	–
ProtoNet	74.98 $\pm$ 0.32	65.58 $\pm$ 1.72	64.54 $\pm$ 0.89	57.50 $\pm$ 2.34	65.88 $\pm$ 4.11	58.31 $\pm$ 3.18	63.70 $\pm$ 1.26	56.36 $\pm$ 1.54	64.93 $\pm$ 1.94	55.79 $\pm$ 1.45
MAML	80.21 $\pm$ 0.24	75.74 $\pm$ 0.48	70.43 $\pm$ 0.76	67.81 $\pm$ 1.12	63.90 $\pm$ 2.28	60.51 $\pm$ 3.12	66.79 $\pm$ 0.85	65.97 $\pm$ 5.04	66.22 $\pm$ 1.31	62.04 $\pm$ 1.73
TPN	76.05 $\pm$ 0.24	60.16 $\pm$ 1.18	67.84 $\pm$ 0.95	62.90 $\pm$ 1.38	65.22 $\pm$ 5.82	50.00 $\pm$ 0.51	62.74 $\pm$ 1.45	50.01 $\pm$ 0.05	–	–
EGNN	81.21 $\pm$ 0.16	79.44 $\pm$ 0.22	72.87 $\pm$ 0.73	70.79 $\pm$ 0.95	65.20 $\pm$ 2.08	62.18 $\pm$ 1.76	63.65 $\pm$ 1.57	61.02 $\pm$ 1.94	69.92 $\pm$ 1.85	62.14 $\pm$ 1.58

Table 1: ROC-AUC (%). CalibHyper: mean

\pm

sample standard deviation over three seeds; baselines from Wang et al. (2026) . ToxCast averages its nine subsets; a dash marks an unreported result.

Ablation	Tox21	SIDER	MUV
CalibHyper (full)	96.82 $\pm$ 1.70	96.89 $\pm$ 2.33	97.19 $\pm$ 1.21
w/o C4RC	90.08 $\pm$ 2.96	90.78 $\pm$ 3.33	93.82 $\pm$ 2.19
w/o MSRHA	87.48 $\pm$ 3.52	86.46 $\pm$ 1.92	67.23 $\pm$ 1.94
w/o C4RC and MSRHA	93.97 $\pm$ 2.80	89.20 $\pm$ 3.90	87.15 $\pm$ 3.53
w/o chance correction	93.00 $\pm$ 3.13	88.39 $\pm$ 1.67	87.47 $\pm$ 3.97
w/o sign separation	95.81 $\pm$ 1.12	88.75 $\pm$ 1.93	67.43 $\pm$ 2.52

Table 2: Component ablation (10-shot ROC-AUC, %, three runs).

Figure 4: Single-run ablations, peak 10-shot ROC-AUC; details in Appendix C . (a) Masked auxiliary labels. (b) Auxiliary-property count

N

(

12^{*}

: 11 during MUV training). (c) Routing count

k

Case	Dataset and target	GT	ReCoG	Pin-Tuning	CalibHyper
C1	Tox21 SR-HSE	Neg.	0.99 Pos.	0.59 Pos.	$7.39\times 10^{-6}$ Neg.
C2	Tox21 SR-HSE	Neg.	1.00 Pos.	0.57 Pos.	$3.77\times 10^{-8}$ Neg.
C3	CEETOX ESTRONE_up	Neg.	1.00 Pos.	0.83 Pos.	$7.98\times 10^{-5}$ Neg.
C4	CEETOX ESTRADIOL_up	Neg.	0.98 Pos.	0.87 Pos.	0.02 Neg.

Table 3: Molecular cases (10-shot): positive-class score and the label predicted at threshold 0.5 (bold: correct; GT: ground truth). CEETOX target names omit the prefix CEETOX_H295R_.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{M}$ , $\mathcal{T}$	set of molecules, set of properties
$\mathcal{T}_{\text{train}}$ , $\mathcal{T}_{\text{test}}$	disjoint meta-training and meta-test properties
$y_{i,p}\in\{0,1,\star\}$	label of molecule $i$ for property $p$ ; $\star$ means unmeasured
$o_{i,p}$	observation indicator $\bm{1}[y_{i,p}\neq\star]$
$E_{\tau}=(S_{\tau},Q_{\tau})$	episode with target $\tau$ , its support set and query set
$A_{\tau}$ , $N$	auxiliary properties of the episode and their number

Appendix

Table B.1: Notation of the main text.

Symbol	Meaning
$I_{pq}$ , $P_{pq}$	joint observation set and the empirical law of the pair on it (Definition E.2 )
$\pi_{p\|q}$	unsmoothed positive rate of $p$ on jointly observed molecules (Definition E.2 )
$b^{\ast}_{pq}$ , $r^{\ast}_{i,p,q}$	baseline and ideal target built from exact unsmoothed marginals (Definitions E.4 and E.6 )
$\chi_{\varnothing}$ , $\chi_{p}$ , $\chi_{q}$ , $\chi_{pq}$	Walsh basis of $\mathbb{R}^{4}$ , with $\chi_{pq}=\chi_{p}\odot\chi_{q}$ (Definition E.5 )
$s_{p}$ , $s_{q}$	labels in $\pm 1$ form, $s_{p}=1-2Y_{p}$ (Definition E.5 )
$P_{\mathrm{swap}}$ , $\mathcal{S}$	swap acting on output coordinates and on inputs (Definition E.7 )

Appendix

Table B.2: Additional symbols of Appendices E to G .

GIN layers / width $d$	5 / 300	Training episodes	2,000	Laplace constant $\alpha$	1
Query batch (train/test)	16 / 64	Routing count $k$	5	Shrinkage constant $n_{0}$	5

Appendix

Table C.1: Hyperparameters of the main experiments.

Tox21
		ROC-AUC			AP
Masked	Ablation setting	Peak	Last-5	Final	Peak	Final
50%	C4RC, unsigned MSRHA	94.87	73.73	86.32	85.53	40.31
50%	w/o MSRHA	94.89	79.70	90.07	66.13	49.88
50%	Head switched to binary	98.80	88.44	80.66	93.30	30.17
70%	C4RC, unsigned MSRHA	85.62	72.15	57.30	41.84	22.39

Appendix

Table C.2: Missing auxiliary labels in the 10-shot setting (%).

Tox21
		ROC-AUC			AP
$N$	Ablation setting	Peak	Last-5	Final	Peak	Final
1	C4RC, unsigned MSRHA	84.46	82.58	82.68	38.22	34.26
1	w/o MSRHA	85.39	82.44	81.59	38.17	32.28
2	C4RC, unsigned MSRHA	88.57	83.13	82.84	47.35	36.14
2	w/o MSRHA	81.46	74.68	75.29	32.45	24.34

Appendix

Table C.3: Number of auxiliary properties in the 10-shot setting (%).

$k$	Tox21	MUV	CEETOX
1	93.01	89.43	76.38
5	99.47	92.32	91.89
10	97.87	86.42	80.69

Appendix

Table C.4: Peak ROC-AUC (%) for different routing counts

k

in the 10-shot setting.

10-shot
Method	APR	ATG	BSK	CEETOX	CLD	NVS	OT	TOX21	Tanguay
ProtoNet	73.58	59.26	70.15	66.12	78.12	65.85	64.90	68.26	73.61
MAML	72.66	62.09	66.42	64.08	74.57	66.56	64.07	68.04	77.12
EGNN	80.33	66.17	73.43	66.51	78.85	71.05	68.21	76.40	85.23
Pre-PAR	86.09	72.72	82.45	72.12	83.43	74.94	71.96	82.81	88.20
Pre-GS-Meta	90.15	82.54	88.21	74.19	86.34	76.29	74.47	90.63	91.47

Appendix

Table C.5: ROC-AUC (%) on the nine ToxCast subsets. CalibHyper: mean over three runs. Baselines are the means reported in Tables 8 and 9 of Wang et al. (2026) ; method groups follow Table 1 . † Ablation setting with binary relation targets and the MSRHA gate fixed at

\gamma=0

(Proposition 5 ).

State	Observed count	Expected under independence
Both negative	3117	3117.0
Only MUV-733 positive	1	1.00
Only MUV-713 positive	3	3.00
Both positive	0	0.001

Appendix

Table H.1: Joint label states of MUV-713 and MUV-733.

	dn negative	dn positive
up negative	230	151
up positive	119	0

Appendix

Table H.2: Joint label states of the OHPROG increase (up) and decrease (dn) assays.

Molecules	Joint observations	Cohen’s $\kappa$
All jointly observed	6657	$+0.018$
Containing phosphorus	213	$+0.240$
Other	6444	$+0.013$

Appendix

Table H.3: Cohen’s

\kappa

between NR-AR and SR-p53 on subsets of Tox21.

Property pair	Joint observations	Joint positives	Original $\hat{\kappa}$	After relabeling	$\|\Delta\hat{\kappa}\|$
MUV-652, MUV-712	3066	1	$+0.2211$	$-0.0013$	$2.2\times 10^{-1}$
PCBA-1460, PCBA-485364	204894	1151	$+0.2231$	$+0.2230$	$1.9\times 10^{-4}$

Appendix

Table H.4: Effect of relabeling one joint positive as

(1,0)

Explore similar work

Semi-Supervised Learning for Molecular Graphs via Ensemble Consensus
Jul 30, 2026Rasmus Tirsgaard, Laurits Fredsgaard, Marisa Wodrich +2Semi-Supervised Learning Ensemble
Cognitive Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark.
MOLAR: Learning Multimodal Molecular Representations from Noisy Labels
Jun 16, 2026Yingxu Wang, Kunyu Zhang, Nan Yin +2Molecular Representation Learning Molecules
Department of Machine Learning, Mohamed bin Zayed University of Artificial Intelligence, AI Diyafah St, 7909, Abu Dhabi, United Arab Emirates · Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China · International College, Zhengzhou University, Daxue North Road, 450000, Henan, China +2
CoMPASS: Collaborative Molecular Property Prediction via Adaptive Small-Large Model Synergy
Aug 31, 2026Wentao Li, Jiangjie Qiu, Yijun Li +2Molecular Property Prediction Chemistry
Beijing Key Laboratory of Artificial Intelligence for Advanced Chemical Engineering Materials · State Key Laboratory of Chemical Engineering and Low-Carbon Technology · Department of Chemical Engineering, Tsinghua University

Jul 30, 2026, cs.LGJ/K move · Enter open · S save

Semi-Supervised Learning for Molecular Graphs via Ensemble Consensus

Rasmus Tirsgaard, Laurits Fredsgaard, Marisa Wodrich, Mikkel Jordahn+1

Cognitive Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark.

Semi-Supervised Learning Ensemble

Open paper AskPDF arXiv

Machine learning is transforming molecular sciences by accelerating property prediction, simulation, and the discovery of new molecules and materials. Acquiring labeled data in these domains is often costly and time-consuming, whereas large collections of unlabeled molecular data are readily available. Standard semi-supervised learning methods often rely on label-preserving augmentations, which are challenging to design in the molecular domain, where minor changes can drastically alter properties. In this work, we show that semi-supervised methods that rely on an ensemble consensus can boost predictive accuracy across a diverse range of molecular datasets, task types, and graph neural network architectures. We find that training with an ensemble consensus objective increases robustness in models and exhibits an effect similar to knowledge distillation; an individual member of an ensemble trained this way outperforms a full ensemble trained in a traditional supervised fashion in almost all cases. In addition, this type of semi-supervised training reduces calibration error.

Abstract

Explore similar work

Semi-Supervised Learning for Molecular Graphs via Ensemble Consensus

MOLAR: Learning Multimodal Molecular Representations from Noisy Labels

CoMPASS: Collaborative Molecular Property Prediction via Adaptive Small-Large Model Synergy