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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, Gadeng Luosang, Nyima Tashi

arXiv:2609.33342v1cs.LGcs.CL

TL;DR

Binary label agreement can mix property dependence with class marginals and merge ordered disagreement states, complicating relation supervision for molecular prediction. CalibHyper estimates shrunk, chance-corrected four-state residuals and uses them to route signed hyperedge messages for each molecule. Across 26 dataset-and-shot conditions, it and its ablation settings are competitive with the strongest reported baselines, with larger margins in 1-shot settings.

  • Problem

    Binary label agreement mixes property dependence with class marginals and merges the two ordered disagreement states, limiting its representation of relations between properties.

    Source: §1 · p. 1, §4 · p. 4

  • Method

    CalibHyper estimates chance-corrected four-state residuals, shrinks them when joint observations are few, and uses them to select, sign, and weight hyperedge messages for each molecule.

    Source: §1 · p. 2, §5.1 · p. 5

  • Results

    Across 26 dataset-and-shot conditions, CalibHyper and its ablation settings are competitive with the strongest reported baselines, with larger margins in 1-shot settings.

    Source: §1 · p. 2, §7 · p. 9

  • Takeaways & Limitations

    Performance margins follow label statistics: they are large on PCBA and CEETOX and small on NVS.

    Source: §7 · p. 9

    Labels missing not at random and extreme class marginals can bias relation estimates; gains vary by dataset and configuration, and the main results cover three seeds.

    Source: §7 · p. 9

Abstract

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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.

1 INTRODUCTION

Auxiliary assay labels can support few-shot molecular property prediction, but binary agreement confounds property dependence with class marginals and merges ordered disagreement states. CalibHyper estimates chance-corrected four-state relations and uses them to drive molecule-conditioned hyperedge messages.

1 INTRODUCTION

  • Binary agreement can be near-perfect even for independent rare-positive properties, confounding class marginals with dependence and motivating chance-corrected relation supervision.MUV-713 and MUV-733 agree on 99.8718% of 3,121 jointly labeled molecules, versus 99.8719% expected under independence.Source: §1 · p. 1
  • Binary agreement also merges the two ordered disagreement states, while molecular-structure-dependent associations and unequal observation counts motivate molecule-specific relation estimates.The introduction contrasts this with ReCoG, where relation estimates affect prediction through an auxiliary loss and a gate weights each auxiliary property once per episode.Source: §1 · pp. 1–2
  • CalibHyper subtracts an independence baseline from the ordered four-state label distribution, shrinks residuals by joint-observation count, and uses them to select, sign, and weight molecule-specific hyperedge messages.C4RC estimates the residuals with a swap-equivariant head; MSRHA applies them to ordered hyperedges connecting a molecule, target, and auxiliary property.Source: §1 · p. 2
  • CalibHyper and its ablation settings achieve ROC-AUC competitive with the strongest reported results across 26 dataset-and-shot conditions, with larger margins in 1-shot settings.The conditions cover thirteen datasets evaluated at 1-shot and 10-shot.Source: §1 · p. 2

2 RELATED WORK

Related work spans few-shot transfer, context-aware prediction, auxiliary-information selection, chance-corrected agreement, and higher-order message passing. CalibHyper combines chance-corrected relation targets with molecule-conditioned messages.

Few-shot and context-aware molecular property prediction

  • Few-shot methods transfer supervision from existing properties to new ones, while context-aware approaches use context molecules, measurements, or graphs to predict unseen properties.The section places CalibHyper near ReCoG, which supervises property relations with binary agreement and compresses auxiliary property nodes conditioned on the target.Source: §2 · pp. 2–3

Selecting and compressing auxiliary information

  • MolGroup and AutAuT select or weight auxiliary information at dataset or task level, while information-bottleneck methods constrain retained representations.CalibHyper combines auxiliary-node compression with a chance-corrected relation target.Source: §2 · p. 3

Chance-corrected agreement and higher-order relations

  • Cohen’s κ corrects agreement for chance, and hypergraphs, signed networks, and dynamic message passing model higher-order, signed, or input-dependent relations.CalibHyper uses ordered molecule-target-auxiliary hyperedges whose supervised relation score sets selection, weight, and sign.Source: §2 · p. 3

3 PROBLEM SETUP AND NOTATION

The setup represents molecules and binary property tasks with a partially observed label matrix, then defines episodes for adapting to a target property. A context graph and predictor process molecule features and auxiliary assay labels while excluding query target labels.

3 PROBLEM SETUP AND NOTATION

  • The label matrix records each molecule-property label as active, inactive, or unmeasured, with an observation indicator marking measured entries.Meta-training and meta-test task sets are disjoint.Source: §3 · p. 3
  • Each episode targets one property and separates a support set for adaptation from a query set for prediction, alongside auxiliary properties drawn from meta-training tasks.The support set usually contains K molecules per class, and the query set contains M molecules.Source: §3 · p. 3
  • A context graph connects molecule nodes with the target and auxiliary property nodes, using observed labels to determine edge types while excluding query target labels.Molecule features come from a pretrained GIN, property nodes use learnable embeddings, and a two-layer context encoder produces node representations.Source: §3 · p. 3
  • The predictor adapts context representations, compresses auxiliary-property representations conditioned on the target, and assigns auxiliary gates during MAML-style bilevel training.The inner loop uses support loss; the outer loop updates shared parameters with query loss and auxiliary objectives.Source: §3 · p. 3
  • A property pair’s joint label is encoded as a four-coordinate one-hot vector ordered 00, 01, 10, 11, with the first digit referring to the first property.Source: §3 · p. 3

4 LIMITS OF BINARY RELATION SUPERVISION

Binary relation supervision can obscure dependence because agreement reflects class marginals and collapses ordered disagreement states. The section illustrates how rare positives and uneven joint observations affect agreement-based relation estimates.

4 LIMITS OF BINARY RELATION SUPERVISION

  • The chance decomposition expresses expected binary disagreement as (1 − cpq)(1 − κpq), so rare-positive marginals limit how strongly dependence moves the binary target.The four-state indicators distinguish ordered disagreements, whose difference from the independence value is 4 Cov(yp, yq).Source: §4 · pp. 3–4
  • When positives are rare, independent properties can agree almost always, while the mean Cohen’s κ is low on MUV and PCBA despite very high rates of joint negatives among agreeing pairs.The median joint-observation count ranges from 235,660 on PCBA to 22 on NVS, and two pairs with κ ≈ 0.22 differ about 1,200-fold in sensitivity to one relabeling.Source: §4 · p. 4, Figure 2 · p. 4
  • ReCoG’s swap-invariant relation input forces equal predictions for ordered states 01 and 10, producing a minimum squared error of 1/2(r01 − r10)^2 on an ordered target.For a CEETOX assay pair, the two states contain 151 and 119 molecules, respectively.Source: §4 · p. 4

5 METHOD

CalibHyper uses C4RC to estimate calibrated four-state relations and MSRHA to turn them into molecule-conditioned signed hyperedge messages for prediction.

5.1 C4RC: CHANCE-CORRECTED FOUR-STATE RELATION CALIBRATION

  • C4RC subtracts an independence baseline from the four-state relation target, shrinks it according to the number of joint observations, and fits residuals with a swap-equivariant head.Swapping the properties exchanges the two disagreement coordinates while leaving the other two unchanged.Source: §5.1 · pp. 4–5

5.2 MSRHA: MOLECULE-CONDITIONED SIGNED RELATIONAL HYPERGRAPH ADAPTER

  • MSRHA selects top-scoring auxiliary properties for each molecule and uses relation-score sign and magnitude to choose message channel and weight on ordered molecule–target–auxiliary hyperedges.The joint triple encoder can express three-way interactions beyond a sum of pairwise terms.Source: §5.2 · p. 6
  • MSRHA aggregates sign- and node-role-specific messages as a weighted average, updating only molecule and target nodes.Normalization by the sum of weights keeps the update scale from growing with the number of retained edges.Source: §5.2 · p. 6

6 EXPERIMENTS

Across 13 datasets and 26 few-shot conditions, CalibHyper exceeds the strongest reported baseline, while ablations examine its components and auxiliary-information routing.

6.1 SETUP

  • Evaluation covers five MoleculeNet benchmarks, 13 datasets, and 26 1-shot and 10-shot conditions, with scratch, pretrained, augmentation, and ReCoG baselines.Table 1 reports ROC-AUC (%) and averages ToxCast across nine subsets.Source: §6.1 · pp. 6–7, Table 1 · p. 7

6.2 MAIN RESULTS

  • CalibHyper exceeds the strongest reported baseline in all 26 dataset-and-shot conditions.Two 10-shot ToxCast entries, CLD and Tanguay, use binary relation targets and fix the MSRHA gate at γ = 0.Source: §6.2 · p. 7, Table 1 · p. 7

6.3 COMPONENT ABLATION

  • Across three datasets, the full model has the highest mean, but neither module helps reliably alone; the ablations indicate the two modules interact.The component ablations use three runs.Source: §6.3 · p. 7, Table 2 · p. 8
  • Four-state encoding without chance correction beats binary targets only on Tox21; merging signed channels gives the best ablated Tox21 score but lowers MUV performance.On MUV, rare positives leave little room for negative dependence, so a separate channel preserves negative messages apart from positive ones.Source: §6.3 · p. 8, Table 2 · p. 8

6.4 ABLATIONS ON AUXILIARY INFORMATION AND ROUTING

  • Masking auxiliary labels reduces joint observations and makes calibrated residuals noisier; on MUV, four-state targets lower the peak to Pre-GNN's level at both masking rates.The masking ablations are single runs, compared within each dataset rather than with Table 1's three-run means.Source: §6.4 · p. 8, Figure 4 · p. 8
  • More auxiliary properties generally raise peak performance; MSRHA has the higher peak in all three settings with N ≥ 8, but those runs lose more by training's end.Both MUV curves dip at N = 2 and decline at N = 12.Source: §6.4 · p. 8, Figure 4 · p. 8
  • Tox21, MUV, and CEETOX peak at k = 5; k = 1 discards complementary evidence, while k = 10 admits weak relations and removes selection on Tox21.The routing-count ablations report single-run peak 10-shot ROC-AUC.Source: §6.4 · pp. 8–9, Figure 4 · p. 8

6.5 MOLECULAR CASES

  • Table 3 shows four post-hoc negative examples classified correctly by CalibHyper but as positive by both baselines; for C3, positive auxiliary labels enter through the negative channel.The table reports positive-class scores and thresholded predictions.Source: §6.5 · p. 9, Table 3 · p. 9

7 CONCLUSION

CalibHyper uses chance-corrected four-state residuals to generate molecule-conditioned signed messages, and the method and ablations are competitive with strong reported baselines across 26 conditions. Performance margins vary with label statistics, while limitations include missing-not-at-random labels, extreme class marginals, dataset-dependent gains, and three-seed main results.

7 CONCLUSION

  • CalibHyper and its ablation settings are competitive with the strongest reported baselines across 26 conditions, with larger margins in 1-shot.Margins are large on PCBA and CEETOX but small on NVS; the ablations show that the relation loss alone does not improve prediction and the modules interact.Source: §7 · p. 9
  • Chance-corrected four-state residuals replace binary agreement and select, sign, and weight molecule-conditioned hyperedge messages.Residuals shrink when joint observations are few.Source: §7 · p. 9
  • Labels missing not at random and extreme class marginals can bias relation estimates; the main results cover three seeds.On MUV, rare positives and weak dependence leave calibrated scores near zero, and four-state targets degrade under label masking.Source: §7 · p. 9
  • The work uses public molecular-property datasets, involves no human subjects or personal information, and intends applications in drug and materials screening.The authors report using language models to assist with experiment scripts, run orchestration, numerical aggregation, and text revision and translation.Source: ETHICS STATEMENT · p. 10, AI USE STATEMENT · p. 10

List of Appendices

The related-work discussion situates CalibHyper among context-aware few-shot methods, auxiliary-information selection and compression, and approaches to agreement correction and relational structure.

A.1 FEW-SHOT MOLECULAR PROPERTY PREDICTION AND CONTEXT-AWARE METHODS

  • Few-shot molecular methods adapt to unseen properties, while context-aware methods use auxiliary observations; CalibHyper estimates deviations of jointly observed labels from their marginal-implied independence baseline.KRGTS adds scaffold and functional-group similarity, while CaMol uses a context graph and assumed causal model.Source: §A.1 · p. 16

A.2 SELECTING, WEIGHTING, AND COMPRESSING AUXILIARY INFORMATION

  • MolGroup and AutAuT select or weight auxiliary information at dataset or task level, whereas CalibHyper learns molecule-conditioned messages within an episode’s auxiliary-property set.CalibHyper combines auxiliary-node compression with calibrated relation supervision and signed propagation.Source: §A.2 · p. 16

A.3 AGREEMENT CORRECTION AND RELATIONAL STRUCTURE

  • CalibHyper carries chance correction into four ordered label states and shrinks the result by the number of joint observations.Its relation head and residual gate follow equivariant-network and zero-initialized residual designs (Propositions 4 and 5).Source: §A.3 · p. 16

A.4 EVALUATION PROTOCOL AND SCOPE OF COMPARISON

The evaluation protocol compares unseen-property prediction in 1-shot and 10-shot settings using mean ROC-AUC and sample standard deviation across independent runs. The appendices provide notation tables for the main text and formal appendices.

A.4 EVALUATION PROTOCOL AND SCOPE OF COMPARISON

  • The main comparison and component analysis use mean ROC-AUC and sample standard deviation across independent runs.The protocol distinguishes these results from single-run ablations.Source: §A.4 · p. 16
  • The evaluation covers 1-shot and 10-shot ROC-AUC on unseen properties.The cited graph prompting and foundation-model methods target adaptation across graphs or tasks.Source: §A.4 · pp. 16–17

B NOTATION

C.1 EVALUATION PROTOCOL AND BASELINE SOURCES

The appendix documents task sampling, metric aggregation, baseline reporting, and archived selection procedures, with separate notes on ablations and ToxCast subset results.

C.1 EVALUATION PROTOCOL AND BASELINE SOURCES

  • Testing covers all held-out properties, and support sets usually contain K molecules per class, with a minority-class exception when its count is at most K.In that case, one minority molecule remains in the query set and molecules of the other class fill support up to 2K.Source: §C.1 · p. 18
  • Dataset ROC-AUC averages held-out properties; the ToxCast aggregate equally averages nine subsets at each episode, and Table 1 reports its three-run mean.AP uses scikit-learn’s average precision score function.Source: §C.1 · p. 18
  • CalibHyper table results use three independent runs, while Section 6.4 ablations are single runs and should be compared within groups, not with three-run means.Baseline methods use differing reporting conventions: some report ten-seed means and standard deviations, while ReCoG’s repetition count and error definition are unspecified.Source: §C.1 · p. 18
  • Archived checkpoints were selected by the highest mean ROC-AUC across meta-test properties among 20 evaluations, without a separate validation split.The resulting statistics retain the effect of test-based selection.Source: §C.1 · p. 18
  • Archived selection records have not been matched to the individual runs behind the current main-table summaries, so those choices remain unverified by these records.Source: §C.1 · p. 18

C.2 MISSING AUXILIARY LABELS AND AUXILIARY-PROPERTY COUNT

  • Many ablation runs peak and then degrade, sometimes below chance; in the N ≥8 count sweep, MSRHA runs peak higher in all three settings but lose more by training’s end.The authors identify stable late training as an open issue.Source: §C.2 · p. 20

C.3 ROUTING COUNT

C.4 RESULTS ON TOXCAST SUBSETS

  • Table C.5 reports ROC-AUC on nine ToxCast subsets; Pre-KRGTS is the best baseline on NVS and ReCoG elsewhere.Daggers mark 10-shot CLD and Tanguay entries with inactive residual paths.Source: §C.4 · p. 20, Table C.5 · p. 20

D IMPLEMENTATION DETAILS AND COMPUTING ENVIRONMENT

This section formalizes pairwise label statistics and describes the relation head, hyperedge encoder, and implementation choices, including how finite observations, marginal imbalance, and batch composition affect the method. It also explains separate mean-score computation for target–auxiliary pairs and how label-statistic cases relate to binary-agreement supervision.

D IMPLEMENTATION DETAILS AND COMPUTING ENVIRONMENT

  • On Tox21, C4RC and MSRHA add 588K parameters, or 19.50%, to the 3.02M-parameter backbone and prediction components.The relation head and adapter use LayerNorm; auxiliary runs use relation dropout of 0.1, and query predictions can depend on batch composition through the context graph and target-node aggregation. The ablation without sign separation also changes normalization because negative scores count twice in its denominator.Source: D IMPLEMENTATION DETAILS AND COMPUTING… · p. 21

E.1 LABEL MATRIX AND EMPIRICAL LAW OF A PROPERTY PAIR

  • For each ordered property pair, the appendix defines an empirical four-state law over jointly observed molecules, compares it with a product-marginal independence baseline, and defines signed agreement for routing.The four states are ordered (00, 01, 10, 11); signed agreement is swap-invariant, whereas the directional component changes sign under a swap.Source: §E.1 · pp. 21–22

F.4 EXPECTATION OF THE C4RC TARGET

  • Under exact marginals, the C4RC target has zero expectation for independent properties, while its signed contrast tracks their dependence and its first-order residuals vary across molecules.The binary relation target, by contrast, is an affine function of the second-order coefficient alone.Source: §F.4 · p. 24

F.3 DEGENERACY OF THE PAIR TERM; F.5 SWAP EQUIVARIANCE OF THE RELATION HEAD

  • For fixed deterministic maps f and g, the relation head is exactly swap-equivariant for every parameter value; nevertheless, symmetric features can collide for distinct property pairs not related by a swap.For example, ((1, 3), (2, 4)) and ((1, 4), (2, 3)) have the same sum, elementwise product, and absolute difference.Source: §F.5 · p. 24

F.6 IDENTITY AT INITIALIZATION

  • At γ = 0, the adapter preserves the predictor’s input, output, and prediction-loss gradients for existing parameters, provided messages and derivatives are finite.This identity depends on normalizing inside the message rather than applying LayerNorm to the residual sum.Source: §F.6 · pp. 24–25

G.1 MARGINAL COMPONENT OF THE BINARY TARGET

  • The binary relation target has a marginal component: predicting from marginals alone can incur excess risk, and rare positives restrict the attainable negative Cohen’s κ.For equal nondegenerate marginals π ≤ 1/2, the stated range is κ ∈ [−π/(1 − π), 1].Source: §G.1 · p. 25

G.2 FINITE OBSERVATIONS, SHRINKAGE, AND SMOOTHING

  • Under the stated i.i.d. sampling model, linear shrinkage balances signal variance against estimation variance, while smoothing shifts the baseline and shrinkage scales that shift with the signal.The appendix treats n0 as an experimental hyperparameter and bounds the independence-case bias from smoothing as a function of joint observation count.Source: §E.2 · p. 23, §G.2 · pp. 25–26

G.3 EXPRESSIVENESS OF THE HYPEREDGE ENCODER

  • Unlike sums of single-layer pairwise functions, the joint ternary encoder can produce a nonzero mixed third-order difference, so its function class is not contained in the pairwise-decomposable class.The appendix demonstrates this with scalar inputs and also gives a nonzero example with LayerNorm.Source: §G.3 · p. 26

G.4 LABEL USE AND MEAN SIGNED SCORES

  • For each target–auxiliary pair, the support-label-conditioned baseline is averaged separately, and the second term vanishes when the auxiliary marginal matches π0_a or target labels are balanced.At each point, d(r_τa) = 2ρ_τa(2Y_τ − 1)(Y_a − π0_a).Source: §G.4 · p. 26

H LABEL STATISTICS BEHIND THE RELATION MODEL

  • Figure 2(a, b) equally weights property pairs with joint observations, sets κ = 0 when independence predicts agreement of 1, and frames the four cases as limits of binary-agreement relation supervision.The four cases appear in panels (c)–(f) and panel D of Figure 1.Source: H LABEL STATISTICS BEHIND THE RELATION… · p. 26

H.1 CHANCE AGREEMENT UNDER SPARSE LABELS: MUV-713 AND MUV-733

The examples show why property relations need more than binary agreement: chance-corrected four-state labels preserve disagreement direction, molecule-dependent association, and support from joint observations.

H.1 CHANCE AGREEMENT UNDER SPARSE LABELS: MUV-713 AND MUV-733

  • 99.8718% agreement versus 99.8719% expected under independence yields κ = −0.0005 for MUV-713 and MUV-733 across 3,121 jointly labeled molecules.The marginals already account for the observed agreement.Source: Table H.1 · p. 27, §H.1 · p. 27

H.2 DIRECTION OF DISAGREEMENT: INCREASE AND DECREASE OF THE SAME READOUT

  • κ = −0.3628 across 500 jointly observed CEETOX molecules; a binary disagreement label merges 151 decrease-only with 119 increase-only cases.The four-state target keeps the two directions of the same readout separate.Source: Table H.2 · p. 27, §H.2 · p. 27

H.3 MOLECULE-DEPENDENT ASSOCIATION: NR-AR AND SR-P53 IN TOX21

  • The NR-AR/SR-p53 association is close to zero overall and without phosphorus, but about an order of magnitude larger among 213 phosphorus-containing molecules.An episode-level weight would assign one of these three association values to every molecule.Source: Table H.3 · p. 27, §H.3 · p. 27

H.4 SUPPORT FROM JOINT OBSERVATIONS AND THE EFFECT OF A SINGLE LABEL

  • About 1,200× greater κ sensitivity occurs for MUV than PCBA after relabeling one joint positive; C4RC instead scales target sensitivity with joint observations and shrinks sparse pairs.The MUV estimate falls to −0.0013, while PCBA κ moves by 1.9 × 10−4. A binary target also counts MUV agreement as dependence, merges CEETOX disagreement directions, and cannot encode support size.Source: §H.4 · pp. 27–28, Table H.4 · p. 28

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