3DCS: Datasets and Benchmark for Evaluating Conformational Sensitivity in Molecular Representations
Authors: Xi Wang
Yang Zhang
Yingjia Zhang
Yejia Cai
Shenji Wan
Venue: ICLR 2026 Poster (2026)
Keywords: Molecule Benchmark
AI for Science
Primary area: datasets and benchmarks
TL;DR: 3DCS: The first benchmark to rigorously evaluate how well molecular representations capture intra-molecular conformational sensitivity across geometry, chirality, and energy.

Abstract: Molecular representations (MRs) that capture 3D conformations are critical for applications such as reaction prediction, drug design, and material discovery. Yet despite the rapid development of molecular representation models, there is no comprehensive benchmark to evaluate their treatment of 3D conformational information.
We introduce 3DCS, the first benchmark for 3D Conformational Sensitivity in MRs. 3DCS evaluates whether representations within the same molecule (i) preserve geometric variation, (ii) capture chirality, and (iii) reflect the energy landscape. To enable this, we curate three large-scale datasets ($>$1M molecules, $\sim$10M conformers) spanning relaxed torsional scans, chiral drug candidates, and AIMD trajectories, and propose a unified Geometry–Chirality–Energy (GCE) evaluation framework.
Empirical analysis reveals that while modern data-driven MRs are highly geometry-sensitive, they inconsistently handle chirality and poorly align with energy, which is often overlooked. 3DCS thus provides the first rigorous benchmark for developing physically grounded, functionally reliable 3D molecular representations. GitHub repository: https://github.com/ComDec/3DCS.

Published as a conference paper at ICLR 2026
3DCS: DATASETS AND BENCHMARK FOR EVALUAT- ING CONFORMATIONAL SENSITIVITY IN MOLECULAR REPRESENTATIONS
Xi Wang', Yang Zhang', Yingjia Zhang', Yejia Shengjie Wangt
[ww3763, yz10442, yc6970, sw5973 ennu.. edu, z 428 pku edu. en
1 New York University
2 Peking University
ABSTRACT
Molecular representations (MRs) that capture 3D conformations are critical for applications such as reaction prediction, drug design, and material discovery. Yet despite the rapid development of molecular representation models, there is no comprehensive benchmark to evaluate their treatment of 3D conforma- tional information. We introduce 3DCS, the first benchmark for 3D Confor- mational Sensitivity in MRs. 3DCS evaluates whether representations within the same molecule (i) preserve geometric variation, (ii) capture chirality, and (iii) reflect the energy landscape. To enable this, we curate three large-scale datasets (> 1M molecules, ~00M conformers) spanning relaxed torsional scans, chiral drug candidates, and AIMD trajectories, and propose a unified Geome- try- Ti-Chiralityy-neee
(GCH) evaluation framework. Empirical analysis reveals that while modern data-driven MRs are highly geometry-sensitive, they incon- sistently handle chirality and poorly align with energy, which often over- looked. 3DCS thus provides the first rigorous benchmark for developing physi- cally grounded, functionally reliable 3D molecular representations. GitHub repos- itory: htttps:///gtitii com/ Saan:/ComDe///ae www.tuuuwb.oo//CCm////3CCCC
INTRODUCTION
Molecular representations (MR) underpin a wide range of design tasks in drug discovery and catal- ysis (Zhang al. 2025a b Yu et al.
2025). Among these, representations derived from 3D confor-
mations are critical (Musaehan et al. 2023 Liao & Smidi 2022 Fang et al.) 2022) because the prop- erties of molecules and the efficacy of drugs are mainly governed by their 3D structures (Aldeghi) eet al.) 2014 Morley et al.) 2013 Chen et al., 2025 Peng al. 2025). In drug design, for example, the success of a ligand often depends on whether its 3D conformation binds precisely and tightly to the target protein (Sousa et al. 2006) Boehr al. 2009 Nicklaus et al. 1995).
Early molecular representations. including hand-crafted and data-driven learned, focus on 1D se- quences (SMILES (Weininger) (988)) or 2D graphs. Well-known examples include SMILES- Fingerprints (ECFP) (Rogers & Hahn 2010). 2022). Although effective in many settings, these approaches cannot distinguish between different 3D conformers because they neglect atomic coordinates. In recent years, research has expanded toward 3D MRs. Manual descriptors such as E3FP (Axen et al., 2017) extend 2D circular fingerprints into three dimensions by encoding neighboring atoms within concentric shells. Data-driven MRs include autoencoder models and transformers that encode atom positions (Zhou et al.] 2023) voxelized 3D grids (Lu et al. (025a). Models inspired by machine-learning force fields (MLFFs) (Unke et al. 2021), such as GemNet, learn energy and force mappings from spherical harmonies (Gasteiger et al. 2024.
BERT (Wang et al. 2019). Extended-Coomectivvi
and MoICLR (Wang
Although 3D MRs have advanced, the lack of corresponding benchmark severely limits our abil- ity to measure progress. Existing molecular benchmarks typically regard molecules static enti- ties and evaluate representations on tasks such as property regression or cross moos--lo classifica- tion (Zhong et al. 2024 Guo et al. 2023). For example, MoleculeNet (Wu et al. 2018) aggregated

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Datasets Pool
Models Pool
Geomelty Sensilivity
Dataset
7
Descriptors
#10,097, 643 Conformers
- Morgan, ESFP...
Chirality Sensilivit
gooogo
Models GemNet, MolAE...
Enantiomers Dataset #52,391 Conformers
Energy
Mult-modal Models MolSpectra...
AIMD Dataset #100,000 Conformers
2 Select model and extract zero-shot representation
1 Generate unified data input
Feed into evaluation pipeline
G-C-E Framework
Geometry
Chirality
Energy
Reference Alignment
Stereochemical Correlation
Landscape Correlation
Distance Correlation
Manifold Consistency
Enantiomer Separation Ratio
Energy Jump Sensitivity
Geometric Error
Torsion Smoothness
Clustering Performance
Distribution Distance
Metrics and performance report
Figure 1: Overview of the 3DCS benchmark workflow. Three curated datasets (relaxed scans, enan- tiomers, and AIMD trajectories) unified and processed through different representation types (descriptor, 3D, and multi-modal). Model's representations are evaluated under the G-C-E frame- work, which includes three dimensions: geometry, chirality, and energy with tailored metrics.
datasets from quantum chemistry and physiology, but overlooked conformational data. Subsequent benchmarks began incorporating conformers but continued emphasize aiter-molecular tasks. For example, Molecule3D (Xu et al. (021] focuses on predicting 3D geometry from 2D graphs, while recent MARCEL (Zhu et al. (023) leverages multiple conformers improve molecular property prediction. We describe these as inter-molecular tasks because they exploit conformer informa- tion across different molecules, yet they do not evaluate whether representations can discriminate between conformers of the same molecule. However, many real-world applications are inherently intra-mon moleclal conformer-sensitive tein pocket with different affinities (Morris & Lim Wilby 2008) show various quantum proper- ties (Zhang et al.) 2018). date, no benchmark systematically evaluates how well MRs capture conformational differences within molecule.
distinct conformers of the same molecule may bind a pro-
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To address this gap, introduce 3DCS, new dataset and benchmark designed to systematically evaluate the sensitivity of intra-molecular 3D MRs with respect to geometry, chirality, and the con- formational energy landscape. Geometric sensitivity requires that representations capture variations in distances, bond angles, and torsions, rather than collapsing distinct 3D shapes into indistinguish- able representations (Gillespie & Popelier 2001] Atz al. (021). Chirality sensitivity is crucial for differentiating enantiomers, which may exhibit vastly different biological activities but are often overlooked or mishandled by both handcrafted descriptors and machine learning models (Adams et al., 2021] H. Brooks et al.) 2011). The energy sensitivity reflects the fact that the Boltzmann weight of conformer governs its probability of occurrence; representations that do not align with relative energies risk mischaracterizing the significance of the conformer (Cercignani 1988) This
work makes three main contributions:
Large-scale datasets for conformer sensitivity. We curate three datasets that contain over IM molecules and 1 11M conformers: (i) a relaxed scan dataset with ~1.5M molecules and ~10 million conformers obtained by rotating an inter-ring bond and relaxing the rest of the structure; (ii) a chirality dataset with 44K chiral drug-like molecules from ChEMBL. where enantiomers and enantiomers are enumerated, yielding ~52K conformers; and (iii) an energy dataset derived from Ab-initio Molecular Dynamics (AIMD) that includes high-quality energies and forces computed with density functional theory.
We propose a unified evaluation framework named GCE with two layers: (i) reference alignment tests whether representation distances align with physical references such as RMSD, dihedral angles, chirality signatures, and energy differences; (ii) manifold consistency assesses whether representations form coherent manifolds, preserving neighborhoods, separating enantiomers, and reflecting energy jumps. The framework is model-agnostic and applies to both handcrafted descriptors and learned representations.
We evaluate classical descriptors (e.g.. E3FP) and broad range of learned representations (UniMol, MolAE, MolSpectra, GemNet, MACE, and the field-based encoder FMG) in zero-shot setting, and additionally study their behavior under supervised fine-tuning. Results show that while learned models effectively capture geometric variations, they inconsistently handle chirality and poorly align with the energy landscape. These findings highlight critical gaps and offer actionable guidance for designing physically faithful 3D molecular representations. In additional fine-tuning experiments, we further show that 3DCS chirality and energy metrics remain informative after training on 3DCS itself.
2 RELATED WORK
Molecular benchmarks. Early benchmarks, such as MoleculeNet (Wu et al. 2018 collate datasets across quantum chemistry, physiology, and biophysics, but treat molecules as single static graphs or structures. Subsequent benchmarks began to probe conformational robustness: Molecule3D (Xu
let al.
2021) evaluates geometry prediction from 2D graphs, while Zhhng & Vitalis (2025)
troduces datasets for benchmarking classification robustness under different conformers. MARCEL
(Zhu 20233 introduces datasets learn conformer ensembles for property prediction, and
GEOM (Axelrod & Gömee--Bomarde 2022) provides energy- annottaed conformations for gener- ative models (Lu al., 2025b). While these efforts mark progress, they still focus on inter-molecular tasks (e.g., property regression or classification across molecules) and do not directly test how well a representation distinguishes conformers of the same molecule. Our 3DCS benchmark explicitly shifts the focus to intra- mole-llae conformational sensitivity.
Molecular representations. MRs can be derived either from handcrafted descriptors that encode chemical domain knowledge or data-driven representation learning. Molecular fingerprints such as ECFP/MMrgan (Rogers& & Hahn 2010), MACCS keys (Durant et al. 2002), and E3FP (Axen al., 2017) are intended to represent the presence (or absence) of substructures within molecules, often in a binary vector. They are explainable and remain strong baselines, but their sparse nature con- tributes to their insensitivity in capturing complex chemistries, such global geometry or potential energy (Wigh et al., 2022 Venkatraman et al. 2024).
In contrast, data-driven approaches learn representations directly from raw molecular modalities, which can broadly be grouped into three categories: ID sequences, 2D molecular graphs, and 3D structures. The most widely adopted 1D representation is SMILES, explored by models such as
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seq2seq (Xu et al. 2017) and SMILES- (Wang et al. 2019). At the 2D level, models such as MolCLR (Wang et al. 2022), MolGNet (Li et al. 2021), and GROVER (Rong et al. 2020) used graph neural networks. Hybrid strategies further enrich 2D encoders with conformational informa- tion, e.g., 3D-Infomax (Stärk et al. 2022) and GraphMVP (Liu et al. 2021). Recently, 3D-based MRs have achieved state-of-the-ar performance on property benchmarks. Some, such as UniMol (Zhou et al. (023) and MolAE (Yang et al. 2024). use Cartesian coordinates directly, while others take pre-defined equivariant basis functions (e.g., spherical harmonies or SO(3) tensor features) to encode geometry (Gasteiger et al.
2024 Fuchs et al.
2020). There are also multi-moda approaches.
2024 Zhao et al. (024) integrates 2D biomedical text with 3D (Wang et al. (025) combines spectral data with 3D informa- tion to enhance representation learning. Despite these advances, most models are trained on a single low-energy conformer, meaning they may not recognize the diversity of conformer ensemble.
For example, MolLM (Tang et al.
molecular structures, while MolSpectra
3 DATASETS
We design the 3D Conformational Sensitivity (3DCS) benchmark based on three well-curated datasets, each targeting a different aspect of conformational representation: geometric flexibility, chirality, and potential energy. All molecules and conformers used in 3DCS will be released to- gether with data-generation scripts and evaluation code in our public GitHub repository.
Geometry Dataset:
Relaxed Scans. To probe MR's ability to capture geometric changes within the same molecule, we curated a large-scale dataset of organic molecules. The dataset is generated through the following steps.
1. Scaffold generation: connect heterocyclic units into diverse scaffolds;
2. Substituent diversification: introduce two specialized substituent libraries, randomly at- taching them to scaffolds, yielding 1,559,779 unique molecules;
3. Relaxed scan: for each molecule, perform a relaxed dihedral scan around the inter-ring sin- gle bond in 2.5' increments, using xTB with the best crude precision level for geometric optimization, recording the single point energies. The constraint done on-the-fly with force constant=C. 05 parameter;
4. Redundancy reduction: apply Density- -Based Spatial Clustering of Applications with Noise (DBSCAN) clustering with eps=0.5 0.. 5 remove redundant conformers for each molecule.
After processing, the dataset comprises 10,097,643 conformers, each annotated with its correspond- ing dihedral and energy values. Implementation details can be found in Appendix C. We use xTB to perform the relaxed scans, which strikes a practical balance between accuracy and scale for our 10n--oofoormerr corpus. Recent systematic studies have shown that GFN-type xTB methods produce DFT-optimized geometries of organic and m-conjugated molecules with high fidelity (c.g.. heavy-atom RMSD and bond/angle statistics with R² 0.99).
Chirality Dataset: Chiral Drug Candidates. To evaluate model sensitivity to chirality, we curate drug-like molecules with annotated stereocenters from ChEMBL (Gaulton et al., (012). We filter drug-candidan molecules with chirality annotations, yielding 4,057 diverse molecules and conduct geometry optimization on each stereoisomer with xTB.
We retain only pairs that pass stereochemical validation (R/S consistency) after optimization, en- suring that observed representation differences reflect chirality rather than failures in geometry op- timization. This protocol yields 15,218 conformers across enantiomer pairs. We apply small tor- sional perturbations within each stereoisomer so that conformer ensembles of different enantiomers overlap in geometry space, preventing models from separating enantiomers using coarse geometric differences alone instead of stereochemistry.
After perturbation and GFN-xTB optimization, recompute the R/S configuration of every stereo- center and discard any conformer whose assignment changes, yielding 52,391 perturbed conformers that strictly preserve the intended stereochemistry for enantiomer separation.
For supervised chirality experiments, we use an 1:1 Murcko scaffold split into train/validation/test sets avoid trivial leakage across enantiomers with similar substructures.
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Energy Dataset: AIMD trajectories. For evaluating energy and foree fidelity, adopt the Re- vised MD17 dataset (Christensen & Von Lilienfeld, (020), which contains high-quality molecular dynamics trajectories of 10 small organic molecules. Each trajectory provides 100K conformers sampled along MD simulations, annotated with DFT-level energies and atomic forces. This bench- mark assesses whether molecular representations remain consistent with the underlying potential energy surface (PES).
4 TEOMETRY-CHRALIT--E
(GCE) EVALUATION FRAMEWORK
Our goal is to quantify how well a MR captures conformational variability. The GCE framework consists of two layers: reference alignment and manifold consistency. Given molecule S with conformers C (2, we have the following metrics.
4.1 REFERENCE ALIGNMENT
We compare pairwise representations distances Aij (See Appendix C.2 vated references:
with three physically moti-
1. Geometry. The reference geometry distance is
D RMSD(c G);
i.e., the Root-Mean-Square Deviation (RMSD) of atom positions after optimal alignment. Throughout this work, RMSD values are reported Angström (A). Geometry-sensitive representations should preserve the relative ordering D(G)
2. Chirality, For a molecule with m stercocenters, each conformer o, has chirality signature
((c:) ( 8m) E {=1)m.
Where +1/ represents relative configurations R/S or D/L. The chirality distance the fraction of mismatched stereocenters:
D Σ ((s((c)) + s((e))
A chirality-sensitive representation should place enantiomers far apart.
3. Energy. The energy distance reflects differences in potential energy:
D E(()) - E(cy)]-
Energy sensitive representations should scale with (E)) and highlight large energy jumps. Energies in the AIMD energy dataset are reported in kcal/mol, while energies in the relaxed-scan dataset are stored Hartree.
We compute Aij as cosine distance for learned representations and Tanimoto distance for binary fingerprints. Alignment is quantified using: Spearman and Kendall rank correlations, RBF kernel centered kernel alignment (CKA) (Kornblith et al. 2019), and Isotonic regression R² (monotonic fidelity). High correlations indicate that representation distances respect physical references.
4.2 MANIFOLD CONSISTENCY
Beyond pairwise alignment, we test whether representations form a coherent manifold. Details for metrics can be found in Appendix C
1. Local Isometry Error (LIE). For each conformer, we compare neighborhoods under DG) and A, computing RMSD of distances normalized by local averages. Low LIE indicates preservation of local geometric neighborhoods.
2. Torsion correlation and smoothness. For the geometry dataset, we correlate angular (dihedral) distances with A. We also compute angular smoothness (AS), the median repre- sentation change per degree dihedral rotation. Moderate AS values indicate responsive yet stable representations. See details in Appendix C.4

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3. Chirality separation. We evaluate enantiomers separation via: Enantiomers Separation AUC (ESA-AUC), Nearest neinrbbu accuracy (NN1-acc), and Silhouette coefficients (with molecule configurations labels). We also compute Hopkins statistics and the best-k silhouette to detect latent clusters without adding labels. See details in Appendix CC.5
4. Energy jump sensitivity (EJS) and smoothness. We measure the conditional probability that large energy differences imply large representation separations, and compute thresh- olded smoothness of representation trajectories relative to energy changes. Thresholded smoothness focuses on segments with significant energy jumps. Additionally, we report Golmogorov-Sminite Smirnov distances between the distributions of representation distances and energy differences. See details Appendix C.6
EXPERIMENTS AND RESULTS
Since conformers the same molecule share identical 1D and 2D structures, we restrict our eval- uation to representations that explicitly encode 3D information. Our benchmark evaluates both handcrafted and learned representations under common framework.
Relative Improvement (%) Compared to E3FP
GemNet
MolAE
MolSpectra
UniMol
Geometry
Chirality
Energy
1NGU-AUC
Issionie Fat
Nentoric Rd
Kandal
Kendial
enves
a/s
Spewnan
188
AJG.AUC
Toraion-
-20% 0%
SCL unsup" .57% 0% 48% 201%
TS
.50% 0% 50%
500%
Figure 2: Radar chart summarizing the benchmark results across GCE dimensions. Each axis corre- sponds to one metric within domain, and values are relative improvements over the E3FP baseline. SCLunsup=: Silhouette coefficients without configuration labels.
Baseline Overview. We evaluate classical 3D fingerprints, field-based encoders, and recent 3D molecular encoders that differ in input modality, geometric inductive bias, and training objectives.
E3FP. E3FP (xxnn al. 2017) constructs alignment-free 3D manual molecular fingerprints by iteratively drawing shells around each atom and hashing the local 3D substructures-incluee non-bonded neighbors and stereochemistry into folded, fixed-length bit vector. Key parame- ters include the shell radius multiplier, the number of iterations, whether to include stereochemistry, and the final bit length.
UniMol. The UniMol framework employs an SE(i)--quivariant Transformer with rotation-invarian positional encoding and pairwise atomic representations (Zhou et al., 2023). Pretraining comprises (i masked atom delfittionmmskinng and recovering atom types and (ii) 3D coordinate denois- ing objective that adds Gaussian noise to fraction coordinates and trains the model to recover the noise-perturbed positions and atom types via equivariant heads.
MolAE. MolAE (Yang et al. 2024) introduces an encoder- decoder architecture with a 3D Cloze Test objective to address two issues in encoder-only coordinate -eeitatte-eoiiiingggg frameworks: objective mismatch between pretraining and downstream tasks, and potential disruption of atom identity caused by coordinate noise. Instead of corrupting coordinates with noise, drops subset of atoms

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and their positions, encodes the remaining structure, and uses decoder with positional encoding to reconstruct the full coordinates and atom types. This preserves the encoder representation and avoids positional bias.
GemNet. GemNet (Gasteiger et al. 2024 is geometric message-passing network that predicts energies and forces by encoding distances, angles, and dihedral angles through direction-aware two-hop message passing. It utilizes spherical Fourier-Besse bases (including radial, circular, and spherical components) and symmetric filters capture geometric features, and trains with a weighted loss on energy and force to learn both the potential and its gradient. Although originally designed for property prediction, its spherical harmonics feature and architectural bias toward rich geometric cues tend to produce informative molecular embeddings.
MolSpectra. MolSpectra (Wang et al. 2025) augments 3D denoising with quantum- mecttnnccc spectrum information via SpecFormer, patch-based Transformer that jointly encodes UV-Vis, IR, and Raman spectra by dividing each spectrum into patches, projecting them with learnable posi- tional encoding, and concatenating them across modalities. Pretraining combines 3D coordinate denoising, masked patch reconstruction on spectral patches, and cross-modal contrastive learning to align spectral and geometric representations, leading to 3D encoders that outperform denoising-only baselines.
MACE. MACE (Batatia et al. 2023 is E()-eqquvarriant architecture for atomistic modeling that combines message passing with spherical harmonic features to predict energies and forces with high sample efficiency. Similar to GemNet, is trained with explicit energy/force supervision MLFF- style datasets, but it uses a different parameterization equivariant tensors and interaction blocks. We evaluate MACE as a strong energy-force baseline on our benchmark.
FMG. FMG (Dumitrescu et al. 2025) is a field-based generative model that represents each molecule multi-channel 3D voxel grids of atom and bond density fields, obtained by placing Gaussian radial basis functions on atom centers and bond midpoints and evaluating them on fixed lattice. To avoid E(3)-cquivariance while still sharing statistical strength across conformations, FMG aligns each molecule to a canonical frame via PCA- reference rotations, thereby sacrificing ro- tational invariance but retaining sensitivity reflections and hence chirality. We treat FMG a strong, chiral-aware field baseline that contrasts our point-cloud encoders by explicitly trading exact rotational symmetry for richer geometric and stereochemical fidelity.
5.1 GEOMETRY EXPERIMENTS AND RESULTS
We observe from Table and Figure 2 that nearly all learned representations outperform hand- crafted molecular fingerprints. Notably, models directly using atomic coordinates outperform Gem- Net with spherical harmonies. We speculate that this is because spherical harmonics composed of relative distances, but necessarily sacrifice some absolute geometric information when we use the RMSD of atom positions as a reference.
At the AS metric level, molecular fingerprints yield much larger values than learned representations. This arises because fingerprints encode the presence or absence of substructure binary vectors: even minor dihedral changes can flip multiple bits, leading to disproportionately large pairwise dis- tances, despite the underlying conformational shift being small. contrast, learned representations distribute structural variation more smoothly across the molecule, dampening local perturbations and producing smaller AS values.
For GemNet, relative spherical harmonics are employed, so torsional changes manifest only as per- turbations a limited set distance and angular descriptors. In contrast, coordinate-based models translate torsional rotations into broader positional shifts across multiple atoms, resulting in higher AS values compared to GemNet. Nevertheless, models that incorporate additional chemical infor- mation-suu SMILES strings energy spectra- avoid excessive sensitivity to minor conforma- tional changes. This reflects a desirable form of robustness: they capture stereochemical variation while remaining stable against slight conformational fluctuations.

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Geometry benchmark metrics comparing learned representations and handcrafted finger- prints. The number of local neighborhoods for LIE@k is 3 by default.
Table 1:
Metric
E3FP
GemNet
MolAE
MolSpectra
UniMol
Spearman (1)
0.406
0.560
0.640
0.682
0.697
Kendall (1)
0.272
0.336
0.483
0.506
0.563
CKA (t)
0.757
0.813
0.862
0.904
0.889
Isotonic R2 (1)
0.521
0.667
0.734
0.770
0.782
LIE@k (L)
0.324
0.390
0.349
0.238
0.306
Torsion- SP (f)
0.313
0.420
0.437
0.508
0.504
AS
2.757
0.0018
0.0048
0.0214
0.006
5.2 CHIRALITY EXPERIMENTS AND RESULTS
We find that nearly all learned representations perform poorly against the chirality reference when evaluated with rank-based correlation metries (see Appendix B.I). This result is unsurprising: the chirality reference inherently discrete, and virtual chirality descriptors such as OPD (Osipov et al.) assume that conform-
1995) are ill-suited for direct correlation analysis. It is not meaningful ers with more stereocenter mismatches should necessarily lie farther apart in representation space. reliably distinguish enantiomers, indepen-
Rather, the key question is whether representations dent of their absolute correlation with discrete chirality distances.
For this reason, in Table 2 we focus exclusively chirality separation results. Here, we find that MolAE achieves the best performance. Notably, both MolAE and UniMol adopt the same SE(3)- invariant framework: the key difference lies in their training objectives. UniMol is trained denoise perturbed conformers by reconstructing the original coordinates. However, random perturbations can easily induce chirality inversion, effectively misaligning the training signal (e.g., the model may learn to map an R conformer back to an Š conformer). In contrast, MolAE employs 3D cloze task, where parts the caatecule-incuudine potential stereocenters-aarc masked and must be reconstructed. Because enantiomers differ subtly around stereogenic centers, this objective naturally encourages the model to capture those differences and learn a faithful mapping. With the addition of the field-based FMG encoder, observe that chirality- architectures indeed exploit the structure of our benchmark. FMG matches or exceeds MolAE ES-AUC despite not being pre-trained on large molecular datasets.
Chirality fine-tuning, Further, on the JDCS-chiralee dataset, we train a supervised contrastive loss encoder's 's embeddings using Murcko scaffold splits. For each model, encourage conformers of the same stereoisomer to cluster tightly while pushing apart conformers of different stereoisomers of the same parent molecule. Fine-tuning improves absolute chirality metrics across all models (see Table 5). but the relative ranking largely persists: MolAE and UniMol remain strong among -Euii-equivariaat encoders, GemNet and MACE improve yet still lag behind the best chirality- aware representations. Notably, GemNet (we use GemNet-Q) benefits from its extra dihedral features and outperforms MACE on chiral discrimination. The field-based FMG encoder achieves the best overall performance, with ES-AUC approaching 0.999.
Table 2: Chirality benchmark. The listed metrics focus on the ability of models to distinguish between stereochemical configurations. Fine-tuned baselines results are reported Appendix table
Metric
E3FP
GemNet
MolAE
MolSpectra
UniMol
FMG
MACE
ES-AUC (t)
0.486
0.577
0.782
0.545
0.622
0.706
0.485
NN@ I-Acc (1)
0.178
0.292
0.497
0.235
0.339
0,412
0.199
Hopkins (t)
0.593
0.602
0.533
0.559
0.752
0.637
SCI (1)
-0.012
0.015
0.115
-0.020
0.012
0.117
-0.094
SCI *(t)
0.033
0.272
0.247
0.127
0.152
0.509
0.369
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5.3 ENERGY EXPERIMENTS AND RESULTS
As shown in Table 3 GemNet and MACE deliver the strongest performance on our energy-based metrics, particularly in the energy jump detection task, reflecting their training objectives that plicitly incorporate energy and force information. Their spherical-harmonic inputs are constructed from relative distances, which naturally map potential energy. likely enhancing their ability to align with energetic variation. In contrast. for most models, correlations between representations and energy differences remain much weaker than those with geometric distances, suggesting that molecular representations generally encode geometric variation while carrying little information about energetic variation if they haven't 't trained on energy or force targets.
By contrast, molecular fingerprint E3FP shows substantially poor correspondence with energy. The reason that counts substructure are energy-unsensitvee so distances in fingerprint space are hard to reflect energetic contrast. Notably, if restrict attention segments of significant energy shifts (our threshold smoothness metric), E3FP's performance improves. At more coarse-graing scales, it retains the capacity to recognize structural changes with significant energy differences.
Energy prediction fine-tuning, On the Revised MD17 dataset, we attach a small MLP head to each encoder and train predict energies the official train/test splits. Since RMD17 does not provide a validation set, we use a fixed training schedule and report the performance checkpoint the held-out test set, avoiding tuning on test data. For the fixed E3FP fingerprint, train a linear head only. We find that models with better 3DCS energy scores (e.g.. MACE, GemNet) consistently achieve lower energy MAE after fine-tuning, and the method ranking induced by 3DCS energy metrics matches the downstream ranking. Detailed results for fine-tuning experiments are reported in Appendix Table
the last
Additionally, we test whether learned representations recover structure in PES. We sample conform- ers from molecular trajectories and select the dihedral angles with the largest variance as collective variables (CVs).. For the representations, nents as proxy CVs. Surprisingly, the resulting 2D representations often reveal energy barriers and minima, suggesting that these learned representations could be useful for analyzing transition states and reaction paths (Appendix A.4).
perform PCA and use the first two principal compo-
Table 3: Energy benchmark measuring correspondence between representation distances and ener- getic variation.
Metric
E3FP
GemNet
MolAE
MolSpectra
UniMol
FMG
MACE
Spearman (1)
0.026
0.078
0.039
0.023
0.043
0.015
0.236
Kendall (1)
0.018
0.052
0.026
0.015
0.028
0.009
0.159
CKA (1)
0.011
0.016
0.024
0.006
0.019
0.011
0.017
iso R² (t)
0.002
0.013
0.003
0.001
0.003
0.001
0.080
EJS (t)
0.184
0.356
0.294
0.271
0.301
0.269
0.578
EJS-ROCAUC (t)
0.531
0.592
0.545
0.526
0.549
0.517
0.764
TS
0.385
0.444
0.346
0.409
0.356
0.582
0.424
KS (t)
0.916
0.998
0.998
0.977
0.997
0.999
0.999
DISCUSSION
Our benchmarks show that most molecular representations behave as compressed encodings of molecule's geometric degrees of freedom-atomee coordinates, bond angles, and torsions. SEC3)- equivariant transformers (Fuchs et al. (020)) enforce rigid-motion symmetry and can propagate in- formation across the whole molecule, whereas standard message- message-passing networks primarily capture local neighborhoods and exhibit strong locality bias. Sparse fingerprints such E3FP focus local substructures and miss many aspects of global geometry.
Across all baselines, enantiomer separation is uniformly weak in the zero-shot setting. This is expected: most models are pre-trained without explicit stereochemical supervision, and coordinate- denoising reconstruction objectives inadvertently encourage mappings that flip chirality. Our

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chirality benchmark, together with the field- basdd FMG encoder, makes this failure mode explicit. FMG, which designed to overcome equivariant limitations on chirality, achieves substantially better enantiomer clustering than conventional ES-AUC after supervised contrastive fine-tuning on 3DCS chiiaaiii
encoders and reaches near- pear-perfect
Energy representation remains major open challenge. For most encoders, correlations between rep- resentation distances and conformer energies are consistently much weaker than those with geomet- ric distances: representations tend to track geometry but only weakly reflect the underlying potential energy surface. GemNet and MACE are notable exceptions: by combining spherical-harmen puts with explicit energy/force supervision, they exhibit much stronger energy alignment and better sensitivity to large energy jumps. Our downstream RMD17 experiments further show that models with higher 3DCS energy scores also attain lower energy prediction error after fine-tuning, indicat- ing that 3DCS energy metrics are predictive of downstream energy-learning difficulty rather than purely diagnostic.
in-
Overall, 3DCS provides starting point and fundamental tool for studying molecules at the conformer-ensemble level. Placing a new model on our geometry-chirallty-ennr radar imme- diately highlights whether its weaknesses lie in geometric smoothness, enantiomer separation, or energy alignment, and thus where to invest modeling effort or hyperparameter tuning. In this work focus unconditional, ligand-side conformational competence; extending 3DCS to conditional settings such as protein-ligand docking, pose prediction, and chirality property prediction natural next step, and public datasets and code designed to make such extensions and cross-correlations with downstream benchmarks straightforward.
Design recommendations. These findings point to three directions for future benchmarks and models: (i) enrich geometry-sensitive objectives beyond Cartesian recovery to include bond angles and torsions; (ii) dataset construction and loss functions should explicitly account for stereochemical integrity. Chirality-preserving preserving augmentations and enantiomers-awei objectives are critical; (iii) using spherical harmonic bases rather than raw coordinates can reduce redundancy and degrees of freedom, making the representation more compatible with energetic features.
CONCLUSION
3DCS focuses molecular representation evaluation around intra-molecular conformational sensitiv- ity. Through three large datasets and the unified GCE framework, we reveal that modern MRs excel at capturing geometry but lag chirality and energy. By identifying these gaps, 3DCS provides molecular encoders that jointly honor
concrete directions for developing the next generation geometry, chirality, and energy. We aim for this benchmark catalyze community-wide efforts in developing pretraining objectives and datasets that more faithfully reflect the dynamic 3D nature of molecules.
THE USAGE OF LANGUAGE MODELS
We used an LLM improve paper writing (grammar and wording); all authors reviewed the edits and take full responsibility for the content.
REPRODUCIBILITY STATEMENT
To promote reproducibility, we release all the original datasets and the scripts used to reproduce baselines. Code for rumning the experiment and charts generation is also provided. Additionally, step-by-step instructions, code examples, and corresponding files are included in the GitHub repos- itory (https:://ithail http:/hwww.ccco/ooo/////////
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A SUPPLEMENTARY FIGURES
In this section, we provide additional figures and commentary to elucidate the constitution of the 3DCS benchmark.
A.1 STATISTIC DATASETS
The geometry dataset summarizes fundamental molecular descriptors and energy annotations for the conformers used in the benchmark. Conformer energies are computed using the semi-empirical GFN2-XTB method within the xTB software. Figure and the xTB energy spectrum for representative subset of conformers.
3 presents the distribution of these descriptors
Energy Distribution
0.016
med 79.4
0.014
Joint Distribution: MolWt vs logP
0.012
0.008
0.004
0.002
15
000
250
200
150
100
-50
(Ha/trae)
10
Ring
02545
60000
53001
50000
Molecule Count
31554
20000
:4016
200
400
600
Molit
800
1000
1200
1400
10000
2853
0
5
6
7
Rings (count)
Molecular Walght Distribution
Distribution
194374
r-196974
ped
med-4
0.0030
0.10
0.0025
Densty
0.00
0.0020
0.06
0015
0.02
0.0000
0.00
600
1400
10
Motecula la Weight (Da)
Crippen log?
Figure 3: Summary of molecular and energetic descriptors for the geometry dataset.
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The chirality dataset focuses stereochemical sensitivity. It includes molecules with more stereocenters and records whether each stereocenter has defined R or configuration. Figure summarizes these general stereochemisttr-relaaee statisties.
Stereo Centers Molecule
3000
Melscute Count
Joint Distribution: MolWt logP
1500
1000
500
10
Stereocenters
Molecular Welght (Da) Distribution
Logo
0.0035
1=1521
(=m050 B1
m23-428.50
0.0025
-5
Densay
0.0020
0.0015
0.0010
1000
0.0005
0,0000
200
400
600
800
1000
1200
1400
1600
Molecular Weight
Count Distribution
Crippen Distribution
1=15216
4000
0.175
med-22 87
0.150
Malezu Count
Dendity
0.125
0.100
2000
0.075
10000
0.050
0.025
0.000
Rings (count)
Crippen ag?
Figure 4: Statistics of the chirality dataset.
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A.2 VIOLIN CHARTS OF GEOMETRY BENCHMARKS
We present violin plots that summarize the distribution of geometry benchmark scores across base- line models. Each violin depicts the kernel density of per-molecule scores, allowing visualize both the central tendency and the spread of results, as well as potential asymmetries in the distri- bution. To assess whether the observed differences between models are statistically significant, conducted pairwise comparisons using the two-sided Mann-Whitney U test on the per-molecule score distributions. See Figure
Spearaa Cormiti between Inibedding and Gesmetii Distancee
Kinds i' benween Emrbedding and Seometic Dittances
3.-
Spuaraa
2.4
04-
Centered betweer Entedding Geametry
2.3
140000
627
lommery
Leca
Linka
12fe
D2P
Service
Figure 5: Violin plots summarizing the geometry benchmark results across baseline models. Pair- wise statistical comparisons were conducted using the Mann-Whitney test. Significance levels are annotated as follows: "ns" for 2 0.05, "* for p 0.05, for p < 0.01, and for p < 0.001.
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A.3 VIOLIN CHARTS OF CHIRALITY BENCHMARKS
We visualize the per-molecule outcomes for chirality-sensitive metrics using violin plots. Similarly, perform two-sided Mann-Whitney U tests the per-molecule chirality scores. See Figure DBI: Davies-Bouldin Index
02
2.9
Naseet
200
Hoad
2013
32-
15
100
Censter
Figure 6: Violin plots summarizing the chirality benchmark results across baseline models. Pairwise statistical comparisons were conducted using the two-sided Kann-Whitney U test on mol-mole score distributions.
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A.4 PES FROM SAMPLED TRAJECTORIES
A potential energy surface (PES) maps molecular energy across conformations. Since the full PES high-dimensional, we visualize 2D versions: reference PES from the most variant dihedral angles, and representation-base try-energy relations are preserved, characteristic ceatuurss-eakkee valleys. and shoules main visible in the representation space (Fig.
PES from PCA projections of learned embeddings. geome-
Relerones PEB (Cliedrrl))
Mc4Sowdre
Paracetomol PES dhedral CV
MoRE
Unioal
48.7
(Dihedral)
Garbill
MrdSowdrN
Figure Potential energy surfaces (PES) comparison for aspirin and paracetamol. Left panels show ground-truth PES as function of the two dihedral angles with the highest variance; right panels show the PES in representation space (learned representations projected via PCA). Red boxes mark energy peaks (barrier regions) that partly captured by representations, illustrating which strueturaa/eneergetic features are preserved versus which are lost or smoothed out.
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B
SUPPLEMENTARY TABLES
B.1 SUPPLEMENTARY CHIRALITY BENCHMARK
Table 4: Chirality metries correlation between representation distance and chirality reference,
including stereochemical labels and OPD index.
Metric
E3FP
GemNet
MolAE
MolSpectra
UniMol
Spearman
0,092
0.009
-0.012
-0,000
-0.025
Kendall
0.078
0.006
-0.012
-0.003
-0.022
CKA
0.789
0.657
0.647
0.715
0.659
OPD-S Spearmannnn
0.011
-0.015
0.006
-0.008
0,008
OPD-dCor
0.833
0.707
0.729
0.793
0.749
OPD-iso R²
0.256
0.240
0,251
0,244
0,255
Table 5: Fine-tuned model performance chirality datasets. We supervised contrastive learn- ing to train the models. E3FP not a trainable model. The result align well with our zero-shot experiment and agreement model architecture, while E(3) network like GemNet and MACE can- not represent chirality well.
Metric
ES-AUC
E3FP
N/A
UniMol
0.976
MolAE
0.971
MolSpectra
0.987
FMG
0.999
GemNet
0.9001
MACE
0.887
B.2 SUPPLEMENTARY ENERGY BENCHMARK
Table 6: Summary of representations' performance the energy dataset. Values reported as
mean + 95% CI.
Metric
E3FP
GemNet
MolAE
MolSpectra
MACE
FMG
Spearman
0.026 1 0.001
0.078 1 0.002
0.039 1 0.001
0.023 1 0.001
0.236 1 0.011
0.015 1. 0.004
Kendall
0.018 = 0.001
0.052
0.002
0.026 + 0.001
0.015 + 0.001
0.160 + 0.008
0.010 + 0.003
CKA
0.011 0.000
0.016
+ 0.000
0.024
0.000
0.006 1 0.000
0.017 1 0.001
0.012 1 0.001
n²
0.002 0.000
0.013
0.001
0.003 0.000
0.001
0.000
0.083 0.010
0.001 0.000
EIS(0.10)
0.151 = 0.006
0.252
0.000
0.251 + 0.000
+ 0.000
0.255 + 0.000
0.250 =
EJS(0.5g)
0.155 + 0.006
0.000 0.263
0.256 1 0.000
0.253 + 0.000
0.286 : 0.002
0.253 1 0.001
EJS(1e)
0.162 + 0.006
0.286
1:00
0.265 1 0.001
0.258 1 0.001
0.350 1: 0.007
0.257 1 0.002
EIS(2ar)
0.184 = 0.007
0.356 +.0004
0.294 = 0.002
0.271 + 0.002
0,578 + 0.019
0.269 + 0.006
EIS(3r)
0.217 0.009
0.451 0.007
0.328 1 0.004
0.289 1 0.004
0.845 0.025
0.283 1 0.016
ROCLAUC
0.531
0.592
0.545 0.001
0.527
0.764 + 0.011
0.517 0.005
Smoothness
0.847 + 0.002
0.998
0.000
0.996 1 0.000
0.001
0,999 1 0.000
0.972 1 0.002
TS
0.385 + 0.010
0.444
0.004
0.346 + 0.001
0.409 + 0.004
0.424 + 0.014
0.583 + 0.007
KS
0.913 = 0.001
0.998 4 0.000
0.998 1 0.000
0.766 + 0.001
0.999 + 0.000
1,00 + 0.000
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Table Number of detected energy jumps.
Energy Threshold
#lumps (mean + 95% CT)
0.1a
1,839,169.111 + 34.666
0.5g
1,232,341 + 61.925
638,505.706 197.971
2x
102,542.184 = 492.257
30
8,929.385 + 167.468
Table 8: DFT energy prediction MAE (kcal/mol) on the Revised MD17 dataset(part I).
Model
Aspirin
Azobenzene
Benzene
Ethanol
Malonaldehyde
E3FP
4.628
4.986
1.845
3.203
3.282
UniMol
5.010
3.509
0.988
0.797
0.801
MolAE
5.759
8.092
1.028
1,439
1.555
MolSpectra
3.525
4.173
0.813
1.554
1.679
GemNet
0.217
0,441
0.222
0,069
0.148
FMG
4.821
5.165
1.863
3.287
3,289
MACE
0.051
0.028
0.009
0.009
0.018
Table 9: DFT energy prediction MAE (kcal/mol) on the Revised MD17 dataset(part II).
Model
Naphthalene
Paracetamol
Salicylic
Toluene
Uracil
Avgerage
E3FP
4.279
4,871
4.425
4,009
3.880
3.941
UniMol
3.648
2.814
6.491
9.289
2.922
3.627
MolAE
2.098
2.814
5.609
4.080
5.570
3.804
MolSpectra
2.868
3.600
3.160
2.683
2.462
2.652
GemNet
0.249
1.312
0.930
0.017
0.106
0.371
FMG
4.550
5.009
4.509
4.015
4.054
4.056
MACE
0.012
0.030
0.021
0.012
0.012
0.020
C IMPLEMENTATION DETAILS FOR DATASETS AND METRICS
C.1 GEOMETRY DATASET: PROGRAMMATIC CONSTRUCTION DETAILS
Pipeline recap. We build bi-ary//heteroary/ backbones and decorate them with merged library of ring scaffolds and small functional groups. RDKit is used for fragment connection, sanitization, and 3D seeding via ETKDG. xTB software used for geometric optimization and relaxed sean. Candidate linkage atoms selected among non-saturated heavy atoms while reserving one position per pair for the final inter-ring bond. To control quality, we cap extra substitution sites per fragment (<2) and stratify ring choices by molecular weight (heavy/light extremes random mid-slice).
Libraries. During generation, we pool ring seaffolds and functional groups into a single sub- stituent library; any entry text. A minimal illustrative subset is shown in TableIo; the complete, machine-readable lists and scripts are in GutHub repository.
backbone unit R-group donor depending
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Published as a conference paper at ICLR 2026
Table 10: Illustrative subset of the merged library used for geometry datasets construction.
Class
SMILES
Functional group C(=0)O
Functional group CO
Functional group CC(=0)C
Functional group C=0
Functional group COC
Functional group C#N
Functional group C=NC
Functional group
CCI
Bulky subumit
CI=CC=CC=CI
Bulky subunit
CI2-CC-CC-CIC=CC-CC2
Bulky subunit
Bulky subunit
C1PC2--0-CCC-2--00--000-0
Bulky subunit
CC(C)C
Ring/scaffold
CICNCCI
Ring/scaffold
CIN=CC-CI
Ring/scaffold
CI=COC=CI
Ring/scaffold
CI=CSC=CI
Ring/scaffold
01CCCCC1
Ring/scaffold
NI=CC=CC=NI
Ring/scaffold
S1CCNCC1
Ring/scaffold
CI=CC=C2CC=CC2-CI
Ring/scaffold
CI=CC-C2C-COC2-CI
Ring/scaffold
CI=0C-C20CCEOJC-CCC2C
C.2 REPRESENTATIONS DISTANCES
For handcrafted descriptors, molecular fingerprints F; = ((x) are compared using Tanimoto dis- tance. For learned representations, extract zero-shot representations 2, g(G) without fine- tuning. The representation distance Ai is defined as:
2. 2j
Cosine distance
1 ||ا
A.j
||:
Zy 1l,,
Euclidean distance
F O Fyl
Tanimoto distance
F. U.UU E51
Cosine distance is the default for learned representations, as most encoders implicitly normalize their representations. Tanimoto is reserved for binary fingerprints, where overlap naturally defines similarity. All the distance matrices are normalized to the ()-1 range.
C.3 CORRELATION METRICS
Rank correlations.
(s(m) = Spcarman(vec (D), voc (A)),
(1)
((m) = Kendall vecl (D), veca (A)).
(2)
Centered Kernel Alignment (CKA). Define RBF kernels
(Dr))²
A?
K:D (D) = exp
K-(A) = exp
20
20
with bandwidths by the median heuristic on upper-triangular entries. Let I K HK K. be centered kernels. Then
1
and
(K(D), R((A)
CKA
||(D | (A) |
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Published as a conference paper at ICLR 2026
Isotonic Regression R We perform isotonic regression fit:
- Jio((A))) Siso monotone non-decreasing,
mapping representation distances Dij onto the reference values Dij- We then compute the coeffi cient of determination.
isoR² =1 (Dj - Dig)2
(Di D)2
high isoR? score indicates that the representation preserves the reference ordering well enough that monotone transformation recovers the reference scale.
C.4 GEOMETRY METRICS
We use /
the RMSD matrix between conformers.
Local Isometry Error (LIE). Global correlations hide distortions at the neighborhood level.
To test neighborhood preservation, for each conformer we identify its nearest neighbors N under (G) and compute
M/P) (i)
D
2
LIE,
Σ
Ag A
D,
JEAN (i)
with D,, A; denoting local averages. The final score is the mean conformers.
Torsion correlation and smoothness. Beyond RMSD, relaxed scan is performed on a controlled axis of conformational change. For torsional scans along a dihedral angle Øi, we define circular angular distance:
A.j = mmmmn(ee +5y 2n - 6 - Qz1).
The torsion-reeressentaion rank correlation is defined as:
Ptor = coorI((ve(AA) vec(A))
The torsion correlation tests global alignment with torsional change.
To further quantify continuity, define angular smoothness (AS) by sorting conformers along the scan and measuring displacement angular increment:
|i+1 - 2i|l
AS = median;
Φ1+1 Φ.1
High Per indicates global consistency with torsional change in conformers, while moderate AS values reflect stable local aeviitivity-voiddingg both insensitivity (collapse) and over-reactivity to small rotations.
C.5 CHIRALITY METRICS
We use (CC) the normalized Hamming distance between chirality signatures, as the stereochemical ground truth. For supervised enantiomers separation metrics, we use the class labels y from the enantiomers' relative configuration tags and pairwise representation distances Ary:
ESA-AUC (Enantiomer Separation AUC). Treat cross-enantiomer pairs as positives and use distance as the score:
to = 1/4 + y,l:
ESA-AUC = AUC([(A.)) to))es))
higher AUC indicates that between clase distances dominate within-class distances, meaning that enantiomers well separated.
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Published as a conference paper at ICLR 2026
Nearest-neighbor Accuracy.
Nearest-neighbor classification under A: NN1-acc 25 1g. yz)
i(i)
arg min Ay. 37
ÿ1 V3(0)
This measures whether local decision boundaries align with stereochemical classes.
Silhouette Coefficient Index. mean,
With a, the intra-class mean distance and b; the nearest other-class
bi max by)
sil sup 1/4 Σ
Larger values indicate tighter intra-class cohesion and wider inter-class margins.
Davies-Booldin Index (DBI). The Sovies--Buldie Index quantifies the trade-off between within- cluster compactness and between-cluster separation. Given partition of the data into K clusters (C,....,Ca, ...,., with centroids { under a Euclidean distance metric d(,,)) ), the within-cluster scatter and the inter-centroid distance
S:
1 - C2
Σ de, ZEC.
M, = du
(i (1+.).
For each cluster i, define its worst-case similarity to other clusters:
S
Ríj
R
max Raj- j
Múj
The DBI is the average of these worst-case similarities:
K
1 K
DBI
R
Lower values indicate better clustering: small S; (compact clusters) and large My (well-separated centroids). DBI is approximately scale-invariant with respect linear rescalings of the distance. practice, one may add small & to Miy the denominator to avoid degeneracy when centroids coincide.
For unsupervised metrics, we aim at evaluate the shape of representations while ignoring the chirality label. we report:
Hopkins statistic. value 0.5 suggests non-uniform, clusterable structure for continuous repre- sentations only.
Best-k silhouette. We scan (2,...,kmaan and report
sil-usup" silhouette A, k-means//e-medoiddss))
using k-means for vector representations and k-medoids (PAM) on precomputed distances for fin- gerprints. A larger value indicates sharper, more coherent clusters that align with latent stereochem- ical organization.
C.6 ENERGY METRICS
Let E R" be the per-conformation energies and let A R=*= denote pairwise representation distances. We write d. = F4 Ezl and dZzz=Aij and evaluate pairs only on the upper triangle.
Half-normal scale of energy differences. We treat (dEi) } as samples from a half nalm-normal distri- bution with scale ay and estimate 0a by:
σa
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Energy-Jump Sensitivity (EJS). For energy-jump level X 0, define the energy threshold ((A) Aā and the jump set Jx = [(1,)) dEi, }. Let r be distance threshold chosen as the 75% quantile of dZ. The sensitivity at level À is the conditional hit rate:
EJS(A) = [dzy > r) (1. E JN = [TAI
Σ (iJ))J
1ídZaj > T).
We evaluate À on the grid {0.1, 0.5, 1.0, 2.0, 3.0} and report all EJS(A) values. By default, we choose À = 2.
EJS-ROC (discrinination under an energy jump threshold). Further, we turn energy-jump detection into binary classification task with labels and scores:
Mij 1ld 0},
8ij dZ,j.
In our evaluation we fix 0 = 2ōd (i.e., X = 2.0) to generate the binary labels. We compute ROC-AUC AUC([(ss) 9t))) using sklearn. www.ics............... roc auc. score.
Thresholded Smoothness (TS). Along ordered conformational trajectories, we verify whether representations vary smoothly with energy. To focus on regions of substantial energetic contrast, we restrict to segments with [xx+] Emal > TE and compute:
A T 1
(A)
TST = R
Σ exp REK
E - Exg 1/Qu. +
This normalizes by robust (90% quantile) scales to enable comparison across molecules and penal- izes representations that change abruptly where the energy landscape is smooth.
Distributional divergence. We ask whether the overall distribution of representation distances resembles that of energy differences. Let FA and FE denote the empirical CDFs of vec(A) and vec(D(E)), respectively. We report the two-sample Kolmogorov-Smimnov statistic:
Dks = sup Fa(x) FF(()),
In our benchmark, these quantities are used descriptive divergences (smaller is better).
25


Reviews:
[{"review_id": "NKfVIJdWBI", "reviewer": "Reviewer_bj3T", "summary": "This paper presents 3DCS, a benchmark framework for evaluating 3D conformational sensitivity in molecular representations. It introduces three datasets (relaxed torsional scans, chiral drug candidates, and AIMD trajectories) and a unified GCE (Geometry–Chirality–Energy) evaluation framework. The benchmark assesses both handcrafted and learned molecular representations (E3FP, UniMol, MolAE, GemNet, MolSpectra) in a **zero-shot** setting, revealing that most models capture geometry well but struggle with chirality and energy alignment.", "questions": "Please refer to my proposed weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The problem studied is meaningful: how well molecular representation models handle 3D conformational variations, rather than just particular molecular properties.", "weaknesses": "1. Lack of model training or adaptation on 3DCS. All models are evaluated in a _zero-shot_ setting using their pre-trained representations. Therefore, the poor chirality and energy performance might not reflect fundamental architectural deficiencies but rather distribution mismatch between 3DCS and their pre-training datasets (e.g., PCQM4Mv2). It would strengthen the claims to:\n    - Split 3DCS into train/validation/test sets and retrain existing models on 3DCS to verify whether their performance improves under the proposed GCE metrics.\n    - Further examine whether training on 3DCS enhances downstream molecular property prediction tasks (e.g., QM9, MD17).\n2. Potential limitation in the geometry sensitivity assumption. The evaluation of geometry sensitivity relies on the assumption that _if two conformers have large atomic coordinate differences (high RMSD), their representation distance should also be large_. This assumption may not always hold physically: Two conformers with large RMSD can have very similar energies or functions. Conversely, small geometric differences can correspond to substantial energetic or functional changes. Thus, the current geometric metrics (Spearman/Kendall correlations with RMSD) may overemphasize purely geometric deviations without distinguishing physically meaningful conformational changes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HEKz2Bhhsv", "reviewer": "Reviewer_CUvk", "summary": "The paper provides a dataset and benchmark for characterizing how molecular representations capture intra-molecular conformational sensitivity. The evaluation framework spans 3 areas of interest: geometry, chirality, and energy, each with their own large-scale datasets that measure how well molecular representations correlate with geometric changes, whether they distinguish stereoisomers, and how well they correlate to the underlying conformational energy landscape.  The empirical results show that while modern data-driven molecular representations are sensitive to geometry, they fail to capture chirality, and don't align with energy variation.", "questions": "The paper is generally clear.  One question is whether the proposed benchmark could eventually serve not only as a characterization tool, but as a metric to help design better molecular representations, for example by suggesting weaknesses that could be overcome by training or modifications of hyperparameters. Although this is beyond the scope of the current work, I would be curious to know if the authors envisioned such a use.\n\nHave the authors thought about ways to link the performance in these benchmarks to the performance in downstream tasks?  For instance, once enough representations have been evaluated, a simple empirical cross correlation between these new metrics and downstream task performance (docking or property prediction) would provide additional insights and help increase the practical relevance of this new characterization.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This is a useful collection of large datasets with a clear analysis process. The methodology is described in a clear fashion and the molecule dataset selection (including processing and augmentation) make sense. The benchmarks across a range of methods highlight the strengths and weaknesses of different types of approaches. The observed lack of proper handling of chirality by all methods aligns well with anecdotal observations and community experience, and the introduction of a specialized dataset for the characterization of this property is timely and important.", "weaknesses": "The current version of the paper lacks the associated dataset and codes, which are critical for reproducibility and use of this new dataset and benchmark.  The emphasis on correlation metrics may not fully capture non-linear relationships between the conformation of the molecule and the molecular representation space, potentially reducing the importance of complex but otherwise valid methods. Furthermore, the present work does not yet demonstrate any relationship between performance of this benchmark and downstream performance on practical tasks, say docking pose prediction, so the main use might would focus on characterizing rather than ranking, new molecular representations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JDXKLKoApx", "reviewer": "Reviewer_37hb", "summary": "This work contributes a benchmark for assessing the capabilities of molecular representations to discern 3D conformers (of the same underlying molecule) in terms of geometric, stereochemistry (specifically chirality), and energy sensitivity (i.e., variability). The benchmark, called 3DCs, consists of three datasets: (1) a geometry dataset obtained by dihedral scan around the inter-ring single bond in small angular increments,  (2) a chirality dataset filtered from ChemBL based on annotation stereocenters, and (3) an energy dataset based on MD17. The authors advocate a two-layer framework: (a) reference alignment between pairs of conformers that takes into account the discrepancy in atomic positions after alignment, fraction of mismatched stereocenters, and difference in potential energy; and (b) manifold consistency between local neighbourhoods. Five baselines, namely, E3FP (classical, non-neural 3D fingerprints), UniMol, MolAE, GemNet, and MolSpectra that encode 3D information are evaluated.  Empirical results demonstrate that molecular representations can reflect the geometric variations rather well but struggle with chirality and energy.", "questions": "--- Could you please include results with strong baselines for (1) chirality,  (2) energy/force, and (3) conditional settings that I mentioned in the weaknesses section? I would be willing to revisit my score if this requested empirical evidence is consistent with the claims of the paper. \n\n--- Could you please address my concerns about potential energy mismatch under relaxed scan and that particular claim about ability of MPNNs to capture long-range dependencies and global structure?\n\n--- How many conformers does your relaxed scan dataset contain - 100 million or 10 million?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "--- The motivation for this paper is clear and important: having good datasets and evaluation strategies for benchmarking the quality of molecular representations is important to advance fields such as drug discovery. \n\n--- Geometry, chirality, and energy are all known to be important factors in the drug design pipelines due to their impact on binding, safety, and stability respectively (and efficacy as a whole).\n\n--- The dataset on chirality seems particularly relevant. I'm not aware of other datasets for quantifying chirality in a meaningful way.", "weaknesses": "--- One of the reasons that hinders the ability of molecular representations to reflect chirality properly is due to equivariance [1]. Specifically, E(3)-equivariant models provably struggle with chirality, while learning chirality-aware features under SE(3)-invariance has high complexity in terms of the number of atoms (O(N^4)).  The current experimental setup already includes the UniMol baseline which implements an SE(3)-equivariant transformer. It would strengthen the paper considerably if the benchmark indeed shows improved performance with a field-based model [1] that is designed to handle chirality better than the equivariant representations. \n\n---The authors claim in the discussion section that “Neural architecture such as SE(3)-equivariant transformers and message-passing networks (MPNNs) capture long-range dependencies and global structure.” I understand why this should hold for SE(3)-equivariant transformers, but do not see how MPNNs capture long-range dependencies and global structure. This is very counterintuitive and goes against conventional wisdom, since MPNNs have a strong inbuilt locality bias and are known to struggle with global properties such as the number of substructures (e.g., cycles) etc.\n\n--- It’s not clear whether/to what extent the estimated energy values pertaining to the geometry dataset obtained with relaxed scan are consistent with the ground truth in the absence of wetlab validation (in contrast to MD simulations, where DFT is employed for reasonably accurate estimates). \n\n--- The methods used for evaluation are not quite state of the art. For example, none of the best-performing methods for predicting energy and force of conformations in the molecular dynamics experiment (such as NequIP, TopNets, MACE) are included.  \n\n--- All three aspects (geometry, chirality, and energy) seem to have been evaluated in unconditional settings (i.e., absent protein targets). In practice, one really cares about target-specific sensitivity of molecular conformations. \n\n--- There seems to be a discrepancy in terms of the stated number of conformers at different parts of the paper. Specifically, in the introduction the authors mention that \"We curate three datasets that contain over 1M molecules and 110M conformers: (i) a relaxed scan dataset with∼1.5M molecules and almost 100 million conformers obtained by rotating an inter-ring bond and relaxing the rest\nof the structure;\". In contrast, in the corresponding section 3, the claim is \"After processing, the dataset comprises 10,097,643 conformers, each annotated with its corresponding dihedral and energy values.\n\n[1] Dumitrescu et al. E(3)-equivariant models cannot learn chirality: Field-based molecular generation. ICLR 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yoWMe3A4Mi", "reviewer": "Reviewer_Ftr9", "summary": "This paper introduces three datasets designed to benchmark molecular representations in their ability to capture 3D structural information. The datasets encompass molecular geometries, chirality-related features, and energy values. The authors evaluate molecular representations by computing pairwise distances between molecules in representation space and correlating these distances with structural, chiral, and energetic differences. A suite of metrics is employed to assess whether the representations sufficiently encode essential 3D information.", "questions": "1. Please clarify the units used for energy and RMSD throughout the benchmarks.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "Overall, the paper addresses an important and timely challenge in molecular machine learning: evaluating the 3D-awareness of molecular representations. The proposed datasets and evaluation framework are novel and potentially impactful.", "weaknesses": "## Dataset Quality and Methodology\n1. Why was xTB chosen for generating molecular geometries? Does this level of theory provide sufficient accuracy for benchmarking purposes?\n2. How does the quality of the xTB-derived geometries and energies compare to those in OMol25, which uses more accurate quantum chemical methods?\n## Chirality Dataset Design\n1. What is the rationale for introducing torsional perturbations in the chirality dataset? Could these perturbations inadvertently alter stereocenters, thereby confounding the intended chirality assessment?\n## Correlation Metrics and Interpretability\n1. While representation distances should ideally correlate with geometric, chiral, and energetic differences, such relationships are likely to be nonlinear or non-monotonic. What would constitute an ideal alignment between representation space and these physical properties?\nAre the selected correlation metrics sufficient to capture these potentially complex relationships? A justification or discussion of metric suitability would strengthen the work.\n## Benchmark Relevance to Downstream Tasks\n1. Do the proposed benchmarks correlate with performance on real-world molecular property prediction tasks? It would be more compelling if representations that perform well on these 3D benchmarks also demonstrate superior performance on established benchmarks for practical property prediction.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)