PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Authors: Fanmeng Wang
Wentao Guo
Qi Ou
Hongshuai Wang
Haitao Lin
Hongteng Xu
Zhifeng Gao
Venue: ICML 2025 poster (2025)
Keywords: Polymer conformation generation
Polymer modeling
Hierarchical generative models
Primary area: applications->chemistry_physics_and_earth_sciences
TL;DR: This study introduces a pioneering method that leverages hierarchical generative models to unlock polymer conformation generation.

Abstract: Polymer conformation generation is a critical task that enables atomic-level studies of diverse polymer materials. 
While significant advances have been made in designing conformation generation methods for small molecules and proteins, these methods struggle to generate polymer conformations due to their unique structural characteristics.
Meanwhile, the scarcity of polymer conformation datasets further limits progress, making this important area largely unexplored.
In this work, we propose PolyConf, a pioneering tailored polymer conformation generation method that leverages hierarchical generative models to unlock new possibilities.
Specifically, we decompose the polymer conformation into a series of local conformations (i.e., the conformations of its repeating units), generating these local conformations through an autoregressive model, and then generating their orientation transformations via a diffusion model to assemble them into the complete polymer conformation.
Moreover, we develop the first benchmark with a high-quality polymer conformation dataset derived from molecular dynamics simulations to boost related research in this area.
The comprehensive evaluation demonstrates that PolyConf consistently outperforms existing conformation generation methods, thus facilitating advancements in polymer modeling and simulation.
The whole work is available at https://polyconf-icml25.github.io.

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Fanmeng Wang 12t
Wentao Guo
Qi Ou
Hongshuai Wang?
Haitao Lin Hongteng Xu 156 Zhifeng Gao
Abstract
High
Polymer conformation generation is a critical task that enables atomic-level studies of diverse poly- mer materials. While significant advances have been made in designing conformation generation methods for small molecules and proteins, these methods struggle generate polymer conforma- tions due their unique structural characteristics. Meanwhile, the scarcity of polymer conforma- tion datasets further limits progress, making this important area largely unexplored. In this work. we propose PolyConf, a pioneering tailored poly- mer conformation generation method that lever- ages hierarchical generative models to unlock possibilities. Specifically, we decompose the polymer conformation into series of local con- formations (i.e., the conformations of its repeat- ing units), generating these local conformations through an autoregressive model, and then gener- ating their orientation transfornations via dif- fusion model to assemble them into the complete polymer conformation. Morcover, develop the first benchmark with a high-quality polymer con- formation dataset derived from molecular dynam- ics simulations to boost related research this area. The comprehensive evaluation demonstrates that PolyConf consistently outperforms existing conformation generation methods, thus facilitat- ing advancements in polymer modeling and sim- ulation. The whole work is available at https: //polyconff cml22. gi github. io.
five repeating units
Energy Landscape Complexity
polymer
protein
AFM Image
Low
small
molecule
Low
Structural FleuurraFFleiiiieee Flexibility
High
Figure I. The comparison of small molecule, protein, and polymer.
Here, the polymer chain comprises series of repeating units, the atomic force microscopy (AFM) image (Roiter & Minko, 2005) is used for direct 3D visualization of various polymer chains.
1. Introduction
Polymers, the macromolecules formed by covalent bonding of numerous identical similar monomers, have already be- come indispensable modern life (Audus & de Pablo, 2017; Kuenneth & Ramprasad, 2023). For example, polyethylene and polypropylene are used as durable and lightweight pack- aging materials, while polystyrene and polycarbonate find applications in electronics for their robustness and flexibil- ity (Chen et al., 2021: Xu al., 2023). The vast chemical space of polymers represents the of molecular condensa- tion that transforms simple building blocks into functional materials. In this context, polymer conformation genera- tion where various deep generative models can be used
WWrk done during internship at DP Technology Gaollin School of Artificial Intelligence, Renmin University of China DD Technology CCalifomiaa Institute of Technology SSINPECC Re- search Institute Petrolcum Processing Co., Ltd. BBiijing Key Laboratory of Research on Large Models and Intelligent Gov- ernance 'Engineering Research Center of Next-Generation In- telligent Search and Recommendation, MOE, Correspondence Zhifeng Gao
to: Hongteng Xu Zhongtengxu@rueecduu <gaozf@ tech.....
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
'This work mainly focuses on generating conformations of linear homopolymers, modeling copolymers and blends involves complexities beyond data modeling.

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Phase-1 Training
Masked Repasting Unit Conformation
Masked Repeating Unit Embeddiings
Condition
Masked Repeating Unit
Polymer SMILES [+[Oelee((C(()))=))eee
Multi-modal Repeating Unit Encoder
MAR Encoder
MAR Decoder
SE(3) Diffusion for Repeating
Unit Conformation
3D Repeating Units
Clone
Clone
Repeating Unit Conformations
Repeating Unit Embedeinge
Multi-modal Repeating Unit Encoder
A2
2D Polymer Graph
MAR Encoder
SO(3) Diffusion 3D Rotations
12
Hi
Rs
Rotations
Polymer Conformation
Real Rlepeating Unit Conformations for Training
Phase-2 Training
Figure 2. The overview of PolyConf: A hicrarchical framework for polymer conformation generation, employing masked autoregressive (MAR) model with a diffusion procodure to sample the conformation of cach repeating unit within the polymer in random order, followed by SO(3) diffusion model assemble these repeating unit conformations into the complete polymer conformation. Here, for the sake of Visualization simplicity, only a small fragment of the whole polymer conformation with five repeating units is presented in this figure.
to obtain the stable 3D polymer structures conditioned on the corresponding 2D polymer graph (Hoseini et al., 2021; Baillif et al., 2023), serves as a fundamental starting point for simulations a crucial step in studying polymer proper- ties (Kremer& & Grest, 1990; Nakano & Okamoto, 2001).
characteristics, thus fundamentally transforming our ability to design polymers and predict their properties.
Technically, a polymer conformation can be decomposed into series of repeating unit conformations, as illustrated in Figure 1. However, unlike proteins that share a common backbone scaffold characterized by similarly distributed dihedral angles between amino acid residues (i.e., the "N C. C - O structure) (Jumper et al., 2021). different polymers are composed of distinct monomers with diverse geometries, leading to various repeating units and structural frameworks (Huang et al., 2016). In addition, although repeating unit conformations within the same polymer share the same SMILES string and scaffold, the monomer itself can be highly complex and the spatial rearrangement of the remaining structure can also vary significantly in 3D space, which indicates that a polymer conformation cannot be simplistically modeled as a rigid assembly of a single predefined repeating unit conformation.
Although conformation generation methods have been tensively studied over the past few years, generating macro- molecular conformations remains challenging (Riniker & Landrum, 2015; Hawkins, 2017). Traditional stochastic methods like molecular dynamics (MD) simulations are widely used (I. et al., 2025a; Wang et al., 2025), but they are computationally expensive and slow, particularly for macro- molecules like polymers (Pracht et al., 2020; Bilodeau et al., 2022), leading to the severe scareity of polymer conforma- tion datasets. Recent advances in artificial intelligence have led to various learning-based methods for conformation gen- cration (Tang et al., 2024; Han et al., 2025). However, these methods are primarily designed for small molecules (Jing et al., 2022; Wang et al., 2024b) and proteins (Janson al., 2023; Lu et al., 2024), leaving polymers unexplored (Kuen- neth & Ramprasad, 2023; Wang et al., 2024a). As shown in Figure 1, polymers present unique challenges distinct from both small molecules and proteins. Unlike proteins, stabi- lized by strong, directional intramolecular interactions, poly- mers typically lack such organizing forces, resulting in more flexible and less ordered conformations. In addition, poly- mers occupy larger chemical space than small molecules, further complicating conformation generation (Martin & Audus, 2023). With fewer prior constraints, the complex conformational behaviors of polymers render protein con- formation generation methods ineffective. Meanwhile, con- formation generation methods designed for small molecules struggle to scale to polymers due to their significantly higher molecular weight (Xu al., 2022). Given these challenges, it is critical to develop tailored polymer conformation generation method to accommodate their unique structural
In this context, we propose PolyConf, the first tailored method for polymer conformation generation, to over- come the above challenges. As shown in Figure 2, we design our PolyConf as a hierarchical generative framework with a two-phase generating process. In the first phase, we leverage the state-of-the-an autoregressive generation paradigm pro- posed recently (Li et al., 2024), which integrates a masked autoregressive model (MAR) with a diffusion procedure (Ho et al., 2020), to generate repeating unit conformations in random order. Specifically, the partial output of the masked autoregressive model, which corresponds to masked repeat- ing units, is used as the condition of the diffiusion procedure designed for repeating unit conformation, thus effectively integrating the abilities of autoregressive modeling and diffu- sion processes to capture the dependencies within repeating unit conformations. In the second phase, building directly the output of the MAR encoder, we employ an SO(3)
2

---

PolyConf:
Unlocking Polymer Conformation Generation through Hierarchical Generative Models
diffusion model 2 designed for repeating unit orientation transformation to generate the required orientation trans- formations, thus facilitating the assembly of repeating unit conformations into the complete polymer conformation.
2.2. Protein Conformation Generation
The emergence of AlphaFold (Jumper et al., 2021; Abram- son et al., 2024) has greatly revolutionized the protein area (Bryant et al., 2022; Hekkelman et al., 2023) which in- spired further protein conformation generation methods (Lu et al., 2024; Wang et al., 2024c) that unlock the multi- conformation capability by modifying AlphaFold predic- tions through MSA perturbations, such as mutations (Stein & Mchaourab, 2022), clustering (Wayment-Stee Steelle al., 2024), and reducing depth (Del Alamo al., 2022). In addi- tion, various deep generative models, particularly diffusion models, have significantly contributed to protein confor- mation generation (Watson et al., 2022; Jing et al., 2023), including protein backhone generation (Huguet et al., 2024; Yim et al., 2024) and side chain generation (Zhang et al., 2024; Lee & Kim, 2024). Since proteins are composed of amino acid sequences with the consistent structural frame- work (i.e., the "N C. C O" structure) (Yue et al., 2025), protein-specific prior knowledge, such as the unified backbone parameterization method (Yim et al., 2023; Bose et al., 2024) and constraints on the number of side-chain torsional angles (Misiura et al., 2022; Visani et al., 2024), has been widely integrated into various protein conforma- tion generation methods. In this context, these methods are unsuitable for polymer conformation generation as they rely on evolutionary information, sequence similarity, and dihedral angle constraints that do not apply to polymers.
Besides designing PolyConf, we devote considerable time and resources to developing PolyBench, the first bench- mark for polymer conformation generation, to address the scarcity of polymer conformation datasets. PolyBench comprises a high-quality polymer conformation dataset ob- tained through molecular dynamics simulations (Afzal et al., 2020) and establishes standardized evaluation protocols. Extensive and comprehensive experiments on PolyBench consistently demonstrate that our PolyConf significantly outperforms existing conformation generation methods and achieves state-of-the-art performance, thus facilitating ad- vancements in polymer modeling and simulation.
The whole work, including code, model, and data, is pub- licly available to facilitate the development of this important yet largely unexplored research area.
2. Related Work
2.1. Molecular Conformation Generation
In recent years, with the significant progress of deep gen- erative models (Cao et al., 2024; Li et al., 2025b), many carming-based methods (Shi et al., 2021; Ganea et al., 2021) have been proposed to generate molecular conformations, thus facilitating traditional molecular dynamics simulations. In particular, CGCF (Xu et al., 2021) generates molecular conformations by combining the advantages of flow-basee and energy-based models. Then GeoDiff (Xu et al., 2022) treats molecular conformations point clouds and Iearns diffusion model in Euclidean space, while TorsionalD- iff (Jing et al., 2022) further restricts the diffusion process only in the torsion angle space to improve performance. Recently, MCF (Wang et al., 2024b) proposes to directly predict the 3D coordinates of atoms using the advantages of scale, and ETFlow (Hassan al., 2024) tries to employ well-designed flow matching tackle this task. However, these molecular conformation generation methods are pri- marily designed for small molecules and typically generate the entire molecular conformation through a single pro- cess (Wang et al., 2023). Although they can be applied to generate polymer conformations, their performance will de- grade significantly as polymers have larger chemical space and higher structural flexibility than small molecules.
3. Proposed Method
3.1. Modeling Principle
Frame-based Polymer Representation. Each polymer with N atoms can be represented as 2D graph G = (V. E), where V = {ur),N1 describes the corresponding atomic features (e.g., atomic type) and & = {eij ) )= describes the corresponding bond features (e.g.. bond type). The polymer conformation can be further denoted as C = [ci] E IR Nx3 where c, E R is the 3D coordinate of the i-th atom.
As shown in Figure 3, the decomposition of polymer con- formation corresponds
series of repeating unit confor- mations. Here, to model polymer structures effectively, we extend the standard definition of repeating units in polymer science, incorporating the two key atoms from the neigh- boring repeating units (i.e., the atom-1 and atom-4 in Figure 3) into the conformation of the current repeating unit. In this context, inspired by the modeling strategy of protein residue (Jumper al., 2021), we further extract the frame from the corresponding repeating unit conformation. In particular, for the i-th repeating unit, its frame contains the corresponding orientation transformation 3, denoted as
"Since the corresponding repeating units in the polymer are defined by their monomers, the bonding atoms between adjacent repeating units are naturally overlapping (as illustrated in Figure 3). Therefore, we only need to train an SO(3) diffusion model to generate rotations, translations be directly derived from the 3D coordinates of those overlapping atoms.
"The corresponding orientation transformation is relative to the standard coordinate system.
3

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Repeating Unit
Frame
Therefore, the polymer conformation generation task can be naturally denoted hierarchical generative process: (I) generating repeating unit conformations C* based on the corresponding 2D polymer graph G, i..., p(C [G), and (2) then generating corresponding orientation transformations O of these repeating units given and C", i... p(O]g, C*).
R
22
R GS v1, V2)
= C3
This hierarchical generative process further leads to the pro- posed PolyConf model and its two-phase learning strategy, as illustrated in Figure 2. In the following subsections, will introduce them in detail.
Polymer SMILES
O RR t) E SE(3)
Key Atoms and Their
Connection Rules
Figure 3. The illustration frame-based polymer representation. In particular. the ID polymer SMILES string represents the monomer's ' SMILES string with two "*" symbols marking poly- merization sites. The 3D polymer conformation comprises series of repeating unit conformations with identical SMILES strings hut distinct 3D structures, overlapping at key atoms (e.g., atom-l aligns with atom-3 of the previous repeating unit). The orientation trans- formation, derived from the key atoms within the corresponding frame, is denoted as O = (R. E) where the rotation R E R gx3 is calculated through the GramSchmidt operation (Leon al., 2013) on vectors Un and 12 and the translation t E R corresponds to the 3D coordinate of atom-3.
3.2. Phase 1: Repeating Unit Conformation Generation
In this first phase, we employ the masked autoregressive model (Li et al., 2024) with a diffusion procedure to gener- ate repeating unit conformations in random order, capturing their complex interactions rather than simple sequential de- pendencies. The distribution p(C"Ig) in Eq. (2) is therefore rewritten as follows:
((C"(g)- P((C)) N. = =p([C]] 9)
III k= P(CK G, (C
O (R,,t,) where R2 E 3x3 denotes the rotation and t; E RR3 denotes the translation. In this context, the polymer conformation can be further denoted as
where === (C.) is the set of repeating unit conforma- tions, and C% is the corresponding subset of C* that contains N₂ repeating unit conformations generated at the k-th step.
C CC", O} =
(1)
K'
Since these repeating unit conformations exist in continuous 3D space, we generate them in random order. Here, model this random order,
where C. = - E ( +3)x3 is the i-th repeating unit's conformation 4, O, (R,, t.) is the i-th repeating unit's 's ori- entation transformation, and N,, is the number of repeating units in this polymer. For the j-th atom in the i-th repeating unit's is conformation, its corresponding 3D coordinates in the polymer conformation can be expressed as R.c,,- + t4.
define random permutation and C can be expressed as:
C (C | E {(k 1)m + 1...., km)),
(4)
where (* the corresponding conformation of the ri)-- th repeating unit, x is the size of the subset, and ensures a random sampling order.
Please note that since each repeating unit involves 2 over- lapping atoms from previous and next units, the number of
atoms in one unit is not N_ but rather N N. 2 N.
The key modules shown in Figure 2 are introduced below.
Hierarchical Generative Modeling, The task of polymer conformation generation is a conditional generative problem, which aims to learn a generative model p(C]g) to model the empirical distribution of polymer conformations C (i.e., the stable 3D polymer structures) conditioned on the corre- sponding 2D polymer graph G. Combined with Eq. (1), this generative model p(Clg) can be expressed as follows:
Multi-modal Repeating Unit Encoder. The multi-modal repeating unit encoder M comprises two parts: the 2D en- coder M for the whole polymer graph G, and the 3D encoder 3d for each repeating unit conformation C in the polymer conformation. The embedding extraction pro- cess can be expressed as follows:
X M(G, (C No )
p(C = =CC",,
= p(C"lg) p(O C"),
= Concat, (M22 Concato (CH))))) (5) Concat, 2d Concato (xdd)NN,)) N2,)
where Ca ( No is the set of repeating unit conforma- tions, and O = J,, is the set of their corresponding orientation transformations.
where X E N. xD. is the multi-modal repeating unit embeddings, X E N.. X.xD is the 2D embedding of the whole polymer graph g, X E R x is the 3D em- bedding of the i-th repeating unit conformation C.², and
'The repeating unit conformation is in the standard coordinate system through applying the inverse orientation transformation to the corresponding sub-structure within the polymer conformation.

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
representations Z mack As shown in Figure 3, repeating unit conformations are a specialized form of molecular confor- mations, characterized by the added complexity of interac- tions between repeating units. Given the recent success of diffusion models generating molecular conformations, leveraging a diffusion model to represent this conditional probability distribution for each repeating unit is highly suit- able. Following previous works (Xu et al., 2022; Li et al., 2024), the corresponding loss function can be formulated as denoising criterion, i.e.,
2
1
2
2
MAR Emarks
3
3
2
3
4
4
4
Z
5
X
knowa
5
5
Figure 4. The illustration of the masked autoregressive modeling in the second phase, where grey blocks represent the corresponding embeddings of masked repeating units.
Cpause = Ee, |||E - -Eo Et((,|t,2")]1 with C² =vā,0"
(8)
Concat,(+) represents the corresponding concatenation op- erator in the i-th dimension.
where C E ( +2)x3 is the conformation of one masked repeating unit (i.e., one element in miac)) ) z" E RR.m the corresponding decoded representation of this masked repeating unit (i.e., the corresponding row of Imus)) ān is the predefined noise schedule, is the time step of this predefined noise schedule, & is the noise sampled from the predefined prior distribution, and Eg is the parameterized denoising network for noise estimator.
In this work, our PolyConf adopts the encoder architecture from MoICLR (Wang et al., 2022) as its 2D encoder M and the Uni-Mol (Zhou et al., 2023) as its SE(3)-invariant 3D encoder Mdd Besides, the entire multi-modal repeating unit encoder M is trainable in the first phase and remains frozen in the second phase.
Masked Autoregressive Modeling. As shown in Figure 2, to generate a random subset of unknown repeating unit con- formations based on known/predicted repeating unit con- formations iteratively (i.e., Eq. (3)), we employ the masked autoregressive modeling in the latent space of the multi- modal repeating unit encoder.
Specifically, we employ the diffusion process defined the torsion angle space to model this probability distribution, and adopt the corresponding diffusion model architecture used in (Jing et al., 2022) the denoising network Eg.
During training, given the random permutation π and multi- modal repeating unit embeddings X" E IR N. ND.,, we ran- domly sample a masking ratio t from the range [0, 1J. and then mask the corresponding repeating units, i.e.,
3.3. Phase 2: Orientation Transformation Generation
As expressed in Eq (2), after generating repeating unit con- formations C" conditioned the corresponding polymer graph G in the first phase, we still need to generate the cor- responding orientation transformations O of these repeating units based on & and C' in the second phase.
X known Concata (1X*))
(+) | E [(TN, N,1)), (6)
where x1) is the permuted repeating unit index used in Eq. (4), X E DN, is the embeddings of unmasked repeating units with known conformations, and X" E I x refers to the π (i)-th row of multi- modal repeating unit embeddings X obtained through Eq. (5).
In particular, as illustrated in Figure 3, repeating unit con- formations within the polymer partially overlap (e.g., the atom-l of the current repeating unit aligns with the atom-3 of the previous repeating unit). Therefore, for cach repeat- ing unit's orientation transformation, i.e., O (R, tz), we only need to consider the generation of rotation R; as the corresponding translation & can be directly derived by aligning those overlapping atoms after applying rotation R,,
Furthermore, as illustrated in Figure 4, we use the MAR en- coder + encode X Known and then use the MAR decoder V to obtain the corresponding representations Z mua of masked repeating units, i.e.,
SO(3) Diffusion for Rotation Generation. According to the above analysis, we further simplify this problem to generating R2 for each repeating unit, i.c. modeling p R. G, C, where R = [R.] E NN x3x3, In this work, we develop an SO(3) diffusion model to generate R, i.e.
Z Zu ( (X known
(7)
where Zünk E NN is the decoded representations of masked repeating units, the MAR encoder & and MAR decoder V are the standard Transformer architecture with the bidirectional attention mechanism.
R (0) = ((O(t), E"), with O = (R()) (()).
Diffussoo Loss. The goal of the masked autoregressive modeling is to generate repeating unit conformations based on the probability distribution of masked repeating unit con- formations C conditioned on the corresponding decoded
Here, & denotes a denoising network, whose architecture is the same the model used in (Yim al., 2023). E R. is the output of the MAR encoder (i.e., the condi- tion concerning and C*). R(0
[R("] E N.333
5

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
obtained through forward diffusion processes on SO(3)N". T(*) = [ E RN x3 is the translations calculated by aligning the overlapping atoms after applying the rotation transformations ((()) the repeating units.
Finally, we can obtain the complete polymer conformation C R.Nx3 by employing the corresponding translation transformation & to C .ie..
C.. Cha +tz
The denoising network yp takes the timestamp t, the trans- formations at time t (i.e.. O(+) (R(") T())), and the con- dition information Ed as input, predicting rotation transfor- mations for the repeating units, denoted R( [
Ö = =1, -O... \\ (c%,
final sinffnall }
(14)
where C E Nx3 is the complete polymer conformation, Čo. R No +2)x3 is the transformed repeating unit con-
TR x3x33 Accordingly, we learn it through minimizing
formation obtained by employing the corresponding transla- tion transformation E,, and is the set difference operation.
the following loss function:
Cphase-2
(0)
RR,,,
(10)
4. Proposed Benchmark
Nu
where R2 is the ground-trume -rutt rotation of the i-th unit.
In this work, we have devoted considerable time and re- sources to developing PolyBench, the first benchmark for polymer conformation generation. Specifically, PolyBench includes high-quality polymer conformation dataset de- rived from molecular dynamics simulations (Afzal et al., 2020) and offers standardized evaluation protocols for vari- ous methods, thus setting foundation for progress in this important yet largely unexplored research area.
3.4. Assembling for Polymer Conformation Generation
After generating the repeating unit conformations {Čr N. in the first phase and the corresponding rotation transfor- mations { (R. Nv in the second phase, the last step is to assemble these repeating unit conformations into the com- plete polymer conformation.
Jiml
)=
4.1. Dataset
As illustrated in Section 3.1, the orientation transformation is relative to the standard coordinate system, meaning that the generated rotation transformations { [R 1 are also relative to the standard coordinate system. Therefore, we first transform each generated repeating unit conformation CT back to the standard coordinate system, i.e.
Since the scarcity of polymer conformation datasets is a major factor causing this important research area to remain largely unexplored, we have invested significant effort to construct a high-quality dataset of over 50,000 polymers with conformations (about 2,000 atoms per conformation) through molecular dynamics simulations (Afzal al., 2020). In particular, the initial polymer structures of molecular dynamics simulations are generated using RDKit (Landrum et al., 2013) and AmberTools (Salomon-Fereee et al., 2013), followed by energy minimization and equilibration in the NVT ensemble with a 1 fs time step for a total duration of 5 ns (5,000,000 steps). Besides, each simulation trajectory is obtained using the General AMBER Force Field with the GROMACS package (Van Der Spoel et al., 2005). In addition, the number of repeating units within the polymer conformation ranges from approximately 20 to 100 for most polymers, with a small portion extending beyond 100. More details about this dataset can be found in Appendix A.
Cue.si (09)-1 Cr = (Cr E (R)- (11)
where O = - t{) is the orientation transformation cal- culated based on those key atoms of the corresponding frame extracted from C.¹, and the corresponding calculation pro-
cess has been illustrated in Figure 3.
Then we employ the generated rotation transformation R. to the corresponding C.. i.e.,
CH std R.
(12)
Furthermore, the corresponding translation transformations of ल. can be obtained through aligning the 3D coordi- nates of those overlapping atoms, i.e.
4.2. Baseline Methods
As mentioned Section and Section 2.2, polymers signif- icantly differ from proteins, thus rendering various protein- specific conformation generation methods unsuitable. In this context, we adapt various molecular conformation gen- eration methods, including GeoDiff (Xu et al., 2022), Tor- sionalDiff (Jing et al., 2022), MCF (Wang et al., 2024b), and ET-Flow (Hassan et al., 2024), to the polymer domain as our bascline methods. Specifically, these baseline meth- ods are implemented using their default settings, treating
0.
if Ti=ll 1, 1
(13)
rot 1.3
if
1.
where i, E 3 represents the corresponding translation au.rot transformation of C.t.ot G,3 E R2 represents the 3D coordinate of a in Cu and ay.e E IR3 represents the 3D coordinate of atom-l in Oy.
6

---

Meanwhile, we compare the efficiency of various methods on the PolyBench benchmark, as illustrated in Figure In particular, the average time required to generate polymer conformations across various methods is computed and com- pared. Our PolyConf achieves the fastest generation time of 0.40 minutes, surpassing TorsionalDifi (0.45 minutes), MCF (1.12 minutes), and GeoDiff, which is significantly slower at PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Table I. The performance comparison of various methods the PolyBench benchmark
Structure
Energy
Method
S-MAT-R +
S-MAT-P
E-MAT-R
E-MAT-P +
Mean
Median
Mean
Median
Mean
Median
Mean
Median
GeoDiff (Xu al., 2022)
93.119
89.767
95.259
91.869
21.249
18.106
64.871
58.711
TorsionalDiff (Jing et al., 2022)
53.210
38.710
70.679
60.744
2.605
1.034
8,402
6.851
MCF (Wang al., 2024b)
248.432
242.866
258.891
253.239
10"h
ET-Flow (Hassan et al., 2024)
94.057
90.475
96.896
92.877
6.733
5.186
53,528
30.125
PolyConf (ours)
35.021
24.279
46.861
37.996
0.933
0.359
6.191
4.122
Remark. We think the widely used Coverage metric (Xu et al., 2022), relying on a fixed RMSD threshold ó for struc- tural comparison in the small molecule domain, is unsuitable for polymer conformation generation as polymers typically exhibit a much larger conformational space with significant diversity arising from their chain length, flexibility, and re- peating units (Chen et al., 2021). Thus, we exclude it from our evaluation metries but still report the corresponding performance under this metric in Appendix B for reference.
GeoDiff
3.54
TorsionalDiff
MCF
1.12
ET-Flow
0.40
PolyConf
4.4. Main Results
0.0
6.5
2.0 25 3.0
35
Average Generation Time (minute)
Table 1 summarizes the performance of various methods on the PolyBench benchmark, demonstrating that our Poly- Conf consistently outperforms baseline methods across both structure (S (S-MAT-R, S-MAT-P) and energy (E-MAT-R, E- MAT-P) metrics with a significant margin. In particular, compared TorsionalDiff (i.e., the best baseline), our Poly- Conf achieves substantial improvements with at least 25% across all evaluation metrics, while eliminating the need for pre-determined polymer structure, highlighting its effectiveness and practicability for generating polymer con- formations that are both structurally accurate and energet- ically realistic. Besides, the suboptimal performance of baseline methods also underscores their limitations in cap- turing the structural complexity of polymers. The above results further validate and demonstrate the critical need for designing tailored polymer conformation generation meth- ods, such as our PolyConf, to accommodate the unique conformational intricacies of polymer systems.
Figure The efficiency comparison (average time) of various methods on the PolyBench benchmark, where compare the average time of generating polymer conformations.
polymers large molecules containing more atoms. Please note that TorsionalDiff requires initial polymer struc- ture as input, which cannot be directly generated like small molecules using RDKit (Landrum et al., 2013), we have to employ the initial polymer structure of the corresponding simulation trajectory as its input, thus unintentionally giving TorsionalDiff biased advantage over other methods.
4.3. Evaluation Metrics
To guarantee the comprehensive and fair comparison, we evaluate various methods based on both structure and energy perspectives. Here, S, and S, denote the sets of generated and reference conformers, respectively. The structure met- rics are defined as follows:
1 | Eoes. min RMSD(C, ČES,
S-MAT-R
(15)
S-MAT-P-
Σ Eees,
min RMSD(C, Ō), CES,
[Sg]
where the generated conformer Č and reference conformer C' have already been aligned before computing their RMSD.
3.54 minutes. Combined with Table 1, these results demon- strate that our PolyConf is capable of both effective and efficient polymer conformation generation.
Meanwhile, the energy metries are defined similarly by replacing the structural difference RMSD(C, C) in Eq. (15) with potential energy difference |E(C)- - E(C)).
In addition, we further present some visualization examples of polymer conformations generated by our PolyConf and
7

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Reference
TorsionalDiff
PolyConf
Figure Several visualizaaion examples of our PolyConf and TorsionalDiff' (i.c., the best baseline).
Table 2. The scalability evaluation of various methods, where the number of repeating units per polymer is doubled.
Structure
Energy
Method
S-MAT-R +
S-MAT-P
E-MAT-R
E-MAT-P +
Mean
Median
Mean
Median
Mean
Median
Mean
Median
GeoDiff (Xu al., 2022)
184.668
175.607
186.861
177.645
52.614
47.872
112.883
105.197
TorsionalDiff (Jing et al., 2022)
119.289
94.075
146.816
126.932
5.219
2,216
11.692
9,227
MCF (Wang et al., 2024b)
227.691
252.796
280.805
260.882
10
ET-Flow (Hassan et al., 2024)
186.132
176.370
188.725
178.977
15.331
12.465
65.116
41,642
PolyConf (ours)
65.040
41.992
84.626
64.445
1.259
0.609
5.785
4.434
the best baseline in Figure 6 to provide qualitative insights. demonstrates that our PolyConf produces polymer confor- mations that more closely align with references, confirming its capability generate high-quality polymer conforma- tions. In contrast, despite leveraging biased prior knowledge of the initial polymer structure, TorfionalDiff (i.e., the best baseline) still fails to capture the unfolded and relaxed poly- mer conformations effectively.
determined by the number of repeating units incorporated during polymerization. Given this inherent variability, it's also essential to evaluate the scalability of various methods, particularly their ability to generate polymer conformations with larger scales (i.e., more atoms repeating units).
Considering various models in Table 1 are trained on poly- mer conformations comprising approximately 2,000 atoms, we further apply these trained models to generate confor- mations with roughly 4,000 atoms by simply doubling the number of repeating units in the inference phase. Here, we use the same pipeline of molecular dynamics simulations generate enlarged polymer conformations on the test set as references. The corresponding evaluations are performed us- ing both structural metrics (S-MAT-R, S-MAT-P) and energy metrics (E-MAT-R, E-MAT-P), as summarized in Table 2. Owing to the advantages of masked autoregressive mod- eling, our PolyConf demonstrates excellent performance,
4.5. Scalability Evaluation
As introduced in Section 1, polymers are macromolecules formed by the covalent bonding of numerous identical or similar monomers. Due to the nature of polymerization, a single polymer chain can vary length depending on spe- cific reaction conditions, resulting chain length distribu- tion rather than uniform chain length. Consequently, the same polymer can exhibit conformations at different scales,
8

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
significantly outperforming baseline methods across all eval- uation metrics. In particular, compared to TorsionalDiff (i.e., the best baseline), our PolyConf improves energy metrics by over 50%. These results validate and support the superior scalability and generalization capabilities of our PolyConf, thus setting it apart as an effective method for varying-scale polymer conformation generation.
Impact Statement
This paper presents work that aims to advance the field of Machine Learning and AI for Science, especially for polymer conformation generation. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
References
5. Conclusion
Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ronneberger, O., Willmore. L.,, Ballard, A. J., Bambrick, J., et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, 630 (8016):4935500, 2024.
In this work, we successfully unlock critical yet largely un- explored task in the context of machine learning polymer conformation generation, which may further trigger a series of downstream research directions. Specifically, we propose PolyConf, the first tailored polymer conformation genera- tion method that leverages hierarchical generative models to tackle this task, and develop PolyBench, the first bench- mark for polymer conformation generation, to overcome the scarcity of polymer conformation datasets and boost subse- quent studies. Extensive and comprehensive experiments on the PolyBench benchmark consistently demonstrate that our PolyConf significantly outperforms existing conforma- tion generation methods in both quality and efficiency while maintaining superior scalability and generalization capabil- ities, thus highlighting its exceptional ability in polymer conformation generation.
Afzal, M. A. F., Browning, A. R., Goldberg, A., Halls, M. D., Gavartin, J. L., Morisato, T., Hughes, T. F., Giesen, D. J., and Goose, J. E. High-throughpe molecular dynamies simulations and validation of thermophysical properties of polymers for various applications. ACS Applied Poly- mer Muterials, 3(2):620 6300 2020.
Audus, D. J. and de Pablo, J. Polymer informatics: op- portunities and challenges. ACS macro letters, 6(10); 1078-1082, 2017.
Baillif, B., Cole, J., McCabe, P., and Bender, A. Deep generative models for 3d molecular structure. Current Opinion in Structural Biology, 80: 2023.
In the future, we will continue to explore this important research area and further develop our method and bench- mark, which may inspire broader research efforts and drive progress in this research area. Moving forward, we aim to extend our method to accommodate more intricate polymer architectures, such as those with 2D topological structures and those constructed by more than one kind of monomer. Meanwhile, we will also consider integrating other advanced deep generative models (e.g., flow-based generative models) to refine polymer conformation generation.
Bilodeau, C., Jin, W., Jaakkola, T., Barzilay, R., and Jensen, K. F. Generative models for molecular discovery: Recent advances and challenges. Wiley Interdisciplinary Reviews: Computational Molecular Science, 12(5) 108, 2022.
Bose, J., Akhound-Sadegh, T., Huguet, G., FATRAS, K., Dector-Brooks, J., Liu, C.-H., Nica, A. C., Korablyov, M., Bronstein, M. M., and Tong, A. Se (3)-stochastic flow matching for protein backbone generation. In The Twelfth International Conference on Learning Representations, 2024.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (92270110), the Fundamental Research Funds for the Central Universities, the Research Funds of Renmin University of China, and the Public Computing Cloud, Renmin University of China. We also acknowledge the support provided by the fund for building world-class universities (disciplines) of Renmin University of China and by the funds from Beijing Key Laboratory of Research on Large Models and Intelligent Governnnce, Engineering Research Center of Next-Generation Intelligent Search and Recommendation, Ministry of Education, and from Intelli- gent Social Governance Interdisciplinary Platform, Major Innovation & Planning Interdisciplinary Platform for the "Double-First Class" Initiative, Renmin University of China
Bryant, P., Pozzati, G., and Elofsson, A. Improved pre- diction of protein-protein interactions using alphafold2. Nature communicatinns, 13(1):1265, 2022.
Cao, H., Tan, C., Gao. Z., Xu, Y., Chen, G., Heng, P.-A., and Li, S. Z. A survey on generative diffusion models. IEEE Transactions on Knowledge and Data Engineering, 2024.
Chen, L., Pilania, G., Batra, R., Huan, T. D., Kim, C., Kuenneth, C., and Ramprasad, R. Polymer informatics: Current status and critical next steps. Materials Science and Engineering: R: Reports, 144:100595, 2021.

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Del Alamo, D., Sala, D., Mchaourab, H. S., and Meiler, J. Sampling alternative conformational states of transporters and receptors with alphafold2. Elife. 11:775751, 2022.
Janson, G., Valdes-Garcia, G., Heo, L.,, and Feig, M. Di- rect generation of protein conformational ensembles via machine learning. Nature Communications, 14(1):774, 2023.
Feng, R., Zhu, Q. Tran, H.., Chen, B., Toland, A., Ram- prasad, R., and Zhang, C. May the force be with you: Unified ferceccentric pre-training for 3d molecular con- formations. In Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., and Levine, S. (eds.), Advances in Neural Information Processing Systems, volume 36, pp- 72750-72760. Curran Associates, Inc., 2023.
Jing. B., Corso, G., Chang, J., Barzilay, R., and Jaakkola, T. Torsional diffusion for molecular conformer generation. Advances in Neural Information Processing Systems, 35: 24240-24255 2022.
Jing, B., Erives, E.,, Pao- Pao-Huang, P., Corso, G., Berger, B., and Jaakkola, T. S. Eigenfold: Generative protein struc- ture prediction with diffusion models. In ICLR 2023- Machine Learning for Drug Discovery workshop, 2023.
Ganea, O., Pattanaik, L., Coley, C., Barzilay, R., Jensen, K., Green, W., and Jaakkola, T. Geomol: Torsional geo- metric generation of molecular 3d conformer ensembles. Advances in Neural Information Processing Systems, 34: 13757-13769, 2021.
Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Zidek, A., Potapenko, A., et al. Highly accurate protein structure prediction with alphafold. nature, 596(7873):583-588 2021.
Grünewald, F., Alessandri, R., Kroon, P. C., Monticelli, L., Souza, P. C., and Marrink, S. J. Polyply; a python suite for facilitating simulations of macromolecules and nanomaterials, Nature communications, 13(1):68, 2022.
Kremer, K. and Grest, G. S. Molecular dynamics (md) simulations for polymers. Journal of Physics: Condensed Matter, ASS): 1990.
Han, J., Cen, J.. Wu, L., Li, Z., Kong, X., Jiao, R., Yu, Z., Xu, T., Wu, F., Wang, Z., et al. A survey of geometric graph neural networks: Data structures, models and appli- cations. Frontiers of Computer Science, 19(11):1113355 2025.
Kuenneth, C. and Ramprasad, R. polybert: a chemical language model enable fully machine-driven ultrafast polymer informatics. Nature Communications, 14(1): 4099, 2023.
Hassan, M., Shenoy, N., Lee, J., Stark, H., Thaler, S., and Beaini, D. Et-flow: Equivariant flow-matching for molec- ular conformer generation, 2024.
Landrum, G. et al. Rdkit: A software suite for cheminformat- ics, computational chemistry, and predictive modeling. Greg Landrum, 8(31.10):528) 10):5281, 2013.
Hawkins, P. C. Conformation generation: the state of the art. Journal of chemical information and modeling, 57 (8):1747-1756, 2017.
Lee, J. S. and Kim, P. M. Flowpacker: Protein side-chain packing with torsional flow matching, bioRxiv, pp. 2024- 07, 2024.
Hekkelman, M. L., de Vries, I., Joosten, R. P., and Perrakis, A. Alphafill: enriching alphafold models with ligands and cofactors. Nature Methods, 20(2):205-213, 2023.
Leon, S. J., Björck, A., and Gander, W. orthogonalization: 100 years and more. Numerical Linear Algebra with Applications, 20(3):492-532, 2013.
Ho, J., Jain, A., and Abbeel, P. Denoising diffusion proba- bilistic models. Advances in neural information process- ing systems, 33:6840 10666666551,,,, 2020.
Li, T., Tian, Y., Li, H., Deng, M., and He, K. Autoregres- sive image generation without vector quantization. arXiv preprint arXiv:2406. 11838, 2024.
Hoseini, P., Zhao, I.., and Shehu, A. Generative deep learn- ing for macromolecular structure and dynamics. Current opinion in structural biology, 67:170- 177707777770 2021.
Li, Z., Cen, J., Huang, W., Wang, T., and Song, L. Size- generalizable RNA structure evaluation by exploring hi- erarchical geometries. In The Thirteenth International Conference on Learning Representations, 2025a.
Huang, P.S.,, Boyken, S. E., and Baker, D. The coming of age of de novo protein design. Nature, 537(7620):
220-327,20 2016.
Li, Z., Cen, J., Su, B., Xu, T., Rong. Y., Zhao, D., and Huang, language-geomeery
W. Large language- geometry model: When LLM meets equivariance. In Forty-secowe International Conference on Machine Learning, 2025b.
Huguet, G., Vuckovic, J., Fatras, K., Thibodeau-Laufed E., Lemos, P., Islam, R., Liu, C.-H., Rector-Brooks, J., Shhound-Sadeghh T., Bronstein, M., et al. Sequence- augmented se (3)-flow matching for conditional protein backbone generation. Advances in neural information processing systems, 2024.
Liu, J., Lin, H., and Li, X. Gmxpolymer: a generated polymerization algorithm based on gromacs. Journal of Molecular Modeling, 30(9)3300, 2024.
10

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Lu, J., Zhong, B., Zhang, Z.,, and Tang. J. Str2str: A score- based framework for zero-shot protein conformation sam- pling. In The Twelfth International Conference Learn- ing Representations, 2024.
Visani, G. M., Galvin, W., Pun, M., and Nourmohammad, A. H-packer: Holographic rotationally equivariant con- volutional neural network for protein side-chain packing. In Machine Learning in Computational Biology, pp. 230- 249. PMLR, 2024.
Martin, T. B. and Audus, J. J. Emerging trends in machine learning: a polymer perspective. ACS Polymers Au, 3(): 239-258, 2023.
Wang. F., Xu, H., Chen, X., Lu, S., Deng, Y., and Huang, W. Mperformer: An se (3) transformer- based molecular per- ceptron. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pp. 2512-2522, 2023.
Misiura, M., Shroff, R., Thyer, R., and Kolomeisky, A. B. Dipacker: Deep learning for prediction of amino acid side chain conformations in proteins. Proteins: Structure, Function, and Bioinformatics, 90(6):1278-1290, 2022.
Wang, F., Guo, W., Cheng, M., Yuan, S., Xu, H., and Gao, Z. Mmpolymer: A multimodal multitask pretraining frame- work for polymer property prediction. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp. 2336-2346, 2024a.
Nakano, T. and Okamoto, Y. Synthetic helical polymers: conformation and function. Chemical Reviews, (12): 4013-4038, 2001.
Pracht, P., Bohle, F., and Grimme, S. Automated explo- ration of the low-energy chemical space with fast quan- tum chemical methods. Physical Chemistry Chemical Physics, 22(14):7169-7199 2020.
Wang. F., Cheng, M., and Xu, H. WGFormer: An SE(3)- transformer driven by wasserstein gradient flows for molecular ground-state conformation prediction. In Forty- second International Conference Machine Learning, 2025.
Riniker, S. and Landrum, G. A. Better informed distance geometry: using what we know to improve conforma- tion generation. Journal of chemical information and modeling, 55(12):2562-2574 2015.
Wang, Y., Wang, J.. Cao, Z., and Barati Farimani, A. Molec- ular contrastive learning of representations via graph neu- ral networks. Nature Machine Intelligence, 4(3):279-287, 2022.
Roiter, Y. and Minko, S. Afm single molecule experi- ments at the solid- liquid interface: in situ conformation of adsorbed flexible polyelectrolyte chains. Journal of the American Chemical Society, 127(45):15688-155 2005.
Wang. Y., Elhag, A. A., Jaitly, N., Susskind, J. M., and Bautista, M. A. Swallowing the bitter pill: Simplified scalable conformer generation. In Forty-first Interna- tional Conference on Machine Learning, 2024b.
Wang. Y., Wang, L., Shen, Y., Wang, Y., Yuan, H., Wu, Y., and Gu, Q. Protein conformation generation via force- guided se (3) diffusion models. In Forty-first Interna- tional Conference on Machine Learning, 2024c.
Salomon-Ferrer, R., Case, D. A., and Walker, R. C. An overview of the amber biomolecular simulation package. Wiley Interdisciplinary Reviews: Computational Molecu- lar Science, 3(2):198-2)) 210, 2013.
Watson, J. L.,, Juergens, D.,, Bennett, N. R., Trippe, B. L., Yim, J., Eisenach, H. E.,, Ahern, W., Borst, A. J., Ragotte, R. J., Milles, L. F., et al. Broadly applicable and ac- curate protein design by integrating structure prediction networks and diffusion generative models. BioRxiv, pp. 2022-12, 2022.
Shi, C., Luo, S., Xu, M., and Tang, J. Learning gradient fields for molecular conformation generation. In Interna- tional conference on machine learning. pp. 9558-9568 PMLR, 2021.
Stein, R. A. and Mchaourab, H. S. Speach_af af: Sampling pro- tein ensembles and conformational heterogeneity with al- phafold2. PLOS Computational Biology, 18(8)e 1010443, 2022.
Wayment-Steele, H. K., Ojoawo, A., Otten, R., Apitz, J. M., Pitsawong, W., Hömberger, M., Ovehinnikov, S., Colwell, L.. and Kern, D. Predicting multiple conformations via sequence clustering and alphafold2. Nature, 625(7996): 832-839, 2024.
Tang, X., Dai, H., Knight, E., Wu, F., Li, Li, T., and Gerstein, M. A survey of generative ai for de novo drug design: new frontiers in molecule and protein generation. Briefings in Bioinformatics, 25 2024.
Xu, C., Wang. Y., and Barati Farimani, A. Transpolymer: a transformer- language model for polymer property predictions. upj Computational Materials, 9(1):64, 2023.
Van Der Spoel, D., Lindahl, E., Hess, B., Groenhof, G., Mark, A. E., and Berendsen, H. J. Gromaes: fast, flexible, and free. Journal of computational chemistry, 26(16):
Xu, M., Luo, S., Bengio, Y., Peng, J., and Tang, J. Learning neural generative dynamics for molecular conformation generation, arXiv preprint arXiv:2 102. 10240, 2021.
1701-1718, 2005.

---

PolyConf:
Unlocking Polymer Conformation Generation through Hierarchical Generative Models
Xu, M., Yu, L., Song, Y., Shi, C., Ermon, S., and Tang. J. Geodiff: A geometric diffusion model for molecular conformation generation. In International Conference Learning Representations, 2022.
Yim, J., Trippe, B. L., De Bortoli, V., Mathieu, E., Doucet, A., Barzilay, R., and Jaakkola, TT. Se (3) diffusion model with application to protein backbone generation. In In- ternational Conference on Machine Learning, pp. 40001- 40039. PMLR, 2023.
Yim, J., Campbell, A., Mathieu, E., Foong, A. Y., Gastegger, M., Jimenez-Luna, J., Lewis, S., Satorras, V. G., Veeling, B. S., Noe, F., et al. Improved motiffscaffolding with se (3) flow matching. In /CLR 2024 Workshop on Generative and Experimental Perspectives for Biomolecular Design,
2024.
Yue, A., Wang, 7., and Xu, H. Reqîoow Rectified quater- nion flow for efficient and high-quality protein backbone generation. arXiv preprint arXiv:2502. 14637, 2025.
Zhang, Y., Zhang, Z., Zhong. B., Misra, S., and Tang, J. Diffpack: A torsional diffusion model for autoregressive protein side-chain packing. Advances in Neural Informa- fion Processing Systems, 36, 2024.
Zhou, G., Gao, Z., Ding, Q. Zheng, H., Xu, H., Wei, Z., Zhang, L., and Ke. G. Uni-mol: A universal 3d molecu- lar representation learning framework. In The Eleventh International Conference on Learning Representations, 2023.
12

---

PolyConf:
Unlocking Polymer Conformation Generation through Hierarchical Generative Models
A. Dataset Details
In this work, considering the scarcity of polymer conformation datasets is a major factor causing this important research area to remain largely unexplored, we have dedicated significant time and resources to developing a high-quality dataset comprising over 50,000 polymers with their conformations (about 2,000 atoms per conformation) obtained through molecular dynamics simulations (Afzal et al., 2020). Here, the specific pipeline of molecular dynamics simulations is described in Appendix A. while Appendix A.2 provides detailed statistics of the obtained polymer conformation dataset.
A.1. Construction Pipeline
While previous studies have introduced DFT-based conformation datasets for polymers (Feng et al., 2023), these datasets are limited to systems with no more than six repeating units, which is far from the realistic scenario where polymer systems can consist of thousands of atoms. Besides, considering the prohibitively high computational cost of DFT calculations for polymer systems of this size (about 2,000 atoms in our work), we employ force-field-aar simulations for polymer conformation generation. Although force fields may have some limitations in accurately predicting properties or energetics, they are well-suited for efficiently exploring the conformational space of large polymer systems, thereby ensuring the generated conformations are realistic representations of polymer structures without compromising the focus of our task.
In partieular, polymer systems are constructed and prepared for molecular dynamies (MD) simulations through combining various molecular modeling tools and custom Python scripts. Monomer structures are generated by RDKit (Landrum et al., 2013) based on the corresponding SMILES strings and then processed to define chain termini and repeat units. The polymer consists of repeating PET unit, capped by head (HPT) and tail (TPT) units. RDKit is utilized to analyze atom connectivity and identify key atoms for polymerization. Hydrogen atoms at the connection points are omitted, and chain termini are explicitly parameterized. Atomic charges and topology files for the corresponding monomer units are generated using the Antechamber and prepgen tools (Salomon-Ferrer et al., 2013), employing the General AMBER Force Field (GAFF). TLeap is used to create Polymer chains with degree of polymerization (Na) are constructed by repeating the PET unit N₂, 2 times and capping the chain with HPT and TPT units at the termini. Chain lengths are chosen to achieve approximately 2,000 atoms per system. AMBER topology and coordinate files are then converted to GROMACSS-Cmppiibl formats using ACPYPE. The resulting files are then organized for subsequent MD simulations.
topology and coordinate files for both individual monomers and polymer chains.
The optimization and MD simulations are conducted using GROMACS (Van Der Spoel et al., 2005) as the usage of GROMACS on polymer simulations has long been reported (Liu et al., 2024; Grünewald et al., 2022). Specifically, the steepest descent method is applied to minimize the system energy, and then 5,000,000 steps (5ns) of MD calculations are performed at 298 K and I atm using the NVT ensemble for equilibrium calculations.
A.2. Dataset Statisties
We collect ID polymer SMIILE strings from various publicly available sources, and further divide their corresponding 3D conformations obtained through the molecular dynamics simulations into training, validation, and test sets. Specifically, the training set comprises about 46k polymers with their corresponding conformations, the validation set comprises about 5k polymers with their corresponding conformations, and the test set comprises about 2k polymers with their corresponding conformations. Meanwhile, as illustrated in Figure 3, the polymer conformation can be decomposed into a series of repeating unit conformation, so we visualize the distribution of the number of repeating units per polymer conformation in Figure to provide insights into the structural complexity and variability of the polymer conformations. As shown in this figure, the number of repeating units ranges from approximately 20 to 100 for most polymers, with small portion extending beyond 100. The distribution across the training, validation, and test sets demonstrates the ability of our dataset to capture wide variety of polymer structures, ensuring diverse and representative conformations for robust evaluation.
B. Additional Results
In the molecular conformation generation task (Xu et al., 2022), Coverage (COV) and Matching (MAT) metrics are widely used to evaluate the diversity and quality of generated conformations. Through fixed RMSD threshold, the Coverage metric can measure the fraction of reference conformations captured by the generated conformations (recall perspective) or the fraction of generated conformations captured by reference conformations (precision perspective). However, its applicability to polymer conformation generation is limited due to the inherent flexibility, polydispersity, and amorphous
13

---

PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models
0.02
0.02
0.05
0.02
Density
Density
Density
9.01
0.01
0.01
0.01
0.01
0.61
0.00
0.00
50
0.9
100
0.00
Number Repeating Units
Number Repeating Units
Number Repeating Units
(a) Training Set
(b) Validation Set
(c) Test Set
Figure 7. The distribution of the number of repeating units per polymer conformation.
Table 3. The structural quality of generated polymer conformations in terms of Coverage (%) and Matching (A). We compute Coverage with a threshold of 25 Å to better distinguish top methods.
Recall
Precision
Method
S S-COV-R
S-MAT-R
S-COV-P t
S-MAT-P 1
Mean
Median
Mean
Median
Mean
Median
Mean
Median
GcoDiff (Xu al., 2022)
0.108
0,000
93.119
89.767
0,008
0.000
95.259
91.869
TorsionalDiff (Jing et al., 2022)
0.172
0.000
53.210
38.710
0.100
0.000
70.679
60.744
MCF (Wang et al., 2024b)
0.000
0.000
248.432
242.866
0.000
0.000
258.891
253,239
ET-Flow (Hassan et al., 2024)
0.089
0.000
94.057
90.475
0.064
0.000
96.896
92.877
PolyConf (ours)
0.515
1.000
35.021
24.279
0.336
0.100
46.861
37.996
nature of polymer systems. Therefore, exclude the Coverage metric from evaluation metrics in Section. 4.3, but still report the corresponding performance of various methods under this metric for reference here.
As shown in Table 3, our PolyConf still significantly outperforms baseline methods in both structural Coverage (S-COV and Matching (S-MAT) metrics. In particular, our PolyConf achieves the highest S-COV-R (Recall) of 0.515 (mean) and 1.000 (median), demonstrating superior diversity and structural coverage over the reference set. Additionally, achieves the lowest S-MAT-R of 35.021 Á(mean) and 24.279 Amedian)) indicating a closer match to the reference conformations compared baseline methods, which show much higher deviations. In terms of precision-based metrics (S-COV-P and S-MAT-P), our PolyConf also maintains the strong superiority with 0.336 S S-COV-P (mean) and 0.100 (median), while achieving the best S-MAT-P of 46.861 Á(mean) and 37.996 Ámmedian). These results consistently indicate that our PolyConf generates polymer conformation with both broader coverage and more accurate conformational matching, despite the inherent difficulties posed by the flexibility and variability of polymer systems.
14


Reviews:
[{"review_id": "KDYQcy2SLb", "reviewer": "Reviewer_9jKE", "summary": "This paper introduces ​PolyConf, a novel hierarchical generative framework for polymer conformation generation. Addressing the unique challenges of polymers—such as high flexibility, large chemical space, and lack of prior datasets—PolyConf decomposes the task into two phases: Repeating Unit Conformation Generation and ​Orientation Transformation Generation\n\nThe authors also present ​PolyBench, the first benchmark dataset for polymer conformation generation, containing over 50,000 polymer conformations derived from molecular dynamics simulations.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your comments. Below, we categorize and resolve your concerns.\n\n**W1&Q1: ​Why not test on proteins?**\n\nOur work focuses on polymers, aiming to explore polymer conformation generation (all-atom conformation). \nPolymers present unique challenges compared to proteins, such as greater structural flexibility (see lines 80-98 for a detailed explanation). In this context, our PolyConf is specifically designed to address and adapt to the distinct structural characteristics of polymers, making it difficult to apply it directly to proteins.\n\nIn addition, while testing on proteins is out-of-the-scope of this work, we believe that PolyConf holds significant potential for application to other macromolecules composed of building blocks, such as proteins (amino acids) and RNA (nucleotides). Due to our limited experience with proteins and the time constraints, it is difficult for us to include them at this stage. We would, however, welcome the opportunity to collaborate with researchers in related fields to further explore and expand the potential applications of PolyConf.\n\n**W2&Q2: Details of PolyBench**\n\nAs described in Appendix A.1, our molecular dynamics simulations are based on polymer SMILES strings. Since most publicly available polymer SMILES strings represent linear polymers, the current PolyBench dataset is also limited to linear polymers. Even though, to the best of our knowledge, PolyBench is the first benchmark for polymer conformation generation.\n\nIn the future, we will continuously maintain and expand PolyBench to include a broader range of polymer data, especially branched and cross-linked polymers. \n\n\n**W3&W4: Reproducibility**\n\nThe code, data, and various scripts for our PolyConf and molecular dynamics simulations are available in this anonymous link (https://anonymous.4open.science/r/PolyConf). We are confident that it has provided enough details to reproduce our work. Due to the repository size limitation, we can only provide a small subset of the complete dataset, but the complete dataset will be provided after acceptance. \n\nIn particular, the training hyperparameters are provided in the corresponding training scripts, all experiments are implemented on eight A100 80G GPUs, and the force-field settings are provided in the `./MD/utils` folder of the provided anonymous repository. We will also explicitly state these details in the revised paper.\n\n\n**W3&W5&W6&Q3: Validation of MD simulations and Quality of PolyBench**\n\nWe have invested significant effort to ensure the reliability of our molecular dynamics simulations, thereby guaranteeing the high-quality of the PolyBench dataset:\n* Under the guidance of highly experienced experts, we design our molecular dynamics simulations using standard pipelines widely adopted in previous works [1]. All scripts and settings related to the molecular dynamics simulations are available in the `./MD` folder of the provided anonymous repository, ensuring that our molecular dynamics simulations are fully transparent and reproducible.\n* We have analyzed the energy changes of various polymers during our molecular dynamics simulations, and the results show that most simulations achieve convergence within 1 ns, while we run the simulations for 5 ns to ensure the reliability and robustness of the PolyBench dataset.\n* We have calculated the density values of typical polymers through our molecular dynamics simulations and compared them with those experimental values provided in [1]. As shown in the following Table, the density values obtained via our molecular dynamics simulations are very close to those experimental values, further supporting the reliability of our molecular dynamics simulations and PolyBench dataset.\n| Polymer                     | Experiment density (g/cc) | MD density (g/cc) |  \n|---|---|---|  \n| [\\*]CC(C)[\\*]              | 0.850                    | 0.837             |  \n| [\\*]CC(C)O[\\*]             | 1.125                    | 1.019             |  \n| [\\*]CC(Cl)(Cl)[\\*]         | 1.630                    | 1.570             |  \n| [\\*]CCCCCCO[\\*]            | 0.932                    | 0.944             |  \n| [\\*]CCCCCCCCO[\\*]          | 0.906                    | 0.927             |\n* In addition, we provide some raw outputs of our molecular dynamics simulations (i.e., `NPT_Cases.tar.xz` and `NVT_Cases.tar.xz`)  in the `./MD` folder of the provided anonymous repository for validation. \n\nWe hope the above responses can resolve your concerns. Since polymer conformation generation remains a relatively unexplored research area, we have invested significant time and effort into developing and refining our PolyConf and PolyBench to boost subsequent studies. Therefore, we kindly request your understanding of the challenges and complexities involved in pioneering work in this field.\n\n[1] High-throughput molecular dynamics simulations and validation of thermophysical properties of polymers for various applications. ACS Applied Polymer Materials, 2020.", "claims_and_evidence": "**Strength**\n\n- Superior Performance Over Baselines: The structural (S-MAT-R/P) and energy (E-MAT-R/P) metrics demonstrate PolyConf’s significant improvements over methods like TorsionalDiff (e.g., ​35.02 vs. 53.21 in S-MAT-R mean).\nResults align with the hierarchical design’s intent to address polymer-specific challenges (flexibility, lack of rigid backbones).\n​\n- Efficiency: Timing comparisons (Figure 5) validate PolyConf’s speed (0.4 minutes vs. 3.54 minutes for GeoDiff).\n​\n- Scalability: Tests on doubled polymer sizes (4,000 atoms) show consistent performance (e.g., ​65.04 S-MAT-R mean vs. 119.29 for TorsionalDiff), supporting scalability claims.\n​\n- Dataset:  PolyBench’s size (50k+ conformations) and diversity (20–100+ repeating units) address the polymer data scarcity problem.\n​\n\n**Weakness**\n\n- It would be beneficial for the paper to also test the proposed model on protein data, as proteins are a specific type of polymer. Given the abundance of available data and the well-established baselines, it is not essential for the proposed method to outperform existing folding models that leverage evolutionary information. However, it would be intriguing to assess where the method’s capabilities stand in comparison.\n\n- It is unclear whether the dataset includes branched or cross-linked systems, or if it is limited to linear polymers only.\n​\n- PolyBench conformations derive from a single force field (AMBER). Force-field inaccuracies or parameterization biases may propagate into the dataset.\n​Reproducibility:\n\n- Missing Details: Training hyperparameters, computational resources, and force-field settings are not fully disclosed.\n​\n- While PolyBench is large, its quality hinges on force-field accuracy. The lack of experimental validation weakens claims about its representativeness.\n\n- The core claims (performance, efficiency, scalability) are supported by internal benchmarks, but external validation (experimental data, broader baselines) is needed for robustness. The dataset’s reliance on simulations and omission of complex polymer types limit its universality. While PolyConf advances polymer informatics, claims about physical reliability and generalization require further evidence.", "methods_and_evaluation_criteria": "The methods and evaluation criteria are ​well-designed for the stated problem", "theoretical_claims": "There are no theorems to verify.", "experimental_designs_or_analyses": "Yes, but I don't identify critical issues.", "relation_to_broader_scientific_literature": "-", "essential_references_not_discussed": "-", "other_strengths_and_weaknesses": "-", "other_comments_or_suggestions": "-", "questions_for_authors": "**Q1:** ​Why was the method not tested on proteins, given the structural similarities between polymers and proteins ?\n\n​**Q2:** Does the PolyBench dataset include branched/cross-linked polymers, or is it limited to linear chain polymers?\n\n**Q3:** ​How was the quality of the PolyBench dataset validated beyond force-field-generated conformations?", "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": "AdOXTd7M9Y", "reviewer": "Reviewer_HPGV", "summary": "Deep learning for polymer design is a severely underexplored area, and this work attempts to address two major challenges: the lack of methodology and the scarcity of high-quality data. In PolyConf, the authors generate polymers autoregressively, generating conformers for individual building blocks and linking them using a diffusion model. This study introduces the first benchmark with a (supposedly) high-quality polymer conformation dataset derived from MD simulations, aiming to advance research in this area. The work is novel and if reproducible would be highly impactful, however, I have quite a few questions and concerns, which I outline below.\n\nThe work aims to address the lack of polymer conformer data by publishing a new dataset; however, I have been unable to review the dataset as it was not made available with the paper (even anonymously), making it difficult to validate its quality. Another limitation of the current evaluation is that all methods compared in the paper are designed for small molecules rather than polymers; however, as far as I understand, there are no deep generative models available for polymers that also handle 3D information, so this may be acceptable. While the contributions are promising and the figures are well-designed and informative, I have currently rated this paper marginally below the publication threshold. I would be willing to increase my score if the authors provide anonymized code for review and address the points raised below.\n\nFeedback and Questions\n\n- **Code availability:** No code is provided, which is a significant drawback. Releasing code (even anonymously for review) would greatly improve reproducibility and impact, especially considering that one of the contributions if the new dataset, but I cannot evaluate it if it is not presented for review. Lack of reproducibility is one of the main reasons I have ranked this work below the acceptance threshold, despite its significant novelty. Without code, it is difficult to determine if the work is fully reproducible, and I am not sure there are enough details in the text to accurately reproduce the results.\n    \n- **Baseline comparisons:** Are there any non-deep-learning baselines for comparison? For instance, a simpler approach that links building block conformers could serve as a useful reference, more-so than comparing to deep generative models designed for small molecules. What would the RMSD be for a method that simply linked the conformers generated by RDKit for the same SMILES in the dataset? This could serve as an interesting dummy model for comparison.\n    \n- **Metric clarity:** \n    - The units for the S-MAT-R and S-MAT-P metrics (both structural and energy-related) should be explicitly stated, I have no idea currently what the units are for the tables in the paper which makes it hard to assess how bad/good the values are.\n    - It is also unclear if the metrics reported in the paper (in the various tables) are for the training, validation, or test set, nor how the metrics differed for the different sets. This should be clarified and unambigious. Have the authors demonstrated, furthermore, that their model is not overfitting?\n\n- **Dataset details:**\n    \n    - The authors mention sourcing data from three different sources. How much data came from each?\n        \n    - PolyInfo is known to prohibit web scraping, so I am confused as to how was data obtained from this source?\n        \n    - A dimensionality reduction method (e.g., UMAP) could help visualize the overlap in building block SMILES from each source, and would make for an interesting analysis to tell us how different the building blocks from each source are.\n        \n- **Validation of MD simulations:** How were the MD simulations used for dataset construction validated? It would be useful to understand how reliable they are for training deep learning models.\n    \n- **Masked autoencoder experiments:** Was there any analysis on how different levels of masking (e.g., percent of masked bits) affect performance? Understanding the limits of masking would be valuable, especially since I assume that increased masking in the latent space would improve inference efficiency. If this is not the case, some clarification would be helpful.\n    \n- **RMSD calculations:**\n    \n    - Were generated and reference polymer structures aligned before computing RMSD?\n        \n    - If so, the reported RMSD values appear high. However, without units provided, it is difficult to assess this properly.\n        \n- **Failure mode analysis:** Can the authors highlight any failure cases? For instance, can the model currently only handle linear polymers, or does it also support other topologies? Are there specific polymers or building blocks where the model struggles?\n        \n- **Objective clarification:** Is the goal to generate low-energy conformers or to match reference structures? If the latter, have the authors verified that the reference conformers are indeed low-energy states?\n        \n- **Future directions:** Could the learned embedding from the masked autoencoder-decoder framework be useful for polymer property prediction? This might be an interesting avenue for future work.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your comments and suggestions. Below are our responses to your questions.\n\n**Q1&Q5: Code availability and Validation of MD**\n\nThe code, data, and various scripts for our PolyConf and MD simulations are available in this anonymous link (https://anonymous.4open.science/r/PolyConf). It has provided enough details to reproduce our work. Due to the repository size limitation, we can only provide a small subset of the complete dataset, but the complete dataset will be provided after acceptance.\n\nAs mentioned in our response to Reviewer 9jKE (https://openreview.net/forum?id=BsTLUx38qV&noteId=KDYQcy2SLb), we have invested significant effort to validate our MD simulations, including seeking guidance from experienced experts, examining the energy convergence, calculating the density values of typical polymers, and comparing them with experiment density values.\n\n\n**Q2: Baseline comparisons**\n\nAs shown in the following Table, we have constructed such a dummy model following your suggestion, and the results demonstrate that our PolyConf can still achieve SOTA performance.\n| Model         | S-MAT-R   | E-MAT-R   |  \n|----|---|---|  \n| Dummy Model   | 68.403    | 18.735    |  \n| PolyConf      | **35.021**    | **0.933**     |\n\n\n**Q3: Metric clarity**\n\nThe units for the S-MAT-R and S-MAT-P are Å, and the metrics reported are all for the test set. We will explicitly state them in the revised paper. \n\nIn addition, we train PolyConf on the training set and select the best checkpoint based on the validation set. It is a widely used practice to avoid overfitting.\n\n\n**Q4: Dataset details**\n\nThe details can be found in Appendix A, with the majority derived from PI1M [1]. Please note that we only need to collect polymer SMILES strings, and all these strings are publicly available from previous works [1]-[5].\n\n\n**Q6: Masked autoencoder experiments**\n\nIn our implementation, the mask rate is randomly sampled from a pre-defined truncated normal distribution, ensuring balanced randomness, avoiding extreme values, and enhancing both robustness and generalization. Details can be found in `./polyconf/models/polyconf_phase1.py` within the provided anonymous repository.\n\n\n**Q7: RMSD**\n\nThe generated and reference polymer structures have been aligned before computing RMSD. While PolyConf has achieved SOTA performance, there is still significant room for improvement in terms of the RMSD. In the future, we are willing to collaborate with researchers to further explore this challenging task.\n\n\n**Q8: Failure mode analysis**\n\nOur method currently only handles linear polymers, as modeling other topologies (e.g., cross-linked polymers) involves significantly greater complexities beyond data modeling.\n\n\n**Q9: Objective clarification**\n\nWe have analyzed the energy changes of polymers during our MD simulations, and the results show that most simulations achieve convergence within 1 ns, while we run the simulations for 5 ns to ensure the reference conformers are low-energy states. Here, we have provided some raw outputs of our MD simulations in the `./MD` folder within the provided anonymous repository for validation.\n\nTherefore, the objectives you mentioned are fundamentally the same: we aim to train the model to match reference structures, thereby enabling it to generate low-energy conformers.\n\n\n**Q10: Future directions**\n\nAs shown in the following Table, directly based on the learned embedding, PolyConf can achieve even better performance than the SOTA polymer property prediction method MMPolymer [5], further demonstrating its great potential. \n| Method      | Egc        | Egb        | Eea        | Ei         | Xc         | EPS        | Nc         | Eat        |  \n|---|---|---|---|---|---|---|---|---|  \n| MMPolymer   | **0.924 ± 0.006** | 0.934 ± 0.008 | 0.925 ± 0.025 | **0.836 ± 0.053** | **0.488 ± 0.072** | 0.779 ± 0.052 | 0.864 ± 0.036 | **0.961 ± 0.018** |  \n| PolyConf    | 0.916 ± 0.006 | **0.937 ± 0.010** | **0.926 ± 0.018** | 0.822 ± 0.052 | 0.422 ± 0.096 | **0.811 ± 0.049** | **0.868 ± 0.041** | **0.961 ± 0.030** |\n\n\nWe hope the above responses help you re-evaluate our work. Since polymer conformation generation remains a relatively unexplored research area, we have invested significant time and effort into developing and refining our PolyConf and PolyBench. We kindly request your understanding of the challenges and complexities involved in pioneering work. We would greatly appreciate it if you could raise your score.\n\n[1] PI1M: a benchmark database for polymer informatics. Journal of Chemical Information and Modeling, 2020.\n\n[2] Graph rationalization with environment-based augmentations. KDD2022.\n\n[3] Polymer informatics at scale with multitask graph neural networks. Chemistry of Materials, 2023.\n\n[4] PolyNC: a natural and chemical language model for the prediction of unified polymer properties. Chemical Science, 2024.\n\n[5] MMPolymer: A multimodal multitask pretraining framework for polymer property prediction. CIKM2024.", "claims_and_evidence": "I do not believe the claims are justified by the current presented results. See my detailed review above.", "methods_and_evaluation_criteria": "Partially. See my detailed review above.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "The analyses in this work are partially sound but require significant clarification. See my detailed review above.", "relation_to_broader_scientific_literature": "This is a novel work that addresses a key gap in polymer design via deep generative models.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Significance is high and the method novel and creative, but the clarity is weak and the experiments/analysis lack rigour. This can be potentially improved.", "other_comments_or_suggestions": "See my detailed review above.", "questions_for_authors": "See my detailed review above.", "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": "SED2xUgUxj", "reviewer": "Reviewer_QQYG", "summary": "In this work, we proposed PolyConf, a pioneering tailored polymer conformation generation method that leverages hierarchical generative models to unlock new possibilities for this task. The authors decompose the polymer conformation into a series of local conformations generating these local conformations through an autoregressive model. The Polymers contain multiple repeats, PolyConf first generates one unit and then generates a series of transformations to locate each repeat. Experimental results demonstrate that PolyConf can generate high-quality, physically reliable polymer conformations, facilitating advancements in polymer modeling and simulation.\n\n## update after rebuttal\nThe authors successfully addressed my concerns. I suggested the authors should clearly pointed out this model is designed specific to the material science. The overall contribution from the machine learning aspect is limited but there are couple of technical improvements for this new task. Therefore, I decide to maintain my overall ranking as 'weak accept'.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your comments. Below, we try to resolve your concerns one by one.\n\n**W1: Clarification of model construction and contribution**\n\nAs shown in Figure 2, we design PolyConf as a hierarchical generative framework with a two-phase generating process. \n\nAs described in Section 3.2, in the first phase, we leverage the masked autoregressive model (MAR) to generate the conformation of each repeating unit within the given polymer in random order. **Please note that the conformation of each repeating unit within the given polymer is not generated independently. They share the same global 2D polymer graph information and can be influenced by each other through the MAR module.** The code is provided in `./polyconf/models/polyconf_phase1.py` within the anonymous repository (https://anonymous.4open.science/r/PolyConf).\n\nAs described in Section 3.3, in the second phase, we employ an SO(3) diffusion model to generate the corresponding orientation transformations of repeating units within the given polymer, thereby assembling those repeating unit conformations generated by the previous phase into the complete polymer conformation. **Please note that the corresponding orientation transformations of repeating units within the given polymer are obtained together through the diffusion processes on $SO(3)^{Nu}$.** The code is provided in `./polyconf/models/polyconf_phase2.py` within the anonymous repository (https://anonymous.4open.science/r/PolyConf).\n\nHere, as mentioned in lines 79-100, PolyConf is specifically designed based on the unique characteristics of polymers, not a simple application of the existing methods. Besides, as shown in our response to Reviewer HPGV (https://openreview.net/forum?id=BsTLUx38qV&noteId=AdOXTd7M9Y), PolyConf can achieve even better performance than the SOTA polymer property prediction method, further demonstrating its potential. In addition, we think PolyConf also has significant potential for other macromolecules composed of building blocks, such as proteins (amino acids) and RNA (nucleotides), thereby driving progress in these related fields.\n\n\n**W2&Q2: Clarification of modeling independence**\n\nAs mentioned in our last response, both conformation and orientation transformation of each repeating unit within the given polymer **are not generated independently**. They share the same global information provided by the 2D polymer graph and can be influenced by each other. \n\n\n**W3&Q3: Stable 3D structures and their applications**\n\nWe analyzed the energy changes of polymers during our MD simulations, and the results show that most simulations achieve convergence within 1 ns, proving that polymer conformations obtained through our MD simulations are low-energy states (i.e., stable). \nAs shown in the following Table, we further calculate the RMSD between conformation obtained in 2ns/3ns/4ns and the final conformation obtained in 5ns within the same MD tracjory, demonstrating that the polymer has a stable 3D structure.\n| RMSD  | 2ns       | 3ns       | 4ns       |  \n|---|---|---|---|  \n| 5ns   | 2.15 ± 1.22 | 2.01 ± 1.09 | 1.84 ± 0.97 |\n\nThese stable 3D structures are critical for various applications. For example, the work in [1] has revealed the relation between the polymer conformation and the elastic modulus of the crystalline region. The works in [2][3] have tried to apply them to calculate glass transition temperatures through experiments and MD simulations. The work in [4] has incorporated polymer 3D structural information into property prediction. In addition, as shown in our response to Reviewer HPGV (https://openreview.net/forum?id=BsTLUx38qV&noteId=AdOXTd7M9Y), PolyConf can achieve even better performance than the SOTA polymer property prediction method, further demonstrating the importance and potential of polymer conformation. \n\n\n**Q1: Clarification of Eq.3**\n\nAs mentioned in our first response, we leverage the masked autoregressive model to generate the conformation of each repeating unit within the given polymer in random order during the first phase. Here, the 2D structure information is known, and we aim to generate the 3D structures of the unpredicted repeating units based on the predicted repeating unit iteratively, thereby obtaining the 3D structures of all repeating units within the given polymer.\n\nWe hope the above responses can resolve your concerns. Since it's a relatively unexplored research area, we kindly request your understanding of the challenges and complexities involved in our work. \n\n[1] Relation between the polymer conformation and the elastic modulus of the crystalline region of polymer. Journal of Polymer Science Part C, 1970.\n\n[2] Prediction of polymer properties. cRc Press, 2002.\n\n[3] High-throughput molecular dynamics simulations and validation of thermophysical properties of polymers for various applications. ACS Applied Polymer Materials, 2020.\n\n[4] MMPolymer: A multimodal multitask pretraining framework for polymer property prediction. CIKM2024.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes. I check all the results in the main article and appendix", "relation_to_broader_scientific_literature": "This part I am not quite sure. I am asking the authors to provide such evidence. I am not quite aware any biological and chemical applications that the prediction of 3D structure of a polymer is necessary.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "First, I would like to thank the authors for contributing a new dataset of polymer 3D structures to the field. In terms of the generated 3D structures, PolyConf clearly has significant advantages over other methods. However, in terms of model construction, there isn’t much innovation in this work. The authors split the generation of a repeat polymer into two parts: the first step is to generate a small molecule’s 3D structure, which has been extensively studied, and the authors should compare different methods for predicting small molecule 3D structures. The second step involves generating the repeat units, which, as far as I know, is new. Therefore, from a purely modeling perspective, the contribution of this work is limited.\n\nAdditionally, during the generation of repeats, each repeat is created independently, at least according to equations (9) and (10). Why would this modeling approach, which seems to lack global information, lead to a reduction in overall RMSD? My guess is that if a repeat is stretched into a straight line, the RMSD won't be too high. Therefore, the second step of the model generation does not necessarily need to learn any special patterns. The authors could provide different 3D structures to address this concern.", "other_comments_or_suggestions": "Related to the previous question, does the polymer have a stable 3D structure? Is there any biochemistry or application related to it? Could you provide some specific citations for its applications?", "questions_for_authors": "1.What is the meaning of ‘To generate a random subset of unknown repeating unit conformations based on known/predicted repeating unit conformations iteratively (expressed in Eq. (3)) ‘  what is the exact meaning of ‘unknown’. Does it mean we do not know the 3D structure or we do not know the 2D structure?\n\t\t\t\t\n2.Is each R-i independent? If they are all independent, could there be collisions between different repeats when the number of repeats is large?\n\n3. What is the RMSD between different conformations in the MD simulation? One possibility is that these polymers themselves do not have a stable 3D structure, and there is a lot of structural variation in the MD simulations. For example, if the RMSD among the MD simulated structures is ~100, then an RMSD of 30 obtained from one computational method would be meaningless.", "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:

Meta-review: This paper proposes a dataset and method for polymer conformation generation. Overall, the reviewers are mildly enthusiastic about the work. The work is interesting in the sense that polymer is not a well studied problem in ML. On the other hand, the technical challenges are similar to those of other materials and molecules. The addition of a new benchmark is valuable given this is a new area. Thus I tend to recommend for accept, but would not be upset if it is not accepted.
Decision: Accept (poster)