Efficient Prediction of Large Protein Complexes via Subunit-Guided Hierarchical Refinement
Authors: Chixiang Lu
Yunhua Zhong
Shikang Liang
Xiaojuan Qi
Haibo Jiang
Venue: ICLR 2026 Poster (2026)
Keywords: Protein complex structure prediction
AlphaFold3
complex modularity
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We introduce HierAFold, a hierarchical pipeline that exploits the modularity of large complexes via PAE-guided (Predicted Aligned Error) subunit decomposition, targeted interface-aware refinement, and confidence-weighted assembly.

Abstract: State-of-the-art protein structure predictors have revolutionized structural biology, yet quadratic memory growth with token length makes end-to-end inference impractical for large complexes beyond a few thousand tokens. We introduce HierAFold, a hierarchical pipeline that exploits the modularity of large complexes via PAE-guided (Predicted Aligned Error) subunit decomposition, targeted interface-aware refinement, and confidence-weighted assembly. PAE maps localize rigid intra-chain segments and sparse inter-chain interfaces, enabling joint refinement of likely interacting subunits to capture multi-body cooperativity without increasing memory. HierAFold matches AlphaFold3 accuracy, raises success rates from 49.9\% (CombFold) to 73.1\% on recent PDB set. While for large complexes, it cuts peak memory by $\sim$25\,GB on a 4,000-token target ($\sim$40\%), successfully models complexes with over $5{,}000$ tokens that are out-of-memory for AlphaFold3, and raises success rates by two-fold compared with CombFold.

Published as a conference paper at ICLR 2026
EFFICIENT PREDICTION OF LARGE PROTEIN COM- PLEXES VIA SUBUNIT-GUIDED HIERARCHICAL RE- FINEMENT
Chixiang Lu', Yunhua Zhong', Shikang Liang", Xiaojuan Qi Haibo Jiang*
DDppartment of Chemistry, The University of Hong Kong
"chooo of Biomedical Sciences, The University of Hong Kong
DDepartment of Electrical and Electronic Engineering, The University of Hong Kong u35905406 connect. hku. hk; xjqi @eee. hku hk; hbj iang@hku. hk
ABSTRACT
State-of-the-art protein structure predictors have revolutionized structural biology, yet quadratic memory growth with token length makes end-to-end inference im- practical for large complexes beyond a few thousand tokens. We introduce HIER- AFOLD, hierarchical pipeline that exploits the modularity of large complexes via PAE-guided (Predicted Aligned Error) subunit decomposition, targeted interface- aware refinement, and confidence-weiglee intra-chain segments and sparse inter-chain interfaces, enabling joint refinement of likely interacting subunits to capture multi-body cooperativity without increasing memory. AFLD matches AlphaFold3 accuracy, raises success rates from 49.9% (CombFold) to 73.1% on recent PDB set. While for large complexes, it cuts peak memory by ~25 GB on a 4,000 token target (r~40%), successfully models complexes with over 5,000 tokens that are Out-Of-Memory for AlphaFold3, and raises success rates by two-fold compared with CombFold. The code available at https: /ttp://///ttttbbt// com www.cccciiccccccccoccc Luchi x aiagg//////nn HrAFolld
assembly. PAE maps localize rigid
INTRODUCTION
The advent of deep learning in protein folding prediction has transformed structural biology (Du et al., 2021; Senior et al., 2020; Jumper et al., 2021). Models such as AlphaFold2 (Jumper et al., 2021; Evans et al., 2021) and RoseTTAFold (Baek et al., 2021) and their successors AlphaFold3 (Abramson et al., 2024) and RoseTTAFole All-Atom (Krishna et al., 2024) now achieve unprece- dented accuracy in modeling biomolecular interactions, including proteins, nucleic acids, and small molecules. Despite these advances, scaling to very large complexes, typically on the order of thou- sands of tokens, remains major bottleneck. Memory usage in transformer-like modules (notably triangle updates and attention) grows quadratically with token length, making end-to-end inference prohibitive beyond ~4-5k tokens on modern GPUs (for example, a 4,500-token complex can require 80 GB of GPU memory) (Abramson et al., 2024).
Current approaches attempt mitigate these limits by by partitioning large tensors (Ahdritz al., 2024), or by predicting pair/triple complexes and relying on Monte Carlo Tree Search (MCTS) (Chaslot, 2010; Bryant al., 2022; Chim & Elofsson, 2024) or combinatorial assembly (Shor & Schneidman- Schneidman-Duhovvn Duhovny, 2024) for global assembly. Consequently, these methods remain insuffi- ciently scalable or miss crucial multi-body cooperativity, limiting the accuracy of the complexes with higher-order coupling (Peng et al., 2023).
Large complexes (e.g., chaperonins, synthetic multi-enzyme circuits) are inherently modular, a prop- erty we exploit for efficient prediction: (i) each peptide chain comprises one more distinct folded subunits and intrinsically disordered regions; and (ii) inter-chain interaction interfaces critical for as- sembly typically restricted to specific subunits and regions, and sparse relative to total residues (Reichmann et al., 2005). This suggests that end-to-end prediction unnecessary: one can first predict interacting interfaces between chains and then assemble chain-level structures accordingly.

---

Published as a conference paper at ICLR 2026
To make this strategy practical, need an automatic way to detect subunits and interfaces. Pre- dicted Aligned Error (PAE) quantifies the expected positional error residue i after aligning on residue and correlates strongly with rigid-body coherence within domains and the reliability of inter-chain interfaces (Jumper et al., 2021). Thus, we explore using PAE to drive automatic mod- ular decomposition and interface detection. We find that coarse predictions yield PAE matrices that naturally partition into low-variance diagonal blocks (coherent subunits) and localized low PAE off-diagonal patches (interaction interfaces) (Fig. 1).
Motivated by these insights, we in- troduce HIERAFOLD (Fig. 2), which exploits modularity to assemble pep- tide chains in a hierarchical, coarse- to-fine manner, drastically reducing memory for large protein complex prediction. (i) Coarse stage. HI- ERAFOLD generates efficient pair- wise predictions, producing PAE ma- trices and initial 3D structures for all chain pairs using a distilled, few-step diffusion model (Song et al., 2023). From the PAE matrices, segments each chain into structurally coherent subunits (dark diagonal blocks) and identifies candidate interface subunits (dark off-diagonal patches) across chains. (ii) Fine stage. For each chain, HIERAFOLD jointly refines its structure with candidate inter- face subunits from other chains, cap- turing multi-body body cooperativity and yielding higher fidelity models while keeping memory bounded. (iii) Assembly. Finally, HIERAFOLD merges the refined partial structures via a confidence-aweee aware alignment module that weights alignment by estimated confidence, priori- tizing well-preeictte residues. By using sparse subunits as cross-chain bridges and explicitly mod- eling higher-order cooperativity among multiple subunits without inflating memory, HIERAFOR overcomes key limitations of prior methods.
Vreect Whee tiee TMI
dlpeed
gray
violet
green
chain
Figure I: Example of dividing subunits along a chain and identifying the inter-chain interface based on the PAE ma- trix. Each color denotes peptide chain. The black lines in PAE are chain borders. The orange square marks a divided subunit in the gray chain. The red rectangle highlights the low-PAE region at an inter-chain interacting subunit, which is sparse relative to the total residues.
HIERAFOLD achieves accuracy par with AlphaFold3 for protein-prove and protein-ligand benchmarks, while cutting GPU memory use by about 40% on large token counts. Unlike baselines that fail with Out-Of-Memory errors, it successfully models complexes exceeding 5,000 tokens, delivering a two-fold improvement success rate compared to CombFold.
In summary, our contributions include:
HIERAFOLD: hierarchical, coarse-to-fe pipeline for large protein complexes that keeps memory bounded while scaling beyond conventional token limits.
PAE-guided modular decomposition: automatically segments chains into rigid subunits and pinpoints localized inter-chain interfaces, removing the need for expert curation.
Interface-aware refinement and assembly: jointly refines each chain with its most likely partner subunits to capture multi-body cooperativity, and aligns chains via subunit inter- faces using a confidence-aware module for greater robustness.
Strong empirical performance: HIERAFOLD matches reproduced AlphaFold3 base- line on the benchmark, successfully models complexes exceeding 5,000 tokens, and out- performs other methods by large margin.
2

---

Published as a conference paper at ICLR 2026
2
RELATED WORK
AlphaFold. Protein structure prediction has progressed from physics-based simulations to data- driven deep learning, with AlphaFold2 (Jumper et al., 2021) establishing a landmark by leveraging multiple sequence alignments (MSAs) and equivariant attention networks to achieve near experi- mental accuracy. AlphaFold3 (Abramson et al., 2024) extends this paradigm multi-chain protein complexes, nucleic acids, and small molecular ligands through unified diffusion- framework (Ho al., 2020).
Tokens in AlphaFold3. To manage memory, AlphaFold3 represents inputs primarily at the token level instead of the atom level. A single token corresponds to one amino acid residue, one nucleotide, or one atom of a ligand/non-standard residue (Abramson et al., 2024).
Large Complex Prediction. The Pairformer module in AlphaFold introduces quadratic memory growth in token number, making end-to-end inference impractical for large complexes. To mitigate memory limits, OpenFold (Ahdritz et al., 2024) splits large tensors and processes them piecewise to trade throughput for lower memory, but the pair representation and attention still dominate memory and scale poorly. Beyond such tensor-level tricks, MoLPC (Bryant et al., 2022) predicts pair/triple subunits and uses Monte Carlo Tree Search (MCTS) (Chaslot, 2010) for global assembly, which underperforms on heteromeric complexes due to reliance on accurate symmetry and stoichiome- try (Shor & Schneidman-Duhenn
2024; Chim & Elofsson, 2024). Similarly, CombFold (Shor & 2024) assembles large complexes via combinatorial and hierarchical assem- bly, but depends high-quality predefined subunits, often requiring expert curation and yielding incomplete or biased models. Because these pipelines emphasize pairwise interactions, they also miss crucial multi- body cooperativity, effects from multiple interacting chains. limiting accuracy on complexes with higher order coupling (Peng et al., 2023).
Satneidmaan-uhhowee
Meanwhile, docking-basse based approaches that rely on pairwise protein-proteie docking (Inbar et al., 2003; Esquivel-Rodit deep learning methods accuracy. Consequently, current approaches remain insufficiently scalable or accurate, overly specialized, insufficiently automated for modeling large complexes.
et al., 2012; Kuzu et al., 2014) are more memory-friendle but lag behind
Protein Subunit/Domain Segmentation. Protein domain segmentation has been studied, with two primary categories of methods: (i) Domain annotation databases, such CATH (Sillitoe et al., 2021) and ECOD (Schaeffer et al., 2017), which provide curated evolutionary classifications and domain boundaries based sequence and structure similarity. (ii) Computational prediction meth- ods, including sequence-basee based predictor (Zhu et al., 2023), structure-based predictor (Zhang et al., 2023; Yu et al., 2022), deep-learning approaches (Lau et al., 2023; Wells et al., 2024). (iii) Large- scale efforts, such TED, which annotate structural domains across the protein universe by integrating these advanced tools (Lau al., 2024). However, these approaches require additional inference-time computation. What's 's more, they are optimized for evolutionary domain definitions and do not iden- tify cross-chaad chain interface subunits.
PRELIMINARIES
Confidence matrices. AlphaFold family models output complementary confidence estimates to assess prediction reliability: (i) PLDDT (predicted Local Distance Difference Test) provides per- residue accuracy estimates (Mariani et al., 2013); (ii) p'TM (predicted TM-score) approximates the expected TM-score to the unknown native structure, measuring overall fold accuracy; (iii) ipTM (interface predicted TM-score) quantifies the relative placement chains or interacting components. In AlphaFold3, weighted combination of ipTM, pTM,, and clash penalties is used to rank multiple samples.
Predicted Aligned Error (PAE). The Predicted Aligned Error (PAE) matrix from AlphaFold esti- mates the positional error (in Angströms) between any two residues after aligning the predicted and true structures on one of them. Low PAE values indicate high confidence in the relative positions of residues, suggesting a structurally well-defined region, while high values imply uncertainty due to either protein flexibility or a poorly predicted region.
Importantly, PAE provides structural cues beyond per-residue scores since it encodes the model's belief about the relative flexibility and coherence of structural regions. Intuitively, when two
3

---

Published as a conference paper at ICLR 2026
Bequences
pairs
Difiuekommduule (24 ligenn)
Parrstes conformtios
Suburt sugmeriition and selection
Inputs modile
Chain
Through Corantory
paritloring
Paiformer
moare
Chain B
Dixtilld Bittutton
ODE based distilled structure prediction
Intercting
Sucunt Selection
module
legers)
Sutunt
C1
C3
Chain
PAE
1A
1A
20A
Coarse stage: pairwise prediction and modular decomposition
Dal
4A
35A
MA
Selected
toous chale
etin
Alignment
m Belected dhiin subentt
cheir
AlphaFokt3 Full-model
Conforce saigted
Pocua chain rouns:
Assembly: confidence alignment
Fine stage: inferface-awas refinement
Figure 2:
An overview of HIERAFOLD. Given the input sequences of peptide chains, the coarse stage generates pairwise conformation of chains with predicted PAE using a distilled diffusion mod- ule. Using the PAE matrices, it divides each chain into structurally coherent subunits (dark diagonal blocks) and detects potential interface subunits (dark off- off-diagonal patches) across chains. Struc- ture of the focus chain with the selected subunits from other chains refined using AlphaFold3 full model. Multiple partial predictions are aligned and assembled by estimating the transformation matrix with a manfidenne-weighheee method.
gions of protein move coherently a rigid unit, the model can predict their relative positions with high confidence, leading to low PAE. Conversely, residues belonging to different domains or flexible linkers exhibit higher relative uncertainty and therefore higher PAE, providing meaningful structural signal for segmentation. As illustrated in Fig. 1: (i) low-value diagonal blocks often align with intrinsic, independently folded subunits within chain, which represent functional domains rather than individual residues. Biologically, these subunits, instead of individual amino acids, rep- resent functional modules and act as units to facilitate interaction between peptide chains (Pawson, 1995). (ii) off-diagonal low-value blocks correspond confident inter-chain or inter-subunit con- tacts, highlighting potential interfaces critical for assembly. This observation suggests that PAE can be leveraged heuristically segment large complexes into subunits and identify interacting interfaces, enabling modular decomposition into tractable parts for scalable structure prediction.
HIERAFOLD
For large protein complex with peptide chains (C,, .,,...,CMM with total of N tokens, end-to- end prediction quickly becomes computationally infeasible as N grows. HIERAFOLD overcomes this by reformulating the prediction problem series of smaller, computationally tractable refine- ment tasks, guided by the protein complex's 's inherent modularity. Instead of processing the entire complex once, iteratively predicts the structure of only its most relevant interacting subunits, denoted as (C..). After all chains are refined in the corresponding localized context, the results are integrated into a complete structure through confidence-awee aware assembly step.
designated focus chain C. in the context
The full pipeline (Fig. 2) proceeds three stages: (i) Coarse stage: generate fast pairwise predic- tions and derive modular decomposition from PAE matrices; (ii) Fine stage: perform high resolution. interface-ane aware refinement of each focus chain C. together with its selected subumits (C.,) from other chains; and (iii) Assembly stage: merge partial structures using confidence- weighted algo- rithm. This hierarchical design captures both local structural accuracy and long longerange cooperative interactions, while keeping memory demands within practical limits.
4

---

Published as a conference paper at ICLR 2026
4.1 COARSE STAGE: PAIRWISE PREDICTION AND MODULAR DECOMPOSITION
The first stage aims to decompose a whole complex into several tractable parts based on the inherent modularity of the complex. This process consists of three steps: fast pairwise prediction, PAE- guided subunit segmentation, and interacting subunit selection.
Fast Pairwise Conformation Prediction To obtain the initial structural and PAE matrix for mod- ular decomposition, given the peptide chain sequences, the first step of HIERFOLD is to perform pairwise structure prediction on every pair of chains (C,, C2). However, running a full AlphaFold3- style inference with hundreds of diffusion steps for all (2) pairs would be prohibitively slow. To accelerate this, we employ a consistency-diise -dittillld structural predictor (Song al., 2023; Song & Dhariwal, 2023). The goal is to train a model fo that can generate coordinates Xo of the chain pair (C,,C)) from a random noise input Xy in a single step or few steps: X = fo (Xy, T).
We train this model using a consistency objective, which enforces that the outputs of the model at different points along the probability flow ODE's trajectory are self-consistent (Song al., 2020b; 2023). Let e be the parameters of target model (an exponential moving average of the model's parameters f)). The loss is defined on pairs of adjacent time steps (ln: la+1): Given noisy coordinates Xt,41 and an ODE-base backstep estimate (Song et al., 2020a) Xt,,;
Leon = EE
tn+1, c). fo (n,,,:t,,))) c)]]
(1)
where represents the conditioning feature extracted from the Pairformer. xt, is the one-step ODE
solution starting from X and is distance metric in coordinate space (c.g., a clamped L2
distance). To further reduce computational cost, the distilled model uses shallower Pairformer (12
vs. 24 blocks). This process yields a set of coarse coordinate predictions {X.x) } and corresponding
PAE matrices (Paz)
ig) } for all chain pairs, which serve the input for the subsequent stages.
PAE-Guided Subunit Segmentation for Biological Modularity With the predicted pairwise PAE matrix, the next step is segment each chain into the intrinsically independent folded subunits. For a chain C; of length T., its intra-chain PAE matrix Pa = P:yl: I,: I.] reveals its internal structural confidence. We observe that diagonal blocks of PAE matrices with low average PAE values corre- spond to compact domains or stable structural motif's (e.g., alpha-helices and beta-sheets), as shown in Fig. 1.
To achieve this automatic subunit segmentation, we employ recursive, top-down partitioning algo- rithm that iteratively identifies the most probable boundaries within protein segment. For any given segment defined by residue indices [ the method searches for the optimal split point & (where i < k < <) that maximizes the uncertainty between the two resulting sub-segments, S [i, k) and S2 J). This uncertainty is quantified by the mean inter-subunit PAE, P (k)), calculated as the average PAE over the off-diagonal blocks of P:
( E (k ii-
EL P (]-b)(k-))
Pinter (k:)
(2)
2
The algorithm proceeds as follows: A queue is initialized with the entire chain segment (0, L). In each step, a segment (i, ) is dequeued. We then identify the optimal split point 'e' that maximizes (k) The split is acceptable if Pimer exceeds predefined split threshold, Tsplit and both new sub-segments are larger than a minimum size Tanin- The new split segments are now queued. This process continues until no more splits can be made, yielding of subunits U,,1, U, for each chain C,-
Interacting Subunit Selection Finally, for each "focus chain" C., we identify neighborhood of relevant interacting subunits N (C.), from all other chains C, b of a, and ignoring other subunits. For subunit Ub.j other chain C2 it is selected if it meets two criteria based on the coarse pre- dictions: high confidence (low PAE) and spatial proximity. which indicates Ub may be at the interaction interfaces of C. and focus chain C.. Specifically for each subunit Ub,7 on other chain C. we compute: (i) Mean Interface PAE: P(Ca, Ub.5). the average PAE value between residues in C, and residues in Ub, from the pairwise matrix Pas- A low value indicates a high probability of interacting. A subunit Un,y is included in the neighborhood set (C,,) if P(C.. Ub,)) < Tp- (ii) Minimum Distance: dmin (Ca; Ubg), the minimum distance between any center atom in C. and any
5

---

Published as a conference paper at ICLR 2026
center atom in Ub, from the coarse predicted structure Xab- Ub. is included if dmin (Ca, Td- This step effectively identifies sparse cross-chail "bridges" for the refinement stage.
4.2 FINE STAGE: ANTERFACE-WARE REFINEMENT
With the pruned context defined for each focus chain, HIBRAFOLD performs high-resolution struc- ture prediction. For each focus chain C. E {C1...., CM J. we execute full AlphaFold3-style in- ference on the composite imput formed by C. and its selected interacting subunits (Ca)). Because the input for each run is limited to one full chain plus only the relevant interface subunits from other chains, the total token count remains well below the memory limits of standard GPUs. This step gen- crates set of M high-resolution, partially overlapping structural predictions, {X,, X2...., XM each capturing the detailed conformation of a focus chain within its interaction context. However, each partial prediction is in its own coordinate frame.
4.3 ASSEMBLY STAGE: CONFIDENCE AWARE GLOBAL ALIGNMENT
The final stage is assemble the M partial, well-predicted structures into single, coherent model of the entire complex. We perform this assembly iteratively. We initialize the global assembly with the highest confidence partial prediction, Xhea- Then, we iteratively align each remaining partial structure X. to the current global assembly. To ensure robustness, we weighted Kabsch algorithm (Kabsch, 1976) instead of a simple global superposition. Specifically, identify the set of atoms that common to both the global assembly and the partial structure found by minimizing the weighted root-mean-
confidence-
X.. The optimal rotation R and translation square deviation (RMSD) over the set of atoms common to both structures, where the contribution of each atom pair is weighted by the product of their pLDDT scores:
argmin R,t
(Rx, +t) X where w/ (x..DD((x.:))PLDDD.. (X (3)
&Coverlup
This method ensures that the alignment is driven by the most confidently predicted regions of the interface, making the assembly resilient to flexible or poorly predicted loops (low pLDDT). After alignment, the refined coordinates of the focus chain C. from X. are merged into the global assem- bly. For multiple samples, the top-ranked one is always aligned with the top-ranked one. The final structure is ranked using composite score, similar AlphaFold3.
IMPLEMENTATION DETAILS
Setup and Terminology Since the official AlphaFold3 training code is not publicly available, all experiments use Protenix (v0.5.0) (Team et al., 2025), an open-source PyTorch reproduction (Paszke et al., 2019), our baseline and core predictive module. "AlphaFold3" in experiments refers to predictions made with the pretrained Protenix model. We acknowledge that any performance differences between our results and the original AlphaFold3 paper may arise from implementation or model weight discrepancies.
5.1 CONSISTENCY DISTILLATION
To enable efficient pairwise conformation prediction within HIERAFOLD, we trained a consistency- distilled version of the Protenix structure module.
Architecture We reduced the computational cost of the structure predictor by halving the num- ber of token-level transformer blocks from 24 to 12. The atom-level transformer stack remained unchanged. All other architectural hyperparameters followed the Protenix v0.5.0 defaults.
Training The distilled diffuuson model was trained using the Adam optimizer (Kingma, 2014) with a learning rate of 1 x 10-5, a 2,000 steps linear warmup, 31 = 0.9, 3r = 0.95, and a weight decay of 1 1 8 The noise scheduler is the same the default in Protenix. Training performed on the preprocessed complex dataset provided with Protenix, with sequences cropped to maximum of 512 tokens fit within GPU memory.

---

Published as a conference paper at ICLR 2026
Table 1: Performance comparison protein-protein and protein-ligand benchmarks. DockQ Suc- cess Rate (%) is reported for protein-protein interfaces, and Ligand RMSD < 2A Success Rate (%) reported for PoseBuster v2 benchmark. "OOM" denotes Out-Or-Memory failure on an 80GB A100 GPU. HIERAFOLLD matches the performance of the full AlphaFold3 baseline while success- fully predicting large complexes where the baseline fails.
Recent PDB
PoseBuster v2
Large Complexes (>5k tokens) Oracle
Method
Oracle
Top-1
Oracle Top-1
Top-1
MoLPC
31.3
CombFold (w/ AFM)
49.9
48.8
20.9
19.9
AlphaFold-Multime (AFM)
71.5
67.1
OOM
OOM
CombFold+AF3
47.5
43.2
20.7
19.8
RoseTTTAFold All-Atom
55.4
41.8
AlphaFold3 (Baseline)
74.4
70.4
78.6
76.0
OOM
OOM
+ (Ours)
72.6
68.4
44.1
43.6
HIERAFOLD (Ours)
73.1
69.0
77.4
74.7
44.5
43.9
Sampling / Inference During the coarse pairwise prediction stage, we run the distilled model for only two iterative refinement steps. For each chain pair, we generate five stochastic samples and select the top-ranked one based on composite score of ip''M, pTT,, and clash penalties. This single, high-ranked coarse prediction is then used for subunit segmentation and selection.
5.2 SUBUNIT SEGMENTATION SELECTION POLICY
For subumit For PAE-guided subunit segmentation, the split threshold Taplit was set to 10.0, and the minimum subunit size Lmin was set to 20 residues.
Selection Policy The selection of subunits or tokens for the high-resolution refinement stage fol- lows a set of hierarchical rules:
Short Chains:
Polymer chains with fewer than 40 tokens are always retained and are not further segmented and selected.
Ligands: For small molecular ligands, all ligand atoms are always retained. All ligands are docked independently with each focus chain and selected subunits from other chains. The final pose is selected based on the highest average atom pLDDT, since we assume the underlying AlphaFold3 scoring sufficiently discriminative to rank the correct binding partner.
Low-Confidence Pairs: If the coarse prediction for chain pair (C,, Cj) yields maxi- mum ipTM score below 0.2, the interaction is considered unreliable, and the partner chain Cj is entirely excluded from the context of C2 because such pairs are unlikely represent a true physical interaction.
For polymer chains with 40 more tokens, we apply the confidence- and proximity-based selection described Section 3.3. subunit is selected if its mean interface PAE is less than TP = 5.0 its minimum distance to the focus chain calculated between the center atoms (Ca for amino
Subunit/Token Filtering:
is less than Tœ 20 A. Distances acids, Cp for nucleotides). subunit segmentation fails for a given chain, the selection logic reverts to operating at the individual token level.
EXPERIMENT
6.1 EXPERIMENTAL SETUP
Baseline Model Again, since the official AlphaFold3 code and weights are not publicly available for training, Protenix (v0.5.0) as core predictive module and primary baseline. All mentions

---

Published as a conference paper at ICLR 2026
HierAFold
CombFold
HierAFold
CombFold
Figure 4: Visualization of complex modeling results comparing HierAFold and CombFold. Left PDB ID is 7na5 and right PDB ID is 8gvi. The gray chains ground truth. Considering only pairwise interactions causes CombFold ignore multi-chain interactions, leading to an inaccurate final assembly.
of "Iiphaoold33 in our experiments refer to this reproduced version. We use the provided pretrained weights for all predictions.
Baselines for Comparison We benchmark HIERAFOLD against several methods: (i)AlphaFold3 (Protenix): The end-to-end Protenix model, representing the state-of-the-art upper bound in aceu- (AFM) (Evans et al., 2021): The v2.3 model, strong baseline for protein-only complexes. (ii)) CombFold: A representative
racy. (ii) AlphaFold-Multinn
shivide-anddconquee method that pre- dicts all pairwise interactions and assembles them. To ensure fair comparison, created variant, CombFold variant using our AlphaFold3 as the prediction engine instead
(iv) CombFold+AFF: of its default AlphaFold-Multimer (v) MoLPC: Another assembly-based based method, primarily de- signed for homomeric complexes. (vi) RoseTTAFold All-Atom: An end-to-end biomolecular com- plex structure predictor (Krishna al., 2024). (vii) MeriZo+HIERAA HIETDD HierAFold variant in which subunit segmentation was replaced by Merizo, a deep learning based method for domain seg- mentation on protein chain (Lau al., 2023), while keeping all other components unchanged. For all methods, the MSA (Edgar & Batzoglou, 2006), baseline details can be found in Appendix A.
Nomory Token Dount
Evaluation Metrics For protein-protede inter- faces, we report the DockQ success rate, defined as the percentage of predictions with DockQ score > 0.23, following AlphaFold3 paper (Basu & Wallner, 2016), (Mirabello & Wallner, 2024). For protein-ligant interfaces, we report the success rate of predictions achieving lig- and RMSD < 2.0 Á after alignment to the na- tive pocket, following established benchmarks. We report both the "Oracle" score (the best re- sult among all generated samples) and the "Top- I" score (the result of the single highest-ranked sample).
Feccoe Seving
1103
19/0
2001
2503
120
03:01
Figure Token number vs GPU memory cost. By default, Protenix inference uses BF16 mixed precision. The decrease when the token number 3000 occurs because SampleDiffusion and ConfidenceHead switch from FP32 to BF16 (set by Protenix). HIERAFOLI saves about 40% GPU memory for large token counts.
6.2 RECENT PDB
Dataset We used the recent PDB benchmark as defined in the Protenix and AlphaFold3 papers. This dataset contains oowhhomlogg protein com- plexes filtered from the Protein Data Bank (PDB) (Bank, 1971) released after the training set cutoff (2021-09-30), providing robust test of generalization for protein-protein interface prediction,
8

---

Published as a conference paper at ICLR 2026
sisting of complexes with up to 20 chains and 5,120 tokens. Following the Alphafold3 and Protenix, for each case, 25 samples were generated using five model seeds (each with five diffusion samples). We report results from model with 4 recycles and from AFM with 5 recycles.
Results As shown in Table I, HIERAFOLD achieves an Oracle success rate of 73.1% and a Top-1 rate of 69.0% the recent PDB benchmark. This performance is nearly identical to the end-to-end AlphaFold3 baseline (74.4% Oracle, 70.4% Top-1), demonstrating that our hierarchical approach almost does not sacrifice accuracy on standard-sized complexes. In contrast, both CombFold vari- ants show a significant drop in performance. CombFold+AI33, despite using the same powerful prediction engine, scores only 47.5% (Top-1) 1), highlighting the importance of our method's 's ability to incorporate multi-chain context during refinement, which purely pairwise methods lack.
The visualizations in Fig. further demonstrate that HIERAFOLD enables more accurate complex prediction. Furthermore, the marginal lower performance of Merizo AITERAFOLE demonstrates that more complex domain segmentation does not yield better downstream structure prediction and confirms that PAE-based segmentation is well aligned with HierAFold's refinement pipeline without additional costs. More results on subunit segmentation are detailed in Appendix A.9. We further evaluate the peak GPU memory usage compared with the baseline shown in Fig. 3. Compared
with the end-to-end baseline prediction, our method saves ~ 40% GPU memory when the number of tokens is large, as each inference step only processes a single focus chain and its selected interface subunits.
Performance Intrinsically Disordered Re- gions Intrinsically disordered protein regions (IDRs), sequences lacking stable tertiary struc- ture, are pivotal in cellular processes (Babu al., 201 1: Oldfield al., 2019). Interactions between IDRs and their partners are character- ized by partial and dynamic binding (Tompa & Fuxreiter, 2008) and are accurately captured by AFM (Omidi et al., 2024). To evaluate how IDRs affect HIERDFOLD, we analyzed the recent PDB dataset following established pro- cedures. Each residue was annotated with disorder probability using AlUPred (Erdös & Dosztányi, 2024), interface residues were iden- tified where any two heavy atoms are within 10 A of each other (Mirabello & Wallner, 2024) and for each complex we computed the mean disorder score the interface. Complexes were then grouped into three bins: low (0. 10.1-00 0.25), medium (0.25 0.5), and high disorder (> 0.5). For both the AlphaFold3 baseline and HIERAFOLD, we measured the mean DockQ for each bin:
Figure 5: Visualization of IDRs prediction. Left: The cyan chain is the IDRs predicted by HIER- AFOLD and the violet chain the ground truth (PDB ID: 7zwa). Right: The corresponding cropped PAE matrix. The orange square marks divided IDRs subunit (lower left and upper right). The red rectangle highlights the low-PAE region the IDRs interface.
Mean Interface IDR Score
AlphaFold3 (Baseline)
HIERA FOLD (Ours)
Mean DockQ
Mean DockQ
Low (0.1 -0.25)
0.55
0.52
Medium (0.25 0.5) High (> 0.5)
0.49
0.44
0.46
0.41
Table 2: Performance comparison on the recent PDB dataset, binned by the mean disorder score of interface residues.
The results (Table 2) reveal consistent trend: as interface disorder increases, DockQ scores decrease for both models. This is expected, because IDRs are flexible, underrepresented in training data, and often participate in transient or fuzzy interactions.
Importantly, HIERAFOLI exhibits almost the same degradation pattern as AlphaFold3, demon- strating that our hierarchical coarse-to- fine pipeline preserves AlphaFold3's 's robustness when han- dling disordered interfaces. In other words, the introduction of subunit segmentation, interface se- lection, and hierarchical assembly does not introduce additional weaknesses for IDRs, shown in

---

Published as a conference paper at ICLR 2026
Fig. 5. This robustness stems from how IDRs behave under our PAE-guided workflow: (i) Segmen- tation: IDRs appear as high-PAE or highly flexible regions and are naturally isolated into their own subunits (orange blocks in Fig. 5). (ii) Interaction Selection: When IDRs genuinely participate in binding, they produce localized low cross-chain PAE signals that ensure their inclusion during fine- stage refinement (red block in Fig. representing the interaction between KU and PAXX protein). (iii) Assembly: Because IDRs generally receive low confidence scores, they are automatically down- weighted during confidence- confidence-wiighted alignment, preventing unreliable geometry from distorting the global structure.
6.3 POSEBUSTER V2
Dataset We evaluated protein-ligand performance on the PoseBuster v2 benchmark (Buttenschoen al., 2024), standard dataset for evaluating small molecule docking accuracy containing up to 4,100 tokens and 4 chains.
Results On PoseBuster v2, HIERAFOLD achieves Top-1 success rate of 74.7%, again closely mir- roring the 77.4% achieved by the full AlphaFold3 baseline (Table 1). This confirms that our subunit selection and assembly process correctly preserves the fine fine-grained atomic interactions necessary for accurate ligand placement, and our special handling of small molecular ligands is effective.
6.4 FILTERED LARGE COMPLEX DATASET
Dataset To test the primary motivation for our work, we curated dataset of protein complexes filtered from PDB, which was released after 2021-09-30 and contains 5,000 10,000 tokens with up to 30 chains. The filtered large complex dataset consists 664 interfaces. These complexes are too large to be processed
80GB A100 GPU by the baseline (AlphaFold3, AlphaFold-Multinee
HierAFold
CombFold
Results The end-to-end baseline failed with Out- Of-Memory (OOM) error.. HIERAFOO FOLD achieved Top-1 DockQ success rate of 43.9 43.9% significantly outperforming Aom (19.8%). This re- sult, combined with the visualization in Fig. 6. demonstrates that by intelligently pruning the con- text for refinement, HIERAFOLD effectively breaks the memory barrier while retaining context needed to resolve complex multi-chain interfaces. The overall performance is lower than on the recent PDB dataset, which can be attributed to two fac- tors. First, the Large Complex Dataset has much higher proportion of protein-antibody interactions (40% 6%), for which AlphaFold3's perfor- mance known to be lower. Second, the maximum sequence crop size during AlphaFold3 training (768 tokens) is much smaller than most of the chain lengths in this dataset, creating a train-test gap. De- spite these challenges, HIERAFOLD still outperforms CombFold by large margin. Finetuning on a large complex dataset with larger crop size could potentially mitigate this performance gap.
Figure Visualization of our method com- pared with the CombFold result on the large complex dataset. The PDB ID 9bj4. The gray chains are ground truth.
CONCLUSION
We presented HIERAFOLD, a hierarchical framework for predicting large protein complexes that overcomes the memory bottlenecks of existing end-to-end models. By leveraging coarse predic- tions and PAE-guided modular decomposition, our method automatically identifies subunits and interfaces, and refines each chain the context of its key interacting partners. This design reduces memory requirements by up to 40% while preserving essential multi-body cooperativity. Experi- ments show that HIERAFOLD matches AlphaFold3 on standard benchmarks and, critically, extends tractable prediction to complexes exceeding 5,000 tokens, achieving substantial gains over prior divide-and-oonueee approuches. Limitations and future work of HIERAFOLD can be found in Ap- pendix A.
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew Ballard, Joshua Bambrick, al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, 630(8016):493-500 2024.
Gustaf Ahdritz, Nazim Bouatta, Christina Floristean, Sachin Kadyan, Qinghui Xia, William Gerecke, Timothy J O'Donnell, Daniel Berenberg, Ian Fisk, Niccolò Zanichelli, et al. Open- fold: Retraining alphafold2 yields new insights into its learning mechanisms and capacity for generalization. Nature methods, 21(8):1514-155 2024.
M Madan Babu, Robin der Lee, Natalia Sanchez de Groot, and Jörg Gsponer. Intrinsically disordered proteins: regulation and disease. Current opinion in structural biology, 21(3):432- 440, 2011.
Minkyung Back, Frank DiMaio, Ivan Anishchenko, Justas Dauparas, Sergey Ovchinnikov, Gyu Rie Lee, Jue Wang, Qian Cong, Lisa N Kinch, R Dustin Schaeffer, et al. Accurate prediction of protein structures and interactions using three-track neural network. Science, 373(6557):871- 876, 2021.
Protein Data Bank. Protein data bank. Nature New Biol, 233(223):10-1066 1971.
Sankar Basu and Bjöm Wallner. Dockq: quality measure for protein-protein docking models. PloS one. 1118)17066 2016.
Patrick Bryant, Gabriele Pozzati, Wensi Zhu, Aditi Shenoy, Petras Kundrotas, and Arne Elofsson. Predicting the structure of large protein complexes using alphafold and monte carlo tree search. Nature communications, 13(1):6025 2022.
Martin Buttenschoen, Garrett M Morris, and Charlotte M Deane. Posebusters: Ai-based docking methods fail to generate physically valid poses or generalise to novel sequences. Chemical Sci- ence, 15(9):3130-31333 2024.
Guillaume Maurice
Chaslot Chaslot. Monte-carlo tree search. 2010.
Ho Yeung Chim and Arne Elofsson. Molpc2: improved prediction of large protein complex struc- tures and stoichiometry using monte carlo tree search and alphafold2. Bioinformaties, 40(6): btae329, 2024.
Zongyang Du Hong Su, Wenkai Wang. Lisha Ye, Hong Wei, Zhenling Peng, Ivan Anishchenko, David Baker, and Jianyi Yang. The trrosetta server for fast and accurate protein structure predic- 2021.
tion. Nature protocols,
Robert C Edgar and Serafim Batzoglou. Multiple sequence alignment. Current opinion in structural biology, 16(3):368-37) 373,, 2006.
Gábor Erdós and Zsuzsanna Dosztányi. Aiupred: combining energy estimation with deep learning for the enhanced prediction of protein disorder. Nucleic Acids Research, 52/W1):116-W188, 2024.
Juan Esquivel-Rodríguee Yifeng David Yang, and Daisuke Kihara. Multi-lzerd: multiple protein docking for asymmetric complexes. Proteins: Structure, Fanction, and Bioinformatics, 80(7): 1818-1833, 2012.
Richard Evans, Michael O'Neill, Alexander Pritzel. Natasha Antropova, Andrew Senior, Tim Green, Augustin Zidek, Russ Bates, Sam Blackwell, Jason Yim, et al. Protein complex prediction with alphafold-multinel biorxiv, pp. 2021-10, 2021.
Lim Heo and Michael Feig. Multi-state modeling of g-protein coupled receptors at experimental accuracy. Proteins: Structure, Function, and Bioinformatics, 90(11):1873-1855 2022.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020.

---

Published as a conference paper at ICLR 2026
Yuval Inbar, Hadar Benyamini, Ruth Nussinov, and Haim J Wolfson. Protein structure prediction via combinatorial assembly of sub-structural units. Bioinformatics-Oye Oxford, 19(1):158- 168, 2003.
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnv,, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Židek, Anna Potapenko, et al. Highly accurate protein structure prediction with alphafold. nature, 596(7873):583-588) 2021.
Wolfgang Kabsch. A solution for the best rotation to relate two sets of vectors. Foundations of Crystallography, 32(5):922-9255 1976.
Diederik P Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
Rohith Krishna, Jue Wang, Woody Ahem, Pascal Sturmfels, Preetham Venkatesh, Indrek Kalvet, Gyu Rie Lee, Felix Horey-Burrows, Ivan Anishchenko, Ian R Humphreys, et al. Generalized biomolecular modeling and design with rosettafold all-atom. Science, 384(66993) 2024.
Guray Kuzu, Ozlem Keskin, Ruth Nussinov, and Attila Gursoy, Modeling protein assemblies in the proteome. Molecular & cellular proteomics, 13(3):887-896) 2014.
Andy M Lau, Shaun M Kandathil, and David T Jones. Merizo: a rapid and accurate protein domain segmentation method using invariant point attention. Nature Communications, 14(1):8445, 2023.
Andy Lau, Nicola Bordin, Shaun M Kandathil, Ian Sillitoe, Vaishali P Waman, Jude Wells, Christine A Orengo, and David T Jones. Exploring structural diversity across the protein universe with the encyclopedia of domains. Science, 386(672 ::addq44494 2024.
Valerio Mariani, Marco Biasini, Alessandro Barbato, and Torsten Schwede. 1ddt: local superposition-fiee score for comparing protein structures and models using distance difference tests. Bioinformatics, 29(21):2722 2722227888222 2013.
Claudio Mirabello and Björn Wallner. Dockq v2: improved automatic quality measure for protein multimers, nucleic acids, and small molecules. Bioinformatics, 40( bt(10)) 2024.
Christopher Oldfield, Vladimir Uversky, A Keith Dunker, and Lukasz Kurgan. Introduction to intrinsically disordered proteins and regions. In Intrinsically disordered proteins, pp. 1-34. Elsevier, 2019.
Alireza Omidi, Mads Harder Møller, Nawar Malhis, Jennifer M Bui, and Jörg Gsponer. Alphafold- multimer accurately captures interactions and dynamics intrinsically disordered protein re- gions. Proceedings of the National Academy Sciences, 121(44))e2406407121, 2024.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- performance deep learning library. Advances in neural information processing systems, 32, 2019.
Tony Pawson. Protein modules and signalling networks. Nature, 373(6115)573-588. 1995.
Chun-Xiang Peng, Fang Liang. Yu-Hao Xia, Kai-Long Zhao, Ming-Hua Hou, and Gui-Jun Zhang. Recent advances and challenges in protein structure prediction. Journal of Chemical Information and Modeling, 64(1):76-95, 2023.
Dana Reichmann, Ofer Rahat, Shira Albeck, Ran Meged, Orly Dym, and Gideon Schreiber. The modular architecture of protein-protein binding interfaces. Proceedings of the National Academy of Sciences, 102(1):57-62. 62, 2005.
R Dustin Schaeffer, Yuxing Liao, Hua Cheng, and Nick V Grishin. Ecod: new developments in the evolutionary classification of domains. Nucleic acids research, 45(D1): D302, 2017.
Andrew W Senior, Richard Evans, John Jumper, James Kirkpatrick, Laurent Sifre, Tim Green, Chongli Qin, Augustin Zidek, Alexander WR Nelson, Alex Bridgland, et al. Improved protein structure prediction using potentials from deep learning. Nature, 577(772))706-710, 2020.
12

---

Published as a conference paper at ICLR 2026
Ben Shor and Dina Schneidman- Duhovny. Combfold: predicting structures of large protein assem- blies using a combinatorial assembly algorithm and alphafold2. Nature methods, 21(3)4477-487, 2024.
lan Sillitoe, Nicola Bordin, Natalie Dawson, Vaishali Waman, Paul Ashford, Harry M Scholes, Camilla SM Pang, Laurel Woodridge, Clemens Rauer, Neeladrí Sen, et al. Cath: increased struc- tural coverage of functional space. Nucleic acids research, 49(D1):D266-D273, 2021.
Jaaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02500 2020a.
Yang Song and Prafulla Dhariwal. Improved techniques for training consistency models. arXiv preprint arXiv:2310. 14.44.9,0 2023.
Yang Song, Jascha Sohl-Dickstein, Diederik Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13455 2020b.
Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. In Proceedings of the 40th International Conference on Machine Learning, pp. 32211-32252, 2023.
ByteDance AML A14Science Team, Xinshi Chen, Yuxuan Zhang, Chan Lu, Wenzhi Ma, Jiaqi Guan, Chengyue Gong, Jincai Yang. Hanyu Zhang, Ke Zhang. al. Protenix-advancing structure pre- diction through a comprehensive alphafold3 reproduction. BioRxiv, pp. 2025-01, 2025.
Peter Tompa and Monika Fuxreiter. Fuzzy complexes: polymorphism and structural disorder in protein-prose protein interactions. Trends in biochemical sciences, 33(1):2-8, 2008
Hannah Wayment- Adedolapo Ojoawo, Renee Otten, Julia M Apitz, Warintra Pitsawong, Mare Hömberger, Sergey Ovchinnikov, Lucy Colwell, and Dorothee Kern. Predicting multiple conformations via sequence clustering and alphafold2. Nature, 625(7996) 883, 2024.
Jude Wells, Alex Hlakins-Hoooke Nicola Bordin, Ian Sillitoe, Brooks Paige, and Christine Orengo. Chainsaw: protein domain segmentation with fully convolutional neural networks. Bioinformat- ics, 40t5),b 2024.
Zhong-Ze Yu, Chun-Xiang Peng, Jun Liu, Biao Zhang, Xiao-Gen Zhou, and Gui-Jun Zhang. Dombpred: protein domain boundary prediction based domain-residue clustering using inter- residue distance. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 20(2): 912 922, 2022.
Jing Zhang, R Dustin Schaeffer, Jesse Durham, Qian Cong, and Nick V Grishin. Dpam: A domain parser for alphafold models. Protein Science, 32(2))e4548 2023.
Kun Zhu, Hong Su, Zhenling Peng. and Jianyi Yang. A unified approach to protein domain parsing with inter-residue distance matrix. Bioinformatics, 39(2):btad070, 2023.
A APPENDIX
A.1 BASELINE DETAILS
In this section, we describe the baseline models employed in our experiments. As most baselines are designed to predict only protein-protein complexes, the evaluation is primarily conducted on the recent PDB dataset.
A.1.1 MoLPC
We utilized the code from the MoLPC repository. The default settings applied without modi- fying any hyperparameters. MoLPC generates single best predicted protein complex, which was used for evaluation.
13

---

Published as a conference paper at ICLR 2026
GT
Visualization of complex modeling results comparing HierAFold and CombFold. Left PDB ID is 7wck, and right PDB ID is 7ow5. The gray chains are ground truth.
Figure 7:
A.1.2 COMBFOLD
We employed the code from CombFold repository. CombFold utilizes a combinatorial assembly algorithm to construct protein complexes from their subunits. Its performance relies the quality and quantity of predicted cubset-complexs provided by the underlying protein complex prediction both AlphaFold Multimee v2 from
method (AlphaFold- Mullimer in default). In this phase, AlphaPuldoown repository and Protenix (a reproduction of AlphaFold3) from Protenix repository as the backhone prediction model, and we notate them CombFold-AFMS and CombFold- Protedd............ CombFold accepts inputs comprising 2 or more subunits and applies its combinatorial method ac- cordingly, and its performance depends on the number of input. To balance performance and time, we included all heteromeric subunit pairs for every unique combination of distinct subunits, along with homomeric subunit pairs for each chain homomer in the protein complex. Trimeric or longer subunit complexes were not utilized; instead, all possible dimeric subunit complexes served as the starting point for the assembly algorithm.
In CombFold, due to potential inaccuracies in pairwise transformations, subcomplexes are evalu- ated for steric clashes among backbone atoms with pL.DDT scores greater than 80. subcomplex filtered out if more than 5% of its atoms exhibit clashes. However, for complexes that fail to yield any valid predictions under this criterion, we disabled the filtering mechanism to generate re- sults. CombFold produces multiple predictions, each accompanied by confidence score, and selected the prediction with the highest confidence for our experiments as Top-1 accuracy, and the highest performance within all samples the oracle accuracy. For the CombFold-AFMvv base- line, we utilized multiple sequence alignments MSAs from the offline AlphaFold Database. For the CombFold-Proute Protenix baseline, we employed online MSA searches via the Protenix server while performing the complex predictions offline.
A.2 ALPHIAFOLD MULTIMER
We utilized the code from the AlphaPulldown repository. We employed AlphaPulldown's default settings, encompassing multiple sequence alignment (MSA) search and complex prediction. The complex prediction process involves a 5-cycle inference that generates a single prediction, which was utilized in experiments. The rank-O prediction sample represents the with the high- est confidence and serves as the Top-1 accuracy metric, while the highest performance among all samples corresponds to the oracle accuracy.
14

---

Published as a conference paper at ICLR 2026
A.3 ROSETTAFOLD ALL-ATOM
We utilized the code from the RoseTTa All-Atom. We employed RFAA's default settings while using the Mlplifold-uullimer''s Database provided in AlphaPulldown repository v2.0.5. We used Uniref30 version at 2023-02 to replace the original 2020-06 requirement in RFAA.
A.4 PSEUDO CODE
Algorithm HIERAFOLD: Hierarchical Protein Complex Structure Prediction
Require: Set of peptide chains {C1, C2.-..; "e.....Cas' with total N tokens
Ensure: Assembled 3D structure of the protein complex
Coarse Stage: Pairwise Prediction and Modular Decomposition
1: for each pair of chains (Ci, Cj), i do
2: Generate coarse predictions using distilled model: Xij. Pij (coordinates and PAE matrix)
3: for each chain C; do
4: Segment C; into subunits {U U....... using PAB-guided recursive partitioning on Pa
5: for each focus chain C. do
6: Initialize neighborhood NCCC,)
7:
for each other chain C, & a do for each subunit Ub,5 in C. do
8:
9:
Compute mean interface PAE: P(Ca, Uh.s) Compute min distance: dani (Ca, Ub.5) P(Ca, Ub,5) < or dinin (Ca, Ub.5) < Ta then Add Ub.j to (C,)
10:
11:
Fine Stage: Interface-Aware Refinement for each focus chain C. do Form composite imput: C. (C,)).)
13:
14:
15:
Perform full AlptaFold3-style inference to get refined structure X.
Assembly Stage: Confidence-Aware Global Alignment
Initialize global assembly with highest-confidence X
for each remaining partial structure X. do Identify overlapping atoms between X, and global assembly Compute confidence weights W' = pLDDT(xx..a) (LDDD(
19:
20:
Find optimal R. minimizing weighted RMSD:
21:
Rank final structures using composite score (ipTM + pTM + clash detection)
A.5 ADDITIONAL COMPARISON WITH COMBFOLD
We further compared HIERAFOLD with CombFold benchmark provided by CombFold, 25 complexes with 5-30 chains and 2,000-18,000 18,000 amino acids. Most of those are included in the recent PDB and filtered large complex data. The top-1 DockQ success rate is 30.2% (CombFold) vs 50.7% (ours).
We further performed an additional analysis to examine how the performance gap between HIER- AFOLD and existing baselines changes as size of the input complex increases. Specifically, we partitioned complexes in the recent PDB benchmark into bins based their total token count and computed the Top-1 average DockQ difference between. The result is summarized Table 3.
A.6 ABLATION STUDY
To validate the effectiveness of the key components in HIERAFOLD, we conducted series of ab- lation studies on the recent PDB dataset. We systematically dismantled our framework to quantify the contribution of the consistency- disttllldd coarse model, the PAE-based subunit segmentation, the PAE-guided subumit selection, and the confidence- aware assembly mechanism. The results are sum- marized in Table 4.
15

---

Published as a conference paper at ICLR 2026
Token Count
HIERAFOLD CombFoll (%)
HIERAFOLD AlphaFold (%)
0- 1,000
+13.4
-0.2
1,000 2,000
+19.4
-10
2,000 3,000
+23.0
-1.4
3,000 - -4,000
+23.9
-1.4
> 4,000
+23.1
-1.7
Table 3: Analysis of the DockQ success rate gap between HIERAFOLDD and CombFold, as well as between HIERAFOLD and AlphaFold, across increasing complex size on the recent PDB set. The positive values indicate HIERAFOLD's advantage.
Table 4: Ablation study of HIERAFOLD on the recent PDB dataset. We report the DockQ Success Rate (%) and average inference time for complex with average of 3,000 tokens. The results validate that each component of our proposed method contributes to the final performance and efficiency.
Method
Oracle (%)
Top-1 (%)
Avg. Time (min)
HIERAFOLD (Ours)
73.1
69.0
46
Ablation Coarse Prediction
w/ Full Diffusion Model
73.3
69.4
125
w/ Mini-rollow (20 steps)
71.0
68.2
52
Ablation on Subunit Segmentation
Taplit (residue level)
72.0
67.8
45
Tsplit
72.9
68.9
46
Tsplit 15
73.1
69.1
46
Tsplit 20
73.2
69.1
47
Taplit (on PDE)
72.4
68.2
45
Ablation Subunit Selection
PAE-Only Selection
71.0
66.9
46
Distance-Onfe Selection
70.4
66.3
46
Tp 10 and TJ = 30
73.4
69.3
50
Ablation on Fine Stage w Distilled Model
69.3
64.9
Ablation on Assembly w/ Unweighted Assembly
71.0
66.5
45
Effeet of Distilled Coarse Prediction The coarse stage is designed to be fast yet accurate enough to guide the decomposition. We tested its importance by replacing it with the full, non-distilled AlphaFold3 model for pairwise predictions. This provides coarse structure prediction process. As shown in Table 4, using the full diffusion model offers a marginal 0.2% improvement in Oracle DockQ success rate the recent PDB dataset but triples the inference time, confirming that our distilled model provides the best trade-off between speed and quality. We further evaluated the mini-rollout method to generate the coarse structure, which degrades the DockQ success rate by 2%, while increasing the inference time, indicating the incorrect pairwise conformation prediction affects the final result.
accurate but significantly slower
PaE-based Segmentation Sensitivity In HIER chain is partitioned into subunits based on low-PAE blocks, controlled by the threshold Tsplit- The default value in our experiments is Teplit 10. Larger thresholds create coarser subunits (fewer boundaries), while smaller thresholds produce finer-grained segmentation. To assess sensitivity Taplit, systematically varied Taptic and evaluated the downstream complex prediction accuracy (Table 4). The results demonstrate that: (i) Performance remains stable across broad and practical range of thresholds. (ii) Extremely fine segmentation (Tsplit = 0) harms performance, confirming that splitting residues individually introduces unnatural discontinuities and disrupts coherent structural modeling. (iii) Very large
16

---

Published as a conference paper at ICLR 2026
HanAFalld
Combiold
HarAFoold
Har
Figure 8: Left: Visualization of large complex modeling results comparing HierAFold and Comb- Fold. PDB ID is 9kt3. Right: Additional visualization of HIERAFOLD on the large protein complex dataset. PDB are 8dxq and 912e. The gray chains are ground truth.
thresholds converge end-to-end behavior, producing single-chain subunits. While accuracy remains stable, memory consumption increases, defeating the scalability benefits of our method.
We further compared PAE with an alternative confidence signal, Predicted Distance Error (PDE), for subunit segmentation. For PDE, we optimized the segmentation threshold to ensure a fair com- parison. However, results indicate that PAE better captures pairwise structural coherence essential for identifying rigid subunits, making the preferred confidence metric for our decomposition pro- cedure.
Importance of PAE-Guided Subunit Selection Our core hypothesis is that PAE-guided subunit selection is superior to simpler heuristics. We evaluated this by ablating the selection criteria: (i)
PAE-Only: Selecting subunits based only on the mean interface PAE (P < Tp). (ii) Distance- Only: Selecting subunits based only on spatial proximity in the coarse structure (dmin Ta). The results show that combining PAE and distance criteria is optimal. The PAE-only approach performs better than the distance-only one, indicating that interaction confidence is more reliable signal than proximity alone. We further evaluate the effect of looser selection policy where we changed the Tp to and тa to 30 to include more subunits from the other chains. The performance increases marginally with the increased peak memory usage and inference time.
Contribution Confidence-Aware Assembly Finally, we assessed the impact our confidence- aware alignment algorithm. We compared our standard method against variant using Un- weighted Assembly, where the Kabsch algorithm applied without PLDDT weighting. The un- weighted method shows a noticeable drop accuracy (69.0% 66.5% Top-1). This highlights that weighting the alignment by local confidence makes the assembly process more robust, espe- cially for complexes with flexible linkers or poorly predicted regions, as correctly prioritizes the well-structured interfaces to guide the overall superposition.
A.7 MORE VISUALIZATION RESULTS
Fig. shows more visualization of HIERAFOLD on the recent PDB dataset compared with Comb- Fold. Fig. 8 shows HIERAFOLI performance on large complex dataset, showing improvement in capturing multiple chain interactions and performing well in monomers.
Table 5: DockQ success rate comparison of AlphaFold3 and HIERAFOLD on homomers and heteromers.
Category
Metrie
AlphaFold3
HIERAFOLD
Oracle
77.3
76.2
Homomers
Top-1
74.0
72.8
Oracle
72.3
70.9
Heteromers
Top-1
67.9
66.3
17

---

Published as a conference paper at ICLR 2026
A.8 PERFORMANCE ON HOMOMERIC VS. HETEROMERIC COMPLEXES
We further examined performance across homomeric versus heteromeric complexes. Complexes in the recent PDB dataset were categorized based on chain composition. As shown in Table 5, both AlphaFold3 and HierAFold achieve higher accuracy on homomers, likely due to stronger co- evolutionary and symmetry-related signals.
subsectioninfluence of the Number of Conformations Our experiments in recent PDB follow the standard inference protocol of Protenix (Team al., 2025), generating 25 conformations. To as- sess the impact of sampling, we evaluated performance when generating fewer conformations. The results are summarized in Table 6
Table 6: DockQ success rate comparison of AlphaFold3 and HIERAFOLD with different numbers of generated conformations.
Category
Metric
AlphaFold3
HIERAFOLD (OuRS)
Oracle Top-1
69.9
68.5
n=5
65.0
63.6
Oracle
72.2
70.9
n=10
Top-1
67.5
66.1
Oracle Top-1
74.4
73.1
n=25
70.4
69.0
A.9 SUBUNIT SEGMENTATION
To contextualize our approach, we compared the segmentation accuracy between our PAF-based segmentation against Merizo (Lau et al., 2023) on the CATH-663 test set (Sillitoe al., 2021). As expected, Merizo achieves higher IoU (0.85 vs. 0.65), since it is explicitly designed and trained for domain parsing, including the detection of discontinuous domains that are prevalent in CATH. In contrast, our segmentation module is not optimized for canonical domain detection, yet still achieves reasonable segmentation quality. It deliberately merges tightly packed regions with uniformly low inter-subunit PAE into single rigid unit-a behavior aligned with our design objective of identifying structurally coherent subunits that matter downstream refinement, rather than reproducing evolutionary domain boundaries.
Despite this difference in segmentation granularity, method achieves boundary MCC of 0.79, closely matching Merizo's 0.84. This demonstrates that PAE provides reliable structural signal for locating true physical boundaries,
without specializing in fine- fine-graine grained domain delineation.
Crucially, these variations in loU have no negative impact on the final complex prediction accuracy shown in Table 1. The results confirm that PAE is effective and sufficient metrie for the type of segmentation required by FFIERAFFLoiddemee boundaries that guide accurate multi-chain refinement.
rigid subunits and interaction-relevant
Combined with the results above, our PAE-based segmentation offers three key advantages:
Computational Efficiency: No additional model database queries are required. Seg- mentation reuses PAE matrices already produced during coarse prediction, making it effee- tively cost-free. Structural Relevance for Complex Assembly: PAE identifies rigid, co- operatively moving structural units, not evolutionary domains. also highlights inter-chain interaction subunits, enabling interface-aware refinement, capabilities absent in existing domain predictors. Competitive or Better Downstream Performance: Despite simpler computation, PAE-based segmentation performs better than Merizo when evaluated in the context of complex structure prediction, the task for which HierAFola is optimized.
A.10 EXTENSION OF HIERAFOLD TO ROSETTAFOLD ALL-ATOM
To evaluate the generalizability HIERAFOLD beyond AlphaFold3, we integrated RoseTTAFold All-Atom (Krishna al., 2024) alternative backbone predictor. On representative subset
18

---

Published as a conference paper at ICLR 2026
of 50 complexes from the recent PDB dataset, the the achieved DockQ success rate of 53.7%, closely matching the 54.8% obtained by the end-to-end TTAFold All-Atom model, while reducing memory usage by ~35%. This demonstrates that HIerAFolD is model-agnostie: it can seamlessly wrap around different backbone predictors and preserve their accuracy while substantially improving scalability. As stronger predictors emerge, they can be incorporated into the HierAFold pipeline to further enhance performance on large complexes.
configuration
A.11 LIMITATION OF HIERAFOLD
A.11.1 COMPUTATION COST AND MITIGATION STRATEGIES
Although HIERAFOLD reduces peak GPU memory usage by decomposing a large complex into manageable subunits, this decomposition introduces extra computation time. We use several strategies to keep this overhead practical: (i) Distilled Coarse Prediction: Running full AlphaFoodd3 for every pairwise coarse prediction would be prohibitively expensive. To address this, introduce a consistency-distilled diffusion model with shallower Pairformer. This replacement significantly reduces latency in the coarse stage while maintaining effective structural priors, as shown in Table 4. (ii) Parallelized Refinement: For complex with M chains, HIERAFOLD runs the fine-stage refinement M times-once for each focus chain-but each run operates substantially smaller imput, lowering per-run memory. This reduction allows: parallel execution across multiple GPUs, or batching execution in the diffusion module single GPU. These options keep total inference time manageable while enabling prediction of complexes far beyond AlphaFold3's memory limit. We benchmarked both methods on a single A100 GPU. The results are shown in Table 7.
Figure Conformation coverage is limited. The left shows the prediction for PDB Scvp (apo), and the right for 8d7u (holo). The apo structure should adopt open conformation, while the holo is closed. Both are predicted in the closed state Hi- ERAFOLD (green box)
Total Tokens
AlphaFold3 (min)
HIERA (min)
2,000
17
3,000
38
46
4,000
74
98
5,000
OOM
170
Table 7: Inference time comparison. While HIERAFOLD introduces extra computation cost, successfully runs on large complexes where the baseline fails due to memory constraints. The baseline inference time is measured on Protenix v0.5.0.
A.11.2 MULTI-STATE ASSEMBLIES
A known challenge for AlphaFold-family models is the prediction of distinct functional states. Since HIERAFOLD uses AlphaFold3 as its predictor, it inherits this limitation. For example, when pre- dicting the structures of an E3 ubiquitín ligase in its apo (PDB: 8cvp, expected open state) and holo (PDB: 8d7u, expected closed state) forms, HIERAFOLD. like the baseline, exclusively predicts the closed conformation for both (Fig. 9). Methods developed for AlphaFold-Famil that assist in
19

---

Published as a conference paper at ICLR 2026
multistate prediction may be adaptable in HIERAFOLD (Wayment-Steele al., 2024; Heo & Feig, 2022).
A.11.3 PERFORMANCE BOUND FUTURE WORK
Despite these advances, performance remains bounded by the underlying AlphaFold3 model, par- ticularly for very large or challenging complexes. Future work will explore training strategies and model enhancements to further improve accuracy on such complex tasks.
A.12 LLM USAGE
Throughout the preparation of this manuscript, Large Language Model (LLM) utilized writing assistant to enhance the quality of the text. The primary role of the LLM was to polish the language by improving grammar, refining sentence structure for clarity, and ensuring stylistic consistency. It is important to state that the LLM's contribution was strictly limited to language enhancement. All conceptual development, research, analysis, and the core arguments presented in this paper are the original work of the authors. Following the guidelines on academic integrity, have critically reviewed and edited all machine-generated suggestions and take full responsibility for the final content and scientific accuracy of this publication.
20


Reviews:
[{"review_id": "xkkneQDAbS", "reviewer": "Reviewer_eHdb", "summary": "The method HIERAFOLD provides a memory-efficient and accurate solution to the prediction of large macromolecular complexes. It uses an optimised version of Protenix, an open-source reproduction of AlphaFold3, to generates 3D models of subparts, a subunit segmentation strategy based on PAE, and a combinatorial algorithm for selecting and assembling subparts. It performs favourably compared to AlphaFold3 and CombFold.", "questions": "- Could the authors discuss other methods for segmenting proteins into domains, or rigid subunits? In particular those developed recently for annotating the AlphaFold Database?\n- Could the authors comment on the influence of the content in intrinsically disordered regions on the performance of the method?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "- The methodology and experiments are sound and clearly explained\n- The success rate is much better than the state-of-the-art methods", "weaknesses": "- The main concern I have is whether this work actually fits within the scope of ICLR. It is not a machine learning contribution per se, as it relies on an already developed diffusion-based SOTA protein structure predictor. The contribution mainly focuses on algorithms for segmenting, selecting and combining subparts, without any representation learning involved.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Qx33eEQwDX", "reviewer": "Reviewer_sJfG", "summary": "The paper introduces a new approach for predicting the structure of large protein complexes by decomposing them into modular subunits using Predicted Aligned Error (PAE) scores. The proposed approach uses a 3-stage process from coarse to split the segments, then performing fine prediction using existing models and the final alignment. It achieves similar accuracy to AlphaFold3 with lower GPU memory requirements for large protein complex.", "questions": "Details of the dataset are very sparse. Provide more details, including the number and lengths of sequences across the 3 datasets, in the manuscript.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper addresses a difficult challenge of predicting the structure of large protein complexes.\n\n- The proposed approach appears to improve both accuracy and reduce memory requirements.\n\n- The three stages of coarse, fine, and assembly are modular and allow for examining individual stages. Overall, the approach is well constructed.", "weaknesses": "- The proposed approaches rely on existing approaches in protein modeling and do not advance the area significantly, nevertheless, they provide an application to an important problem. \n\n  - The reliance of PAE for segmentation is one of the main drawbacks of this approach. PAE is an estimated alignment error and may not fully capture the inter-domain interactions, leading to errors in clustering based only on PAE.\n\n  - Since the main comparison in this paper was done between hierafold and combfold, it would be helpful to compare against the dataset used in the combfold paper.\n  \n  - Description of the dataset and performance variation with respect to homology, number of conformations, or known multi-state assemblies is missing. The paper would be strengthened if it explicitly demonstrated performance on disordered/flexible domains.\n\n  - A better quantification or analysis of the identified sub-unit from segmentation is not provided. This will also allow to examine if common sub-structures are being identified as subunits across different proteins.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MvwGgBSTYF", "reviewer": "Reviewer_EYwv", "summary": "HIERAFOLD: Hierarchical pipeline for efficient large complex prediction using PAE decomposition & refinement.", "questions": "1.Addressing Intra-Subunit Errors: Given that the method assumes correct intra-subunit structure, how would HIERAFOLD perform if the base model prediction for one of the subunits was highly inaccurate (e.g., due to novel topology or unusual folding)? Could the targeted refinement be adapted to dedicate a small amount of computational budget for intra-subunit refinement based on a local confidence score (e.g., pLDDT)?\n\n2.Decomposition Sensitivity Analysis: How is the threshold for PAE-guided subunit decomposition determined? Is it a fixed value, or is it dynamically tuned? Please provide a sensitivity analysis showing the final accuracy (e.g., TM-score, Interface TM-score) as a function of this PAE decomposition threshold to address the concern about structural breaks.\n\n3.Assembly Mechanism for Flexibility: Can the \"confidence-weighted assembly\" mechanism explicitly handle the difference between rigid-body movements of subunits (which require global transformation) and local, flexible changes (which require local backbone/side-chain adjustments)? How does the assembly process prevent structural strain introduced during the re-assembly of independently refined subunits?", "limitations": "", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "The work addresses a critical and well-known scalability bottleneck in modern protein structure prediction models, which suffer from quadratic complexity (O(N^2)) for large protein complexes. The originality of the method is high, centered on the Predicted Aligned Error (PAE)-guided hierarchical decomposition of large complexes into smaller, manageable subunits. This is a creative, biologically motivated, and highly relevant solution that directly exploits the inherent modularity of protein structures. The quality of the method is evidenced by the thoughtful design, particularly the targeted interface-aware refinement strategy, which focuses computational power precisely where inter-chain interactions are most critical, thus optimizing the accuracy-efficiency trade-off. The significance of HIERAFOLD is substantial, as it practically extends the application of highly accurate prediction methods to systems exceeding a few thousand residues, which is a major advancement for predicting large, biologically relevant assemblies.", "weaknesses": "1.Sensitivity to Initial Subunit Quality：The hierarchical pipeline is fundamentally limited by the quality of the initial prediction for the subunits. The current approach implicitly assumes the intra-subunit structure is largely correct and focuses its efforts on inter-subunit interfaces. The method lacks a mechanism to effectively identify or recover from errors in the internal structure prediction of the subunits themselves. This poses a significant failure mode, as local structural errors within a subunit cannot be easily rectified during the refinement or re-assembly steps, especially if they are far from the interface.\n\n2.Decomposition Robustness and Structural Breaks: While efficient, the PAE-based decomposition strategy carries a risk of introducing structural discontinuities or breaks at the boundaries of the artificially created subunits, particularly in cases of highly dynamic, ambiguous, or tightly interwoven (non-modular) interfaces. This potential for introduced structural artifacts needs a more robust discussion and mitigation strategy.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jVACbfYMDm", "reviewer": "Reviewer_E9v3", "summary": "This paper presents HIERAFOLD, which exploits the modularity of large complexes via PAE-guided (Predicted Aligned Error) subunit decomposition, targeted interface-aware refinement, and confidence-weighted assembly. By leveraging coarse predictions and PAE-guided modular decomposition, the method automatically identifies subunits and interfaces, and refines each chain in the context of its key interacting partners. Experiments from various benchmarks clearly show that HIERAFOLD matches AlphaFold3 on standard benchmarks and, critically, extends tractable prediction to complexes exceeding 5,000 tokens, achieving substantial gains over prior divide-and-conquer approaches.", "questions": "1. What is the computation cost of HIERAFOLD? Though the decomposition of long tokens into several small subunits is effective at reducing the memory cost. It ends up with a lot of extra computation. Is the extra computation cost acceptable compared to the saved memory usage?\n\n2. How will the split k in PAE-Guided Subunit Segmentation for Biological Modularity affect the performance? And how much difference for the split part? Is the split showing a significant difference between the two split parts?", "limitations": "", "rating": 4, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The challenges and motivation of the proposed method are clearly shown and demonstrated.\n\n2. Various experiments are conducted to show the effectiveness of the proposed method.\n\n3. The paper is well written and organized.", "weaknesses": "1. The decomposition is a good way to save memory usage. However, the paper only uses AlphaFold3 as the backbone model to test the method. An extension to other backbone methods will help better demonstrate the effectiveness.\n\n2. More baselines should be added, such as OpenFold and MoLPC, to demonstrate the effectiveness of the proposed methods better.\n\n3. The code is not publicly available.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "NunVZw0836", "reviewer": "Reviewer_XQxJ", "summary": "This paper addresses the computational complexity issue in AlphaFold by presenting a hierarchical pipeline, refered to as HieraFold, which decomposes the end-to-end structure prediction task in a coarse-to-fine manner.\nHieraFold first performs a coarse global prediction using a \"lightweight\" version of AlphaFold with a smaller diffusion module, and then locally refines critical subunits identified via the pAE matrix.\nExperimental results on protein-protein and protein-ligand benchmarks demonstrate the effectiveness of the proposed method.", "questions": "1. A fundamental question: why do low-pAE regions naturally correspond to critical subunits? Please provide an intuitive explanation of the rationale behind this choice.  \n\n2. In Figure 2, why is C1 retained while C2 and C3 are omitted?  \n\n3. How does the performance gap between HieraFold and the baseline change as the size of the input complex increases?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. This paper addresses an important research problem: reducing the peak computational complexity of AlphaFold, which is critical for real-world applications involving very large protein complexes.\n\n2. The proposed method for identifying critical subunits does not rely on expert curation, making it more generalizable and practical.\n\n3. Experimental results on large complexes demonstrate substantial improvements over existing methods.", "weaknesses": "1. **Writing and organization.** Although generally well structured, the manuscript would benefit from improvements in writing. Specific issues include:  \n   * Incorrect use of hyphens and dashes;  \n   * Some paragraphs are overly wordy;  \n   * The Introduction section discusses the literature extensively but there is no separate “Related Works” section. It is important to maintain the distinct roles of these sections rather than combining them;  \n   * Line 249: “focus chai” should be corrected to “focus chain.”  \n\n2. **Computational and time cost.** The multi-stage pipeline leads to higher computational overhead and longer runtime. A more detailed analysis of the trade-off between the ability to handle large complexes and the additional time and computation required would strengthen the paper.  \n\n3. **Insufficient validation of design choices.** Some key design decisions are not thoroughly supported by ablation studies, including:  \n   * The choice of pAE over other confidence metrics output by AlphaFold;  \n   * Whether confidence-metric-based subunit identification indeed outperforms manually designed approaches;  \n   * The necessity of the refining stages (Stages 2 and 3), i.e., how much improvement does the full pipeline provide over the coarse stage alone.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)