UniIF: Unified Molecule Inverse Folding

Authors: zhangyang  gao
jue  wang
cheng  tan
lirong  wu
yufei  huang
siyuan  li
zhirui  ye
stan z li
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-15 06:47:31

Abstract: Molecule inverse folding has been a long-standing challenge in chemistry and biology, with the potential to revolutionize drug discovery and material science. Despite specified models have been proposed for different small- or macro-molecules, few have attempted to unify the learning process, resulting in redundant efforts. Complementary to recent advancements in molecular structure prediction, such as RoseTTAFold All-Atom and AlphaFold3, we propose the unified model UniIF for the inverse folding of all molecules.  We do such unification in two levels: 1) Data-Level: We propose a unified block graph data form for all molecules, including the local frame building and geometric feature initialization. 2) Model-Level: We introduce a geometric block attention network, comprising a geometric interaction, interactive attention and virtual long-term dependency modules, to capture the 3D interactions of all molecules. Through comprehensive evaluations across various tasks such as protein design, RNA design, and material design, we demonstrate that our proposed method surpasses state-of-the-art methods on all tasks. UniIF offers a versatile and effective solution for general molecule inverse folding.

Main paper: 
 introduction: 
 Molecule inverse folding plays a pivotal role in drug and material design, enabling scientists to synthesize novel molecules with the desired structure. Previously, many studies focus on either macromolecules [19, 33, 21, 9, 17, 4, 10, 17, 8, 34] or small molecules [6, 26, 16, 28, 14, 31] separately, leaving the challenge of inverse folding general molecules. For example, the advanced small molecule model [6, 31] take atoms as basic units; the macromolecule models [8, 10] consider predefined microstructures (such as amino acids and nucleotides) as the basic units. Additionally, even for the same molecule, different models employ varying strategies to extract geometric features. Complementary to the great success of RoseTTAFold All-Atom [25] and AlphaFold3 [1] in molecular structure prediction, we propose a unified model, UniIF, for the inverse folding of all molecules. By comparing small-and macro-molecules, we identify three challenges toward the unified model:(1) Unit Discrepancy: The macromolecules takes predefined microstructures (amino acids and nucleotides) as the basic units, while small molecules takes atoms as basic units.(2) Geometric Featurizer: Different studies employ various strategies for extracting geometric features from structures, such as distance, angles and tensor product; there are lack of unified featurization strategy. (3) System Size: The small-molecules allow the full attention transformer to learn long-term dependencies, but the quadratic computing cost limits the mechanism scalling up to macro-molecular systems. Alternatively, previous research use sparse GNN, which suffers from the limited local receptive field that causes over-smoothing and oversquashing [29] . In addition, developing a unified model working well for all molecules is challenging.The unit discrepancy makes it challenge to adapt methods across small-and macro-molecules, which explains the divergence between these two research lines. As a solution, we propose a frame-based block to unify the representation of amino acids, nucleotides, and atoms: a group of atoms with varying size is treated as a block with fixed size. Each block includes decoupled equivariant basis and invariant features, generalizing the representation of AlphaFold2 and other small-molecule methods.The geometric featurizer is necessary to capture the geometric interactions between blocks. We initialize the equivariant block basis using predefined rules or a learnable GNN layer, and then constructing invariant block features based on these basis. The key operation is to use local coordinates and dot product to capture the geometric interactions between virtual atoms. We reuse the featurizer in each model layer to interactively learn updated geometric features, where the concept of directed virtual atom is introduced to enhance the pairwise interactions. We show that the unified featurizer works well across protein design, RNA design, and material design.We use sparse GNN to address the system size issue, while maintaining the ability to capture longterm dependencies. The transformer-style protein models like AlphaFold and RosettaFold require a substantial amount of GPU memory. Sparse GNNs, on the other hand, are criticized for their tendency to over-smooth and over-squash due to their limited local receptive field. To be efficient while preserving the ability to capture long-term dependencies, we introduce global virtual blocks. Each virtual block is connected to all real blocks, serving as an information exchange agent.We conducted comprehensive experiments across various tasks, including protein design, RNA design, and material design, to demonstrate the effectiveness of UniIF. The results show that UniIF achieves state-of-the-art performance on all the tasks, which is non-trivial and may benefit the machine learning, drug discovery, and material science communities.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? Answer: [Yes] Justification: Our experimental results support the claims. Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
related work: 
 Unification. Unified molecular learning has attracted increasing attention in recent years. RoseTTAFold All-Atom (RFAA) [25] and AlphaFold3 [1] are two representative models that have achieved remarkable success in protein structure prediction. RoseTTAFold All-Atom uses an atombond graph for small molecules and a frame graph for macromolecules. AlphaFold3 uses a bi-level representations, i.e., atom representation and token representation, for all molecules. The token concept is requivalent to the block concept in this paper, which means a group of atoms, such as a amino acid or a nucleotide. GET [24] and EPT [20] are two recent models that use a block representation for both small and macromolecules and introduce a new equivariant transformer backbone. Unlike RFAA [25] , which specifies a atom-bond graph for small molecules, our model employs a unified block graph for all molecule types and do not require the atom-bond graph. Our model also differs from AlphaFold3 [1] , GET [24] and EPT [20] in the that we introduce the vector basis for each block.Protein Inverse Folding. Recent research use k-NN graph to represent the 3D structure and employ graph neural networks for protein inverse folding. GraphTrans [19] uses the graph attention encoder and autoregressive decoder for protein design. GVP [21] proposes geometric vector perceptrons to learn from both scalar and vector features. GCA [33] introduces global graph attention for learning contextual features. In addition, ProteinSolver [32] is developed for scenarios where partial sequences are known while not reporting results on standard benchmarks. Recently, AlphaDesign [9] , ProteinMPNN [4] , ESMIF [17] , LMDesign [40] , KWDesign [8] , VFN [27] achieves dramatic improvements. A benchmark [11] is proposed to comprehensively evaluate protein design models.RNA Inverse Folding. RNA inverse folding is a challenging task due to the complex secondary structure and tertiary structure. Traditional methods [3] include colony optimization and constraint programming, in addition to adaptive walk, simulated annealing and Boltzmann sampling. Recent deep learning method RDesign [34] has achieved promising results and build a benchmark for AI researchers to follow-up. RiboDiffusion [18] use diffusion decoder to generate RNA sequences conditioned on the backbone structure embeddings.Material Design. Deciding which chemical compositions are likely to form compounds is a critical task in material design [28, 26, 14] . An important application is to substitute lattice-site elements or ionic species within existing compounds that exhibit similar chemical behaviors. Wang et al. [36] successfully employed the elemental substitution method to discover 18,479 stable compounds out of a pool of 189,981 potential candidates. Recently, Jensen et al. [6] introduced a open dataset for material design and established a benchmark for evaluating deep learning models in this domain.3 MethodQuestion: Does the paper discuss the limitations of the work performed by the authors? Answer: [No] Justification: The limitation is that we do not do wet-experiments. But we think this is out of scope for the AI paper. Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
overall framework: 
 As shown in Fig. The model treat all types of molecules as block graphs. For macromolecules, we use predefined frames based on amino acids and nucleotides; for small molecules, we learn the local frame of each block by one-layer GNN. (2) A geometric featurizer is used to initialize the geometric node feature and edge features. (3) We propose the block graph attention layer, based on which we build the block graph neural network to learn expressive block representations. (4) Finally, we show that the UniIF can achieve competitive results on diverse tasks, ranging from protein design, RNA design and material design.We introduce the block graph to represent all types of molecules, where the key insight is to transform irregular set of atoms (varying size) as regular block representation (fixed size). Atom-based Block Representation.P ! O5 ! C5 ! C4 ! O4 ! C1 ! C2 ! C3 ! Base O3 ! O2 ! O3 !"# P !$#A block B = {(x i , z i )} |B| i=1 contains a set of atoms {x i , z i } |B| i=1, where x i ∈ R 3 and z i ∈ R d represent the equivariant coordinate and invariant features, such as the atom type. The common block types include amino acids, nucleotides, and atoms, which are represented as B f old , B rna , and B smol , respectively. Formally, we write B f old = {(x i , z i )} i∈V f old and B rna = {(x i , z i )} i∈V rna , where V f old = {N, C1, C2, O} and V rna = {P, C5, C4, C3, C2, C1, O5, O4, O3, O2} are the sets of atoms for amino acids and nucleotides, respectively. For small molecules, each atom a represents a block B smol = {(x a , z a )}, where 1 ≤ a ≤ 118. As the block size |B| varies for different types of blocks, the atom-based blocks representation could not directly be applied for unified modeling. Frame-based Block Representation. We introduce frame-based block representation to unify the modeling of all molecules. A block B = (F, f ) contains the equivariant frame F and invariant feature vector f ∈ R d . The local frame F (R, t) contains the axis matrix R = [e 1 , e 2 , e 3 , • • • , e u ] and translation vector t. We set t as the coordinate of the representative atom, i.e., C1 of macromolecules and the atom itself of small molecules. Following AlphaFold2, we consider the special case that R ∈ R 3,3 is orthogonal. However, additional experiments show that the model can also work well with non-orthogonal axis matrix. For macromolecules, the axis matrix R is predefined based on amino acids and nucleotides, while for small molecules, we learn the axis matrix R as it does not have prior common structure patterns. The frame-based block representation decouples geometric information: (1) the local frame basis describe the equivariant pose; (2) the invariant feature vector could embed the atom type and invariant local structure patterns for different tasks. More importantly, the dimension of the frame-based block representation is fixed, which is beneficial for the unified modeling; we build block features in Sec. 3.3.Frame-based Block Graph. Given a molecule M = {B s } n s=1 containing n blocks, we build the block graph G({B s } n s=1 , E) using kNN algorithm. In the block graph, the s-th node is represented as B s = (F s , f s ), and the edge between (s, t) is represented as B st = (F st , f st ). The relative frame is defined as [22, 10, 27] , we modify PiFold featurizer to initialize the geometric node feature f s and edge feature f s,t ; refer to Sec. 3.3.F st = F -1 s • F t . Inspired byRelation to Other Methods. The frame-based block is a generalized data form of AlphaFold2 and other methods. If R is required to be a rotation matrix, the frame-based block is equivalent to AlphaFold2's local frame; otherwise, it is equivalent to represent the atom as invariant feature h and equivalent vector x, similar to GVP [21] and DimeNet [12] .Learning Local Frame. For small molecules, there is no predefined local frame, and we need to learn the local frame for each atom. Given the the molecule M = {(x s , z s )} |M| s=1 , we use a 1-layer of GNN to initialize the atom representation{z s } |M| s=1 ← BlockGAT({x s , z s } |M| s=1 ), where the inital local frames are T (I, 0). The rotation vector r s of the s-th atom is constructed by message passing:EQUATIONN s is the s-th atom's neighbor system. Let the direction (r x , r y , r z ) = rs ||rs|| and magnitude θ = ||r s || represent the rotation axis and angle, we compute the quanternion q s and rotation matrix R s :EQUATIONFinally, the local frame of the s-th atom is T s (R s , t s ), where t s is the atom coordinate. Experiments show that learning rotation vectors consistently outperforms learning Schmidt-orthogonalized axises.Node Geometric Feature. The invariant block feature captures the atom type and the local structure:     z pos i = R T s (x i -t s ) = F -1 s • x i Equivalent to invariant features, local structure f s = 1 |B s | i∈Bs MLP(z i , z pos i )Pooling atom features as block features, embed atom typeThe inverse frame operation T -1 s project the equivalent global coordinates to the invariant local coordinate, i.e.,x local = F -1 s • x global = R T s (x global -t s ).We use MLP to embed atom type and local coordinates. All atom features in the same block are pooled to get the block feature f s .Edge Geometric Feature. We initialize pairwise features following the principle that Edge features capture the directed 3D interactions.Instead of using mutually constructed distance and angle features, we concatenate the local coordinates of two blocks to fully describe their 3D positions. Given B s and B t with global coordinate matrices as X s ∈ R |vs|,3 and X t ∈ R |vt|,3 , the invariant edge features following s ← t direction isEQUATIONwhereT -1 s = (R T s , -R T s t s )projects equivariant global coordinates to invariant local coordinates. Frame-based SE-(3) Module Design. Given the geometric transformation y = W x, we decompose W = R t ΣR T s using SVD and explain y = R t ΣR T s x as:1. Projecting x as the local coordinate x local using the frame F s (R s , 0), i.e., x local = R T s x. 2. Updating local coordinates via gated attention, i.e., x local ← Σx local .3. Translating x local as the global coordinate using frame T t (R t , 0), i.e., y = R t x local .If we parameterize Σy as f θ (y), and considers the effects of translation, i.e., T s (R s , t s ), T t (R t , t t ), the general principle of designing SE-(3) networks could be:   ẑ = R -1 s (x -t s ) = T -1 s • x Equivalent to invariant ẑ ← f θ ( ẑ) Invariant update, one can use GNN or Transformer x = R t ŷ + t t = T t • ẑ Invariant to equivalent (5)The well-known AlphaFold actually follows such a design, where they parameterize f θ as the IPA module. In this work, we replace f θ with an enhanced graph neural network:EQUATIONwheref (l) s and f (l)st represent the input node and edge features of the l-th layer. In Fig. 5 , we show the design of the Block Graph Attention Module, consisting of three components: (1) geometric interaction extractor, (2) virtual block for long-term dependencies, and (3) the edge attention mechanism. We show the detailed design of the Block Graph Attention Module in the following sections.Long-term Dependency via Virtual Blocks. The GNN is criticized by local receptive field, yielding the problem of over-smoothing and over-squashing [2, 5, 29, 13] . Transformers overcome these problems using direct paths between distant nodes, while suffering from the O(n 2 ) computing cost. We introduce n ′ virtual blocks {B i } n+n ′ i=n as information agents for a graph. Each virtual block directly connects to all the real blocks, resulting in (2 • n • n ′ ) additional directed edges. As n ′ ≪ n, we claim that the computing cost is close to original GNN. All the virtual blocks, i.e.,T n+1 (R ′ , t ′ ), T n+2 (R ′ , t ′ ), • • • , T n+n ′ (R ′ , t ′ ), share the same rotation R ′ and translation t ′ :          X = [x 1 , x 2 , • • • ] All the coordinates of the molecule X T X = U ΛV T SVD R ′ = U V T = [e x , e y , e z ] t ′ = N i=1 xi NCenter of Mass (7) The invariant features of virtual blocks are different, as we hope they learn diverse interactions. We encode the index to initialize block featuresf ′ i = Embedding(i) for i ∈ {1, 2, • • • , n ′ }.Local Position Interaction Dot Product Interaction Geometric Interaction Extractor. We enhance edge features with geometric interactions using the local coordinates of virtual inter-atoms and dot products of virtual intra-atoms. Previous works, such as PiFold [10] , introduced virtual atoms in the featurizer to capture informative side-chain geometry beyond protein backbones, resulting in performance gains. VFN [27] extended this idea by allowing GNN layers to update the virtual atoms. However, these efforts are limited to learning virtual intra-atoms conditioned on node features. Instead, we propose virtual inter-atoms conditioned on edge features, allowing the same node to exhibit different virtual states specified by edges. Additionally, inspired by small molecule modeling, we use the dot product of virtual intra-atoms to capture angle information. We show the geometric interactions in Fig. 6 , and formulate it as:EQUATIONt = MLP(f (l) st ), MLP(f (l) t ) ∈ R m,3 Edge feature ẑ(l) st = (T st • h (l) st )∥h (l) stLocal coordinates of virtual inter-atomsEQUATIONwhereT st = T -1 s • T t = (R -1 s R t , R -1 s (t t -t s )), q st = vec(R st ) ∈ R 9is the flatten rotation matrix of T st , and r st = ||t s -t t || indicates the pairwise distance. All q st , r st an a st are invariant features. We highlight the difference to previous researches in color.Gated Edge Attention. We modify PiFold's GNN to capture the geometric interactions when updating node features. For molecular design tasks, we find that aggregating edge features only leads to consistent performance gains. We understand this phenomenon as the model can pay more attention on learning 3D interactions under such a model design. In addition, we use a gated mechanism to control how the edge features are injected to node features. The gated edge attention module is:               w st = AttMLP(f (l) s ||f (l) st ||f (l) t ) a st = exp wst k∈Ns exp w sk h (l) t = EdgeMLP(f (l) st ) Only conditiond on edge ∆f (l) s = t∈Ns a st h (l) t f (l+1) s = f (l) s + σ(MLP(∆f (l) s )) ⊙ ∆f (l) sUpdate node feature via forget gate (9) where ⊙ is element-wise product operation, and σ(•) is the sigmoid function. We highlight the difference between PiGNN and the proposed module in color.FFN & Edge Updating. Analogous to the transformer model, the FFN is a MLP. The edge updating layer remains the same as PiFold:EQUATIONThe proposed module could be equivalently implemented as a transformer module using matrix multplication. However, we find that padding proteins to the maximum length would grealy increase the computing cost in both GPU occupancy and runtime; We suggest using GNN without padding.Regularization. We find that the proposed model fit training data better than PiFold and more likely to suffer from overfitting. To address this issue, we randomly drop out the nodes/edges with a probability of p to prevent overfitting. We find that controlling the dropout rate could result in models with different fitting abilities. The best performance is achieved when p = 0.05.Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? Answer: [NA]Answer: [No] Justification: The code will be released upon acceptance.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 
experiments: 
 We show the effectiveness of UniIF via multiple inverse folding tasks and ablation studies. We briefly introduce molecular design tasks as follows:• Protein Design (T1): Designing protein sequences folding into the target structure.• RNA Design (T2): Designing RNA sequences folding into the target structure.• Material Design (T3): Discoverying stable composition from a known material structure.Task Description Protein design aims to design protein sequences that fold into target structures. Given a protein backbone structureX = {X i ∈ R m,3 : 1 ≤ i ≤ n},where m is the maximum number of points belonging to the i-th residue, n is the number of residues and the natural proteins are composed by 20 types of amino acids, the goal is to learn a function F θ :EQUATIONThe parameters θ are learned by minimizing the cross-entropy loss, i.e., L(F θ (X ), S) = -n i=1 log s i p(ŝ i |X , θ). The task is challenging due to the combinatorial search space of amino acids and the complex relationship between sequence and structure.Settings We evaluate of UniIF on the CATH4.3 dataset [30] following prior works [11, 8] . The dataset is split by the CATH topology classification code, yielding 16,631 training, 1,516 validation, and 1,864 testing samples. To assess generalization, we adopt a time-split strategy, considering the use of pretrained ESM2 models by some baselines, which risk data leakage. The time-split evaluation assigns data before a specific date to the training set and data after that date to the test set. For structural time-split evaluation, we use the CASP15 dataset [11] , containing novel crystal structures not seen during training. For sequence time-split evaluation, we use the NovelPro dataset [8] , which includes 76 protein sequences released within 30 days before November 23, 2023, with structures predicted by AlphaFold2. UniIF consists of 10 layers of BlockGAT with a hidden dimension of 128. It is trained using the Adam optimizer with a learning rate of 1e-3 and a batch size of 8 for 50 epochs.We report the median recovery rate of the top-1 predicted sequences, representing the percentage of correctly predicted residues. The ESM2-free baselines include StructGNN [19] , GraphTrans [19] , GCA [33] , GVP [21] , AlphaDesign [9] , ProteinMPNN [4] , and PiFold [10] . The ESM2-based baselines include LMDesign [17] and KWDesign [8] . While we prefer open-source baselines, we also re-implement VFN [27] for a comprehensive comparison.We provide results under different settings (with and without ESM2) and across diverse datasets (CATH4.3, CASP, NovelPro). Using a pure inverse folding model without ESM2, UniIF achieves the best performance on all datasets, demonstrating its effectiveness. Notably, UniIF outperforms the strong baseline PiFold with fewer learnable parameters. In time-split evaluations, UniIF surpasses all baselines, including ESM2-based methods, by a significant margin. On NovelPro, which features novel sequences, UniIF outperforms LMDesign and KWDesign that use ESM2 for sequence refinement. This indicates UniIF's superior generalizability, crucial for real-world means that we replace the geometric interaction operation with VFN's operation [27] . "-GDP" means that we remove the geometric dot product features. "-EAttn" means that we replace the gated edge attention with PiGNN's attention module [10] . "-VFrame" means that we remove the global virtual frames.applications. Ablation studies show that the proposed geometric featurizer, gated edge attention, and global virtual frame enhance performance. On CATH4.3, the overall improvement is slight due to strong baselines, but time-split evaluation highlights UniIF's superiority in generalization.Task Description Similar to protein design, RNA design aims to design RNA sequences that fold into target structures. Specially, previous work [34] use the RNA secondary structure as additional input to guide the design process, since the tertiary structure is limited. In this work, we only use the tertiary structures as input for the reason of unification, which is more challenging than the baselines.We conduct experiments RNA on the dataset collected by RDesign [34] , consisting of 2218 RNA tertiary structures, which are divided into training (1774 structures), testing (223 structures), and validation (221 structures) sets based on their structural similarity. Following RDesign's benchmark, baseline methods include SeqRNN, SeqLSTM, StructMLP, StructGNN, and StructGNN, GraphTrans [19] , PiFold [10] and RDesign [34] . Given the small number of data samples, we report the median recovery and its standard deviation for theree independent runs. Conclusion As shown in Table 2 , UniIF achieves the best performance in all cases. The improvement is significant, as previous strong baselines like PiFold only excelled in protein design. To our knowledge, UniIF is the first model to achieve state-of-the-art performance in both protein and RNA design tasks, demonstrating its versatility and effectiveness. Compared to RDesign, which uses additional secondary structure features, UniIF relies solely on tertiary structure input and still performs better. UniIF successfully unifies the protein and RNA design processes, paving the way for a unified inverse folding model for protein-RNA complexes in future developments.Task Description Discovering stable atom compositions from known material structures is crucial for new material discovery [28, 26, 14] . This task is challenging due to the large composition space and the lack of large-scale data. Thanks to recent benchmark efforts [6] , we can evaluate the performance of UniIF on this novel task.Method Rec % ↑ Random 1.6±0.0 GCN [23] 49.6±0.1 PMLP [39] 46.1±0.0 GraphSAGE [15] 49.1±0.4 GAT [35] 46.1±0.0 GraphUNet [7] 55.2±7.9 GIN [38] 58.7±0.2 EdgeCNN [37] 63.2±0.9 UniIF (ours) 75.3±1.2 -frame 54.9±2.8 -quat 65.2±3.9Table 3 : CHILI-3K Results.Datasets & Baselines We evaluated UniIF on the CHILI-3K dataset [6] , which consists of nanomaterial graphs derived from mono-metal oxides. The dataset includes 53 metallic elements and one non-metallic element (oxygen), comprising 3,180 graphs, 6,959,085 nodes, and 49,624,440 edges. Following the official benchmark, the dataset is randomly split into training (80%), validation (10%), and testing (10%) sets. Baselines include GCN [23] , PMLP [39] , GraphSAGE [15] , GAT [35] , GraphUNet [7] , GIN [38] ,and EdgeCNN [37] . Experiments are repeated three times with different seeds, using early stopping with a patience of 50 epochs, and trained up to 1000 epochs.In Table 3 , UniIF outperforms all baselines by a large margin. Ablation studies demonstrate the crucial role of the learned local frame in enhancing interaction feature extraction. In addition, how to learn the local frame is also important. In the "-quat" ablation, we try to learn the x, y, and z axes with Householder orthogonalization directly, but found it less effective, with the recovery rate dropping from 75.3% to 65.2%. This highlights the value of the proposed local frame learning mechanism.In Fig. 7 , we show the designed protein and RNA sequences.In addition, we use AlphaFold3 [1] to re-fold the designed sequences into structures. The ground truth (gray), PiFold (green), and UniIF (pink) structures are alinged and compared. We observe that UniIF improves both the recovery and RMSD of the designed protein and RNA, demonstrating its effectiveness in inverse folding tasks.  
conclusion: 
 We propose the first unified model, dubbled UniIF, for general molecule inverse folding. The key points include unifying the data representation, the featurizer and the model architecture without a drop in performance. Extensive experiments show that UniIF surpasses baseline methods on all tasks. Ablation studies reveal that the geometric interaction extractor, gated edge attention, and virtual long-term dependency modules contribute to performance gains. We believe that the proposed model can benefit multiple domains, such as machine learning, drug design, and material design. 
experimental setting/details: 
 Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes] Justification: We have provided such information in the experimental section.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [Yes]Justification: We provided the standard deviation in the RNA design and material design tasks.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors).• It should be clear whether the error bar is the standard deviation or the standard error of the mean. Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [NA]Justification:Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification:Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. 
 
 Appendix:  


Decision: This paper considers the problem of inverse folding, which is the design of a chemical (such as a small molecule or a protein) to conform to a given 3D structure. Traditionally, the modelling approach used for this task would depend on whether the object to be designed is a small molecule, protein, or material; here the authors propose the UniIF architecture, which shows competitive results on any of the subdomains of inverse folding.

After mixed initial reviewers, some of the reviewers increased their ratings after author rebuttal, with three in favour of accepting the paper, and one leaning towards rejection. Generally, most reviewers agreed that the paper is interesting, well-written, and relatively novel. They enjoyed the model unification idea, although questioned to what extent it is a useful contribution, given that (as shown by the authors during rebuttal) there seems to be no positive transfer between the domains, and best results are achieved by training UniIF for each task separately. The reviewers also discussed the strength of the empirical results, noting that (a) protein design tasks investigated in this work seem close to saturated, and (b) employed materials design tasks are somewhat uncommon and the results are harder to contextualize due to the choice of baselines. Reviewers continued discussing during the private discussion period, debating whether improvements on top of prior work are clear enough, and whether unification without positive transfer is useful in itself. They noted wetlab results could be a potential way to increase the impact of this work, although they agreed this would not be required for acceptance at NeurIPS. During this phase, two of the positive reviewers decided to lower their scores to borderline accept.

After all of the discussion, the paper ended up with exclusively borderline ratings, albeit not due to lack of opinion on the side of the reviewers, and rather them carefully weighing the pros and cons of this work. On the positive side, it is clear that UniIF is an interesting architecture, and while no advantage from co-training on multiple modalities was observed so far, it could encourage downstream work to investigate this idea further, potentially moving towards a “foundation model” for science. Due to this potential, and generally promising performance, I am willing to lean into the positive aspects of this work and support its acceptance despite borderline ratings. I would encourage the authors to carefully consider the feedback from the reviewers and include relevant discussion in the final version of their paper; in particular, I would recommend highlighting the lack of positive transfer between domains as an avenue for future work.

Reviews: review: paper_summary: paper_summary: This paper addresses the challenge of inverse folding, i.e. the design of novel molecules or macromolecules with specific desired 3D structure, with the goal of improving real-world drug and material design. The authors point out that this challenge has been addressed independently for different contexts, such as inverse folding for small molecules vs inverse folding for large macromolecules. They argue that this has resulted in redundant efforts. To address this issue, they propose a unified model for the inverse folding of all molecules. They demonstrate the efficacy of their novel unified approach across three benchmark molecular design tasks involving protein, RNA and material design.
strength_weakness: strength_weakness: While the unified approach is elegant, it is not clear (and the authors do not assert) that the unification is responsible for any performance improvements. However, it is easy for the reader to be left with the impression that the improved results stem from unification. The authors should make it clear that either (i) unification is satisfying but is not connected to performance improvements, or (ii) unification leads to performance improvements and explain clearly the data supporting this. 

The recovery metric is confusing, since it is not clear that higher recovery actually corresponds to the ability to design novel molecules. Indeed, the recovery metric penalizes the model for novelty, which seems to contradict the stated goal ('enabling scientists to synthesize novel molecules with the desired structure'). This undermines the claim that the approach presented in the paper 'can benefit multiple domains, such as machine learning, drug design, and material design'. Specifically, rediscovering existing macromolecules does not benefit these domains. 

Moreover, even if the metric were aligned with the stated goals, it is not clear to this reviewer that existing inverse folding methods are not good enough to solve any real world application of inverse folding such as the stated goals described in the introduction to this paper of improvements in drug and material design. This leads me to wonder what problem this paper is trying to solve.

While the paper focuses on maintaining the structure of the target molecules (or material), no attempt is made to ensure that the function is maintained. This does not bode well for applications such as drug design, that require that the designed molecule functions correctly. 

The paper does not include any wetlab experiments, instead relying on performance at benchmark tasks to demonstrate improved performance. The authors argue that this is the only limitation of this paper, and that wetlab experiments are by definition out of scope for an AI paper. This raises the question of whether improvements on the benchmark tasks and associated metrics used in this paper corresponds to progress on the stated goals of the paper.
questions: questions: In the absence of wetlab experiments, please could the authors address this limitation by providing data that demonstrates that improved performance at the specific benchmark tasks in inverse folding cited in this paper results in improved performance at novel molecule design. This data can be extracted from previously published work, with appropriate citation. 

There have been a series of recent works presenting improvements at inverse folding. These works, including this paper, make lofty claims about the impact that such improvements will have on drug and material design. Please could the authors point to any realized impact on drug and material design resulting from improvements at inverse folding as measured by performance on these benchmark tasks. 

If such realized impact is difficult to find, please could the authors identify and address this limitation. 

Please could the authors propose strategies to mitigate the risk that further improvements in performance on benchmark tasks, such as the improvements reported in this paper, will not result in realized impact in drug or material design. 

Please could the authors propose strategies to mitigate the risk that the metric used in this work penalizes the model for the design of novel molecules, thereby undermining the stated goals. 

Please could the authors identify a set of real world applications for inverse folding, describing the problem, how inverse folding will contribute to solving this problem, and why existing inverse folding methods are not good enough to solve each specific real world problem identified (NB inferior performance on benchmark tasks does not demonstrate that existing methods are not good enough).

I note that the number of sequences for CATH 4.3 differs from the referenced papers - please could the authors explain this discrepancy. 

For the time split protein tasks, it would be helpful to establish how similar each test sequence is to those used in training, both in terms of proximity in sequence space and in terms of 3D structure. Please then stratify performance as a function of each distance for each held out test set. It would be helpful to also compute these distances for the CATH topology-based split, to provide a watermark for comparison.
limitations: limitations: In addition to the questions above, please could the authors describe limitations of their work that may prevent improvements at inverse design as measured by performance on benchmark tasks using a recovery metric from having impact on real-world challenges such as drug and material design.
paper_summary: paper_summary: Previous approaches on molecule inverse folding (IF), which is crucial for drug and material discovery,  focus separately on either macro-molecules or small molecules, leading to the lack of a unified approach for different molecule types. To this end, the paper proposes UniIF to unify the IF from a data and model perspective. Specifically, by introducing a unified block for processing different molecules and a geometric block to capture their 3D interactions, UniIF shows improvements in various tasks across different molecules.
strength_weakness: strength_weakness: - The ablation experiments in Table 1 (-GDP), which remove the geometric dot product features, show miner drawbacks in proteins with longer sequences. This makes the geometric interaction extractor mainly capture the interaction of the virtual inter-atoms. The idea for capturing long-range dependency or interaction using virtual blocks has been studied in [1,2,3,4]; the authors could consider providing a discussion on how their proposed techniques differ from these referenced works.
- In addition, the UniIF adopted both node and edge feature extractors as feature augmentation, which is model-agnostic. However, the comparison of all three tasks does not show the potential benefit of introducing such a featureizer. 
- The paper could provide further insight into the benefit of employing a unified framework for protein, RNA, and material design. For example, could the UniIF model different molecules in a unified latent space, allowing the researchers to investigate their underlying interactions?

[1] Neural Message Passing for Quantum Chemistry. In ICML, 2017

[2] An analysis of virtual nodes in graph neural networks for link prediction. In LoG, 2022

[3] On the Connection Between MPNN and Graph Transformer. In ICML, 2023.

[4] Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel. In ICLR, 2024.
questions: questions: 1. Could you provide some discussions or experiments on the effectiveness of the proposed featureizer?
2. Is it possible to train UniIF with mixed molecule datasets?
3. For Equation 7, the SVD decomposition could be time-consuming when scaling the input size. Could the author explain the motivation for such a design and why a simple approach, like "mean," does not work?
limitations: limitations: The proposed UniIF offers a unified framework for learning different molecules, such as protein and RNA. However, it still models different molecules individually, hindering the proposed framework's potential impact.
paper_summary: paper_summary: This paper propose a unified framework for inverse folding. Their model is applicable to small molecules, proteins and RNA.
More specifically, they propose a unified frame representation for amino acid, atom and nucleotide. They further propose a GNN-based model to learn the structure information. 
Results show that their model can outperform other baselines in protein design, RNA design and material design.


---

I changed my score to 5 after the discussion with other reviewers and AC.
strength_weakness: strength_weakness: Major points:

1. Some important experimental details are missing. For instance, while the paper proposes a unified inverse folding framework, it's unclear whether the model is trained on a combined dataset from different types of molecules. Specifically, the training sets for RNA design and material design are quite limited. If the model is trained with protein data, it would be beneficial to demonstrate whether incorporating data from other types improves performance.

2. Additionally, if I understand correctly, the paper does not explain the decoder part of the inverse folding model.

Minor points:

1. It would be helpful if the paper included a comparison of perplexity, as related works such as PiFold have used this metric.
   
2. The performance on protein design looks comparable with other models to me.
questions: questions: (1) As illustrated in the previous part, do you train the model on three types of molecules?

(2) What decoder model is used?
limitations: limitations: The limitations are not discussed.
paper_summary: paper_summary: This paper proposes representing molecular systems as blocks of atoms and designs a neural network architecture that processes such representations. The method is applied for benchmark inverse folding tasks for protein/RNA. A materials-related task is also explored.
strength_weakness: strength_weakness: - The protein inverse folding ablation seems to show the various introduced techniques do not influence model performance much. The insights of the models seem obscured from this perspective, especially considering block-based representations and architectures have already been explored in previous works (GET/EPT). The RNA design task does not include ablation, and this reviewer is not convinced by the materials-related task (see below). It is rather unclear what a reader can take away from this work in terms what techniques actually contribute to improved performance.

- If "unified" is the key word of the method, perhaps the authors should include experiments where the model is trained on various data modalities and see if that improves performances on individual tasks.

- The materials sections are rather strange in this paper. Inverse folding for proteins/RNAs can be understood as inferring the sequence from a given structure. The materials task is not introduced in great detail. What is being predicted? How is it "inverse folding?"

- To follow up on that, the baselines that the proposed model is compared against are not what's considered state-of-the-art in materials representation. For materials, there are popular benchmarks such as Matbench (https://matbench.materialsproject.org/), JARVIS (https://pages.nist.gov/jarvis_leaderboard/), or Open catalyst (https://opencatalystproject.org/index.html), where results of SOTA models are readily available. This reviewer is not convinced by the materials-related results presented as significant details regarding the dataset/goals are missing, and the baselines are not really used for materials.
questions: questions: - In the experiments, what exactly does with/without ESM mean? How is ESM used? Why can't the proposed method also become "with ESM"? Why is it valuable to consider "without ESM"? Are models "with ESM" more expensive or what?
- Can the author clarify the materials task and why it is inverse folding? Can the authors compare to materials-focused SOTA methods in the space?
limitations: limitations: The authors did not write about the limitations of the proposed method.

Comments: title: Rebuttal Summary
Thanks for your comments!
Thanks for your reply!
Looking forward to your reply
Thank you
Thank you very much
Thank you
Further clarifications
Author Rebuttal
comment: We thank the reviewers for their insightful and constructive reviews of our manuscript. We are encouraged to hear that the reviewers found the unified framework is **interesting and novel** (Reviewer r3pY,Aoua,kcUc,m3n9), the paper is **well written** (Reviewer Aoua,kcUc) and the proposed **method is effective** (Reviewer r3pY, Aoua, kcUc, m3n9). They think the **method is elegant** (Reviewer r3pY, Aoua, kcUc, m3n9), and extensive experiments have been conducted to provide justification for the **effectiveness** of the proposed method (Reviewer r3pY, Aoua, kcUc, m3n9). During rebuttal, we tried our best to address each reviewer’s concerns point by point, and received major positive comments:
- Reviewer r3pY: I like the idea of a Unified framework across these different tasks but not sure whether individual tasks benefit from training on the datasets for the other tasks.
- Reviewer Aoua: I retain my score (weak accept) considering the contribution of the submission.
- Reviewer kcUc: Thanks for your reply. I have no further comments. (weak accept)
- Reviewer m3n9: There are some new ideas in the paper and the performance metrics seem to outperform existing works.  The reviewer increases the score from 4 to 5 (borderline accept).


We thank all reviewers again for all the efforts that help us improve the manuscript. In case our answers have justifiably addressed your concerns, we respectfully hope that you can increase your score to support the acceptance of our work.

========================================================================


Regarding the remaning question raised by reviewer r3pY, that is "whether individual tasks benefit from training on the datasets for the other tasks", the answer is no. For example, we have tried to train UniIF in mixed protein and RNA dataset, which achieve slightly lower performance than training on single dataset. However, we would like to highlight the merits of the unified framework:

1. One can train UniIF model on different molecules in a unified latent space, allowing the researchers to investigate their underlying interactions, as suggested by reviewer Aoua. Just like what AF3 did, and we will extend this in the future.

2. Currently, UniIF achieves SOTA performance on single tasks, thanks to the carefully model design. 

3. One can take UniIF as the strong baseline and incoorpatate their domain-specific knowledge to further enhance the performance, i.e., adding secondary structure information for RNA design.

We believe that incorporating more specific domain knowledge can lead to a stronger model within its domain. However, the unified approach is elegant, and our method already achieves state-of-the-art performance, suggesting that further integrating domain knowledge could unlock even greater potential of UniIF.
Dear Reviewer r3pY,

Thanks for your review. We have tried our best to address your questions and we respectfully thank you for supporting the acceptance of our work. Also, please let us know if you have any further questions. Look forward to further discussions!

Sincerely,

The Authors
Dear reviewer r3pY,

Thank you once again for your reply! We agree with you that AI researchers should consider reaching out to potential collaborators from other fields, particularly those already equipped with funding, equipment etc. We are also looking for such opportunities.

We're glad to hear that you appreciate the unified framework and that we have the chance to clarify your question regarding whether individual tasks benefit from training on datasets for other tasks.

> The answer is no, based on our experiments. But our method already achieves SOTA performance on each single task.

For example, we attempted to train UniIF on a mixed dataset of proteins and RNA, which resulted in slightly lower performance compared to training on a single dataset. However, we would like to emphasize the benefits of the unified framework:

- UniIF can be trained on different molecules within a unified latent space, allowing researchers to explore underlying interactions—similar to what AF3 accomplished. We plan to  extend this in the future.

- UniIF currently achieves state-of-the-art  performance on individual tasks, thanks to the careful design of the model, including  the interaction operator, GNN layer, and virtual frame. To evaluate the effectiveness of UniIF, we also provide the ablation results of RNA design. The performance gain obtained by virtual frame (VFrame) and geometric dot product (GDP) is more significant in RNA dataset. This is because the protein design performance has reached a bottleneck stage where any improvement is difficult. Things will be more clear on RNA dataset.  Here is the RNA ablation results:

>| model      | short | medium | long  | all   |
>|------------|-------|--------|-------|-------|
>| w/o VFrame | 44.44 | 49.25  | 37.40 | 45.45 |
>| w/o EAttn  | 47.89 | 49.00  | 36.71 | 48.28 |
>| w/o GDP    | 46.88 | 48.00  | 37.19 | 47.06 |
>| UniIF      | 48.21 | 49.66  | 37.29 | 48.94 |



- UniIF can serve as a strong baseline that can be further enhanced by incorporating domain-specific knowledge, such as adding secondary structure information for RNA design. That is, individual tasks can be enhanced by adding domain-specific knowledge to UniIF, although UniIF has already achieved SOTA performance.

We sincerely hope this could clarify  your concerns, and we would be happy to answer any additional questions. If we have adequately addressed your concerns, we kindly hope that you consider raising the score to support acceptance. Your comment and suggestion are important and valuable for us. Thank you.

Best,

Authors.
Thank you for the considered response to my review. I fully agree with the authors that the lack of well curated datasets that would allow AI researchers to address key issues in this domain is a significant issue. 

I also fully agree with the authors that AI researchers should collaborate with bio-labs to validate their algorithm, and increase their impact on the field - indeed carrying out wetlab experiments is not simply a matter of getting funding and equipment, there is significant technical expertise and experience required, so I would not suggest that AI researchers try setting up experiments from scratch.

Navigating collaborations with bio-labs is crucial to achieving significant impact, and I urge these authors to consider reaching out to potential collaborators from other fields, particularly those already equipped with funding, equipment etc. 

More generally, while I like the idea of a Unified framework across these different tasks, it still remains unclear to me that the unification itself results in improved performance - i.e. that individual tasks benefit from training on the datasets for the other tasks.
Dear reviewer r3pY,

We express our sincere gratitude for your constructive feedback in the initial review. It is our hope that our responses adequately address your concerns. Your expert insights are invaluable to us in our pursuit of elevating the quality of our work. We are fully aware of the demands on your time and deeply appreciate your dedication and expertise throughout this review.

We eagerly anticipate your additional comments and are committed to promptly addressing any further concerns.

Once again, we extend our heartfelt thanks for your time and effort during the author-reviewer discussion period.

Best,

Authors
Thanks for your review service and appreciation!
Thanks for your response. I retain my score considering the contribution of the submission.
Thanks for your review service and raised score!
Thank you for the response and efforts for the rebuttal. It is challenging for this reviewer to evaluate the performance of the model on the protein/RNA tasks due to lack of experience in these fields, while the materials task is relatively new and not commonly benchmarked. Since there are some new ideas in the paper and the performance metrics seem to outperform existing works, this reviewer would give the benefit of the doubt for a rating increase from 4 to 5, but with a confidence of 1.
Thanks for your review service and good questions. Have a good day!
>> **Reply to W1** In the task of protein design,  GET can achieve 38.3% recovery. This is because GET is designed for protein-molecule interactions learning, and do not responsible for protein design. 

 
Here is the citation of CHILI:

>> [1] Friis-Jensen, Ulrik, et al. "CHILI: Chemically-Informed Large-scale Inorganic Nanomaterials Dataset for Advancing Graph Machine Learning." arXiv preprint arXiv:2402.13221 (2024).
Thanks for your reply. I have no further comments.
> **Q5** Could the authors identify real-world applications for inverse folding, detailing the problem, how inverse folding could help, and why existing methods fall short for each specific application?
>> **R4** If the computing benchmark is not recognized and only wetlab experiments are considered, it becomes difficult for us to explain why existing methods fail in applications due to limitations in money, time, equipment, and experience.  Here are some real-world applications of inverse folding:
- Binding site design[2]: Designing binding sites for small molecules starting from previously characterized designs generated using Rosetta.
- Membrane protein design[6]: Creating soluble and functional analogues of integral membrane proteins uisng AF2+ProteinMPNN.
Inverse folding methods are used for sampling new amino acid sequences for a given fold, where improving the recovery is an important goal in these research. By reducing the temperature, one can balance the recovery and diversity. In comparison, our proposed UniIF could balance recovery and diversity better than baselines. 

> **Q6** I note that the number of sequences for CATH 4.3 differs from the referenced papers - please could the authors explain this discrepancy.
>> **R6** Previously, the protein number of CATH4.3 follows the extual description from ESMIF[7].  However, it was recently discovered that they released a dataset with a different number of proteins than what they described. Hence, we correct the description, but actually use the same dataset as in the baseline.

> **Q7** For the time split protein tasks, it would be helpful to establish how similar each test sequence is to those used in training, both in terms of proximity in sequence space and in terms of 3D structure. Please then stratify performance as a function of each distance for each held out test set. It would be helpful to also compute these distances for the CATH topology-based split, to provide a watermark for comparison.
>> **Q8** There is no way to find the CATH code for novel protein sequences. Following your suggestion, we can provide hirachical performance in terms of sequence and structure similarity using mmseq and foldseek in CASP15 dataset. We found that the sequence similarity positively correlated with the recovery more significantly.

| seq cut |  rec | struct cut |  rec |
|:-------:|:----:|------------|:----:|
|   <0.3   | 0.48 | <0.1        | 0.51 |
|   <0.5   | 0.51 | <0.3        | 0.49 |
|   <0.8   | 0.52 | <0.8        | 0.52 |