PoinnCARE: Hyperbolic Multi-Modal Learning for Enzyme Classification
Authors: Kun XIE
Peng Zhou
Xingyi Zhang
Wei Liu
Peilin Zhao
Sibo Wang
Biaobin Jiang
Venue: ICLR 2026 Poster (2026)
Keywords: EC number prediction
enzyme function
hyperbolic space learning
multi-modal learning
enzyme structure
enzyme active site
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Enzyme Commission (EC) number prediction is vital for elucidating enzyme functions and advancing biotechnology applications. However, current methods struggle to capture the hierarchical relationships among enzymes and often overlook critical structural and active site features. To bridge this gap, we introduce PoinnCARE, a novel framework that jointly encodes and aligns multi-modal data from enzyme sequences, structures, and active sites in hyperbolic space. By integrating graph diffusion and alignment techniques, PoinnCARE mitigates data sparsity and enriches functional representations, while hyperbolic embedding preserves the intrinsic hierarchy of the EC system with theoretical guarantees in low-dimensional spaces. Extensive experiments on four datasets from the CARE benchmark demonstrate that PoinnCARE consistently and significantly outperforms state-of-the-art methods in EC number prediction.

Published as a conference paper at ICLR 2026
POINNCARE: HYPERBOLIC MULTI-MODAL LEARNING FOR ENZYME CLASSIFICATION
Kun ;ie'; Peng Zhou', Xingyi Zhang', Wei Liu', Peilin Zhao Shao"|Sil Sibo Wang Biaobin Jiang" 'Tencent, AI for Life Sciences Lab, Shenzhen, China;
Huuna University, Changsha, China;
MMBZUA,, Masdar City, Abu Dhabi, UAE;
*Shanghai Jiao Tong University, Shanghai, China;
'The Chinese University of Hong Kong, Hong Kong
gennyxie@tencent. com, zhoup 1 3660 foxmail.com.
xingyi zhangembzuai. ac ae, Eopliuêtencent com, peilinzhaods edu. cn, swangêse cuhk. edu. hk,
ABSTRACT
Enzyme Commission (EC) number prediction is vital for elucidating enzyme fune- tions and ad advancing biotechnology applications. However, current methods struggle to capture the hierarchical relationships among enzymes and often overlook critical structural and active site features. To bridge this gap, we introduce PoinnCARE]] novel framework that jointly encodes and aligns multi-modal data from enzyme sequences, structures, and active sites in hyperbolic space. By integrating graph dif- fusion and alignment techniques, PoinnCARE mitigates data sparsity and enriches functional representations, while hyperbolic embedding preserves the intrinsic hierarchy of the EC system with theoretical guarantees in low-dimensional spaces. Extensive experiments on four datasets from the CARE benchmark demonstrate that PoinnCARE. consistently and significantly outperforms state-of-the-arr meth- ods in EC number prediction.
INTRODUCTION
Enzymes are fundamental biological catalysts that drive nearly all biochemical reactions essential for life (Berg) 2022 van Beilen and Li 2002). and they underpin a wide range of industrial applications,
including pharmaccutical synthesis Karan et al. 2012;) Nandanwar et al. 2020), food processing (Ku- mar et al. 2024 Kumari et al. 2021), and environmental cleaning (Gupta al. 2002. Kumari et al. 2019). Central to understanding and harnessing enzyme function is the Engyme Commission (EC)
number system (Kraut 1988 Copeland 2023). which hierarchically classifies enzymes based on the chemical reactions they catalyze. Each EC number is a four-digit code, progressing from broad functional classes (1st digit) to highly specific activities (4th digit). For example, illustrated in Fig. T the enzyme with EC number 3.111 catalyzes the hydrolysis of DNA, producing fragments with defined chemical groups at their termini. Accurate EC number prediction not only facilitates the annotation of newly discovered proteins but also enables the exploration of the vast and largely uncharacterized protein universe.
Despite recent advances YYnng et al. 2024a Yu et al. 2023), existing computational approaches for EC number prediction face two major limitations. First, most methods either ignore or inadequately model the intrinsic hierarchical structure of the EC taxonomy. typically representing enzymes in Fuclidean space (Li et al.) 2018 Ryu et al. 2019 Sanderson al. (023).. As shown in Fig. 2 (left), the F.C. system forms a tree-like hierarchy, which is theoretically diffiult to embed in Fuclidean space without significant distortion or high- high-dimensional overhead, limiting prediction accuracy. Second, current methods predominantly rely on sequence alignment (Stephen 1990), overlooking critical structural and active site information that fundamentally determines enzymatic specificity and
"Work done while the author was PhD student CUHK and research intern Tencent. CCoresponding authors.
Code is available httpt::t/////// pettps://githee wttp:tttwwwcccccctttotoeote i nnCARK

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Substrate
Encyme-subsirate subsirule
Products
level 1
16 1I =
complex
level
|6=²]|
Active
level
16 - 245
lovel
[ 4963
Enzyane
Enzyme
Figure 2: The tree structure of the EC system (left) and the catalytic mechanism of enzymes (right),
function. As depicted in Fig. (right), enzyme catalysis depends on the precise liceedimmnnionnll arrangement of active site residues, which govern substrate binding and reaction specificity (Riziotis)
ct al. 2025). Ignoring these modalities obscures the full complexity of enzyme function.
To address these challenges, we propose PoinnCARE framework that integrates multi-modal information from protein sequences, structures, and active sites, and projects them into hyperbolic space. We augment the CARE benchmark (Yang et al. 2024a) with comprehensive structural and active site an- notations. While most enzymes can be assigned structures via experimental data or AlphaFoldd/ESMMFol predictions, experi- mentally validated active site annotations are available for only small subset, leading to modality imbalance. To overcome this, PoinnCARE constructs pairwise similarity graphs for struc- ture and active site modalities, leveraging intra-modality graph
Active site
P49183 in UniProt with EC 3.1.1.11
EC3:: Hydrolases
3.1:1: Acting on ester bonds
FC 3.121 Fndivdosynhommlleess producing S-
plosphonsnoesles
EC 3.1.211111 deoxynibomullusse
Figure 1: An example enzyme.
diffusion and inter-modality dual-graph alignment to alleviate annotation sparsity and bridge modality gaps. These graph representations are then projected into hyperbolic space to preserve the hierarchical relationships of the EC system. Our analysis shows that hyperbolic embeddings represent tree-like structures with lower distortion and in fewer dimensions than Euclidean approaches, while yielding better accuracy. Finally, comprehensive experiments on four test sets in the CARE benchmark (Yang) ctt al. 2024a) show that PoinnCARE consistently outperforms sfate-of-the-art methods.
In summary, the main contributions of our work include:
We augment the CARE benchmark with comprehensive structural and active site information, enabling richer multi-modal learning for enzyme function prediction.
We construct similarity graphs and use graph diffusion to address annotation sparsity and enhance functional representation.
We introduce a hyperbolic multi-modality encoding and alignment mechanism, which preserves the hierarchical relationships of the EC system with low distortion.
We demonstrate, through extensive experiments, that PoinnCARE achieves state-of-the-ar perfor- mance on four challenging EC number prediction benchmarks.
RELATED WORK
Enzyme function prediction. Historically, sequence similarity has been the foundation for protein function annotation (Finn et al. 2015), with BLAST (Stephen 1990) serving primary tool for similarity searches. With the advancement of machine learning (ML), several methods have been proposed leverage traditional MI technologies, such as SVM (Chang and Lin 2011]. CNN (Li
et al. 2021), and ResNet (He et al. 2015)), to enhance the accuracy of enzyme function annotation
2023). The contrastive framework was first utilized to enhance enzyme function prediction performance in CLEAN (Yu et al., 2023). Specifically, triplet margin loss was employed to minimize distances between positive samples while maximizing distances between negative samples. Building on this simple yet powerful framework. CLEAN-Concal (Yang et al.] (024c) integrated structural information by using ResNet (He et al.) 2015) to encode protein contact maps. Subsequently, several methods were introduced to augment this contrastive paradigm, including HiFi-NN (Ayres et al. 2023), FEDKEA (Zheng et al. 2024).
2018 Ryu et al. 2019; Dalkiran et al. 20188] (Snndesson
Muuti-moodl learning with Poincaré model-based hyperholic graph neural networks for enzyme function prediction CARE (Yang al. 2024a) henchmark.
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EnzHier (Duan al. 2024). and Yim et al.'s approach (Yim et al. 2024). by improving positive and negative sampling strategies based on the hierarchical characteristics of EC numbers. Recent approaches have expanded beyond protein sequences to improve the enzyme function classification results. To be specific, Top-EC (van der Weg et al. 2025) integrates enzyme structure information with 3D graph neural network, learning from interplay between biochemical features and local shape-dependent features. ProteinF3S (Yuan et al. (025) consolidates sequence, structure, and surface information through a two-phase fusion strategy. Despite these advances, existing methods fail to comprehensively utilize critical information that directly determines the catalytic functions, such as active sites. These limitations motivate us explore a novel approach incorporating multi- modal information for enhanced EC number prediction.
Hyperbolic representation learning. Hyperbolic geometry, characterized by negative curvature, exhibits exponential volume growth that naturally accommodates hierarchical structure and entailment relations, and thus has been successfully adopted across various domains, including computer vision Liu et al. (2020); Desai al. (202)), natural language processing Xiong et al. (0022); Yang ct al. 2024b), and graph-based tasks Sun et al. (00TT) Bai et al. (2023).
In terms of the biological domain, many studies have extensively validated the superiority of hyper- bolic geometry in capturing the latent hierarchical structures of biological data, successfully applying it to Gene Ontology representation Kim et al. (202T), cell lineage inference Tian et al. (2023), , genomic sequence modeling Khan et al. (2025). taxonomic classification Gong et al. (2025). and protein-ligand binding Wang et al. (2025). These works collectively demonstrate that hyperbolic embeddings offer more geometry-awan inductive bias than Euclidean approaches for modeling complex evolutionary and functional relationships. However, despite the evident hierarchical structure inherent in EC num- bers, existing computational approaches heavily rely on traditional Euclidean space representations for EC number prediction, highlighting significant gap the field and inspiring our effort to embed enzymes, along with the rich associated information, within hyperbolic space.
PRELIMINARIES
3.1 PROBLEM FORMULATION
Let y denote the set of EC numbers, where each element of E y represents the i-th EC number at hierarchical level E {0, 1, 1,2, 4). Here, y serves as a virtual root node, acting as the common ancestor of all EC numbers. To capture hicrarchical relationships among EC numbers, we establish edges (u'- yj between nodes that share the same prefix, representing parent-child relationships. The virtual root yd connects to all first-level EC numbers y¹. With edge set g((), the hierarchical structure of the EC number system forms a tree T = (Y, g()) as illustrated in Fig. (left)
For any enzyme x E X, we represent its multi-modal information as a tuple (yo, 82, az), corre- sponding to sequence, structure, and active site features, respectively. EC number prediction aims to learn a classifier f(.) : X + y mapping enzymes to their corresponding EC numbers. Importantly, since individual enzymes can catalyze multiple reactions associated with different EC numbers, this prediction task is inherently a multi-class, multi-label classification problem.
3.2 HYPERBOLIC SPACE
Hyperbolic space represents a class of Riemannian manifolds characterized by its constant negative sectional curvature (Grigor' yan and Noguchi 1998, Dong et al.) (025). Following previous stud- ies (Ganea et al. 2018 Yue et al. 2023] Zhang et al. 2021c), we elaborate on our method based on the Poincaré ball model. Specifically, an n-dimension Poincaré ball model with constant negative curvature x(x < 0) can be denoted as (B%. got where E = {a E [d]| < <1/kk} represents an open ball, - 4/(1 x||==||))2/ is the Riemannian metric tensor, and || denotes the Euclidean
norm. Equipped with this metric tensor, the induced distance between u, v E B% is denoted as:
which changes smoothly w.r.t the positions of and v. This locality property of the hyperbolic distance is key for embedding hierarchical topologies. More details provided in Appendix A.T
d(u, v) arcosh(1 [I+x|]u][")[[xx][]))))
2=][==v/||
Vln
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3.3 TRKE-LIKE RELATIONSHIPS AMONG ENZYMES
Unlike conventional flat classification with independent categories, the tree-structured EC system naturally endows enzymes with intrinsic hierarchical relationships. By connecting each enzyme to its corresponding EC number node v E y/ these inherent hierarchical relationships can be quantitatively characterized through Gromov's 's 5-hyperbolicity (Bridson and Haefliger 2013 Gromov (987). as shown in Table The EC system topology exhibits strong hyperbolic characteristics with value close to zero, in contrast to random topologies. The computation of 8 ô-hyperbolicity is detailed in Appendix A.2
Embedding this tree-like structure into Euclidean space poses fundamental challenges. In tree structure, the number of nodes grows exponentially with depth, while the volume of an n-dimensional Euclidean ball only grows proportionally to the n-th power of its radius. This inherent mismatch between growth rates implies that accurate tree embedding in Euclidean space necessitates high dimensions, with limited dimensions resulting in significant distortion. In contrast, the volume of ball hyperbolic space grows exponentially with its radius, offering natural geometric framework for embedding tree structures with faithful embeddings. An
Table ò-hyperbolicity.
EC
Random
Training set
0.01
0.92
Test set
0.00
0.73
illustrative example is presented in Appendix A.3 A.33 fundamental difference:
The following theorem formally establishes this
Theorem Let T be tree with nodes and dr be the associated tree distance. Then:
(T, dr) can be embedded in Ollogn) dimensional Euclidean space with O(log n) distortion (Bour gain 1983).
(T, dr) can be embedded in hyperbolic space with dimension 2 2 with 1 + distortion, where can be arbitrarily small (Sarkar 2017
4 METHOD: POINNCARE
In this section, we present PoinnCARE, a novel hyperbolic space-based multi-modal learning framework for EC number prediction. We first augment single-modality benchmarks with critical structural and active site information (S) Next, we propose a graph diffusion-enhancee topology modeling approach capture modality similarity relationships (Sec|4.2). Finally, we encode dual similarity graphs in hyperbolic space, preserving inherent hicrarchical enzyme relationships while capturing rross-modal semantic correlations through inter-modality alignment (Sec 4.3
4.1 MOLTI-MODAL DATASET CURATION
As shown in Fig. (right), the structure and active sites of enzymes directly involved in catalytic specificity determination, and thus are crucial for understanding enzyme catalytic mechanisms (Rizi) otis al. 2025). However, the existing benchmark CARE (Yang al. 2024a contains only sequence information, which is insufficient and indirect for enzyme function inference. Therefore, we supplement the benchmark with structure information and active site annotations, augmenting the single sequence modality to multiple modalities. Specifically, for each enzyme, we obtain the experimentally determined structures from PDB or structures predicted by AlphaFold2 (Jumper et 202I/ESMFold (Lin et al., (2022). Active site annotations are obtained from UniProt (Consortium 2024), which specify the residues directly involved catalysis. Detailed dataset statisties are pro- vided in Appendix [C.1] Based on supplemented information, EC numbers for query enzymes can be inferred from sequeecce/truccuurllacciis site information through similarity search algorithms or ML/DL-based classifiers. However, the scarcity of reliable active site annotations in UniProt leads to incomplete modality information, introducing a notable gap between structural and active site modalities. which further intensifies the difficulty of multi-modal learning (Wang al.) (2024b). To address these challenges, we develop a dual similarity graph encoding framework that mitigates data sparsity from both intra-modality and mnter-modality perspectives.
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4.2 GRAPH-BARE BASED MEDR-IY RELATIONSHIP MODELING
In this section, we capture pairwise similarity under structural and active site modalities and construct two independent similarity graphs. We then employ graph diffusion operations to mitigate data sparsity by incorporating both direct and indirect connections within the graphs.
Similarity graph under structure modality. We employ Foldseek (Van Kempen et al. 2024) to extract pairwise structural similarity. Specifically, Fold- seek discretizes structures in continuous space and re- duces 3D structure comparison to ID sequence compari- son through VQ-VAE (Van Den Oord al. 2017). We denote the structural similarity returned by Foldseck simi, (2,,, xz) = FFoldseek (82, S2,), where TG E denoting the enzymes from the dataset, and 8x repre- sents the corresponding structure. Based on the score simi,,(;)). )) construct a similarity graph under the struc- ture modality, denoted G (D, Ele).. An edge (z) ) is included in the edge set g(,) if simi,,(;, 22y 5", where 8 is a predefined threshold. Graph construction details and statistics are provided in Appendix B
42431
orver Woren messa
OOSE KIRTT
poges ESEVE ASUEL VENEE Rouse
EVEVO GREXA VEEGH
GIAA grou...
Bqsagy BUDAA VODDE FLURS-
Figure 3: Active site illustration.
Similarity graph under active site modality. We derive the enzyme similarity from the perspective of active sites using Folddisco (Kim al. 2025), an unverted-inder -ed--index---eedd method for fast structural motif detection within databases. Given the geometry and amino acid types of the active sites of z;, Folddisco first identifies whether a similar motif exists Ty. If local structure in 2; is identified, Folddisco computes the similarity between the query active sites and the identified one, denoted as simi, 22y) = fooddiacc ((9x, $z.: ). (gz,, $2,)). We denote the similarity graph under active site modality as G = (D, g(")), where edge set E (() includes (x,, x.)) if there a local motif in Ty sharing high similarity with the active sites of vi, i.e., sirmia(1;; xz) 8".
Active site information provides complementary insights beyond sequence and structural features. As illustrated in Fig. 3 enzymes can share identical EC numbers and active sites while exhibiting distinct sequence and structural patterns. This phenomenon arises because active site residues are typically scattered and discontinuous in the sequence (Hu et al. 2024), and their local structural features may deviate from the global protein structure distribution (Riziotis et al. 2025).
Remark. When learning over these similarity graphs, we follow the inductive learning paradigm (Hamilton et al., (017), strictly ensuring that only training enzymes and relationships among training enzymes are visible during the training phase, as further detailed in Appendix [D.4
Graph diffusion. Let A., A, be the adjacency matrices of the structural and active site similarity graphs, respectively. We augment the topology of these two graphs by aggregating information from multi-hop neighbors through a graph diffusion operation:
A'
P W
A
w pk
k=U
k=0
Specifically, P. is the transition matrix of the active site similarity graph and w is the weighting coefficient at k-th hop satisfying Ex k=0 w = 1. Graph diffusion can be instantiated into different formulations (Gasteiger et al.) 2018 2019 Kipf and Welling. 2016; et al.) 2019). Let D. be the degree matrix of A,, In this work, we set P. D A- w aa((1 )² and restrict the sum to a finite number T.a, yielding the personalized PageRank distribution (Wang et al. 2017 ZZhang et al.,
2021b 2024 Xic al.) 2024 2025 Hou al. 2021). Similar notations are adopted for the structure similarity graph.
The enhanced distributions A and A can be viewed as weighted and directed graphs, with edge weights reflecting the connection strength between node pairs, taking into account both their direct connections and indirect connections through multi-ho hop neighbors. Following (Gasteiger et al.) 2019). we preserve these weights and use the resulting weighted graphs for subsequent hyperbolic encoding and alignment.
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modality
CARE benchnack
Stracture modality
VABLLESCYHL....
Hypeholl
diffeskot
fapp
Decoler
Strcttrr
Active silcs
Active site modality
B
Hypnttlic CNN
Griph
diffinion
Tayp
Daander
curation
similarity gruph consinuction diflussio
Hyperbolic modality alignment
Figure 4: Overview of PoinnCARE framework: Curation multi-modal dataset by augmenting existing benchmarks with structure and active site information; II. Capturing intra-modality relation- ships with graph modeling and graph diffusion; III. Encoding enzyme similarity in hyperbolic space using dual hyperbolic GNNs capture inter-modality relationships with modality alignment.
4.3 MULTI-MODAL LEARNING AND ALIGNING IN HYPERBOLIC SPACE
Subsequently, we encode the augmented similarity graphs with independent GNNs in hyperbolic space to preserve the intrinsic hierarchical topologies, guided by cross- coos-modalityy alignment loss to capture the inter-modality invariance.
Standard GNN layer updates node representations in three sequential stages: linear transformation. neighbor aggregation, and non-linear activation (Liu et al. 2023 Wu et al., 2019. Zhang al.) 2023). However, these foundational operations are not readily applicable in hyperbolic space. To address this issue, a local Euclidean approximation within hyperbolic space commonly adopted as compromise (Ganea et al. 2018, Shimizu et al. 2020).
Definition (Tangent Space) For point x 8 in hyperbolic space, its langent space TB provides a first-order approximation of B% and is isomorphic to Euclidean space.
The exponential map operation exp, TT > B" projects vectors from the tangent space back to the hyperbolic space, while the logarithmic map log, 8 + T. performs the inverse operation. Furthermore, the parallel transport PT T + T, defines a way of transporting the local geometry along smooth curves that preserve the metric tensors. The detailed mathematical formulations are provided in Appendix AA.4
Based these definitions, update node embeddings in hyperbolic space by first projecting them onto the tangent space, performing standard operations (linear transformation and neighbor aggregation), and finally mapping results back to hyperbolic space (Chami et al., (209)] Ganea et al.) 2018 Shimizu et al.) [2020; Zhang et al.) (2021c). For simplicity, the langent space of the origin node selected to perform standard operations. Specifically, the matrix multiplication with W and the bias translation with b in hyperbolic space can be formulated as:
W
exp, ( (x)), æ + b exp, (PT (b)).
(2)
Then, the message passing procedure at the I-th layer is:
h WV = ftrane (n." = W ② h @b.
(3)
h (++1) = 8 (Jags (nr = expo
Σ JEN())
az log, (n (n)0))
(4)
where N(i) denotes the neighbor set of node i, and 5(-) a non-linear activation function, such as ReLU, We set the weight di according the normalized Laplacian matrix (Kipf and Welling) 2016
Liu et al. 2019). The input features (1) are initialized using a Protein Language Model (PLM), such
ESM (Lin al. 2022) used in (Yang al. 2024c Yu et al. 2023). Compared Fuclidean GNNs,

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the hyperbolic overhead introduces additional computational cost of O(nd), increasing the total computational complexity from (mnd) in a standard model to O + nd) in the hyperbolic GNN, where n, m, and d denote the number of nodes, edges, and feature dimensions, respectively.
We separately encode structural and the active site information with two independent hyperbolic GNNs. Specifically, feed the adjacency matrices augmented by graph diffusion, A' and Ay along with PLM embeddings H into the dual hyperbolic GNNs:
hyp (A H))),
H(a) - Srup (A H)).
(5)
We then align the representations under two modalities by minimizing the divergence between structural and active site embeddings of the same enzyme (Zhang al. (021a):
Catign (s) H(a) + wa( I H(s) H (6) + 1 H (.)))
(6)
The first term of Culign maximizes the correlation between representations from two modalities and captures the invariance between different views. The subsequent decorrelation terms prevent learning degenerated embeddings (Liu et al. 2023), with wa controlling the weight of decorrelation.
The representations from both modalities are then combined to derive the EC number prediction y. which is formulated as weighted sum the modality-specific predictions, governed by the trade-off parameters 8, and Ba (He et al. 2023):
= 3. fa) (H()) + 8a fal] H (a)).
(7)
Finally, the overall model is optimized by minimizing a joint objective function that balances the alignment loss and the cross-entropy loss: Lalign GCe-
EXPERIMENTS
5.1 EXPERIMENTAL SETTINGS
Dataset. We evaluate PoinnCARE on the standardized enzyme function benchmark CARE (Yang al., 2024a) curated from Swiss-Prot (Consortium, 2024), comprising enzymes with validated digi- EC number annotations. To rigorously assess the generalizability of a model to unseen proteins, CARE defines four distinct test sets, each presenting unique challenges:
<30% Identity test set: All enzymes the test set share less than 30% sequence identity with enzymes in the training set, ensuring stringent low-homology testing conditions (Rost] 1999).
30-50% Identity test set: Enzymes in this test set share sequence identity between 30% and 50% with those in the training set, representing an intermediate homology zone.
Previously Misclassified (Price) test set: A collection of enzymes that were initially misannotated in established databases such as KEGG by automated annotation methods, but were subsequently experimentally validated and correctly reclassified by Price et al. (Price et al.) 2018).
Promiscuous test set: A collection of enzymes capable of catalyzing multiple distinct reactions that are classified under different EC numbers. In this dataset, a single enzyme can be associated with up 9 different EC numbers.
All four test sets share common training set. Statistics of training and test sets presented in T Following the recommendation in the CARE benchmark, we use 50% sequence clustering of the training
increase the diversity. We follow the inductive setting (Hamilton al., 2017). ensuring that only training enzymes are accessible during training, while test enzymes are withheld until inference. Appendix D.4 provides more explanations and the performance comparison.
Baselines. We compare PoinnCARE with 12 SOTA competitors belonging to four categories:
Similarity search algorithms: BLASTp (ttephen 1990), Foldseek (Van Kempen et al. 2024).
Folddisco (Kim et al. 2025);
Contrastive learning methods: CLEAN (Yu et al. 2023), CLEAN-Concal (Yang et al.) 2024c):
PLMs for general proteins: ESM-2 (Li et al.
2022). ESM-c (ESM Team 2024), ProtTS (Elnaggar
et al. 2020), ProtBert (Elnaggar et al.] 2020), S-PLM (Wang al. 2024a);
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Table 2: Performance regarding accuracy <30% Identity and 30-50% Identity test sets. The best and second- beett results are shown in bold and underlined, respectively.
Identity Level 3
30-50%
Identity Level
Level (K-s-))
Level 2
Level 4 (xxxx.x)
Level
Level
Level (x.X.x.)
Avg.
rank
(xx.--))
(x.xx.))
(X-rn-))
(X....-)
(x.xX.-)
Random*
0.194
0.032
0.012
0,000
0.225
0.036
0.007
0.000
13.38
BLASTp
0.697
0.590
0.569
0.475
0.923
0.879
0.850
0.773
7.00
Foldseek
0.815
0.722
0.667
0.544
0,932
0.841
0.755
4.13
Folddisen
0.756
0.600
0.511
0.378
0.798
0.755
0.723
0.564
9.88
CLEAN
0.806
0.729
0,678
0,535
0.946
0.905
0.870
0.798
2.50
CLEAN-Concat
0,810
0.704
0.646
0,507
0.946
0.893
0,859
0.777
3.63
ESM-2
0.783
0.781
ESM-c
0.691
0.574
0.527
0,436
0.911
0.848
0.808
0.745
9.25
ProfTS
0.755
0.649
0.604
0.492
0.929
0.873
0.833
0.765
6.38
ProtBert
0.672
0.546
0.502
0.410
0.874
0.804
0.767
0.709
10.38
S-PLM
0.751
0.637
0,582
0,921
0.861
0.823
0.752
7.75
CharGPT*
0.278
0.016
0.000
0.000
0.336
0.030
0.014
0.000
13.38
Pika
0.616
0.461
0.377
0.206
0.738
0.600
0,502
0,377
12.00
PoinnCARR
0.900
0.827
0.779
0.648
0.961
0.926
0.887
0.822
1.00
Table 3: Performance regarding accuracy on Price and Promiscuous test sets. The best and second-best results are shown in bold and underlined, respectively.
Previously Misclassidied (Price)
Promiscuous
Level
Level 2
Level 3
Level 4
Level (N----))
Level (X.X-.))
Level
Level (x.x.x.)
Avg.
(X----)
(xXx---)
(x.x.x.))
(xxx..x)
(x.x.x.))
Random
0,223
0.047
0.007
0.000
0.411
0.090
0.041
0.005
12.88
BLASTp
0,824
0.811
0.710
0.341
0.843
0.784
0.733
0.682
5.63
Foldseek
0.939
0.878
0.797
0.314
0.769
0.689
0.638
0.561
6.38
Folddisco
0.000
0.000
0.000
0.000
0,656
0.526
0.484
0.318
12.25
CLEAN
0.858
0.797
0.696
0,280
0.873
0.816
0.768
0.691
5,00
CLEAN-Concal
0,905
0.872
0.770
0.348
0.776
0.659
ESM-2
0.918
0.849
0.762
0.362
0.861
0.780
0.724
0.629
4.00
ESM-c
0.791
0.726
0,666
0,343
0,818
0.730
0.672
0.579
8.13
ProfTS
0,895
0.827
0.761
0,380
0.843
0.754
0.694
0,596
5.38
0.554
0,549
S-PLM
0.872
0.789
0.719
0.238
0.848
0.761
0.709
0.606
6.50
CharGPT*
0.365
0.169
0.088
0.000
0.196
0.055
0.036
0.002
13.00
Pika*
0.824
0.649
0.507
0.041
0.618
0.473
0.372
0.164
11.00
PoinnCARE
0.955
0,909
0.827
0.349
0,911
0.871
0.849
0.785
1.25
LLMs for general protein-related question answering: GPT-4o-mini (Hurst al. 2024). Pika (Car
rami and Sharilzadeh 2024).
brief introduction to the baseline methods provided in Appendix C.2 with Table T summarizing the modalities employed by each bascline method. The results of LLMs and the random baseline are directly adopted from the CARE benchmark and marked with an asterisk *
Metrics. For evaluation, we adopt sets of metries: the accиracy score as defined in the CARE benchmark (Yang et al.) 2024a), and the precision, recall, and F, scores adopted in CLEAN Yu
al. (023). Following the evaluation protocol established in (Yang et al. 2024at Yu al.) 2023 Yang et al. (024c), we evaluate the classification performance at all four EC number levels. Level
evaluation solely examines the correctness the first digit, while level 4 evaluation requires
accurate prediction of all four digits in the EC number. Further implementation details are provided in Appendix
5.2 CLASSIFICATION RESULTS
Tables and
present a comprehensive comparison between PoinnCARE and 12 state-of-the th-tth--rtt methods on the CARE benchmark in terms of accuracy. Across all four evaluation levels and test sets, PoinnCARE consistently achieves the highest accuracy in nearly all cases, demonstrating robust and superior performance. Compared to the strongest baseline CLEAN, PoinnCARE achieves
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substantial improvements of 10.4% and 2.4% in level 4 accuracy on <30% Identity and 30-50% Identity test sets, respectively, demonstrating its exceptional capability in EC number prediction under low sequence similarity conditions. On the challenging Price test set, PoinnCARE outperforms the second-best method, with accuracy improvements of 1.7%, 3.1 %,, and 3.0% at levels through 3, respectively. Furthermore, for enzymes with promiscuous functions, PoinnCARE surpasses the second competitor CLEAN by a significant margin of 9 9.4% in level 4 accuracy. In terms of precision, recall, and Fi score, PoinnCARE also demonstrates a similar outstanding performance. with detailed results presented in Appendix D.1 The standard deviation values are in Appendix D.2
As illustrated in the left sub-figure of Fig 2 the classification space expands from main classes at level to over 4,900 distinct EC numbers at level 4, indicating a notable increase in classification complexity across levels. Nevertheless, PoinnCARE consistently outperforms existing methods across all four levels, demonstrating remarkable robustness. Among the 12 baseline methods, Foldseek, S- PLM, and CLEEAN-Concat incorporate structural information of enzymes. Notably, Foldseek exhibits promising performance on the <30% Identity test set, highlighting the effectiveness of structural information, especially when sequence similarity is highly limited. We also report the performance of valid Folddisco predictions. While BLASTp utilizes full sequence information containing hundreds of residues, Folddisco achieves comparable performance by leveraging only several residues in local active site motifs. This comparison demonstrates the crucial role of active sites in determining enzyme function, particularly in cases of low sequence similarity.
5.3 CLASSIFICATION RESULTS IN A LIMITED-DIMENTE
SPACE
As shown in Theorem compared with Euclidean space, hyperbolic space can achieve arbitrarily low distortion even in low dimensions. Following this theoretical analysis, we evaluate the dimensional efficiency of PoinnCARE. against CLEAN, the strong baseline, by systematically reducing the embedding dimension from 512 to 32, and the results on the <30% Identity test set are presented in Figure As the embedding dimension decreases from 512 to 32, CLEAN's classification accuracy at level 4 drops significantly from 0.535 to 0.354, suffering an 18. 1% performance degradation. In contrast, our PoinnCARE maintains robust performance across different dimensions. Notably, even with a compact 32-dimensional representation, PoinnCARE achieves a strong accuracy of 0.597 at level 4. Appendix D.3 provides detailed results on the <30% and 30-50% Identity test sets.
Cupeouood CLEANEUU CLEABE of
1.
Figure 5: Varying dimensions.
5.4 POINNCARE AS A GENERAL FRAMEWORK
In this section, we explore the generalizability of PoinnCARE by treating it as a general framework that can be combined with different sequence en-
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0.8
coders. For ESM2 Lin et al., 2022), ESMc (ESM Team 2024), and ProtT5 (Heinzinger et al.) 2024), we present the standalone performance, the performance in hyperbolic space, and the performance when inte- grated into our PoinnCARE framework in Figure 6 Compared to the standalone performance, transform- ing into hyperbolic space yields notable improve- ments in level-4 accuracy: 10.6% for ESM2, 1 11.8% for ProTT5, and 19.0% for ESMc. Integrating with
088
0.6
04
Suadstiona
hymecbolo
Figure 6: PoinnCARE as a framework. the full PoinnCARE framework further boosts performance, achieving up to an additional 8.2% improvement in level-4 accuracy.
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5.5 ABLATION STUDY
In this section, we conduct ablation studies in a boltom-up man- ner. Starting from a naive MLP classifier, we progressively incorporate key components to demonstrate their individual contributions, culminating in the full PoinnCARE framework. Figure 7 shows how the accuracy evolves during this process on the <30% Identity test set. First, transforming the ML.P into hyperbolic space yields substantial improvement of 9.3% in level-4 accuracy. Subsequently, the independent incorporation of the active site and the structural similarity graph each further enhances performance. Finally, integrating modality alignment to fuse both information notably boosts overall results, achiev- ing a 2.6% improvement over the variant with only structural information in level-4 accuracy. A case study illustrating the complementarity between the modalities is presented in Appendix E Furthermore, Appendix [ppendix[D.A]proool providds a comprehensive parameter analysis, including investigations into the inductive learning setting, the curvature of the underlying hyperbolic space, and the graph diffusion settings.
LAXX
1.0
04
Hipamall
PAROARE
Me
Figure 7: Ablation study.
6 CONCLUSION
In this paper, we present PoinnCARE, a hyperbolic multi-modal learning framework for enzyme function prediction. By effectively incorporating both structural and active site information through graph-based modeling and diffusion, PoinnCARE captures comprehensive enzyme characteristics beyond sequence features. Motivated by the theoretical advantages when embedding trees, we adopt hyperbolic geometry instead of traditional Fuclidean space for enzyme representation learning. Then we align and fuse information from these two complementary modalities, capturing comprehensive en- zyme characteristics. Extensive experiments the CARE benchmark demonstrate that PoinnCARE consistently outperforms existing methods across various challenging scenarios.
ACKNOWLEDGMENTS
Sibo Wang is supported by the RGC GRF grant (No. 14217322) and the "I+1+1" CUHK-CUHK(SZ)- GDST Joint Collaboration Fund.
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A HYPERBOLIC GEOMETRY
A.1 POINCARÉ BALL MODEL
As we presented before, an n-dimension Poincaré ball model with constant negative curvature s(x= < 0) can be denoted as (B% 9*), where B% (x E R=||==||2 < -1/K] is an open ball with denotes the radius (-1/k)1/2, - = 4/(1 2 is the Riemannian metric tensor, and Euclidean norm.
The metric tensor in Euclidean space is yf I. This implies that the metric tensor of Poincaré model conformal to that in Euclidean space, meaning that the angles defined Poincaré ball model are the same as those in Euclidean space. The conformal factor between them is A 2/(1 =||==|?)) and the Poncaré model's 's metric tensor can be rearranged as of A2I.
The distance between u, E B% is denoted as:
1 |
2x u 2112
d(u, v)
arcosh(1 (1 + K /|u (1 x1|1|12)
The hyperbolic distance is determined by both the relative positions of points u and v (llu- - vll in the numerator) and their absolute positions (//u||2 and ||e||2 in the denominator). Notably, for points approaching the boundary of the Poincaré ball (where their norms approach -1/k), the hyperbolic distance grows significantly faster than the corresponding Euclidean distance. This fast growth of space near the boundary is particularly advantageous for embedding tree-like hierarchical structures. Leaf nodes belonging to different subtrees can be placed far apart in this boundary space, while maintaining their relative distances within the same subtree, thus accurately preserving the structure of the hierarchy.
A.2 GROMOV HYPERBOLICITY
Gromov 1987 Narayan and Saniee 2011) a notion from group theory, measuring how tree-like a graph is. Specifically, let (G, do) denote the input graph with its associated distance function. Let a, b, c, d be four vertices of the input graph, and define S1, S2, S3 as:
Gromov's 5- d-hyperbolicity (Bridson and Haefliger 2013
S (a, do(d,c), S2 = do + do(b, d), S3 = da d) + do(b,c). c).
Then we can calculate 5(a, b, c, d) as the difference between largest and the second largest largest S., denoted as M1 and M2, respectively:
8(a, b, c, M1 M2.
We analyze the hyperbolic characteristics of graph G using the mean of sampled 5(a, b, c, d) values, where a, b, d are randomly selected nodes in G, provide statistical view of the graph's 's geometric properties. While the classical 6-hyperbolicity defined as the supremum of all 5(a, b, c, d), we use this mean-based metric capture the average hyperbolic behavior of the topology.
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For tree topologies, have d 0. A ó value that is close to zero indicates that the imput structure of the graph more closely resembles a tree-like hierarchical organization. The closer the to zero, the more tree-like (or more hyperbolic) the given topology is.
A.3 EMBEDDING REGULAR TREE TWO-DIMENSIONAL SPACES
To demonstrate how Euclidean and hyperbolic spaces fundamentally differ in their capacity for embedding hierarchical structures, we analyze a concrete example: embedding a regular tree in two-dimensional spaces.
Consider regular tree with branching factor where each node has exactly b child nodes. The total number of nodes an I-layer tree is Σi=o b", exhibiting exponential growth with respect to the depth 1. When embedding such a tree into geometric space, can place the root node at the origin with leaf nodes extending outward. In Euclidean space, however, the available area grows insufficiently: a disc of radius has 2x11², scaling only quadratically with 1. In contrast, the area of disc with radius in hyperbolic space (with curvature 1) is 2m 22 + 6 e- /2- - 1), providing exponential growth that matches the tree's expansion rate.
A.4 TANGENT SPACE RELATED OPERATIONS
In this section, we provide brief introduction to the tangent-space related operations, starting from basic concept, Möbius addition (Ungar) 2007), that is utilized deriving the closed-form expression of other operations.
Möbius addition. For x. y E B Möbius addition defined as:
1xx y (1 2x(xr, v)2 x||y|>>>> + (1 + x||b>|>)
(8)
(x. 8/2 + x=? - 13
Note that when 0, the Möbius addition degenerates to the Euclidean addition. Based on the Möbius addition, we can define the Möbius subtraction æ ex y x @x (-y). Next, we present the detailed mathematical formulation of the exponential map, logarithmic map, and parallel transport (Ganea et al. 20188; Yang et al. 2023).
Exponential map. For B% and E T T. + O, the exponential map exp, T B is defined as:
expx.v) (v) = x @w (tanh( Vkl
2
16
where X, 2/(1 [<|==1 is the conformal factor.
Logarithmic map. For x. y E B x * y. the logarithmic map log, : .B + Ta B defined as
2
tanh (V]xlll @x 5/1) -I θx y
log, (3) M X
(10)
4N M
Parallel transport. Here present the parallel transport PT vector e E To to a another tangent space T.
TToB%. TT that transports
Ao
PTo-e (v) log. (or @N expo(u))
X,
u.
(11)
B SIMILARITY GRAPH CONSTRUCTION DETAILS
B. STRUCTURE MODALITY
For the structure modality, we employ Foldseek VVan Kempen et al. 2024) to compute pairwise similarities. For enzymes 2;, Fy D with their corresponding structures 8s, and Sxys the similarity is measured by the normalized bit score:
bits(Sa,, Say)
simi,(z;, 2z)) = Fooldeokk (Sa,, $2,)
bits (82, 8z.)
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where bits(Sa; $2y) is Foldseek's default scoring metric measuring the structural alignment be- tween 8z, and $2,- The normalization by self-alignment score ensures the similarity measure is bounded between 0 and 1. The edge set (+)) includes an edge between enzymes 2; and zy when simi, (2i, xz)) 8%, where 8 0.3.
B.2 ACTIVE SITE MODALITY
Fig. 8 illustrates the distribution of active site annotations from UniProt across our enzyme dataset, where more than half of the enzymes have no annotated active site residues. Based on the available annotations, we construct the active site modality graph using Folddisco (Kim et al.) 2025) identify similar local motifs. For enzyme 2; with sequence Gz., structure Sag and active site annotation Oz Folddisco first identifies whether similar motif exists in enzyme x.y. If match is found, Folddisco returns two metrics; RMSD (Root Mcan Square Deviation), measuring the geometric similarity, and IDF (Inverse Document Frequency), quantifying the rarity of the identified local structural patterns. We filter out matches with IDF < 0.7 to focus on meaningful structural patterns, then define the similarity between enzymes using the RMSD score:
20000
cogytes
1.900
1000
0
Figure 8: Distribution.
simii (Zi, xT)) = F'olddiscoo (4o, 8 Oz2) (qz,, b2,)) = RMSD 2;))
The edge set {(a) includes an edge between enzymes 24 and zj when simia x,) > 8", where 8 = 0.05.
B.3 GRAPH STATISTICS
TableApresent the key statistics of both similarity graphs. The homophily ratio, defined as the proportion of edges connecting enzymes with identical EC numbers (Zhu et al. 2020), indi- cates that the structure modality graph Gla) exhibits stronger homophily than the active site modality graph G(a), The node set contains enzymes in both the training and test sets. Fol- lowing the recommendation in the CARE benchmark, we use 50% sequence clustering of the training set to increase the set diversity. We also analyze the distribution of structural and active site similarity graphs, as shown in Fig. 9 which reveals a modest number of shared relationships, indicating that each modality captures distinct and unique information.
4K2,404
10305 momnraatppeoo pif
scbitendape 6770
Figure 9: Edge distribution.
Table 4: Statistics of similarity graphs G(s) and G(a).
# nodes
# edges
Homophily Ratio
G(s)
29,531
189,369
0.808
G(a)
29,531
17,800
0.514
C ADDITIONAL EXPERIMENTAL SETTINGS
C.I DATA STATISTICS
Table the detailed statistics of the utilized benchmark CARE.
C.2 BASELINES
We include the following SOTA methods as baselines:
BLASTp (Stephen 1990) is a fast sequence alignment algorithm that can search for database sequences similar given query sequence.
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Table 5: Dataset statistics.
# enzymes
unique EC numbers
Training set
184,529
4936
<30% Identity test set
432
333
30-50% Identity test set
560
389
Previously Misclassified (Price) test set Promiscuous test set
148
56
209
384
Foldseek (Van Kempen et al. 2024) is fast structure alignment algorithm. By reducing 3D
structural information to ID sequence information, Foldseek can search for database structures similar to given query structure.
2025) is a fast local motif detection algorithm that can search and identify local structures from the database that similar to given motif.
Folddisco (Kim et al.
CLEAN Yu et al. 2023) initializes enzyme embeddings with ESM-2 (Lin et al. 2022). and then optimizes embeddings with triplet margin loss, where the distance between pairs with the same EC class is minimized and the distance between pairs with different EC classes is maximized.
CLEAN-Concat (Yang et al. 2024c) improves the CLEAN method by utilizing both sequence information in ESM-2 embedding and the structure information encoded by ResNet (He et al. 2015).
ESM-2 Lin ct al.
2022) is protein language model trained on sequences of natural proteins with the aim of designing protein structures.
ESM-c (ESM Team
2024) scales up data and training compute, achieving performance improve-
ments over ESM-2.
ProtT5 (Elnaggar et al. 2020) trains T5 (Raffel et al. 2020), auto-encoder language model, on
UniRef and BFD data to capture biophysical features from protein sequences.
ProtBert (Elnaggar et al. 2020) trains BERT (Devlin al. 2019) on the UniRef and BFD data.
S-PLM (Wang et al. 2024a) is a 3D structure-awarg protein language model (PLM) that enables the sequence-based embedding to carry the structural information through multi-view contrastive learning.
GPT-4o-mini (Hurst et al. 2024 is large language model that demonstrates promising capabilities in understanding and generating human-like text.
Pika (Carrami and Sharifzadeh 2024) finetunes LLMs on curated, debiased dataset tailored for protein question answering and a biochemically relevant benchmarking strategy. Protein embeddings by ESM-2 (Lin et al.) 2022) are utilized to provide comprehensive understanding of the target protein in the given question.
For similarity search algorithms, we first establish a reference database comprising enzymes from the training set. Test enzymes then queried against this database, and the EC numbers of top-retrieved enzymes serve as predictions. For PLM baselines, we freeze the pre-trained weights while training The reported results for PLMs and
task-speeific classification head based on the training PoinnCARE are averaged over five independent runs. We implement all baselines using their official code repositories as documented in Table except for LLMs, which directly predict EC numbers through prompting.
C.3 IMPLEMENTATION DETAILS
Accuracy is computed using the original code from CARE benchmark (Yang et al., 2024a), whereas precision, recall, and Fi scores calculated using the scikit-learn library (Pedregosa et al. 2011).
Our PoinnCARE is implemented in Python using the Py Torch framework (Paszke 2019 The model optimized using the Adam optimizer (Kingma and Ba 2014) with a learning The hidden dimension is set to 512, consistent with the baseline implementations. The hyperbolic encoders are implemented based on the Poincaré model with fixed curvature of 1. The graph diffusion operation over the active site similarity graph (()) instantiated two-layer personalized
of 0.01.
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Table 6: Summarization on the modality used in baselines.
Modality
Category
Methods
Sequence
Structure
Active site
BLASTp Foldseek
Similarity search
Folddisco
CLEAN
Contrastive learning
CLEAN-Concat
ESM-2
ESM-c
PLM
ProTT5
ProtBert
S-PLM
LLM
Pika
Table 7: The links to the baseline repositories.
Category
Method
Github link
BLASTP Foldseek Folddisco
http://gulabb.omm/hcchhhiiiinnit
Similarity search
CLEAN
Contrastive learning
CLEAN-Concat
ESM-2
ESM-c
PLM
ProfT5
ProtBert
S-PLM
https//ggghabbcccom/ddool/innnns M/tre//mman
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Table 8: Hyperparameters details.
?
Wa
<30% Identity test set
0.8
0.2
0.001
30-50% Identity test
0.8
0.2
0.001
Previously Misclassified (Price) test set Promiscuous test set
0.2
0.8
0.0001
0.5
0.5
0.0001
Table 9: Performance in terms of precision The best and second-best results are shown in bold and underlined, respectively.
<30% Identity and 30-50% Identity test sets.
<30% Identity
30-50%
Identity Level
Level (K.-.v>)
Level
Level
Level 4 (x.X.X.)
Level
Level
Level (x.X.X.))
Avg.
rank
(X.X.x))
(x.X.X.))
(X.->-)
(x.X.--)
(x.X.X.))
Random
0.176
0.038
0.005
0.000
0.146
01018
0.002
0.000
13.25
BLASTp
0.706
0.629
0.582
0.503
0.915
0.897
0.854
0.789
5.38
Foldseek
0.794
0.642
0.743
4.50
Folddisco
0.662
0.418
0.455
0.368
0.662
0.718
0.694
0.505
11.25
CLEAN
0.793
0,716
0.680
0.517
0.931
0.911
0.861
0.804
2,75
ESM-2
0.785
0.675
0.620
0.486
0,943
0.883
0.819
0.770
4,88
ESM-c
0.690
0.548
0.527
0.402
0.902
0.854
0.778
0.738
9.00
ProtBert
0,676
0.521
0.503
0.378
0.872
0,806
0.728
0.691
10.00
S-PLM
0.738
0.604
0.563
0.428
0.907
11.875
0.799
0.742
7.63
CharGPT
0.091
0.001
0.000
0,000
0.123
0.022
0.011
0.000
13.50
Pika
0.587
0.483
0.357
0.196
0.714
0.588
0.498
0.354
11.75
PoineCARE
0.885
0.826
0.778
0.616
0.951
0.924
0.875
0.818
1.00
PageRank algorithm with = 0.8. The values of other hyperparameters on four test sets are listed in Table 8 including:
Bg and Ba: trade-off parameters of modality fusion: H = H()) Ba H()
y: trade-off parameters the compound loss: L = Las + Lalign.
Wd: weight of de-correlation terms in alignment loss 6
D ADDITIONAL EXPERIMENTAL RESULTS
D.1 PERFORMANCE REGARDING PRECISION, RECALL, AND F1 SCORES
In this section, we provide additionally comprehensive evaluation results other standard metrics:
precision scores Tables 9 and TO recall scores in Tables II and 12 F1 scores Tables 13
and [4
The performance distributions across these metrics align with our previous accuracy analysis: our PoinnCARE demonstrates superior performance under most cases and maintains the highest average rank across test sets, further validating the effectiveness of our hyperbolic multi-modal learning framework. Notably, on the Promiscuous set, BLASTp achieves marginally higher precision than method, which can be attributed to the high sequence similarity between this test set and the training data (with nearly 50% of enzymes sharing >90% sequence identity). Nevertheless, PoinnCARE still surpasses BLASTp in both recall and Fj metrics, achieving a substantial 4.4% improvement in level 4 Fi score on the Promiscuous set.
D.2 PERFORMANCE STABILITY
In this section, provide the standard deviation results for the top three end-to-end prediction methods, PoinnCARE, ESM-2, and ProtT5, on the <30% Identity test set regarding accuracy. For the similarity search and contrastive learning baselines, the standard deviation applicable because
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Table 10: Performance in terms of precision score on Price and Promiscuous test sets. The best and second-bes, best results shown in bold and underlined, respectively.
Previously Misclassidied (Price)
Promiscuous
Level
Level
Level
Level
Level (X.ve.))
Level
Level
Level (x.X.x.)
Avg. rank
(Kouse)
(X.X..))
(x.X.X.))
(XXX...)
(X.X..))
(x.X...))
Random
0.220
0.051
0.007
0.000
0.363
0.081
0.036
0.005
13.13
BLASTp
0.818
0.784
0.696
0.341
0,968
0.960
0,951
0,874
4.25
Foldseek
0.939
0.878
0.797
0.318
0.846
0.808
0.799
0.704
4.25
Folddisco
0.000
0.000
0.458
12.13
CLEAN
0.858
0.794
0.686
0.307
0,909
0.873
0.848
0.691
5.38
CLEAN-Conen
0.905
0.868
0.767
0.348
0.917
0.860
0.834
0.639
3,75
ESM-2
0.362
ESM-c
0.787
0.720
0.661
0.343
0.822
0.737
0.712
0.579
9.13
ProfT5
0.891
0.824
0.757
0.380
0.846
0.766
0.734
0.596
6,38
ProtBert
0.674
0.551
0.512
0,200
0.794
0.691
0.658
0.549
11,00
S-PLM
0.867
0,788
0.718
0.238
0.851
0,780
0.756
0.606
7.13
CharGPT
0.372
0.176
0.095
0.000
0.292
01,866
0.067
0.005
12.63
Pika*
0.824
0.649
0.507
0.041
0.890
0.794
0.742
0.354
9,00
PoineCARE
0.953
0.906
0.824
0.349
0.943
0.925
0.917
0.785
1.75
Table 11: Performance in of recall score <30% Identity and 30-50% Identity test sets. The best and second-best results are shown in bold and underlined, respectively.
Identity Level
30-505 Identity
Avg.
Level (K.rrr))
Level (x.X..))
Level (xxx...)
Level (X.re-)
Level 2
Level 3
Level (x.x..x)
(x.x.x.)
(X.X.)))
(x.X.X.)
Random
0.151
0.024
0.014
0.000
0,152
0.022
0.007
0.000
13.13
BLASTp
0.660
0.545
0.546
0.478
0.931
0.877
0.841
0.779
5,88
Foldseck
0.783
0.660
0.634
0.533
0.939
0.875
0.823
0.740
3.88
Folddisco
0.611
0.466
0.473
0.346
0.648
0.670
0.676
0.497
11.13
CLEAN
0.782
0.653
0.659
0.523
0.955
0.885
0.854
0.797
2.50
CLEAN-Conch C-Concat
0.768
0.481
ESM-2
0.745
0.632
0.618
0.494
0.955
0.868
0.828
0.771
4.63
ESM-c
0.650
0.507
0.505
0.413
0.925
0.839
0.782
0.737
9.00
ProfTS
0.723
0.468
0.939
0.857
0.752
ProtBert
0.636
01488
0,480
0.383
0.895
0.788
0.729
0.693
10.00
S-PLM
0.708
0.573
0.557
0.443
0.933
0.847
0.801
0.738
7.50
ChatGPT
0.135
0.008
0.000
0.000
0.148
0.013
0.000
13.63
Pika
0.581
0.402
0.355
0.187
0.763
0.562
0.477
0.350
11.88
PoinnCARE
0.885
0.787
0.761
0.632
0.969
0.909
0.870
0.825
Table 12: Performance in terms of recall score on Price and Promiscuous test sets. The best and second-bes best results are shown in bold and underlined, respectively.
Previously Misclassidied (Price)
Promiscuous
Level 1
Level
Level 3
Lovel
Level (x----)
Level
Level 3
Level (xxxx.x)
Avg.
rank
(X-e-)
(xxx--)
(X.x..-)
(x.x...)
(X.X-.-)
(x.xx-))
Random
0.223
0.054
0.007
0.000
0.405
0.085
0.037
0.005
12.88
BLASTp
0.818
0.784
0.696
0.341
0.834
0.780
0.730
0.682
6.00
Foldseek
0.939
0,878
0.797
0.314
0.762
0.675
0.632
0.561
6,38
Folddisco
0.000
0.000
0.000
0.000
0.641
0.510
0.464
0.318
12.25
CLEAN
0.858
0.307
0.691
CLEAN-Concat
0.905
0.872
0.770
0.348
0,868
0.805
0.770
0.659
3.13
ESM-2
0.918
0.849
0.762
0.362
0.857
0.771
0.716
0.629
4,00
ESM-c
0.666
0.343
0.579
ProTTS
0.895
0,827
0.761
0,380
0.837
0.745
0.686
0.596
5,38
ProtBert
0.678
0.554
0.515
0.200
0.810
0.699
0.630
0.549
10.00
S-PLM
0.872
0.789
0.719
0.238
0.844
0.754
0.702
0.606
6.38
ChatGPT
0.372
0.176
0.095
0.000
0.192
0.052
0.033
0.002
13.00
Pika*
0.824
0.649
0.507
0.041
0.611
0.465
0.362
0.164
11.00
PoinnCARE
0.955
0.909
0,827
0.349
0.908
0.866
0.844
0.785
1.25
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Published as a conference paper at ICLR 2026
Table 13: Performance in terms of Fi score <30% Identity and 30-50% Identity test sets. The best and second- bestnd-best results are shown in bold and underlined, respectively.
<30% Identity
30-50%
Identity Level
Level (K---v))
Level 2 (XX.-))
Level
Level (x.X.X.)
Level (X.->-)
Level
Level (x.X.X.)
Avg. rank
(x.XXX))
(XXX-:))
(x.X.X-)
Random
0.150
0.023
0.007
0.000
0.143
0.018
0.003
0.000
13.13
BLASTp
0.673
0.551
0.528
0.484
0.921
0.872
0.830
0.778
5.63
Foldseek
0.871
0.736
4.25
Folddisco
0.604
0.430
0.448
0.354
0.648
0.673
0.665
0.498
11.13
CLEAN
0.783
0.661
0.641
0.511
0.942
0.885
0.842
0.795
2.63
CLEAN -.FA-CConcat
ESM-2
0.752
0.629
0.589
0.483
0.948
0.865
0.809
0.766
4.88
ESM-c
0.659
0.500
0.479
0.398
0.912
0.834
0.762
0.732
9.00
ProTTS
0.730
0.604
0.555
0.455
0.932
0.854
0.785
0.745
6.25
ProtBent
0,642
0.478
0.456
0.373
0.880
0.779
0.703
0.685
10.00
S S-PLM
0.714
0,559
0.525
0.427
0.917
11,46
0.783
0.735
7.75
ChatGPT
0.085
0.002
0.000
0.000
0.100
0.013
0.008
0.000
13.63
Pika
0.570
0,382
0.318
0.184
0.726
0.540
0.447
0.340
11.88
PoineCARE
0.883
0.787
0.742
0.617
0.959
0.910
0.859
0.816
1.00
Table 14: Performance in terms of Fi second-best results are shown in bold and underlined, respectively.
Price and Promiscuous test sets.
The best and
Previously Misclussidied (Price)
Level
Level
Level
Level 4 (xXXx..)
Level (X.--.)
Level 2
Level
Level (x.Xx.x)
Avg.
(X-->))
(xX--))
(x.X.X-)
(x.X.:-)
(x.X..-)
Random
0.221
0.052
0.007
0.000
0.364
0.080
0.036
0.005
13.00
BLASTP
0.818
0.784
0.696
0.341
0.879
0.840
0.804
0.746
4.75
Foldseek
0.939
0.797
0.315
0.783
0.717
0.686
0.609
$.50
Folddisco
0.000
0.000
0.000
0.000
0.688
0.582
0.541
0.366
12.38
CLEAN
0.858
0.795
0.687
0.307
0.871
01823
0.789
0.691
5.25
CLEAN ELEACCCnnaat
0.905
0.768
0.348
0.659
3,63
ESM-2
0.917
0.847
0.761
0.362
0.839
0.766
0.730
0.629
4.13
ESM-c
0.788
0.722
0.663
0.343
0.798
0.713
0.676
0.579
8.50
ProfT5
0.892
0.825
0.759
0,380
0.820
0.596
5.63
ProtBart
0.676
0.552
0.513
0.200
0.778
0.679
0.634
0.549
10.25
S-PLM
0.869
0.788
0.719
0.238
0.826
0.749
0.716
0.606
6,63
ChatGPT
0.372
0.176
0.095
0.000
0.224
0.063
0.044
0.002
12,88
Pika*
0.824
0.649
0.507
0.041
0.703
0.573
0.486
0.223
10.88
PoindCARE
0.954
0.907
0,825
0.349
0.912
0.880
0.867
0.785
1.25
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Published as a conference paper at ICLR 2026
Table 15: The standard deviation values of the top three ene-to-end prediction methods.
PoinnCARE
ESM2
ProtT5
Mean
Std
Mean
Std
Mean
Std
0.900
0.003
0.783
0,014
0.755
0.009
-.X.-.-
0.827
0.006
0.695
0,014
0.649
0,015
X.X.X.-
0.779
0.010
0.643
0.013
0.604
0.012
X.X.XXX.
0.648
0.006
0.518
0.015
0.492
0.018
Table 16: Performance under varying dimensions.
Test sct Dimension
<30% Identity
30-50% Identity
256
128
512
256
128
64
X.
0,806
0.831
0.817
0.752
0.694
0.946
0.948
0.948
0.941
0.902
CLEAN
X.X.--
0.729
0.738
0,731
0.664
0.560
0,905
0.911
0.909
0.678
0.701
0.685
0.593
0.486
0.870
0.877
0.870
0.848
0.788
X.X.X.X
0,535
0.532
0.546
0.458
0.354
0.798
0.804
0.780
0.755
0.673
0,900
0.895
0,888
0.880
0.862
0,961
0.963
0.96
0,959
0.951
0.827
0.824
0.817
0.812
0.787
0.926
0.924
0.925
0.921
0.909
PoineCARE
X.X.K.-
0.779
0.776
0.768
0.757
0.734
0.887
0.888
0.885
0.880
0.865
X.X.X.X
0.648
0.641
0.633
0.622
0.597
0.822
0.816
0.818
0.811
0.792
these methods are deterministic and do not exhibit variability across different runs. As shown in Table 15, our PoinnCARE demonstrates superior and also stable performance with low standard deviation values.
D.3 PERFORMANCE UNDER VARYING DIMENSIONS
The accuracy performance of PoinnCARE and the strongest baseline, CLEAN, on the <30% and 30-50% test sets under varying dimensions, ranging from 512 down to 32, is presented in Table T6
D.4 PARAMETER ANALYSIS
Inductive transductive settings. Our main experiments adhere to the inductive learning paradigm (Hamilton et al.) 2017), enforcing strict information constraints whereby only training samples and their inter-relationssips subsequently generalizes to previously unseen test instances during inference. We further investigate performance under the transductive setting (Kipf and Welling 2016). wherein test samples are made available during training while their labels remain concealed. The main distinction between these two paradigms lies in the exploitation of train-test similarity relationships in the training stage. Table 17 presents accuracy comparisons across four test sets under both settings. Our PoinnCARE demonstrates robust generalizability even under the strict inductive learning paradigm.
accessible during the training phase. The learned model
Table 17: PoinnCARE performance under inductive and transductive settings regarding accuracy.
<30% Identity
30-50%
Identity
X.-...-
X.X.-.-
X.X.X.-
X.X.X.X.
X.-...-
X.X.-.-
X.X.X.-
X.X.X.X.
Inductive
0.900
0.827
0.779 0.784
0.648
0.961
0.926
0.887
0.822
Transductive
0.902
0.833
0.650
0.961
0.929
0.888
0.828
Previously Misclassidied (Price)
Promiscuous
X.-...-
X.X.-.-
X.X.X.-
X.X.X.X.
X.+...-
X.X.-.-
X.X.X.-
X.X.X.X.
Inductive
0.955
0.909
0.827
0.349 0.359
0.911
0.871
0.849
0.785
Transductive
0.962
0.917
0.829
0.915
0.876
0.852
0.790
23

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Published as a conference paper at ICLR 2026
Table 18: Performance under different hyperbolic space cuvatures.
Leanable c
c= 0.5
c= -1
c
-5
X-----
0.896
0.894
0.902
0,900
X.X.--- 0.826
0.832
0.833
0.825
X.X.X.- 0.781
0,780
0.784
0.777
X.X.XXX. 0.649
0.648
0.650
0.637
Table 19: Performance with variour graph diffusion settings.
PPR
HKPR
a 0.8
= 0.5
a = 0.2
t= 2
t = 5
t= 8
<30% Identity
0.902
0.894
0,897
0.890
0.892
0.896
X.X..--
0.833
0.834
0,837
0.832
0.833
0.836
X.X.X.-
0.784
0.791
0.788
0.789
0.787
0.789
X.X.X.X.
0.650
0.656
0.652
0.656
0.655
0.652
30-50 Identity
X.n...-
0.961
0.966
0.964
0.967
0.965
0.965
X.X.-.-
0.929
0.932
0.929
0.933
0.931
0.929
X.X.X.- 0.888
0.891
0.889
0.890
0.889
0.889
X.X.X.X.
0.828
0.832
0.831
0.830
0.830
0.830
Curvature of the hyperbolic space. our main experiments, we fix the curvature of the underlying hyperbolic space to -1. The larger the absolute value of curvature, the more strongly curved the hyperbolic space becomes. The traditional Euclidean space corresponds to zero curvature (c = 0). We investigate performance sensitivity different curvature values by setting learnable parameter optimized jointly with the model. Table presents accuracy results on the <30% Identity test set. Our findings indicate that curvatures closer to zero yield comparable performance, while = 5 creates a strongly curved space that leads to slightly decreased accuracy.
-0.5, -5, and
Graph diffusion. To address the sparsity of enzyme active site annotations, apply graph diffusion over the active site similarity graph ((a), Our main experiments employ two-layer personal- ized PageRank (Wang et al. 2017) with a = 0.8 as the graph diffusion mechanism. We further investigate alternative parameter configurations and diffusion instantiations, such as Heat Kernel PageRank (Kloster and Gleich 2014), to evaluate the impact of different diffusion strategies. As presented in Table PoinnCARd maintains superior performance across various graph diffusion settings, demonstrating the stability and effectiveness of our approach.
E
CASE STUDY
In this section, present case, D4APQ6, from the <30% Identity test set, to demonstrate how active site information helps complement structural information. D4APQ6 is from the <30% Identity test set, where its sequence identity with all training samples is de- liberately restricted to less than 30%. The structural similarity with training samples returned by Foldseek also falls below the pre-defined threshold, preventing the formation of effective edges in the structural sim- ilarity graph. When relying solely on the structural graph, the enzyme D4APQ6 is misclassified as EC 3.2.1.67. However, Folddisco successfully identifies that D4APQ6 shares a similar local motif with the active sites (Cys-454 and Cys-457) of 022229 from the training set, illustrated in Figure TO This similarity results in the formation of homophilic
C457
maining
VLGEE SPRVE KPICN
SPIEE PERTL
LORMP GROTY KCPMC DOKER.
KOVDE YHROW SEVET..
Figure correctly classified case.
24

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Published as a conference paper at ICLR 2026
E174
DE09
RAKZET
3.4.3..0
.EEDY VERGH BAUWI HEPLE ..YVCYY GELDY Q2A2R DOCML
LOERD RGAAD CKERY
TDPY7 LDEVD GELYG SGATO
P75735 PO0193, QACPV', ORGXRO fom wutning ser, with EC 1.6.99
KOUNY GOBRI, ERGPING L.RRET..
TXPT" KIMHER AGE
Figure 11:
Examples heterophilic structure (left) and active site (right) similarities, with the normalized bit score (nbit) and the motif RMSD provided.
edges in the active site similarity graph G(*), which facilitates information aggregation between test samples and known training samples, thereby enabling accurate classification D4APQ6. Conse- quently, by integrating both structural and active site modalities, D4APQ6 is correctly classified as EC 1.8.1.9 by PoinnCARE.
F LIMITATION AND FUTURE WORK
In order to identify potential directions for future work, we first explore the reasons behind enzyme misclassification. Specifically, we collected enzymes from the <30% Identity test that misclassified by PoinnCARE. In this test set, sequence identity scores with training samples are strictly limited to below 30%. We further analyzed the structure and active site similarities associated with these misclassified enzymes and derived the following observations. First, we found that 53.3% (81 out of 152) these misclassified enzymes lack both structural and active site similarity. Second, 45.3% (54 out of 152) of misclassified enzymes possess either structural similarity or active site similarity, However, the majority of these edges are heterophilic, meaning they connect to enzymes with different EC numbers. The homophily ratio among these edges is only 0.078, which significantly lower than the overall homophily ratios. The absence of effective information and the presence of misleading, heterophilic relationships make the classification of these enzymes particularly challenging.
We further examined those enzymes that misclassified at the deepest EC level, and present the examples where our model can be misled by heterophilic edges. Specifically, enzyme P73735, whose true EC number is 1.6.5.12, was misclassified BC 1.6.5.9, as three out of four edges in the structural similarity graph connect to enzymes with EC 1.6.5.9 (Q8CPV5, Q8GXR9, and PO0393), as shown in the left part of Fig. IT Similarly, enzyme B2KZE7, with EC number 3.4.13.22. was incorrectly assigned EC 334.13.20. In this case, the only edge for B2KZE7 in the active site similarity graph links Q8BUG2 from the training set, which also has an EC number of 3.4.13.20. The right part of Fig. 11 demonstrates the identified similar local motifs. Based on the above observations, we believe that improving both the quantity and quality of similarity ellatonnshpss-especiilll through more precise structural and active site information-wiin enhance performance in these difficult cases.
G BROADER IMPACTS
Our method contributes to more effective enzyme function prediction, which could facilitate the understanding of enzyme roles in various biological processes. The improved prediction accuracy has potential implications for both fundamental research in biotechnology and downstream industrial applications.
25

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Published as a conference paper at ICLR 2026
H
LLM USAGE
Per author guidelines, we disclose the use of Large Language Models for only writing polish.
26


Reviews:
[{"review_id": "UFt1iIVS9M", "reviewer": "Reviewer_znFn", "summary": "This paper introduces PoinnCARE, a hyperbolic multi-modal learning framework for enzyme function classification. PoinnCARE integrates three modalities — protein sequence, 3D structure, and active site motif — into a unified representation. The representations are used to train a hyperbolic GNN in order to model the hierarchical relationships of the Enzyme Commission (EC) classification tree. Trained on an updated CARE benchmark dataset, PoinnCARE achieves state-of-the-art enzyme classification accuracy across several test sets, including low-homology and promiscuous enzymes.", "questions": "- How sensitive is the performance to the choice of hyperbolic dimension or curvature parameter?\n- How does the model handle noisy or missing active-site data?\n- What is the training time and computational cost compared to CLEAN?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Originality: The integration of hyperbolic geometry with multi-modal structural representations (global structure + active site graphs) for enzyme classification is novel and elegant.\n- The hierarchical nature of EC numbers fits naturally with hyperbolic geometry.\n-  Combining sequence, structure, and active site information offers richer functional understanding than sequence-only baselines.\n- Strong empirical performance: PoinnCARE consistently outperforms 12 state-of-the-art methods (ProtT5, ESM-2, CLEAN, etc.), especially on low-similarity and multi-functional enzyme subsets.\n- Hyperbolic representations are robust and efficient: achieve comparable or better accuracy at much smaller dimensions (e.g., 32 vs. 512) compared to CLEAN representations.\nExpanded the CARE dataset with active sites and structure for the protein-ml community.", "weaknesses": "Presentation clarity:\n- While well-written, the methods section could better explain the intuition behind “graph diffusion” and “dual hyperbolic alignment” for readers unfamiliar with those concepts.\n\n-Requiring active site motif limits generalization to unknown enzyme reactions or reactions that lack detailed enzymology studies.", "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": "SYsL3j2lvC", "reviewer": "Reviewer_e3qB", "summary": "This paper presents PoinnCARE, a novel framework for Enzyme Commission (EC) number prediction. It compellingly argues that existing methods fail by (1) not adequately modeling the hierarchical, tree-like structure of the EC classification system and (2) overlooking critical multi-modal data, specifically protein structure and active site information. The core proposal is to solve this by embedding multi-modal enzyme data (sequence, structure, and active site) into hyperbolic space, which is theoretically well-suited for hierarchical data.", "questions": "Is it possible to further simplify the framework so that the overall complexity could be lower.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "(1) The paper's greatest strength is its clear and theoretically-grounded motivation. The introduction clearly identifies two major limitations of prior work: ignoring the EC hierarchy and overlooking multi-modal data . They also provide a strong theoretical case for why using hyperbolic space. \n\n(2) The experimental section is thorough, rigorous, and provides powerful evidence for the paper's claims. PoinnCARE consistently achieves the highest accuracy in nearly all cases. The authors have also provided extensive ablation studies to support the effectivness of their framework.", "weaknesses": "The most significant con I see of this paper is that it seems to require heavy hyperparmeters tuning. Table 8 lists the final hyperparameters, which is good for reproducibility. However, it reveals a potential weakness: the modality-weighting parameters are different for each test set. \n\nBefore any learning occurs, the framework requires running multiple computationally intensive bioinformatics tools. This includes using Foldseek to compute all-vs-all structural similarity and Folddisco to compute all-vs-all active site motif similarity. This is more complex than a model that simply takes a protein sequence as input.", "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": "MyIZoZDtwt", "reviewer": "Reviewer_B891", "summary": "This paper introduces PoinnCARE, a hyperbolic multi-modal learning framework for enzyme function prediction. By combining information from enzyme sequences, structures, and active sites, the approach leverages graph diffusion and dual-graph alignment within hyperbolic space to encode hierarchical relations informed by the Enzyme Commission (EC) system. Extensive experiments on the CARE benchmark demonstrate that PoinnCARE achieves improved accuracy over a strong set of baselines across several challenging test splits.", "questions": "1. Could the authors please clarify the reasoning behind the exclusion of state-of-the-art specialized models from the evaluation?\n2. What is the rationale for choosing to perform GNN operations in the origin's tangent space rather than the local node's tangent space? Beyond \"simplicity,\" is there any theoretical or experimental evidence (e.g., a comparison of these two aggregation methods within the PoinnCARE framework) to support this decision?\n3. Given the extreme sparsity of $G^{(a)}$ and the shared $H^{(0)}$ input, how can the authors demonstrate that $H_{(a)}$ has learned \"active site\"-specific information that is meaningful for prediction and distinct from $H_{(s)}$? Is there any qualitative or quantitative analysis of the differences between the $H_{(a)}$ and $H_{(s)}$ embedding spaces (e.g., t-SNE visualization or mutual information analysis)?\n4. Why was a simple linear weighted sum chosen as the final modality fusion method? Did the authors experiment with more complex fusion mechanisms (e.g., concat + MLP, or cross-modal attention)?\n5. In constructing $G^{(s)}$ and $G^{(a)}$ (Sections B.1 and B.2), how were the similarity thresholds $\\delta^s=0.3$ and $\\delta^a=0.05$ chosen? How sensitive is the model's performance to these thresholds?\n6. Could the authors analyze cases where PoinnCARE makes errors at the deepest EC digit level (level 4), and provide qualitative examples? Are there biological patterns (e.g., convergent evolution) that systematically challenge the model?\n7. How do the computational and memory costs of the hyperbolic GNN approach compare empirically to standard Euclidean GNNs, given the noted $O(nd)$ overhead?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Integration of multiple modalities: The paper goes beyond sequence-based modeling by integrating experimentally determined or predicted enzyme structures and active site annotations, which addresses the intrinsic complexity of enzyme function prediction.\n2. Hyperbolic embedding with theoretical justification: Embedding enzyme representations in hyperbolic space is both theoretically motivated  and practically validated. The paper rigorously discusses why hyperbolic geometry is ideal for modeling the EC system's hierarchy.\n3. Comprehensive and robust empirical evaluation: The method is benchmarked across four different and increasingly challenging test scenarios from CARE, with comparisons to a wide range of recent and classical baselines, including CLEAN, CLEAN-Concat, various PLMs, and LLM approaches. Tables 2, 3, and supplemental metrics (precision, recall, F1; Tables 9–14) consistently show improvements of PoinnCARE, validating its robustness to sequence diversity and test set complexity.\n4. Ablation and dimensionality studies: The results in Figure 6 and Table 16 demonstrate that performance gains are attributable to each design component, and PoinnCARE's effectiveness persists even at smaller embedding dimensions, reinforcing the theoretical claims regarding hyperbolic geometry.\n5. Reproducibility efforts: The authors provide detailed data and implementation information, facilitating future reproduction.", "weaknesses": "1. Lack of comparison with advanced models: This paper uses enzyme structure and active site information, but the specialized models it compares against are limited to the sequence-based CLEAN and its derivatives. It does not include comparisons with structure-based models such as EnzymeCAGE (Liu et al. 2024) and GraphEC (Song et al. 2024).\n(1) Liu, Yong, et al. \"EnzymeCAGE: a geometric foundation model for enzyme retrieval with evolutionary insights.\" bioRxiv (2024): 2024-12.\n(2) Song, Yidong, et al. \"Accurately predicting enzyme functions through geometric graph learning on ESMFold-predicted structures.\" Nature Communications 15.1 (2024): 8180.\n2. Questionable choice of hyperbolic GNN architecture: PoinnCARE adopts the Poincaré Ball Model and performs GNN aggregation and transformation in the tangent space at the origin ($o$). The authors state this choice was made \"For simplicity\". However, HGCN (Chami et al., 2019) explicitly argues for and demonstrates the superiority of aggregation in the local tangent space of each center node ($x_i^H$). PoinnCARE's architectural choice seems to be a simplification that may lead to suboptimal representation power. The paper does not provide sufficient justification that this \"simple\" choice is reasonable or equivalent to local-space aggregation.\n(1) Chami, Ines, et al. \"Hyperbolic graph convolutional neural networks.\" Advances in neural information processing systems 32 (2019).\n3. Concerns about the efficacy of the active site modality: The paper admits that the active site data is extremely sparse, with \"more than half of the enzymes have no annotated active site residues\". Despite using graph diffusion, the information foundation for this modality is very weak. Furthermore, the input features $H^{(0)}$ for both hyperbolic GNNs are identical. This introduces a risk: the representation $H_{(a)}$ learned by the GNN on $G^{(a)}$ ($f_{hyp}^{(a)}$) might just be a variant of the $H^{(0)}$ features on a highly smoothed (post-diffusion) graph structure, without capturing much genuinely unique \"active site\" functional signal. The contribution of this modality may be overestimated.\n4. Oversimplified modality fusion: The final fusion method for prediction is a simple weighted sum: $\\beta_{s} \\cdot H_{(s)} + \\beta_{a} \\cdot H_{(a)}$. Given the heterogeneous nature and different sparsity levels of the two modalities (structure vs. active site), this linear, static fusion method is likely suboptimal. The paper does not explore more dynamic fusion mechanisms (e.g., attention, gating).\n5. Positioning in relation to closest prior work: Several highly relevant recent papers are not cited or discussed, particularly those specifically focusing on hyperbolic multimodal taxonomy or hierarchical enzyme function prediction. This weakens the contextualization and differentiation of the method’s originality.\n(1) Gong, ZeMing, et al. \"Hyperbolic Multimodal Representation Learning for Biological Taxonomies.\" arXiv preprint arXiv:2508.16744 (2025).\n(2) Li, Nan, et al. \"Hyperbolic hierarchical knowledge graph embeddings for biological entities.\" Journal of Biomedical Informatics 147 (2023): 104503.\n6. Insufficient analysis of failure cases: The analysis leans heavily on aggregate metrics. It would be helpful to present examples or qualitative analysis, where the method fails, especially at deeper EC levels. There’s a lack of introspection on possible errors, such as misclassification of enzymes with convergent functions but divergent structures or sequences (a case hinted at by Figure 3, but not explored in error analysis).", "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)