Fast and Interpretable Protein Substructure Alignment via Optimal Transport
Authors: Zhiyu Wang
Bingxin Zhou
Weishu Zhao
Yang Tan
Jing Wang
Pietro Lio
Liang Hong
Venue: ICLR 2026 Poster (2026)
Keywords: Protein substructure alignment
Residue-level representation
Optimal transport
Deep learning
Structural bioinformatics
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: PLASMA efficiently aligns protein substructures at the residue level using differentiable optimal transport, producing interpretable alignment matrices and similarity scores for clear analysis..

Abstract: Proteins are essential biological macromolecules that execute life functions. Local motifs within protein structures, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution and enabling protein engineering. Existing computational methods struggle to identify and compare these local structures, which leaves a significant gap in understanding protein structures and harnessing their functions. This study presents PLASMA, the first deep learning framework for efficient and interpretable residue-level protein substructure alignment. We reformulate the problem as a regularized optimal transport task and leverage differentiable Sinkhorn iterations. For a pair of input protein structures, PLASMA outputs a clear alignment matrix with an interpretable overall similarity score. Through extensive quantitative evaluations and three biological case studies, we demonstrate that PLASMA achieves accurate, lightweight, and interpretable residue-level alignment. Additionally, we introduce PLASMA-PF, a training-free variant that provides a practical alternative when training data are unavailable. Our method addresses a critical gap in protein structure analysis tools and offers new opportunities for functional annotation, evolutionary studies, and structure-based drug design. Reproducibility is ensured via our official implementation at https://github.com/ZW471/PLASMA-Protein-Local-Alignment.git.

Published as a conference paper at ICLR 2026
FAST AND INTERPRETABLE PROTEIN SUBSTRUCTURE ALIGNMENT VIA OPTIMAL TRANSPORT
Zhiyu Wang 1.2 Bingxin Zhou'
Jing Wang'
Yang Tan'
Weishu Zhao'
Pietro Liò² Liang Honglt 1 Shanghai Jiao Tong University.
2 University of Cambridge.
ABSTRACT
Proteins are essential biological macromolecules that execute life functions. Lo- cal structural motifs, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution and enabling protein engineering. Existing computational methods struggle to identify and compare these local structures, which leaves significant gap in understanding protein structures and harnessing their functions. This study presents PLASMA, seep-learning-beee based framework for efficient and interpretable residue-level lo- cal structural alignment. We reformulate the problem as regularized optimal transport task and leverage differentiable Sinkhorn iterations. For pair of in- put protein structures, PLASMA outputs clear alignment matrix with an in- terpretable overall similarity score. Through extensive quantitative evaluations and three biological case studies, we demonstrate that PLASMA achieves ac- curate, lightweight, and interpretable residue-level aligmment. Additionally, we introduce PLASMA-PF, tive when training data are unavailable. Our method addresses a critical gap protein structure analysis tools and offers new opportunities for functional anno- tation, evolutionary studies, and structure-bui drug design. Reproducibility is ensured via our official implementation at https: htt//gittt thub. com/ 2W471/ - www.gnment..ggeemmmmmmme
training-free variant that provides a practical alterna-
P
INTRODUCTION
Proteins are essential macromolecules responsible for life functions, from catalysis and signal trans- duction to structural support and transport. Local structural motifs (e-g., catalytic residues, binding pockets, metal metal-binding sites) are critical for understanding mechanisms, designing therapeutics, and guiding protein engineering (Mills et al. 2018). Structural conservation three to ten times stronger than sequence conservation across evolution, suggesting that local structural comparison reveal functional relationships invisible to sequence-based methods (Hvidsten et al. 2009).
Despite their importance, existing computational methods primarily emphasize global structure comparison or sequence alignment. The inability to detect local structural motifs, i.e., compact three-dimensional residue arrangements that often concentrate around catalytic pockets interac- tion sites, prevents researchers from understanding protein evolution, predicting functions un- characterized proteins, and rationally designing proteins with desired properties. While large-scale resources like AFDB (Jumper et al., 2021 Varadi et al., 2022) open a unique opportunity to un- cover conserved motif's across the protein universe, active sites often comprise spatially proximate residues that may be widely separated in sequence or embedded within different overall fold archi- tectures (Lu al. 2018). Addressing this gap is key to advancing our understanding of protein function and evolution.
The development of robust local structure aligmment methods specifically targeting local structural motifs is not merely a technical challenge but a fundamental requirement for advancing multiple areas of biological research and application. Existing methods for protein substructure alignment
"Equal contribution first authors. Corresponding authors (bingxin.zhou@e @st..esssuu.nn.... (ang((liang@suu.cdu...)

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Query Frotein
Aligmmnt Matrix
Aligned Substructures
Pa
H
Pretrained PRI Rackhnnn
Representations
PLASMA
Pc
H
0.969
K
Describes the regited substructure siilanty
Algnment Score
Candidate Protei
Siamese Network
Tranport Plan [Alggment Matric)
Substructure Similarity
Alignment Score K
Cost Matrik
8
C
Ω
Sinkhom
H
Confidence Weight
Output
Dageraal Consiiaiion
Output
TRANSPORT PLANNER
PLAN ASSESSOR
Figure 1: PLASMA Overview. PLASMA converts residue-level protein embeddings into substruc- ture alignments using optimal transport. Transport Planner learns cost matrices with Sinkhorn iterations, and Plan Assessor produces similarity scores. The framework provides alignment ma- trices and quantitative scores without requiring model-specific designs.
can be broadly divided into three categories. The first relies on template-based searches, where predefined motifs are used to identify similar substructures (Bittrich et al., 2020, Kim et al. 2025). These approaches are effective for detecting well-characterized patterns but cannot uncover novel similarities, making them unsuitable for pairing novel structural motifs. The second category estimates substructure similarity based on the global similarity of entire protein structures. Several studies leverage structural superposition (Zhang] 2005) or structural tokenization (Holm) 2020 to produce residue-level matches with sequence alignment, but they are computationally demanding and difficult to scale to large datasets. More recent embedding-based methods (Hamamsy et al., 2024) are enabled by advances in protein representation learning, which make alignment faster and competitive for whole-protein comparison. However, they compress residue-level information into coarse embeddings, which causes problems in producing interpretable local alignments. The third category directly addresses substructure alignment by constructing pairwise similarity matrices and using dynamic programming to find matching regions. This approach captures local similarities more accurately than global methods and produces scores that reflect substructure correspondence
(Kaminski et al. 2023 Liu et al. 2024 Pantolini et al. 2024). However, the results can be influenced by overall structural patterns, and alignment matrices have limited interpretability since they are optimized for algorithmic performance rather than clarity. Additionally. these methods are typically untrainable and cannot adapt specific alignment tasks incorporate domain knowledge, limiting their ability to improve through experience or be customized for particular biological contexts.
The challenges above point the need for novel protein substructure alignment method that com- bines accuracy, efficiency, and clarity. To this end, we explore optimal transport (OT), a mathe- matical framework proven effective in alignment problems (Mena al. 2018). In particular, the differentiable Sinkhorn algorithm (Sinkhorn & Knopp 1967| Cuturi] (013) 3) has shown strong ability uncover meaningful correspondences in 3D shape analysis (Eisenberger et al., 2020) and sub- graph matching (Ramachandran et al., 2024). Notably, these Of-based alignment methods assume strict one-to-one correspondences between all residues or that one of residues is fully contained within the other. These constraints do not hold for protein substructure alignment, functionally similar regions may only partially overlap and vary length across proteins.
To address the aforementioned limitations, we reframe protein substructure alignment an OT problem and introduce PLASMA (Pluggable Local Alignment via Sinkhorn MAtrix), As illustrated in Figure I PLASMA operates residue-level embeddings from pre-trained protein representa- tion model and identifies the residue-level alignment between protein pairs. The Transport Planner computes the pairwise matching using learnable cost matrix and differentiable Sinkhorn iterations (Section B) and the Plan Assessor then summarizes the resulting alignment matrix into a single similarity score reflecting the overall similarity of the matched substructures (Section PLASMA
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functions lightweight, plug-and-play module for protein representation models. It is capable of efficiently aligning partial and variable-length matches between local structural regions.
Our work addresses these limitations through three contributions. First, we introduce formulation of residue-lovel local structural alignment based on regularized optimal transport with a learnable geometric cost, which provides principled and flexible way define correspondence and enables efficient, fully parallel implementation. Second, this formulation enables clear and interpretable residue-residue correspondences and naturally supports partial, variable-length, and non-sequential motif alignments, resolving the difficulty of obtaining reliable local alignments. Third, PLASMA produces a normalized and interpretable similarity score through its OT-based objective, overcom- ing the limitations of existing approaches whose alignment matrices or similarity measures lack a consistent probabilistic meaning. Our experiments show strong generalization to low-homology structures, and the case studies demonstrate the biological interpretability and practical utility of the resulting alignments.
PROTEIN SUBSTRUCTURE ALIGNMENT VIA OPTIMAL TRANSPORT
N residues and a candi- date protein P. = (Tr.1....,,, Pe.M. } of M residues. Suppose the two proteins contain local structural motifs F, = [fg....... fq.n] Pg and F. = ffe.1..... f..mm. S Pe. where n S N and m I M. The objective of protein substructure alignment is: (1) to identify the corresponding fragments F, and F. within P, and Pe.. and (2) to score their level of similarity.
Problem Formulation Consider query protein P. = (Tg.1....::
The task is challenging for several reasons: the overall structures of Pg and Pa may differ substan- tially, the fragments F, and J. may vary in sequence length or composition, and alignments require remaining meaningful in a biological context. In particular, biologically relevant alignments should capture functional similarities, such as common enzymatic activities or conserved structural roles.
Optimal Transport Reformulation To address the protein substructure alignment problem, reformulate as an regulay--e OT problem between the residues of two proteins Pg and P.. Each protein is represented as a of residue embeddings that capture local biochemical and structural context. The OT solver then computes a soft alignment matrix Q E IR N X.M by assigning weights between residues so as minimize the overall transport cost C. This formulation bypasses explicit fragment enumeration, naturally accommodates partial and variable-length matches, and produces interpretable alignment matrices that highlight the underlying substructures (Appendix A
Overview of PLASMA We implement regropy-regularizzed OT and propose PLASMA, module that transforms H,, E xd xd and H. E xx residue-level d-dimensional hidden representations of P. and Pa (e.g., from pre-trained protein language models), into soft alignment matrix Ω e N.M and a similarity score E [0, 1]. In our experiments, we instantiate Hg and He with seven diverse protein representation backbones (Section G). and observe consistent alignment behavior across them, indicating that PLASMA is not tied to particular choice of encoder. Formally.
(2, x) PLASMA(H, Ho).
PLASMA consists of two complementary components (visualized in Figure D with details intro- duced in the next two sections). The first component, the Transport Planner, produces Q to highlight local correspondences between P, and P.. The second component, the Plan Assessor, summarizes this aligmment matrix into a similarity score k E [0, 1], providing a quantitative measure of align- ment quality. The framework achieves computational complexity of O(N2) (Appendix B
TRANSPORT PLANNER
The Transport Planner module handles the core OT computation. It defines cost functions between residue pairs and solves the regularized OT problem to produce an Q that captures residue-level matching between query and candidate proteins (P,, P.).
Cost Matrix We formulate a learnable cost matrix with a siamese network architecture to capture complex residue-level similarities. This approach enables PLASMA to learn task-specific represen-
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tations that optimize alignment quality through end-to-end training. The cost from rg.. to reg is denoted by Cij in the learnable cost matrix, defined as
Ci = [ooo
de (e(LN(ho.a))
(2)
Here hg and fo.j denote the hidden representations of residues fg and Te.j. respectively. The operator [+]+ applies hinge non- non-linearity, shown to outperform dot-product similarity in subgraph matching tasks (Raj et al. 2025). The layer normalization LN(.) facilitates robust optimization dynamics with numerical stability and scale-invariant representations. The siamese network do(-) processes query and candidate residues using a twin architecture with shared parameters 0.
Learnable and Parameter-Free Implementations The siamese network architecture can be cho- sen flexibly, ranging from Transformer-basee (Hamamsy et al. 2024) models to graph neural net- works (Jamash al. 2024), depending on the inductive bias of the input data and the computational budget. Here we also provide a simple implementation using fully connected layers:
be (h) ReLU(h. W1) W2.
where W1 E Rdxd and W2 E Rdd xd' are learnable transformation matrices with hidden di- mension. For simplicity, omit the subscript of H as the siamese network applies the same set of parameters to both the query and candidate proteins. This lightweight design serves as an ef- fective default while allowing more sophisticated architectures be substituted without modifying the overall PLASMA architecture. In addition, for scenarios with a lack of labeled data, we in- troduce parameter-free variant, PLASMA-PF, which bypasses the siamese network and operates directly on residue embeddings. The cost used in the OT objective follows Ø with no architectural components removed other than the encoder. PLASMA-PF preserves the fundamental alignment functionality and offers a fast baseline for substructure similarity evaluation. Notably, the learnable version remains preferable for improved stability and extrapolation (See Section and Figure
Sinkhorn Alignment Matrix Based on the cost matrix C defined in we formulate the cor- responding OT problem (Appendix A and solve it using the Sinkhorn algorithm (Cuturi 2013). The algorithm approximates the OT plan by iteratively scaling the matrix to satisfy the marginal constraints with row and column normalizations, ensuring that the total alignment weights of each residue are properly distributed across residues of the other protein:
(t)
1(++1)
ij
where 2
(4)
ΣM 0
(1)
IN
2
The iteration is initialized as ()) exp(-C/r) where is temperature parameter controlling the alignment sharpness (Appendix Dp. The optimal 52" = (T) after T iterations serves as the Sinkhorn alignment matrix. For simplicity, we denote as 92 in the subsequent discussions.
The original Sinkhorn algorithm converges to fully doubly stochastic matrix, forcing each query residue to distribute across all candidate residues (and vice versa). This strict matching is often bio- logically meaningless, most residues lack relevant counterparts. PLASMA achieves implicit par- tial alignments via two mechanisms. First, early termination preserves sparsity by limiting Sinkhorn iterations. letting poorly matching residues retain low weights. Second, the temperature parameter T controls alignment mass, with lower values producing sparser, focused alignments. Together, these mechanisms emphasize biologically relevant correspondences while avoiding forced matches, without hard constraints on the transport budget (Caffarelli & McCann 2010, Figalli 2010). Rep- resentative alignment matrices demonstrating these patterns are shown in Appendix
PLAN ASSESSOR
The Plan Assessor receives the alignment matrix Ω from the Transport Planner and transforms it into an interpretable single similarity score [0, 1] that quantifies the existence and degree of similarity of the aligned substructures. This is computed by first calculating a substructure similarity score for the aligned regions, then adjusting with confidence weight correct potential bias.
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Substructure Similarity We calculate the alignment score matched substructure. With threshold p. a residue pair rq.a E Pg and re.f E Pe is treated as matched if 2, > p. The matched residues then form two sets, R2 = (r, Vi, substructure is a subset of these residues. The representation of the matched substructure can be ap- proximated by summing the embeddings of residues from Ry and R.. Therefore, the substructure similarity score s E [-1, 1] is defined as the cosine similarity between the summed representations:
p} and R. {rej] Vi, S4y > p}. A matched
EiER, hag EjER. haj 8 1EiER, hegill EJER, hesll
(5)
This substructure similarity score is effective when sufficient number of residues matched between the two proteins. However, it becomes less reliable when only a few residues are aligned or when the matched residues are dispersed along the sequence rather than forming continuous region. In such cases, the score reduces to a residue-level similarity measure, which may appear deceptively high even though the aligned residues do cluster into structurally interpretable substructure. We thus introduce a confidence weight to adjust the initial similarity score.
Alignment Score with Confidence Weight Correction The confidence weight a E [0, 1] is de- rived from Ω using 2D convolution with identity kernel K = T1 TR of size k:
1-1 Oij Σ
A
Pitus+o Kwo
Σ Rinas+a
(6)
This convolution operation highlights continuous diagonal segments l and emphasizes core re- gions where consecutive residues in the query align with consecutive residues in the candidate. A max-poot max-pooling layer then produces a scalar confidence weight a = max,,; aij. summarizing the strongest local alignment signal used to weight the similarity score and obtain the final alignment score ń. = 8 E [0, 1]. Here 8+ is the non-negative substructure similarity score. This formulation provides an intuitive and interpretable measure:
0 indicates residue matches and resents perfect substructure alignment. We follow the convention of established alignment methods (e.g., TM-align (Zhang. 2005)) and exclude negative similarity values, since matched substructures with opposite orientations in the representation space lack meaningful biological interpretation. See Appendix [ for visual examples of alignment matrices with different similarity scores.
rep-
MODEL OPTIMIZATION
PLASMA trained with two complementary objectives: predicting the presence of aligned sub- structures via the alignment score and recovering precise residue-level matches via the alignment matrix Q2 Training data consists of protein pairs (P,, Po), where a subset of pairs contains matched substructures with shared functions. For each input protein pair, two mask vectors Mg E {0, 1)M and Me E {0, 1 M are respectively defined to indicate the position of target substructures F, and F., where 1 marks the residues that belong to the substructure of interest.
Alignment Score Optimization The alignment score & serves as the model's prediction on whether the input protein pair contains aligned substructures. We define the ground truth y if the pair contains matched substructures and = 0 otherwise. The prediction is optimized by LBCE y (k)) (1 - y) log(1 (x)). where (-) is the sigmoid function.
Alignment Matrix Optimization Unlike the alignment score, optimizing the alignment matrix is challenging because unlabeled residues may correspond to valid but unannotated matches. Treating these residues negative examples would impose inappropriate penalties the model. To address this, we propose the Label Match Loss (LML) to focus exclusively on the labeled substructures. Specifically, when ||Melli I 0 and ||M > 0, the LML for protein pairs is defined
LIMI. II[ - 22 M,l+ll//||Molls
where [+]+ retains only non- non-negative elements, and || denotes the & norm. This loss evaluates how well the constructed alignment matrix Ω aligns the labeled substructures FF). in (Pq. ; P.). For
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each residue ry E Pe. (2 Mg)g gives the alignment weight with respect to labeled residues in Py-- The non-negative contributions by [Me- - ?2 M,]+ are normalized by ||Mella across all labeled residues. When no labeled substructures exist, LLML = O, which allows the model to focus on known substructures without penalizing unlabeled but potentially valid matches. This loss provides an optional bias toward annotated local structural motifs when such labels exist. These regions are typically small and structurally meaningful (e.g., catalytic or binding motifs), and emphasizing them helps the model avoid being dominated by background alignments.
The final L LACE + LLML. jointly detects substructure existence by k. and localizes known substructures by Ω while staying robust to missing or incomplete labels in the training data.
6 EMPIRICAL ANALYSIS
We conduct extensive quantitative and qualitative evaluations comprehensively assess the valid- ity and advancement of PLASMA in local structural motif alignment tasks. All experiments are programmed with PyTorc v2.5.1 and run on NVIDIA RTX 4090 GB GPU.
6.1 EXPERIMENTAL SETUP
Prediction Tasks and Benchmark Datasets Our experiments are based on residue-level func- tional alignment benchmark, VenusX (Tan et al. 2025a). We consider three common classes of functional substructures: activation sites, binding sites, and motifs. Across all test sets, the sequence identity between training and test proteins is kept below 50%. For quantitative evaluation, two levels of difficulty: (i) interpolation (test_ing inter), where the test set contains proteins from InterPro families already present in training; and (ii) extrapolation (test_extra), where the test set only includes novel substructures from unseen families, Further details are in Appendix C.T
design
Baseline Methods We compare PLASMA with popular baselines in protein structure alignment, including structure-based methods (FOLDSEEK (Van Kempen al.) 2024). TM-ALIGN (Zhang 2005), and TM-VEC (Hamamsy et al. 2024 and seteedding-bseed methods (EBA (Pantolini et al, 2024 and COSINESIM, a cosine similarity over protein embeddings). For all embedding- based methods, we implement seven popular pre-trained models to extract residue-level sequence and structure representations, including PROTTS (Elnaggar al. 202Ip. PROSTTS (Heinzinger al. 2024), ANKH (Flnaggar et al. 2023), ESM2 (Lin et al. 2023) PROTBERT (Brandes et al. 2022).
T'M- VEC (Hamamsy al. 2024), and PROTSSN (lan et al. 20255 All baselines use the authors'
official code and checkpoints (see Appendices D for details).
To assess the ability to detect the existence of local structural motifs, we use standard binary classification metrics, including ROC-AUC, PR-AUC, and F1-Max. Additionally, to evaluate alignment quality, we introduce the Label Match Score (LMS) by 7 with LMS = 1 1- LML to measure correspondence between predicted alignments and annotated functional regions.
Evaluation Metries
6.2 QUANTITATIVE PERFORMANCE EVALUATION
Table reports performance on test_extra which contains functional substructures from pro- tein f'amilies not seen during training. This setting evaluates the generalizability of the alignment framework, which is essential in practice because new functional substructures are continuously discovered. Full results on seven backbone models are provided in Appendix [F] and all hyperpa- rameter and dataset details are summarized in Appendix on cest_inted nter are reported in Appendix
Corresponding interpolation results
Across all three substructure detection tasks and all evaluation metrics, PLASMA achieves consis- tent top performance, highlighting its robustness in capturing fundamental local structural similar- ities for novel substructures beyond the training distribution. PLASMA-PE also performs strongly and remains competitive without task-specific training. However, unlike in the interpolation setting, PLASMA-PF does not surpass the learnable PLASMA variant test.extra; this emphasizes the value of supervised examples in improving alignment accuracy for entirely new functional sub- structures. In contrast, baseline methods show large performance variation across backbone models.

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Table I: Model performance on test_ext (mean + std over three independent seeds). Colors indicate relative performance versus TM-ALIGN.
Motif
Binding Site
Active Site
Metries
Methods
ANKH
ESM2
PROTSSN
ANKH
ESM2
PROTSSN
ANKH
ESM2
PROTSSN
PLASMA
98 008
997.003 1013
.96 016
99 n08
98 013
98g
.98_ 0112
.98, 010
.97
ROC-AUC
PLASMA-PP
98
g3 u0s
g00
92 002
_9
_6g.uo
97. ous
EBA
90 053
92+.00 021
322.04 043
97+ 021
301 060
97=.018
97+ 012
13 one
252.019
2433
770.00 018
2,010
724.000
.70
012
79
- 083
Foldseek
894.003
90g.0m o1a
.8 002
TM-Align
.114.014
+ 4.040
403,000
PLASMA
.98 011
.97. 0..4
.96 017
.98
.97 01e
010
.97=
.98.; 011
.97
PLASMA-PP
_30
.951.000
192..00
.981
.901.on
195
_18_008
.96 n06
.97
PR. PRA
EBA
91g
.93 o1n
388
.98
.96 nas
.8
.97 012
.97 012
Backbone
86
774.041
82
2.2
67
.6
96
84g.000
80
Foldseek
7,6.000
.81
TM-Align
86
80
.04 0.12
PLASMA
97=.009
.5s 018
92
.91
96+ 090
.984. no0
98 018
97=.001
.9:
PLASMA-PP
962.013
.90,.000
844..00
.02
.85 082
.00
-7
.94g.010
.90
FL-MAX
EBA
86 033
.87g
000 00c
97 021
.93 009
000
99
.7 008
.00g
Backbome
.7 008
.70
.73g 013
.0.4.04
.24 087
60
92 0.0
75g 044
.71g
Foldseek
97 001
.96 015
TM-Align
.76 015
.87g
.00g
LMS
PLASMA
.75g 015
69 018
.2 648
.82g.oo 000
.77 105
1 onn
900_ 054
.87 nae
.7. ost
PLASMA-PF
78 005
48
23 021
85 .08
49
33...mn
029
.68g.057
13g
Best
Baseline (TM-Align)
Worst
EBA performs reasonably well with sequence-based ANKH and ESM2 yet drops substantially with structure-based PROTSSN, especially under the extrapolation split. FOLDSEEK and TM-ALIGN remain consistently below PLASMA across nearly all conditions, reflecting the limited usefulness of global structural similarity for residue-level motif detection.
Beyond accuracy, PLASMA demonstrates exceptional computational efficiency. As shown in Figure 2 PLASMA achieves the best performance while requiring minimal time per protein pair- approxiaxxiy 10ms for PLASMA and 7ms for PLASMA-PF. This represents roughly 50 times speedup over global structure alignment methods like TM-Align and Foldseek, which require costly structural superposition, and about times faster than EBA due to PLASMA's fully dif- ferentiable OT formulation that is efficiently accelerated on GPUs, compared to EBA's inherently sequential dynamic programming approach.
6.3 QUALITY OF PREDICTED ALIGNMENTS
Beyond quantitative metrics, assess PLASMA's robustness in identifying biologically meaning- ful substructures by examining both alignment scores and alignment matrices.
PLASMA effectively distinguishes proteins with shared local functional substructures overall structural similarity is low. Figure provides evidence from two perspectives, with all embedding-bee methods obtaining protein representations from ANKH. Figure B compares sim- ilarity score distributions for protein pairs from test_inted where PLASMA and PLASMA-PF clearly separate positive and negative pairs. This advantage comes from the OT framework. which emphasizes local correspondences independent of overall similarity. In contrast, EBA and COSI- NESIM show substantial overlap between positive and negative distributions. EBA in particular lacks an upper bound on its scores, making them difficult to interpret and subject to calibration problems (i.e., scores cannot be directly used as probabilities and lead to unstable thresholds). Fig- ure B further groups test-set alignment scores by TM-score to assess performance under different levels of global similarity for protein pairs. Although all methods degrade as TM-score decreases, PLASMA and PLASMA-PE consistently maintain high ROC-AUC values above 0.9, whereas base- line EBA, COSINESIM, Foldseck, and Tllali deteriorate sharply on similaarty samples when TM-score is sufficiently small (e.g., lower than 0.5).
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Motif
Binding Site
Active Site
1.0
PLASINA
ROC-AUC
PLASMA
0.9
EBA
TM-Vec
0.8
Foldseek
TM.Align
200
400
600
800
200
400
600
200
400
Time Cost (ms)
Time Cost (ms)
Time Cost (ms)
Figure Performance versus computational efficiency comparison. ROC-AUC scores plotted against inference time (milliseconds) for motif and binding/active site detection using PROSTT5 embeddings. Points represent averages across three splits with standard error bars on both axes.
B
Motif
Binding
Active
ERG Soow
10
0.0
0.7
Fiieee Poeeoessroo Scoee
Ti4-ston
Store
TM Score
TK Score
Binding
Figure 3: Alignment quality analysis across different approaches. A. Distribution of alignment scores for positive and negative protein pairs. B. ROC-AUC score trend at different global structural similarity levels.
Motif
Binding Site
Active Site
Backbone
Ankh
ESM2
Prot5SN
PLASMA Pf
0.0
0.6
0.8
0.0
0.2
0.6
0.8
0.0
0.5
0.8
Label Match Score
Label Match Score
Label Match Score
Figure 4: Label Match Score comparison between PLASMA and PLASMA-PE across different substructure types, demonstrating the improved alignment quality achieved through training.
While both PLASMA variants demonstrate strong performance in score-based discrimination, their alignment quality differs. This is evident in Figure $ which compares their performance using the LMS score evaluate correspondence between predicted alignments and annotated regions. PLASMA consistently outperforms PLASMA-PF across motifs, binding sites, and active sites, demonstrating that learning improves the prediction of local structural motifs. By contrast, while EBA also produces alignment matrices, it cannot be meaningfully assessed with LMS: its uncon- strained formulation yields a maximal LMS of 1.0 regardless of true alignment accuracy.
6.4 REPRESENTATIVE ALIGNMENT EXAMPLES
The next experiment evaluates PLASMA's utility in real biological applications. We examine three protein pairs of different substructure sizes (independent of the training set), including simple local motifs, complex rofactor-binding domains, and extended multi-element substructures. In each case, we provide UniProt identifiers. functional descriptions, alignment results, and visualizations from PLASMA and EBA, and corresponding analyses. Appendix N provides additional visualizations that further illustrate the generality of these conclusions. Collectively, these cases show PLASMA detects biologically meaningful local similarities across diverse sequences, structures, and functions.
Conserved Small Helical Motifs Across Functionally Diverse Protein Structures The first case matches local structures between P40343 (Vps27, yeast ESCRT-0 complex component) and
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QRKOLD v5 P40543
PLASMA (Ouns)
EBA
A
AAgrren: Store 2:51
Aigrmeet Score
Query (ONCIOn
Ye
(PR003903 Liquitn meceocingeet
248
250 KE
130
P64215 us COH410
Abgrant Scare
grrnnnt
B
X
(9902008): Sotiy attchnint
Canditule polllc
Longi
Q86W92 Q60258
Nignnert Scare 0.58
Algament Score
(0900032) Lengph
100
200
PRO13NO Starlllllsaaae moot
Card 0808 (065258) Langtt 770
Figure 5: Representative alignment examples across three protein pairs. A, P40343 vs Q8KOLO. B. P64215 vs COH419, C. Q69ZS8 Q86W92. Left: 3D structures with highlighted aligned regions. Center and right: alignment matrices from PLASMA and EBA with zoomed insets. A higher resolution version of this figure can be found at Appendix H
Q8KOLO (ASB2, a mouse E3 ubiquitin ligase substrate-recognition component). The two proteins share apparent sequence homology (21.0% identity) and participate in distinct cellular processes (endosomal sorting versus proteasomal degradation), yet both use analogous helical arrangements for wwwpproooorooiiieooe protein interactions: Vps27's s GAT domain forms coiled-coils for ESCRT-1 recruitment (Curtiss et al., 2007), whereas ASB2 employs ankyrin repeat helices for substrate recognition in the F3 ligase complex. PLASMA assigns high-confidence scores to residues mediating these inter- actions (Figure A). The 3D structure visualization also confirms the alignment of the conserved Leu-X-X-Leu-Leu motif for both proteins (Ren et al. 2008), with aligned RMSD of 0. A. This finding suggests potential convergent evolution of helical protein- protein-binding interfaces across distinct cellular machineries. By contrast, EBA identifies multiple helices, but most correspond nonfunc- tional scaffold regions rather than the relevant interaction motifs.
Structurally and Functionally Relevant motifs of Different Sizes and Metabolic Contexts The second case examines P64215 (GevH, glycine cleavage system H protein from Mycobacterium tu- berculosis) and COH419 (YngHB, biotin/lipoyl attachment protein from Bacillus subtilis) (Cui et al. 2006). These proteins have different overall sequences (25.2% sequence identity) and metabolic functions: GevH shuttles methylamine groups in glycine cataholism, while YngHIB accommodates both biotin and lipoic acid in a single-domain architecture. Despite these differences, both bind similar cofactors and exhibit conserved 3-sheet arrangements necessary for post-translational mod- ification. As shown in Figure 5B, PLASMA successfully aligns the four-stranded 3-barrel archi- tectures. highlighting the critical lysine-containing f-turns with an overall alignment score 0.69 and RMSD of 0.83, whereas the baseline EBA misaligns nonfunctional regions. The alignment of complex conserved structural motifs across protein families demonstrates the potential of PLASMA in revealing modular evolution and conserved cofactor-binding architectures.
Extended Multi-Element Substructures in Cell Adhesion Regulators The third case investi- gates Q69ZS8 (Kazrin, a scaffold protein in Mus musculus) and Q86W92 11prin-31//PFIBBB a human focal adhesion regulator). Despite their different cellular localizations and interaction part-

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ners, they regulate distinct but mechanistically related aspects of cell-cell adhesion: Kazrin organizes desmosomal components in keratinocytes, and Liprin-31 modulates focal adhesion disassembly and cell migration. Yet both proteins rely extended a-helical regions for protein -pretenn interactions (Groot et al.] 2004). As in Figure 5 C. PLASMA successfully aligns complex multi-coil substruc- tures spanning multiple helical segments interspersed with flexible linkers, with overall align- ment score of 0.98 and RMSD 0.82 Å. The alignment highlights conserved leucine-rich motif's and hinge regions that stabilize oligomerization interfaces, revealing analogous scaffolding strategies. In contrast, EBA identifies plausible structures but often misaligns helices or matches nonfunctional scaffold regions, failing to capture more than just biologically meaningful substructures.
7 RELATED WORKS
Protein Global Structure Alignment Global structure alignment methods evaluate overall pro- tein similarity. Classic approaches like TM-ALIGN (Zhang, 2005) are foundational, while modern methods increase efficiency by abstracting structures into ID sequences (FOLDSEEK (Van Kempen
et al. 2024)). representing them as fixed vectors for rapid search (TM-VEC (Hamamsy al. 2024)). or using advanced spatial indexing (GTALIGN (Margelevičius 2024 D. The field has also expanded
to align multiple structures (MTM-ALIGN (Dong et al. (0188), multi-chain complexes (MM-ALIGN
MMukherjee & Zhang 2009)), and diverse macromolecules universally (US- (US-ALIGN (Zhang et all
).22). However, their global nature limits the detection of conserved motif's in dissimilar proteins.
Substructure and Sequence-based Alignment To find local similarities, Lubstructure-basee methods use graph-based residue embeddings (Tan et al. 2024). focus on active-site environments
(Castillo & Ollila 2025), or apply finear-assignmen
formulations (Zhang al. 2025 PLM--ased
residue representations are also widely used from raw embedding similarity scoring (Kaminski et al.)
2023 Liu al. 2024) learned alignment models and embedding-awwin dynamic programming
Llinares-Lppez et al., 2023 lovino & Ye 2024h. OT-based differentiable graph matching has been used to learn structure/function- aware substitution matrices (Pellizzoni et al., [2024), with primary focus on learning matching costs. PLASMA instead targets residue-level local substruc- ture alignment, producing explicit mappings with practical speed and interpretability. Meanwhile, embedding- seres-corr--aaeee based alignment methods remain hard to interpret quantitatively, as their scores are essentially unbounded (Pantolini et al. 2024).
8 CONCLUSION AND DISCUSSION
This work presents PLASMA, a local structural motif alignment framework leveraging regularized optimal transport to detect biologically meaningful local similarities across proteins with diverse sequences, structures, and functions. PLASMA consistently outperforms baseline methods in ac- curacy, efficiency, and interpretability, capturing subtle structural correspondences often invisible global alignments. Its trainable variant benefits from supervision to improve alignment precision, while the training-free variant achieves robust performance without task-specific labels.
Beyond quantitative performance, PLASMA provides clear, residue-level alignment matrices that support mechanistic insights into protein function, evolutionary relationships, and structure-guided protein engineering. Its ability to handle varying substructure sizes and complexities (e.g.. from short helices to extended multi-element domains) demonstrates versatility and practical relevance. Overall, PLASMA establishes new standard for accurate, efficient, interpretable, and practically applicable protein local structural motif alignment.
ACKNOWLEDGMENTS
This work was supported by the grants from National Science Foundation of China (Grant Num- ber 92451301; 62302291), the Al for Science Program by Shanghai Municipal Commission of Economy and Informatization Development Program of China 12024Y and Computational Biology Key Program of Shanghai Science and Technology Commission (23JS 400600).
-TBXX-220XX99 the National Key Research and
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Reproducibility Statement To promote reproducibility, release all source code and trained models under an open-source license, which is available at httpps:/ggithu. com/ 2W4 71/ qit Details of data sources provided in Ap- Task definitions, evaluation protocols, and hyperparameter settings are described in Sections 6. and Appendices (22 Implementation details and instructions for reproducing experi- ments are included in the project repository to facilitate independent verification.
PLASMA-
pendix C.I
Ethics Statement All experiments are conducted on publicly available protein sequence and struc- ture databases. We follow established ethical guidelines in data usage and acknowledge that histori- cal biases present in these resources may be reflected in our results, which is independent of model development.
The Use of Large Language Models (LLM) In the preparation of this manuscript, GPT-5 and GPT-4o were utilized writing assistants. The usage strictly limited improving grammar, clarity, and overall readability. All scientific ideas, experimental results, and conclusions were con- ceived and formulated exclusively by the authors. All text polished modified by the LLM was subsequently reviewed and edited by the authors to ensure that the original scientific meaning was accurately preserved.

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15


Reviews:
[{"review_id": "mDoGDEp0IB", "reviewer": "Reviewer_e2jA", "summary": "PLASMA is novel protein local structural alignment algorithm that uses differentiable optimal transport method with trainable cost matrix. The method is very fast at inference and outperforms baselines on the presented examples. Unfortunately, only one (yet unpublished) benchmark has been used for evaluation, excluding more traditional choices used in the community.", "questions": "- please see Weaknesses\n- \"the sequence identity between training and test proteins is kept below 50%.\"  such a split may not be sufficient to exclude data leakage. Anyway, the authors provide performance data for TM-score similarities below 0.5.\n- can you also show TM-align and FoldSeek results at different levels of TM-score similarity as additional baselines in Fig. 3B?\n- the classical Sinkhorn algorithm has the complexity of O(N^2 log N) for a fixed tolerance. Can you please support your O(N^2) claim, provide more details on the chosen tolerance and provide additional numerical experiments?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The manuscript is well written and motivated\n- The SOTA is exhaustive and correct\n- The baselines are well chosen\n- Both interpolation and extrapolation results are presented\n- The method provides interpretability by normalized similarity scores and alignment matrices\n- Parameter-free version of the network is also presented and demonstrates a strong performance", "weaknesses": "- The individual components and ideas of the method are not novel\n- The paper does not discuss nor demonstrates examples with non-sequential alignments. This can be the actual advantage of the presented algorithm. While traditional sequence alignment (like SW or NW algorithms) is order-preserving (they align sequence A on B while preserving the residue order in both A and B), the optimal transport (OT) is in general not order preserving. Please consider case of fold-switching proteins, for example.\n- More traditional structural alignment benchmarks could have been also used, examples include BALIBASE 2, BALIBASE 3, HOMSTRAD, OXBENCH, SISYPHUS\n- no multiple structural alignment is discussed\n- Training/test splits based on InterPro families may have data leakage, as different families may still share identical local structural motifs or even domains.", "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": "vRZTXxJoZY", "reviewer": "Reviewer_WJJf", "summary": "This submission introduces PLASMA, a method to obtain protein substructure alignment. By embedding each residue of a pair of proteins with a pLM, a soft alignment matrix coupled with an overall alignment score. The alignment matrix is obtained by passing the pLM embeddings through an optional siamese network yielding a cost matrix, to which Sinkhorn iterations are applied. From the resulting alignment matrix, an interpretable score is calibrated to surface regions of high structural similarity. Experiments show very high performance when benchmarked on substructure identification tasks.", "questions": "The plan assessor does a kxk identity deconvolution to detect motifs, but this assumes sequence continuity on both proteins, which would downweight cases where there are structural motifs that are non continuous. Is it possible to remove this component and obtain confidence values on the motifs without it? Can the authors show that diagonal patterns still emerge from diagonal motifs for pLMs?\n- Is it possible to have ablations on the different components of the plan assessor? There are a few elements in there and it would be good to have some insights into the impact of those elements on performance.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper tackles a relevant problem in the field of protein representation learning. The paper is clearly written, the benchmarks are sound and convincing, and the methodology is original. PLASMA clearly demonstrates superior performance while simultaneously also being much faster than some of the previous methods. The VenuX benchmark is a strong set of experiments that clearly show generalization abilities. The testing of various pLMs show that the method is robust and adaptable.", "weaknesses": "Major comments:\n- The claim that PLASMA is \"the first deep learning framework for efficient and interpretable residue-level protein substructure alignment\" is overstated. Clearly there is prior work for the kind of task tackled here (EBA, pLM-BLAST). Foldseek also falls under the category of models described here. epLSAP-Align (https://doi.org/10.1093/bioinformatics/btaf309) is also very similar and should be cited given it leverages the OT formulation on structures directly. Another related method is ActSeek, which should also be cited: https://pmc.ncbi.nlm.nih.gov/articles/PMC12343037.\n- Although a preprint, I would already cite Folddisco as concurrent work, as it fulfills the same nice and needs https://www.biorxiv.org/content/10.1101/2025.07.06.663357v1. If the authors can benchmark against this method it would be great, but not strictly necessary. \n- More generally, I have a feeling that the writing could benefit from a tighter list of contributions in the introductions to clearly contrast the contributions of the work (mostly the machinery on top of the pLM and siamese networks as well as some other mentioned technical contributions like the losses and scores) to other works.\n\nMost of the weaknesses are nitpicks, here are some things I would like to see improve in terms of presentation:\n- I think the results of test_extra currently in Appendix G are the most relevant results since effective generalization is most relevant. Swapping this with table 1 is I think more appropriate, especially considering those results still show strong performance.\n- It would be great to have a concrete percentage for the colors relative to TM-Align.\n- The contrast ratio for the colors in figure 5 is pretty bad and barely readable when printed. The squares subsetting the proteins could be also bigger for the proteins.\n- There is some interchangeable terminology which can be made more precise. \"substructure,\" \"local structure,\" \"motif,\" \"functional site,\" \"active/binding site\" are used interchangeably but they are not completely: motifs can be discontinuous, binding sites often involve side chains only, “substructure” could mean a whole domain.\n- The description of the diagonal kernel could be made a bit more explicit by highlighting it surfaces continuous diagonal elements.\n- \"which causes troubles\" needs to be reformulated, e.g. to \"which causes problems\".\n- appendix references should be made more explicit, indicating more precisely what's in each of them.", "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": "8lIxZ5JM3b", "reviewer": "Reviewer_NvT1", "summary": "This paper works on identifying and understanding protein structure for efficient and interpretable residue-level protein substructure alignment. The authors reformulate the problem as a regularized optimal transport task and leverage differentiable Sinkhorn iterations to solve the alignment problem. Besides, the authors use extensive quantitative evaluations and three biological case studies to demonstrate that the proposed method, PLASMA, achieves accurate, lightweight, and interpretable residue-level alignment. Moreover, the authors propose a training-free variant as an alternative when training data is not available.", "questions": "Please refer to the weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The challenges behind protein alignment are well defined, and the motivation is clearly demonstrated.\n2. Extensive experiments on various datasets, baselines, and backbone models clearly prove the effectiveness of the proposed method.\n3. The paper is well written and organized, with code published.", "weaknesses": "1. Using optimal transport to align two graphs is not a novel idea, as can be seen in papers[1][2][3]. What are the differences and advances of PLASMA compared to other methods?\n\n2. The authors claim that PLASMA can sufficiently address the variable length alignment challenge, but there are no experiments to prove this statement. What is the performance of PLASMA when the query and target protein have different lengths?\n\n3. There is no ablation study to show the effectiveness of each component in PLASMA.\n\n4. In Eq. 7, the authors want to introduce a loss that focuses exclusively on labeled substructures. Then how does the number of labeled substrcutres affect the performance of PLASMA? And is it necessary to let the model focus on these labeled substructures? What are the reasons to include this loss?\n\n[1] Lee, John, et al. \"Hierarchical optimal transport for multimodal distribution alignment.\" Advances in neural information processing systems 32 (2019).\n[2] J. Tang, W. Zhang, J. Li, K. Zhao, F. Tsung and J. Li, \"Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport,\" 2023 IEEE 39th International Conference on Data Engineering (ICDE), Anaheim, CA, USA, 2023, pp. 1638-1651, doi: 10.1109/ICDE55515.2023.00129.\n[3] A. T. Riahi, G. Woollard, F. Poitevin, A. Condon and K. D. Duc, \"AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps,\" in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 20, no. 6, pp. 3842-3850, Nov.-Dec. 2023, doi: 10.1109/TCBB.2023.3327633.", "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": "3BRm31dy0S", "reviewer": "Reviewer_4sr4", "summary": "This paper addresses the challenge of identifying and comparing local protein substructures, such as active sites, which is critical for understanding protein function but difficult with existing global alignment or sequence-based methods. The authors introduce PLASMA, a deep learning framework that reformulates residue-level substructure alignment as a regularized optimal transport (OT) problem. The method consists of a \"Transport Planner\" that uses differentiable Sinkhorn iterations to generate an alignment matrix and a \"Plan Assessor\" to compute an interpretable, overall similarity score. The paper presents both a trainable (PLASMA) and a training-free (PLASMA-PF) variant. Experimental results on benchmark datasets show that PLASMA outperforms existing structure-based (e.g., TM-Align) and embedding-based (e.g., EBA) methods in detecting motifs, binding sites, and active sites, especially in cases of low global similarity. The method is also demonstrated to be significantly more computationally efficient than baselines.", "questions": "Could the authors please clarify the exact mathematical formulation of the cost matrix $\\mathcal{C}$ used in the parameter-free PLASMA-PF variant? How is the cost computed \"directly... from $LN(H)$,\" and how does this computation relate to Equation 2?\n\nCould the authors elaborate on the claim that the LMS metric cannot be meaningfully applied to the EBA baseline? Since EBA produces residue-level alignments, it seems this metric should be applicable and would provide a valuable head-to-head comparison of alignment quality, not just score-based classification performance.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "Overall, the formulations are clear.\n\nThe prosed method is efficient and effective.\n\nThe reformulation of substructure alignment as a regularized optimal transport problem is a novel and well-justified approach for this domain. This formulation naturally accommodates the partial and variable-length matches common in biological substructures, which the paper correctly identifies as a limitation of standard OT-based alignment methods.\n\nThe strong performance of PLASMA-PF, which requires no task-specific training, makes the method highly practical for scenarios where labeled data is scarce.\n\nThe qualitative case studies presented in Section 6.4 and Figure 5 are convincing. They effectively demonstrate PLASMA's ability to identify biologically meaningful local alignments between proteins with very low sequence identity and different global structures, and correctly contrast these interpretable results with the baseline EBA.", "weaknesses": "The approach relies on embedding models like protein language models, which may be biased to certain types of proteins. This reliance would potentially result in problems the downstream alignment task. It would be beneficial to test PLASMA on underrepresented proteins, e.g., orphan proteins.\n\nIn table 1, the results are tested over 3 different seeds. More repetition would make the results more robust.\n\nThe justification for the \"Plan Assessor\" design (Section 4) feels somewhat heuristic. Specifically, the confidence weight $\\alpha$ is derived using a 2D convolution with a fixed identity kernel to detect diagonal patterns. The rationale for this specific operator over other potential methods (e.g., a learnable kernel, or a different path-detection algorithm) is not fully explored, nor is the sensitivity to the kernel size.\n\nThe paper does not provide an ablation study on the key hyperparameters of the Sinkhorn algorithm. The temperature parameter $\\tau$ and the number of iterations $T$ (Section 3) are critical for controlling the sparsity and accuracy of the final alignment matrix $\\Omega$, as the paper itself notes. While Appendix D.2 mentions hyperparameter setup, no results are shown to demonstrate how performance (e.g., accuracy and alignment sparsity) varies with these choices.\n\nThe formulation of PLASMA-PF is ambiguous. The paper states that it \"bypasses the siamese network and directly computes costs from $LN(H)$\". It is not explicitly stated how this cost is computed. It is unclear if it still uses the hinge-loss formulation from Equation 2 with $\\phi_{\\theta}$ as an identity function, or if it uses a different distance metric (e.g., cosine distance) entirely.", "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)