ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search
Authors: Mengdi Liu
Xiaoxue Cheng
Zhangyang Gao
Hong Chang
Cheng Tan
Shiguang Shan
Xilin Chen
Venue: NeurIPS 2025 spotlight ()
Keywords: protein design
Primary area: machine_learning_for_sciences

Abstract: Designing protein sequences that fold into a target 3D structure—known as protein inverse folding—is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering native sequences, they often overlook the one-to-many nature of the problem: multiple diverse sequences can fold into the same structure. This motivates the need for a generative model capable of designing diverse sequences while preserving structural consistency. To address this trade-off, we introduce ProtInvTree, the first reward-guided tree-search framework for protein inverse folding. ProtInvTree reformulates sequence generation as a deliberate, step-wise decision-making process, enabling the exploration of multiple design paths and exploitation of promising candidates through self-evaluation, lookahead, and backtracking. We propose a two-stage focus-and-grounding action mechanism that decouples position selection and residue generation. To efficiently evaluate intermediate states, we introduce a jumpy denoising strategy that avoids full rollouts. Built upon pretrained protein language models, ProtInvTree supports flexible test-time scaling by adjusting the search depth and breadth without retraining. Empirically, ProtInvTree outperforms state-of-the-art baselines across multiple benchmarks, generating structurally consistent yet diverse sequences, including those far from the native ground truth. The code is available at https://github.com/A4Bio/ProteinInvBench/.

ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search
Mengdi Liu!?, Xiaoxue Cheng", Zhangyang Gao², Hong Chang!
Cheng Tan Shiguang Shan 22an'2,Xilin Xilin Chen
State Key Laboratory of Al Safety, Institute of Computing Technology, CAS, China
2 University Chinese Academy of Sciences (CAS), China
AI Lab, Research Center for Industries of the Future, Westlake University 4 Gaoling School of Artificial Intelligence, Renmin University of China {liumengdi 23z, changhong, sgshan, xlchen ac. cn,
chenxxiaoxue@ruc edu. en, (gaozhangyang, tancheng Bancheng@@westlaale @westlake. edu.
Abstract
Designing protein sequences that fold into target 3D structure known protein inverse folding-is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering native sequences, they often overlook the one-to-man nature of the problem: multiple diverse sequences fold into the same structure. This motivates the need for generative model capable designing diverse sequences while preserving struc- tural consistency. To address this trade-off, we introduce ProtInv ProtInyTree, the first ewward-guided tree-search framework for protein inverse folding. ProtInvTres Tree re- formulates sequence generation as deliberate, step-wise decision-making process, enabling the exploration of multiple design paths and exploitation of promising candidates through self-evaluation, lookahead, and backtracking. We propose a two-stage wawus-and-groundde and residue generation. To efficiently evaluate intermediate states, we introduce a jumpy denoising strategy that avoids full rollouts. Built upon pretrained protein language models, ProtInvTree supports flexible test-time scaling by expanding the search depth and breadth without retraining. Empirically, ProtInv Tree outperforms state-of-the-an baselines across multiple benchmarks, generating structurally con- sistent yet diverse sequences, including those far from the native ground truth. The code is available at atthtps::/ /////tttttbb//// wtw..h...ooo...a..ooo..........t A4Bio/ htt.///BB/PPoteinnnBeeeeee
action mechanism that decouples position selection
1 Introduction
Proteins are 3D folded linear chains of amino acids that perform essential biological functions, such as metabolic control, transmitting signals, and regulating cellular processes [1 Designing sequences of amino acids that fold into desired protein structure, also known as protein "inverse folding" (IF) [58), is crucial task with great potential for protein engineering and synthetic biology [27 62
Recent deep learning approaches typically recover the native sequence conditioned on a target structure through the following three paradigms: autoregressive generation, which models sequence 10]; one-shot prediction, which directly maps structure to [5]; and iterative refinement, which progressively improves an initial design through multiple passes [6ll 12 63]. Despite of achieving impressive recovery performance, these methods often overlooked the inherently one-to-many nature of the problem 38 33 16), where multiple distinct amino acid sequences are capable of folding into the
dependencies step-by-step 22 23 20
sequence in single forward operation [2
*Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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B
The energy landscaape torms atracduaa consielenccy
Seeq uequeenee
Ona State
Ground Trush
Sequence
Selected
States
Candicate Sequenoss
(8) generation refinement
Reward-guided Search Tree
Space
Figure 1: (A) Schematic illustration various approaches of structure-basee protein design. (a) One-shot generation that directly predicts full sequences from structure in one step, (b) Iterative refinement that first generates full sequence and then improves it through multiple steps, and (c) our method that applies tree search to perform deliberate design. Each node denotes an intermediate sequence conditioned on the target structure, progressively expanding toward full generation. See the complete framework and details in Figure 2 (B) Energy landscape E = e scTMScore over the sequence space with respect to the target structure, where the ground-truth sequence is marked and candidate sequences cluster around several local optima.
same protein backbone structure. As a result, rather than predicting a single native sequence, is often desirable generate a diverse set of sequences while preserving structural consistency.
This goal, however, reveals an inherent trade-off: while diversity prefers broad exploration of the sequence space, structural consistency strictly requires feasible subspace that has good local residue compatibility and global foldability. To address this challenge, we advocate for a deliberate, step-wise design process that progressively explores the solution space of feasible sequences. Inspired by dual process theory in cognitive science [25]
43 40], where System characterized by fast, automatic, and heuristic-driven responses, while System 2 involves slow, deliberate, and analytical reasoning, we propose to model the protein design process as deliberate and iterative decision- making process that should (I) explore multiple alternatives at each design step rather than one single candidate, (2) dynamically assess and revise each design step through lookahead and backtracking to optimize the overall designed sequence, and (3) maintain structured decision history support effective credit assignment and multi-step planning.
To this end, we propose ProtInv Tree, training-free framework for seuuctrr--bsee protein design that formalizes the design process as sequence of branching decisions and leverages Monte Carlo Tree Search (MCTS) during generation. Specifically, we iteratively perform the design process, sampling multiple decisions each step and looking ahead to compute reward signals that evaluate the quality of current choices, thereby guiding the overall sequence design. At each decision step, introduce two-stage focus-and and-grounding action mechanism that first selects the positions in the sequence to modify (focus) and then generates new residues at these positions (grounding). Moreover, we employ fast, jumpy denoising as an evaluation mechanism, efficiently estimating trajectory quality without costly forward model rollouts. Through these designs, ProtInvTree is capable of making globally optimal decisions rather than settling for locally optimal ones, which allows to design novel yet plausible sequences that may deviate significantly from the native sequence (as shown in Fig. T.. Additionally, the explicit exploration of design paths may offer potential insights into the interpretability of protein sequences. To knowledge, this is the first work to apply tree-search framework to Eructure-hased protein sequence design.
Empirically, comprehensively evaluate ProtInv Tree across sred-bbackbone and de novo protein design tasks. We demonstrate that ProtInvTres outperforms state-of-the-art baselines and excels in the design of plausible proteins with high structural consistency. Besides, it achieves Pareto-optimal trade-offs both the seTMscore- diverrity and McTMse nixcore-novelyy... Notably, we observe that existing approaches aggressively optimizing for sequence recovery achieve limited novelty at the same TMscore level. Further analyses reveal that increasing planning depth and expansion width can effectively improve structural consistency, demonstrating that the paradigm of test-time scaling can effectively unlock the potential of pretrained protein language models (PLMs).
In summary, contributions follows:

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We propose ProtInvTree the first test-time reward-guri guided tree search framework for protein inverse folding. It formulates protein design deliberate, step-wise decision process, enabling exploration of multiple trajectories and exploitation of promising candidates.
We introduce two-stage ceuus-nndgrouuneee mechanism decoupling position selection and residue generation and a fast, jumpy denoising strategy for efficient reward evaluation.
We demonstrate that ProtInVTre achieves state-of- of-the-art performance across multiple bench- marks, with a test-time scaling capability that improves both structural consistency and sequence diversity without retraining fine-tuning.
2 Related Works
2.1 Protein Inverse Folding
Recently, AI algorithms have spurred a major revolution in modeling protein inverse folding, enabling accurate sequence design conditioned on target structures. Existing approaches can be broadly categorized into the following three paradigms based on their generation strategies.
Autoregressive models generate sequences esiiue-bb--rssduu conditioned on both the 3D structure and previously generated tokens. Pioneering models like GraphTrans [22] and GVP [23] introduced SE(3)-invariant graph encoders with attention or geometric modules. Later, models such GCA 44,
ESM-IF 20) and ProteinMPNN (T] incorporated global context and fine-grained pairwise distance modeling. These models offer accurate recovery but suffer from slow inference long sequences.
One-shot models bypass iterative steps by directly predicting full sequences from structure. Pi- Fold 13 introduced an efficient graph encoder with an MLP decoder, achieving significant speedups and improved accuracy on long proteins. Uni-IF [5] generalizes this to multiple molecule types. These models are highly efficient but face challenges in maintaining global structural consistency.
Iterative refinement methods address this by first generating full sequence and then improving through multiple steps. AlphaDesign [12] and LMDesign [6] use confidence-aware predictors and pretrained sequence models for guided refinement. KWDesign [ combines sequence and structure pretraining with uncertainty-awan
update mechanism. Recent works such BridegIF [63 and GraDe-IF (57) apply diffusion to enhance diversity and structural compatibility. Fast non- autoregressive diffusion models like PMPanDiff' (54) accelerate inference while preserving accuracy.
Despite notable advances in protein inverse folding, most efforts focus on training-time improve- ments, while the inference phase remains underexplored. As large protein foundation models emerge, harnessing test-time computation boost sequence quality and diversity becomes crucial for in- centivizing their full potentials. To this end, we propose novel paradigm based on tree-structured generation, which departs fundamentally from the three existing categories of approaches.
2.2 Test-time Scaling and MCTS
Test-time scaling refers to increasing computational resources during inference to enhance model output without modifying its parameters. This approach has gained significant attention in the field of large language models (L.LMs), where performance is improved by generating multiple samples Various test-time search methods have been proposed [26] 46), including random sampling [49], self- self-consistency, and tree-search
and using reward models for best-solution selection [4] 53
methods [56] 17
59
36 Among them, MCTS, a heuristic search algorithm designed for decision-
39,, has emerged as powerful technique for structured exploration in the output space of large language models. It enables deliberate reasoning by simulating multiple generation trajectories, selectively expanding promising paths, and integrating reward feedback to guide inference toward high-quality outputs. Inspired by these advances, we are the first to extend the paradigm of test-time scaling to PLMs. Our proposed framework, ProtIny Tree, leverages reward- guided tree search to perform deliberate, step-wise protein sequence generation, enabling test-time scaling for improved structural consistency and diversity.
making tasks 55
50
7
3

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3 Preliminaries
Problem Definition. The protein inverse folding problem seeks determine the amino acid sequence that folds into a given target structure c. Here, x [2), ................................ IT represents the sequence of residues, where x; {1, 2, ..... ......... 20} denotes the type the i-th residue. The structure c = [c1 C2...., Gn] E | specifies the Cartesian coordinates of the backbone atoms (N, C-a, C, and optionally O) for each residue c, The inverse folding problem can be formally expressed as:
So Jo:c-1 X,
(I)
where is the learnable parameter. Given that homologous proteins invariably exhibit similar structures, the solution for a given structure is unique [T6]. Hence, ideal model should be capable of learning the underlying mapping from protein backbone structures to their corresponding sequence distributions pa (x(c).
35 30 have demonstrated remarkable 48 31 and have achieved notable success in protein inverse folding [1 61 63 These methods, including iterative refinement models, formulate the task this paradigm, we adopt this strategy to progressively construct the sequence. Formally, starting from an initially corrupted sequence Xo. the model iteratively denoises the sequence into complete design Xy through series of conditional reverse transitions, where X and Xy differ from the definition in diffusion modeling:
Iterative Denoising. Recently, diffusion models 19.42
capabilities in the field of life science [1 2 47
iterative denoising process that refines the sequence step by step. Following
(x( Xo, c)
II pa (x(+1+1 Xr: c)2
where X₂ represents the intermediate sequence at step t, with subset of amino acids remaining unfilled (e.g., represented by [MASK] tokens), and denotes the target backbone structure. Each reverse step pa (x Xr, c) refines the current sequence while preserving the structural context.
ProtInyTree: Deliberate Protein Inverse Folding Framework
In this section, we propose a reward-guided tree-search framework for deliberate protein inverse folding. We first formulate the iterative denoising as a tree-based Markov decision process (MDP), enabling structured exploration over multiple trajectories (Section 4.1. Then we describe the MCTS procedure employed to identify diverse and high-quality sequences that are consistent with the target backbone structure (Section 4.2) Finally, we introduce two designs of the action and reward components (Sections 4.3 [.d 4.4) which define how the sequence is updated at each step and how intermediate states are evaluated during the search process. We present the detailed algorithm to formalize the entire framework in the appendix.
4.1 Tree-based MDP Formulation
As described in Section 3 while the step-wise denoising process is effective, it lacks the ability to incorporate intermediate feedback, track uncertainty, and revise previous decisions. To overcome these limitations, we reformulate the iterative denoising process as a tree-based Markov decision process for structured, feedback-aware generation. In this tree structure, each node represents a state S,, each branch corresponds to action a, and each node is assigned value that reflects the reward rt at that state. Specifically, we define the concepts in the tree search framework as follows:
8: A (c, xt),
a: {(ix, 2i, K rt A R(s,, at), x(a
ss)) A po (x xt, c).
Here, the state s, consists of the target backbone structure c and partially generated sequence x;- The action a, corresponds the selection of positions in the sequence and modification of new residues, as detailed in Section 4.3 The reward Ft is computed by a reward function R(S,, ar). which evaluates the structural consistency of the modified sequence, as described in Section 4.4 The policy model π (aa Se) generates the next partial sequence X++1 based on the current state St- It is parameterized by structurally modulated protein language model (PLM). A trajectory in the transitions:
multi-step Markov decision process is defined as sequence of state-action-rewwe
[[S0, ao, ro), (S1, (i,,,,,77 T1)..)...., (ST, ar, Br,rT)),

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Stepwise Dendising
[M]
Protein Sequence
stato
[M]
[M]
[M]
[M]
[M]
[M]
Focus
[M]
A
[
M
[M]
[M]
action
Denoleing
Selected
Grounding
[M]
A
[M]
N
[M]
Focus and Grounding
Fast Jumping
Value Updating
Fast Jumping
(1) Selection
22) Expansion
(3) Evaluation
(4) Backpropagation
(a) Reward-guided Tree Search Framework
(b) Step-wise Protein Design
The framework of ProtInvTree. (a) The four steps of reward-guided tree Baurch-Selcctions Expansion, Evalution, and Backpropagation are illustrated on a partial denoising tree. Each node corresponds to partially denoised subsequence. After performed to quickly estimate its value, which is then backpropagated along the path in the tree. (b) Illustration of how sequence is generated step by step. Masked tokens in the sequence progressively infilling through a focus-and-groundiin mechanism.
Figure 2:
node is expanded, "jumpy" denoising
where each transition corresponds to an incremental update of the sequence. By reformulating the sequence design process from linear chain into tree structure, our framework enables deliberate planning over multiple generation trajectories, facilitates the incorporation of intermediate feedback from structural evaluations, and supports systematic revision of prior design decisions.
4.2 Reward-guided Tree Search
In our approach, the reward-guided tree search process operates as an iterative procedure. As illus- trated in Figure 2 it comprises four key steps: selection, expansion, evaluation, and backpropagation. The details of each step are described as below.
Selection. The selection process begins the root node and identifies the leaf node with the highest exploration potential, determined by the UCT (Upper Confidence Bounds applied to Trees) 28 score. The UCT score is computed follows:
In N())
UCT(s:) = (s,) + w
(3)
N(s,)
where w is a hyperparameter that balances exploitation (i.e., node value V(ss)) and exploration (i.e., visit count N (s:)), and p denotes the parent node of s,.
Expansion. After selecting the node with the highest UCT score. expanded by generating multiple child nodes. Conditioned on the current state which consists of the target structure e and current sequence x,, the policy model samples K candidate sequences for the next step:
(x {x
3k (a, s.) A po (x 1 x,, c).
(4)
Each candidate sequence X constitutes new child state s (c. x x which is added the search tree as an expansion of the selected node. The details of the candidate construction process by policy model are described in Section 4.3
(1)
Evaluation. Each expanded node is evaluated to determine its value V(s,41). As described in Equation [2] we first perform rollouts that complete the state s via sampling fully generated sequences, and then assess them with reward model, assigning the average reward r++1 as the node value (s(+1). The details of the reward function and evaluation process are provided in Section 4.4
Backpropagation. After evaluating the expanded nodes, their values are backpropagated along the traversal path to update the visit counts and value scores of the ancestor nodes sy (0 S S t). The updates are performed using the following equations:
5

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Nnow (sy) = Nola(s,) + 1, View (sy) = (di(ss))Nola + r2+1
(5)
(6)
Noew (s;)
where Vou(())) and (s))(s;) represent the previous visit count and value score of node sy. respectively, and re+1 is the reward obtained during the evaluation step.
The four stages described above are performed iteratively until the terminal state reached. We define two termination conditions for MCTS as follows: (1) The maximum number of MCTS iterations, M. reached. (2) A terminal node is encountered with a reward exceeding a predefined threshold, indicating strong structural consistency and high-quality design. Once the tree search is complete, the optimal path is selected greedily by prioritizing nodes with the highest scores.
4.3
Geeus-and-Groundingg Action
To generate candidate transitions from each intermediate state St, we propose a two-stage Focus- and-Grot und-Grounding action mechanism (see illustration in Fig. (2)). At each denoising step, the model explicitly decomposes the sequence updating process into identifying where to modify (Focus) and determining what token generate the selected position (Grounding).
Formally, the Focus operation F(-) defines position selection distribution p 8t) over all positions, from which the K positions with the highest probabilities are selected:
F(s:) = argsort,e (I......)) (po(i ss), K(),
where L denotes the sequence length and indicates the targeted position for refinement. Conditioned on the focused positions {i...... iN the Grounding operation defines distribution over amino acid types, specifying the generated token:
G(s,, i) = Po (z; ss, i E F(st).
(8)
where each Pal (2; 8t, i) predicts the residue æ; V for position and V denotes the amino acid vocabulary. The overall policy is factorized as the product of the Focus and Grounding distributions:
To Ta(a
5t)
Poli (s)) (2( (EF((;))
II
Se, i),
In practice, the selected position set fir...., iN } is a random subset of sequence positions (more selection strategies comparison is provided in appendix), and each token r, is generated by structurally modulated PLM conditioned on the backbone structure and the partial sequence context. This two-stage action design enables precise localization of modifications, ensuring structural coherence and enhancing search efficiency throughout the generation process.
4.4 Jumpy Denoising for Fast Reward
In the MCTS procedure, evaluating a node far from a leaf node is challenging, as the intermediate nodes are not fully expanded. This is typically addressed in one of two ways: employing forward dynamics models to simulate complete trajectories, which is computationally expensive. or approx- imating node values via bootstrapping methods, which are faster but less accurate. Effectively integrating these evaluation strategies into ProtInyTree Tree remains an open challenge.
To address this, we introduce a Jumpy Denoising strategy to accelerate the evaluation process, which a rapid, single-step DDIM-based 442 sampling process:
XT~ J(x++1,c).
(10)
where J(.) approximates the reverse denoising distribution p(xr Xx+1, c). Here, X++1 is obtained through action a, step f. We define the reward function R(s,, a,) the structural consistency feedback obtained by comparing the folding results from the sampled sequence Xy and the input structure c, formulated as:
R(s,, a,) = TMScore (f (xr c),
(11)
where / is the protein folding algorithm. TMScore(:; .) is a widely used metric for measuring protein structure similarity. This jumpy denoising strategy significantly reduces computational overhead while maintaining reliable approximation of the final reward.

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Table Structure consistency performance comparison between ProtInvTree and different baseline approaches on the CATH 4.2 dataset. The split of "Short,, "Single-chain and "All" is the same as previous works. The best and second-best results are labeled with bold and underline.
scT-Mscore (1)
RMSD (1)
Models
Trainable/Total
Params.
Short
Single-chain
All
Short
Single-chain
All
StructGNN
22
L4M//1 .MM
0.616
0.646
0.751
2.439
2.702
2.327
Graph Trans
1.5M/1.5M
0.590
0.635
0.744
2.356
2.678
2.351
GCA 45
2.1M/2. 1M
0.606
0.646
0.755
2.430
2.596
2.226
GVP 24
0.9M/0.9M
0.611
0.662
0.771
2.289
2.542
2.181
ProtcinMPNN 10
1.M/1 .MM
0.636
0.692
0.795
2.310
2.370
2.009
AlphaDesign 12
3.6M/3 6M
0.646
0.693
0.814
2.271
2,422
1.969
PiFold 13
5.8M/5 8M
0.655
0.700
0.842
2.203
2.355
1.723
UnilF 15
5.4M/5 4M
0.660
0.709
0.845
2.168
2.298
1.680
LM-Design (ESM-Ib) 61
6.9M//50M
0.663
0.714
0.849
2.150
2.240
1.638
KW-Design (ESM-2)
54,49M/6S0M
0.676
0.729
0.858
2.101
2.148
1.566
ESM-3 [8
1.4B/L.4B
0.668
0.692
0.816
2.060
2.387
2.135
ProtIny Tree (ESM-3)
OM/1.4B
0.768
0.800
0.881
1.902
2.136
1.513
Table 2: Structural consistency comparison be-
Table 3: De novo protein design results on TS45 datasets. We compare structural consistency of the following methods. The best and second-best
tween ProtInvTree and baseline approaches on
CATH 4.3 datasets. The best and second-best
results are labeled with bold and underline.
results are labeled with bold and underline.
Model
se-TMseore (1)
RMSD (1)
Model
se- se-TMscore (?)
RMSD (L)
StructGNN
0.693
2.563
22 StructGNN
0.631
3,336
GraphTrans
0.690
2.614
Graph
0.618
3.276
GCA
0.698
2.525
GCA
0.660
3.226
GVP 24
0.713
2.509
GVP 24
0.652
3.245
ProtcinMPNN 10
0.743
2.238
ProteinMPNN 10
0.668
3.142
AlphaDesign
12
0.749
2.230
AlphaDesign 22
0.660
3.167
PiFold 1
0.785
1.949
PiFold 13
0.699
2,875
KW-Design (ESM-2)
0.818
1.711
KWDesign (ESM-2) 11
0.711
2.643
ESM-3 [8]
0.775
2.074
ESM-3 [
0.690
2.958
ProtinyTrec (ESM-3)
0.835
1.702
Proteinlny Tree (ESM-3)
0.724
2.513
5 Experiments
5.1 Experimental Setup
Datasets. We conduct experiments on both CATH v4.2 and CATH v4.3 34 where proteins categorized based the CATH hierarchical classification of protein structure,
comprehensive analysis. Following the standard data splitting 222 20). CATH v4.2 dataset consists of 18,024 proteins for training, 608 proteins for validation, and 1,120 proteins for testing: CATH v4.3 dataset consists of 16,153 proteins for training, 1,457 proteins for validation, and 1,797 proteins for testing. We also include a more realistic assessment. Following the previous work ProthnyBench 14, we download the public TS-domains structures from CASP15 which consists 45 structures, namely TS45.
of de novo proteins collected from the CASP15 competition provide
Evaluation Metrics. For evaluation metrics, we use sc-TMscore 600 and RMSD 6 evaluate structural consistency. We define diversity the average proportion of differing residues across all pairs of generated sequences and define novelty as recovery. Details of all metrics are provided in the appendix. Following previous studies (22 20), we report them on three settings, namely short proteins (length < 100), single-chain proteins (labeled with chain in CATH), and all proteins.
Baselines. We compare ProtInvTres with several state-of -ott---a-t-h-ttttt- baselines, categorized into three
groups: (1) autoregressive models, including StructGNN (22), GraphTrans (22) GCA 45) GVP 224,
and ProteinMPNN [T0;; (2) the one-shot model, PiFold 13] UnilF 15 (3) iterative models,
including AlphaDesign 112] LM-Design (61) KW-Design

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0.7
0.8
AlphaDesign
0.6
Diversity
Novelty
0.6
PiFold
0.4
KW-Design
ESM3
0.5
ProtinvTree
0.0
0.6
0.7
0.8
0.9
0.6
0.7
0.8
0.9
sc-TMScore
SC-TMScore
Figure Pareto comparison structural consistency (M-ore) against diversity (left) and novelty (right) across different protein sequence design methods. Each curve represents a specific method evaluated under different sampling temperatures.
Diversity
Diversity
Diversity Novelty
Diversity Novelty
Novelty
Novelly
sampled equences
Diversity range
ground truth sequence
(a) Hign Diversity, Low Novelty
(b) Low Diversity. Hign Novelty
(c) Hign Diversity. Hign Novelty
(d) Low Diversity, Low Novelty
Figure 4: Conceptual illustration of the difference between diversity and novelty of the generated sequences. Each blue dot represents generated sequence, and the purple dot represents the ground truth sequence. Assuming generated sequences this plane share similar structural consistency, The gray circular boundary indicates the diversity range among the generated samples, while the gray lines connecting each sample to the ground truth reflect their novelty.
Implementation Details. All experiments are conducted on NVIDIA-A100 GPUs with 80G memory. We choose ESM-3 [18 as our policy model because it is the first protein foundation model that directly supports inverse folding without task-specific fine-tuning. The Jumpy Denoising strategy also leverages it, which is capable of filling in arbitrary mask ratios. Building on this capability, we focus on unleashing the potential of PLMs through test-time scaling. ensure fast structural feedback for reward computation, we use ESMFold [29] to predict the 3D structures of candidate sequences. For ProtInyTree, we set the maximum number of MCTS iterations M to 50. The selection numbers K, at each step follow a cosine schedule. In the UCT algorithm, the weight balancing the exploration and exploitation set to 0.01.
5.2 Benchmarking Fixed Backbone Protein Design
Structural Consistency. We benchmark the fixed backbone protein design task in CATH4.2 and CATH4.3 datasets, reporting the sc-TMscore and RMSD in Tables and ProtInyTres demonstrates superior performance over previous methods. We highlight the following: (1) Although iterative refinement models have significantly outperformed previous autoregressive and one-shot baselines, the proposed tree-based generation framework (ProtIny Tree) further achieves substantial improvements, demonstrating the effectiveness of branching exploration over linear refinement. (2) ProtInvTree enhances inference based on the frozen ESM-3 model, requiring no additional trainable parameters, yet achieving the strongest performance. Compared plain ESM-3 run for the same number of denoising steps (no tree search), ProtInvTree improves the se- T-Moore by 18.3% (short), 17.6% (single-chain), and 7.8% (all) in CATH 4.2. (3) We further evaluate RMSD structural metric, which consistently supports the effectiveness of ProtInvTrree.
independent
Balance between Structural Consistency and Diversity Novelty, Figure the Pareto frontier between structural consistency (measured by sc-TMScore) and two key sequence-level objec- tives: diversity (left) and novelty (right). We highlight our primary findings as follows: (1) ProtInyTree achieves Pa Pareto-optimal performance in both the diversity-sTTMeeee and weelty-sTMMscoe

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0.880
scTMscore
0.24
0.860
scTMscore
0.35
0.875
Diversity
0.22
ScTMscore
0.855
Diversity
ScTMscore
0.30
Diversity
0.870
0.20
Divers
0.850
0.18
0.25
0.865
0.845
0.16
0.860
0.14
0.840
0.20
0.855
0.12
0.835
0.15
2
4
Expand Number
Depth
Figure 5:
Test-time scaling laws analysis of our ProtInv Tree under different expansion numbers (left) and search depths (right).
spaces, outperforming all baselines across the trade-off frontier. (2) Compared to ESM-3, we observe that Protlny'Tree also achieves significantly higher diversity and novelty even comparable levels of structural consistency. (3) Notably, when at comparable sc-TMScore levels, the baselines of AlphaDesign, PiFold, and KW-Design exhibit progressively higher diversity and lower novelty. This highlights a f'undamental distinction between the two metries: diversity measures variation within the set of generated sequences, whereas novelty reflects deviation from the native (ground-truth) sequence. As shown in Fig. 4 baseline methods optimized with a recovery loss tend to converge around local optima near the ground-truth sequence, illustrated in case (a): by contrast, our method can escape this regime and explore multiple diverse and structurally consistent solutions, including those far from the ground truth sequence, as shown case (c).
5.3 De Novo Proteins Design
Evaluating models on the TS45 dataset allows us to gain better understanding of the potential of AI models designing de novo proteins and reveals that different models exhibit non-trivial differences in generalizability. We present the quantitative results in Table which reveal the following: (I) ProtInvTre outperforms all baseline methods terms of both sc- TMscore and RMSD, highlighting its superior ability to maintain structural consistency and achieve accurate geometric reconstruction. (2) We additionally compare ProtInyTree Tree with ESM-3 [8] to assess the effectiveness of our overall framework beyond the pretrained language model itself. Despite sharing the same pretrained model, ProtInvTre achieves substantially better results, suggesting that test-time sward-gguied planning plays key role in unlocking the full potential of pretrained PLMs.
5.4 Analysis: Diving Deep into ProtInyTree
Test-time Scaling Analysis. To understand how test-time computation scales with performance, investigate the effect of two key planning hyperparameters our framework: the number of candidate expansions and planning depth, shown in Fig. [ We observe that, as the expansion number and planning depth increase, sc-TMscore gradually improves, although the average time cost also rises moderately. This indicates that scaling test-time computation can effectively enhance sequence quality through more deliberate search. However, as the number of planning depths further increases, the sc- sc-TMscore tends to be saturated, as the search converges to high-confidence regions, the diversity of refinable sequences becomes limited, and further refinements yield diminishing structural gains. Moreover, the diversity in both settings decreases as the expansion number and planning depth increase, revealing the trade-off between structural consistency and sequence diversity.
Computational Efficiency The analysis of test-time computational efficiency is critical, particularly for methods that involve large pretrained models and structure prediction. We provide detailed analysis of the compute-performance performance trade-off. Specifically. for each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as shown in Table E We also scaled the number of sampling iterations for ESM-3 assess its performance-efficienee trade-off. The resulting Sc-TMScore and average inference time per design are summarized in Table We observe that, although inference

---

time increases with larger expand number or planning depth, the aefformance-efficcin trade-off remains superior to simply scaling the base ESM-3 sampler.
Table 4:
The performance--fficienny trade-off of ProtInv Tree (Our method)
Expand Number
3
4
5
6
se-T'Mcore
0.859
0.865
0.868
0.872
0.878
Inference Time / design
11.43
21.20
32.29
43.92
Table 5: The performancce-fficinncyy trade-off of ESM3 (base model)
Iteration Number
10
100
sc-TMScure
0.816
0.822
0.825
0.824
0.826
Inference Time / design (s)
0.438
0.706
3.397
5.481
6.897
Case Study. To facilitate understanding of the entire workflow of our proposed ProtInvTree we visualize a reward-guided search tree in Figure Each node represents partially generated sequence with its predicted reward r, reflecting structural consistency. The tree showcases how ProtInvTree performs branching exploration guided by reward scores. Two high-reward sequences, S1 and S2, emerge from different trajectories, with high diversity and novelty, yet achieve high structural rewards (r 0.99, 0.98). We further compare their predicted 3D structures with the ground truth structure in Figure 7 Its high sc-TMScore and low RMSD demonstrate ProtInv Tree's ability to generate diverse sequence candidates while maintaining structural consistency. This case illustrates how the reward-guide guiddd tree search enables efficient exploration of the solution space and selection of structurally faithful, non-trivial designs beyond native recovery.
89
(-f) AS
M0.57
F-0.99
140.88
M0
S1
$2
1-0.88
DOVADY LOTYHKLPD 82: MAMMMMMNNTT MTMLNTVVR VDEVADY VKNKKLPD NTVVDVADY
S1&GT sc-TMScore:0 99; RMSD:0.33 S2&GT sc-TMScoree0.B8 RMSD:0.38
Reward-guidd guided search tree visualization.
Figure 6:
Figure 7: Structural align- ment visualization.
Conclusion
We present ProtInvTree, a novel reward-guided tree-search framework for protein inverse folding that explicitly addresses the trade-off between structural consistency and sequence diversity. By reformulating sequence design as step-wise, decision-making process, ProtInv Tree enables the exploration of diverse design trajectories through self-evaluation, lookahead, and backtracking. ProtInv Tree shows superior performance across multiple benchmarks, achieving state-of-the-ar structural consistency while generating diverse and novel sequences beyond the native ground truth. Future work will focus on extending our framework to a broader range of protein-related tasks beyond -aedbbbakkbone inverse folding. One limitation of the proposed ProtIny Tree the computational efficiency, particularly for methods that involve large pretrained models and structure prediction. Another potential limitation is its current lack of experimental validation real-world biological settings. We will seek collaborations with experimental laboratories to test the viability and functional relevance of the designed sequences.
Acknowledgments
This work is partially supported by the program of The Robotie Al-Scientist Platform of Chinese Academy of Sciences.
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References
[1] Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneherger, Lindsay Willmore, Andrew Ballard, Joshua Bambrick, et al. Accurate structure prediction of biomolecular interactions with alphafold 3. Nature, pages 1-3, 2024.
[2] Sarah Alamdari, Nitya Thakkar, Rianne van den Berg, Alex Xijie Lu, Nicolo Fusi, Ava Pardis Amini, and Kevin K Yang. Protein generation with evolutionary diffusion: sequence is all you need. bioRxiv, pages 2023-09, 2023.
[3] Minkyung Back, Frank DiMaio, Ivan Anishchenko, Justas Dauparas, Sergey Ovchinnikov, Gyu Rie Lee, Jue Wang, Qian Cong, Lisa N Kinch, R Dustin Schaeffer, et al. Accurate prediction of protein structures and interactions using three-track neural network. Science, 373(6557):871-8777 2021.
[4] Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoe V Le, Christopher Ré, and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv:2407.21787, 2024.
[5] James W Bryson, Stephen F Betz, Helen S Lu, Daniel Suich, Hongxing X Zhou, Karyn O'Neil, and William F DeGrado. Protein design: hierarchic approach. Science, 270 941, 1995.
[6] Oliviero Carugo. How root-mean-square distance (rmsd) values depend on the resolution of protein structures that are compared. Applied Crystallography, 36(1):125-122 2003.
[7] Xiaoxue Cheng, Junyi Li, Wayne Xin Zhao, and Ji-Rong Wen. Think more, hallucinate less: Mitigating hallucinations via dual process of fast and slow thinking. arXiv preprint arXiv:2501.012 2025.
[8] Alexander E Chu, Tianyu Lu, and Po-Ssu Huang. Sparks of function by de novo protein design. Nature Biotechnology. 42(2):203-215, 2024.
[9] Rémi Coulom. Efficient selectivity and backup operators in monte-carlo tree search. In International conference on computers and games, pages 72-83. Springer, 2006.
[10] Justas Dauparas, Ivan Anishchenko, Nathaniel Bennett, Hua Bai. Robert J Ragotte, Lukas F Milles, Basile IM Wicky, Alexis Courbet, Rob J de Haas, Neville Bethel, al. Robust deep bearningbbsse protein sequence design using proteinmpnn. Science, (78(6615):49-22) 2022.
[11] Zhangyang Gao, Cheng Tan, Xingran Chen, Yijie Zhang, Jun Xia, Siyuan Li, and Stan Z. Li. KW-design: Pushing the limit of protein design via knowledge refinement. In The Twelfth International Conference Learning Representations, 2024.
[12] Zhangyang Gao, Cheng Tan, and Stan Z Li. Alphadesign: A graph protein design method and benchmark on alphafolddb. arXiv preprint arXiv:2202.01077 2022.
[13] Zhangyang Gao, Cheng Tan, and Stan Li. Pifold: Toward effective and efficient protein inverse folding. In The Eleventh International Conference on Learning Representations, 2023.
[14] Zhangyang Gao, Cheng Tan, Yijie Zhang, Xingran Chen, Lirong Wu, and Stan Z. Li. Pro- teininvbench: Benchmarking protein inverse folding on diverse tasks, models, and metrics. In Thirty-eventhh Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2023.
[15] Zhangyang Gao. Jue Wang, Cheng Tan, Lirong Wu, Yufei Huang, Siyuan Li, Zhirui Ye, and Stan Z Li. Uniif: Unified molecule inverse folding. Advances in Neural Information Processing Systems, 37:135843-135860 2024.
[16] Tymor Hamamsy, James Morton, Robert Blackwell, Daniel Berenberg, Nicholas Carriero, Vladimir Gligorijevic, Charlie EM Strauss, Julia Koehler Leman, Kyunghyun Cho, and Richard Bonneau. Protein remote homology detection and structural aligoment using deep learning. Nature biotechnology, pages 1-11, 2023.

---

[17] Shibo Hao, Yi Gu, Haodi Ma, Joshua Jiahua Hong, Zhen Wang, Daisy Zhe Wang, and Zhit- ing Hu. Reasoning with language model is planning with world model. arXiv preprint arXiv:2305. /4992, 2023.
[18] Thomas Hayes, Roshan Rao, Halil Akin, Nicholas Sofroniew, Deniz Oktay, Zeming Lin, Robert Verkuil, Vincent Q Tran, Jonathan Deaton, Marius Wiggert, al. Simulating 500 million years of evolution with language model. Science, page cads0018, 2025.
[19]
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 53:6840-6855 2020.
[20] Chloe Hsu, Robert Verkuil, Jason Liu, Zeming Lin, Brian Hie, Tom Sercu, Adam Lerer, and Alexander Rives. Learning inverse folding from millions of predicted structures. International conference machine learning, pages 9976- PMLR, 2022.
[21] Po-Ssu Huang, Scott E Boyken, and David Baker. The coming of age of de novo protein design. 2016.
Nature, 537(7620):320-
[22] John Ingraham, Vikas Garg, Regina Barzilay, and Tommi Jaakkola. Generative models for graph-based protein design. Advances in neural information processing systems, 32, 2019.
[23] Bowen Jing, Stephan Eismann, Patricia Suriana, Raphael John Lamarre Townshend, and Ron Dror. Learning from protein structure with geometric vector perceptrons. In International Conference on Learning Representations.
[24] Bowen Jing, Stephan Eismann, Patricia Suriama, Raphael John Lamarre Townshend, and Ron Dror. Learning from protein structure with geometric vector perceptrons. In International Conference on Learning Representations, 2021.
[25] Daniel Kahneman, Shane Frederick, et al. Representativeness revisited: Attribute substitution in intuitive judgment. Heuristics and biases: The psychology of intuitive judgment, 49(49-81):74 2002.
[26] Jikun Kang, Xin Zhe Li, Xi Chen, Amirreza Kazemi, and Boxing Chen. Mindstar: Enhancing math reasoning in pre-trained Ilms at inference time. arXiv preprint arXiv:2405.16265 2024.
[27] Hamed Khakzad, Ilia Igashov, Arne Schneuing, Casper Goverde, Michael Bronstein, and Bruno Correia. A new age in protein design empowered by deep learning. Cell Systems, 14(11):925-93) 939, 2023.
[28] Levente Kocsis and Csaba Szepesvári. Bandit based monte-carlo planning. In Johannes Fürnkranz, Tobias Scheffer, and Myra Spiliopoulou, editors, Machine Learning: ECML 2006, 17th European Conference on Machine Learning, Berlin, Germany, September 18-22, 2006, Proceedings, volume 4212 of Lecture Notes in Computer Science, pages 282-293. Springer, 2006.
[29] Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Allan dos Santos Costa, Maryam Fazal-Zarandi, Tom Sercu, Sal Candido, et al. Language models of protein sequences the scale of evolution enable accurate structure prediction. BioRxiv, 2022:500902, 2022.
[30] Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747, 2022.
[31] Mengdi Liu, Zhangyang Gao, Hong Chang, Stan Z. Li, Shiguang Shan, and Xilin Chen. G2pdiffusion: Cross-species genotype-to-phenotype prediction via evolutionary diffusion. arXiv preprini urXiv:2502.0440: 2025.
[32] Weian Mao, Muzhi Zhu, Zheng Sun. Shuaike Shen, Lin Yuanbo Wu, Hao Chen, and Chunhua Shen. De novo protein design using geometric vector field networks. The Twelfth International Conference Learning Representations, 2024.
[33] Grant S Murphy, Jeffrey L. Mills, Michael J Miley, Mischa Machius, Thomas Szyperski, and Brian Kuhlman. Increasing sequence diversity with flexible backbone protein design: the complete redesign of a protein hydrophobic core. Structure, 1066) 2012.
12

---

[34] Christine A Orengo, Alex D Michie, Susan Jones, David T Jones, Mark B Swindells, and Janet M Thomton. Cath-a hierarchic classification of protein domain structures. Structure, 1093 1997.
[35] Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas Müller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952, 2023.
[36] Zhenting Qi, Mingyuan Ma, Jiahang Xu, Li Lyna Zhang, Fan Yang, and Mao Yang. Mutual reasoning makes smaller Ilms stronger solvers arXiv preprint arXiv:2088.06195, 2024.
[37] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684-10695, 2022.
[38] LUCA Silva, Barthelemy Meynard- Piggaaea, Carlo Lucibello, Christoph Feinauer, et al. Fast uncovering of protein sequence diversity from structure. In The Thirleenth International Conference Learning Representations. (seleziona...), 2025.
[39] David Silver, Aja Huang, Chris Maddison, Arthur Guez, Laurent Sifre, George Van Den Driess- che, Julian Schrittwieser, loannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al. Mas- tering the game of go with deep neural networks and tree search. nature, 529(7587):484 2016.
[40] Steven A Sloman. The empirical case for two systems of reasoning. Psychological bulletin, 1 119(1):3, 1996.
[41] Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling Ilm test-time compute opti- mally can be more effective than scaling model parameters. arXiv preprint arXiv:2408.08 03314, 2024.
[42] Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 2020.
[43] Keith E Stanovich. Who is rational?: Studies of individual differences reasoning. Psychology Press, 1999.
[44] Cheng Tan, Zhangyang Gao. Jun Xia, Bozhen Hu, and Stan Z Li. Generative de novo protein design with global context. arXiv preprint arXiv:2204. 10673, 2022.
[45] Cheng Tan, Zhangyang Gao, Jun Xia, Bozhen Hu, and Stan Z Li. Global-context aware generative protein design. In ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1 1-5. IEEE, 2023.
[46] Chaojie Wang, Yanchen Deng. Zhiyi Lv, Shuicheng Yan, and An Bo. Q*: Improving multi-step reasoning for lims with deliberative planning, 2024.
[47] Xinyou Wang, Zaixiang Zheng, Fei Ye, Dongyu Xue, Shujian Huang, and Quanquan Gu. Diffusion language models are versatile protein learners. arXiv preprint 47X2 2024.
[48] Xinyou Wang. Zaixiang Zheng, Fei Ye, Dongyu Xue, Shujian Huang, and Quanquan Gu. Dplm-2: A multimodal diffusion protein language model. arXiv preprint arXiv:2410.1378. 2024.
[49] Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoe V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations, 2023.
[50] Yi Wang, Hui Tang, Lichao Huang, Lulu Pan, Lixiang Yang, Huanming Yang. Feng Mu, and Meng Yang. Self-play reinforcement learning guides protein engineering. Nature Machine Intelligence, 5(8):845-860) 2023.
13

---

[51] Kevin E Wu, Kevin K Yang, Rianne van den Berg, Sarah Alamdari, James Y Zou, Alex X Lu, and Ava P Amini. Protein structure generation via folding diffusion. Nature communications, 1501) 2024.
[52] Ruidong Wu, Fan Ding, Rui Wang, Rui Shen, Xiwen Zhang, Shitong Luo, Chenpeng Su, Zuofan Wu, Qi Xie, Bonnie Berger, et al. High-resolution de novo structure prediction from primary sequence. BioRxiv, pages 2022-07, 2022.
[53] Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. An empirical analysis of compute-optimal inference for problem-solving with language models. arXiv preprint arXiv:2408.00724, 2024.
[54] John J Yang, Jason Yim, Regina Barzilay, and Tommi Jaakkola. Fast non-autoregressive inverse folding with discrete diffusion. arXiv preprint arXiv:23/2.02447, 2023.
[55] Huanjin Yao, Jiaxing Huang, Wenhao Wu, Jingyi Zhang, Yibo Wang, Shunyu Liu, Yingjie Wang, Yuxin Song, Haocheng Feng. Li Shen, et al. Mulberry: Empowering milm with oi-like reasoning and reflection via collective monte carlo tree search. arXiv preprint 1rXiv:2412.1831, 2024.
[56] Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad- vances in Neural Information Processing Systems, 36, 2024.
[57] Kai Yi, Bingxin Zhou, Yiqing Shen, Pietro Lio, and Yu Guang Wang. Graph denoising diffusion for inverse protein folding. In Thirty-seventh Conference on Neural Information Processing Systems, 2023.
[58) Kaizhi Yue and Ken A Dill. Inverse protein folding problem: designing polymer sequences. Proceedings of the National Academy of Sciences, 89(9):1633416)) 1992.
[59] Di Zhang, Jiatong Li, Xiaoshui Huang, Dongzhan Zhou, Yuqiang Li, and Wanli Ouyang. Accessing gpt-4 level mathematical olympiad solutions via monte carlo tree self-refine with 3 8b. arXiv preprint arXiv:2406.07333 07394, 2024.
[60] Yang Zhang and Jeffrey Skolnick. Tm-align: a protein structure alignment algorithm based on the tm-score. Nucleic acids research, 33(7):200--2399, 2005.
[61] Zaixiang Zheng, Yifan Deng, Dongyu Xue, Yi Zhou, Fei Ye, and Quanquan Gu. Structure- informed language models are protein designers. In International Conference on Machine Learning, pages 92317-42336 PMLR, 2023.
[62] Yiheng Zhu, Zitai Kong, Jialu Wu, Weize Liu, Yuqiang Han, Mingze Yin, Hongxia Xu, Chang- Yu Hsieh, and Tingjun Hou. Generative ai for controllable protein sequence design: A survey. arXiv preprint
20V::2402.10111 2024.
[63] Yiheng Zhu, Jialu Wu, Qiuyi Li, Jiahuan Yan, Mingze Yin, Wei Wu, Mingyang Li, Jieping Ye, Zheng Wang, and Jian Wu. Bridge-if: Learning inverse protein folding with markov bridges. In The Thirty-eighth Annual Conference on Neural Information Processing Systems.
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A Algorithms
The overall workflow of the ProtInVTree is provided Algorithm
Algorithm ProtlavTree: Reward-Guided Tree Search for Protein Inverse Folding
Input:
Backbone structure c, ground truth sequence Xgts initial sequence Xo, folding model f(-),
PLM policy Te, reward function R), max iterations M, tree depth T', expansion number per node K, reward threshold
Output: A set of generated sequences S = {x;] where Z denotes the number of generated sequences.
1: Initialize root node So = Xo), search tree T with So, and result set S + Ø
2: for m to M do
3: Selection: Traverse the tree from So using UCT to select a promising node Sy (Eq.
4: for k = 1 to K do
5: Expansion:
6: Sample action a, (k) ~ (a [s)
Focus-and-Grounding strategies (Sec. 4.3 (k) Apply (*)) to obtain updated sequence X++1
7:
Construct child state s(4) (c, x(())
8:
(k)
9:
Add $,+1 to tree T as child of st
10:
Evaluation:
11:
Sample completed sequence: X7
(k) J [xx+11:0)
Jumpy denoising (Sec. 4.4)
12:
Compute reward: (k)
rz+1 TMScore ( (xxt))
13:
Set node value: (( [++
14:
Backpropagation:
15:
Update visit count N (sy) and value Vss,) (Eq. 5
Backpropagate r241 update all ancestors of s (Eq.
(k)
(K)
17:
ift + 1 = T and ri+1 2 then
[kk
18:
Add x;+1 to result set S end if
19:
20:
end for
21:
end for
22:
Return: Sequence set S 2 containing Z high-quality candidates
B Evaluation Metrics
In the main paper, we report evaluation results using four metrics: se- sc-TMscore, RMSD, novelty, and diversity. The descriptions of these metries are detailed follows.
sc- sc-TMScore. The structural similarity is the ultimate standard for measuring the quality of the designed sequence. However, the structures of designed protein sequences needed to be predicted by other algorithms, such as AlphaFold [1, RoseTTAFold 3. OmegaFold [52) and ESMFoll (29]. The protein folding algorithm itself has a certain inductive bias and will cause some prediction errors, which will affect the evaluation. To overcome the inductive bias, we adapt the self-consistent TM-score (sc-T (eeTrMs metric:
sc-TMScore = (x))
(12)
where f is the protein folding algorithm and TMScore(:;)) is widely used metric (60] for measuring protein structure similarity. Since the structures of the designed sequence and reference sequence predicted by the same protein folding algorithm, the model's inductive bias is expected to be canceled out when calculating the TM-score. This approach results in a more robust metric, called the sc- oMMore,, that is less affected by the inductive bias of the protein folding algorithm.
RMSD. The standard dissimilarity measure for protein structures the root mean square deviation (RMSD) of representative atom positions such as a-carbons. RMSD is caleulated as the square root
22

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of the average squared distance between corresponding atoms in two 3D structures:
n 1/4 w. w;l1
RMSD(V, w)
(13)
n
where v = fx) and w = fxx are the predicted 3D structures of the designed sequence x and the reference sequence x, respectively, obtained using structure prediction algorithm f. Here, i and w; denote the 3D coordinates of the i-th atom in each structure, and n is the total number of atoms considered (typically backbone or a-carbon atoms). RMSD provides fine-grained comparison of atomic positions after optimal rigid-body alignment of the two structures, However, it is sensitive to local deviations, such as flexible loops or inaccurate predictions side-chain packing, and may not fully reflect the overall fold similarity. As a result, RMSD is typically used in conjunction with other metries such as TM-score to provide a more comprehensive assessment of structural quality.
Novelty. We define novelty as the complement of sequence recovery, reflecting the extent to which the generated sequences deviate from the native ground truth:
Novelty = Recovery
where recovery is the fraction of amino acids in the predicted sequence that exactly match the ground-truth sequence at each position, defined as:
n 1 16; xx, 12
Recovery
Diversity.
The average fraction amino acids that differ between pairs of sequences:
M j-1
2
Diversity( ...... x)
1 + +
NM
1)
2 M(M - j=1k=1
dH d x*)
where dæ is the Hamming distance. We note that sequence diversity alone is not a sufficient measure of IF method's quality, as it can be increased arbitrarily at the expense of sample quality (e.g. as measured by structural consistency).
C Analysis of the Planning Components
We investigate how explicit planning components-innermmddaaat intermediate feedback, uncertainty tracking. and backtracking-aaa affect test-time protein design quality. We compare our MCTS-based planner (ProtInvTrree) against two commonly used test-time strategies: Best-of-N and Beam Search sampling.
ESM-3: base model without any planning feedback:
Best-of-N: generates N independent candidates and returns the one with the highest reward;
incrementally expands partial solutions while keeping only the top-B (beam width) candidates, iterating step-by-step with intermediate feedback until complete se- quence/design found;
Beam Search:
ProtInyTree (ours): Monte Carlo Tree Search with intermediate feedback, uncertainty
tracking, and backtracking.
Table summarizes the results and the presence of each planning component. We find that (1) Intermediate feedback (Beam Search) improves convergence over purely independent sampling (Best-of-N), indicating that partial evaluations guide more promising local expansions. (2) Uncer- tainty tracking further boosts reliability by prioritizing candidates with stable scores, reducing variance in final structures. (3) Backtracking enables recovery from suboptimal branches and better global exploration, yielding the best overall accuracy.
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Table Comparison of planning strategies under equal computational budgets. Checks (V) indicate the presence of the corresponding planning component.
Models
sc- se-TMscore (1)
RMSD ())
Intermediate Feedback
Uncertainty Tracking
Backtracking
ESM-3
0.816
2.135
Best-of-N
0.839
1,974
Beam Search
0.853
1.724
ProtInv'Tree
0.881
1,513
D Selection Strategies Comparison
To analyze the impact of different position selection strategies in the SuuusanndGroundee action mechanism, we evaluate several variants for computing the position distribution ( sy), which determines the set of positions {ii,..., [k, to modified at each denoising step.
Specifically, we compare the following approaches:
Random sampling: Positions are selected uniformly at random from the sequence.
Autoregressive sampling: Positions are visited sequentially from left to right in an autore- gressive manner.
Entropy-based selection: Positions with the lowest predictive entropy, representing the model's most confident predictions, are prioritized for update.
We integrate each strategy into the Focus module F(s)), keeping the Grounding step unchanged. Table / summarizes the quantitative results, showing that all three strategies achieve competitive performance, with random sampling performing surprisingly well despite its simplicity. This may be because exploring a broader space in the early stages helps avoid premature convergence and encourages greater sequence diversity, which ultimately benefits overall generation quality.
Table 7: Comparison of different sampling strategies on structure consistency (scTM-score).
Sampling Strategy
Random
AR
Entropy
Sc TMscore (f)
0.881
0.877
0.870
E Structure Complexity Effects
We also provide additional breakdowns across fold classes and protein lengths, revealing meaningful differences in performance and novelty trends. Table summarizes the breakdown by fold class and length-basee based results are given Table [
Table 8: Performance trends across the Fold class.
Fold Class
sc- sc-TMscore (t)
RMSD (L)
Novelty (t)
Mainly Alpha
0.855
1.548
0.616
Mainly Beta
0.830
1,710
0.503
Alpha-Beta
0.908
1.488
0.448
Few Secondary
0.764
1.349
0.553
F
Broader Impacts
Inverse protein folding models, positioned at the intersection of bioinformatics and computational biology, offer significant potential for advancing both basic research and real-world applications. By enabling the design of protein sequences that reliably fold into desired three-dimensional structures, these models can drive progress across diverse domains. Broader impacts include facilitating structure- based drug discovery, enabling the rational design of enzymes with novel functionalities, and advancing synthetic biology through the creation of custom proteins with tailored properties.


Reviews:
[{"review_id": "1T8eN33KeQ", "reviewer": "Reviewer_mTNz", "summary": "This paper presents ProtInvTree, a reward-guided tree search framework for protein inverse folding. It reformulates sequence generation as a step-wise decision process using Monte Carlo Tree Search, enabling exploration of diverse sequences consistent with a target structure. Key innovations include a two-stage focus-and-grounding mechanism for position and residue selection, and a jumpy denoising strategy for efficient evaluation. Built on pretrained models without retraining, ProtInvTree achieves state-of-the-art performance in terms of structural consistency, diversity, and novelty. Experimental validation is pending.", "questions": "A)\n1. **Intermediate Feedback and Uncertainty**: Section 4.1 emphasizes the benefits of incorporating intermediate feedback, tracking uncertainty, and enabling backtracking via tree-based search. Could you provide empirical evidence to isolate these contributions? For example, how much do they improve performance over simpler strategies?\n\n2. **Beam Search Baseline**: Have you considered comparing ProtInvTree to a **beam search baseline** that does not include backtracking or uncertainty estimation? Including such a baseline would clarify whether the proposed advantages of tree search are essential or incremental.\n\n3. **Ablation of Planning Features**: Can you ablate specific planning features—e.g., removing backtracking, removing jumpy denoising, or using greedy selection—to assess their individual impact on structural consistency, diversity, and novelty?\n\n4. **Uncertainty Quantification**: How is uncertainty explicitly tracked and used during search in your implementation? If applicable, showing how this improves exploration or stability would help justify its inclusion.\n\n\n\nB)\n1. **Novelty Collapse Analysis**: Have you evaluated how novelty changes alongside diversity as planning depth and expansion width increase (e.g., in Figure 5)? Including novelty plots would clarify whether deeper search also leads to convergence toward native sequences.\n\n2. **Failure Mode Characterization**: It would strengthen the work to systematically identify conditions under which ProtInvTree collapses to native-like sequences. Could you analyze thresholds (e.g., depth ≥ X or expansion ≥ Y) beyond which the method fails to explore novel solutions?\n\n3. **Parameter Sensitivity Study**: Consider conducting a controlled sweep over planning parameters to map the diversity–novelty–consistency landscape. This would help practitioners tune the method for different design goals (e.g., conservative vs. exploratory designs).\n\n4. **Recovery-Oriented Trade-off**: Would adding an explicit recovery-based reward term bias the search toward the native sequence? A comparison with and without such terms could reveal how tightly ProtInvTree adheres to or diverges from native recovery.\n\n5. **Structure Complexity Effects**: Does the convergence behavior vary across protein types (e.g., different lengths, fold classes, or disorder levels)? Reporting such breakdowns might uncover structure-specific tuning needs.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n\n**Quality:**\nThe paper proposes ProtInvTree, a reward-guided MCTS framework for protein inverse folding that operates entirely at test time. Built on top of pretrained models (ESM-3), it delivers strong performance across benchmarks (CATH 4.2/4.3, TS45) without additional training. The method achieves state-of-the-art structural consistency while improving sequence diversity and novelty. Jumpy denoising offers an efficient approximation for reward evaluation.\n\n**Clarity:**\nThe paper is clearly written, with intuitive diagrams and a detailed description of the method. \n\n**Significance:**\nTest-time compute scaling is a key strength. The method enables more deliberate search at inference without retraining.\n\n**Originality:**\nApplying MCTS to protein sequence design is novel. The focus-and-grounding mechanism and jumpy denoising strategy are also original contributions.\n\n\n### **Weaknesses**\n\n* The claimed benefits of planning (intermediate feedback, uncertainty tracking, backtracking) are not directly validated. There is no comparison to beam search or other simpler baselines that lack these features.\n* Figure 5 shows a drop in diversity with deeper planning, but the paper does not analyze how **novelty** changes under the same conditions. This limits insight into when and how the method converges toward native-like sequences.\n* The test-time compute–performance trade-off is not quantified in practical terms (e.g., runtime vs. accuracy).\n* There is no experimental or functional validation of designed sequences.", "was_revised": true, "final_justification": "I maintain my score of **5: Accept**, as the authors have adequately addressed key concerns raised in the initial review and demonstrated the technical strength and potential impact of the work.\n\n**Resolved Issues:**\n\n* **Beam Search and Simpler Baselines:** The authors added comparisons against both Beam Search and Best-of-N baselines under matched compute budgets. This helps contextualize the gains from MCTS, particularly with respect to structural consistency and novelty.\n\n* **Planning Feature Ablations:** A thorough ablation study was provided, showing the individual contributions of intermediate feedback, uncertainty-driven exploration, and backtracking. This validates the benefit of each planning component.\n\n* **Novelty Collapse and Scaling Behavior:** The authors added novelty plots and extended the planning depth/width experiments. Results indicate a gradual, not abrupt, decline in novelty, and no evidence of full collapse to native-like sequences.\n\n* **Test-Time Compute Trade-off:** The authors now report detailed timing vs. accuracy data, which quantifies the inference cost of deeper planning.\n\n* **Uncertainty Quantification:** The reply clarifies that uncertainty is handled via the standard UCT mechanism. Ablation of this term showed a measurable drop in performance, supporting its utility.\n\n* **Structure-Specific Analysis:** The authors provided additional breakdowns across fold classes and protein lengths, revealing meaningful differences in performance and novelty trends.\n\n**Partially Addressed or Remaining Issues:**\n\n* **Functional Validation:** As noted, experimental validation is out of scope, and while structural fidelity is a strong proxy, it limits confidence in real-world utility. This is common in protein design papers but remains a caveat.\n\n* **Recovery-Biased Rewards:** The authors rightly note that adding recovery-based rewards would leak ground truth. However, an approximate alternative (e.g., homology-guided regularization) could be explored in future work to assess biases in the method.", "rebuttal": "Thank you for your thoughtful and detailed feedback. We appreciate your positive assessment of the strengths of our work, as well as your suggestions for areas of improvement. We address each of your comments in detail below:\n> **W1 & Q1 & Q2:** The claimed benefits of planning (intermediate feedback, uncertainty tracking, backtracking) are not directly validated. There is no comparison to beam search or other simpler baselines that lack these features. Add Beam Search Baseline.\n\n**Reply:** We compare our MCTS-based planner (ProtInvTree) against two commonly used test-time strategies: Beam Search and Best-of-N sampling. To ensure a fair comparison in computational cost, all methods are restricted to approximately the same number of model calls per design.\n\n| Models        | scTM-score (↑) | RMSD (↓) | Intermediate Feedback | uncertainty tracking | Backtracking |\n|---|---|---|---|---|---|\n| ESM-3         | 0.816          | 2.135    | ×                     | ×                   | ×            |\n| Best-of-N     | 0.839          | 1.974    | ×                     | ×                   | ×            |\n| Beam Search   | 0.853          | 1.724    | √                     | ×                   | ×            |\n| ProtInvTree   | 0.881          | 1.513    | √                     | √                   | √            |\n\n\n\n> **W2 & Q5:** Novelty & Collapse “Figure 5 shows diversity decreasing with deeper planning, but novelty is not reported. How does novelty behave and when does the search collapse to native‑like sequences?”\n\n**Reply:** We will add novelty curves in the revised Fig. 5. The key trend is a smooth trade‑off—better scTM comes with a gradual, not abrupt, drop in novelty. Even at our most aggressive settings the average fraction of mutated residues remains > 49 %. A condensed view of the sweep is below:\n\n| Metric                     | N=2   | N=3   | N=4   | N=5   | N=6   |\n|----------------------------|------:|------:|------:|------:|------:|\n| sc-TMScore                 | 0.859 | 0.865 | 0.868 | 0.872 | 0.878 |\n| Novelty                    | 0.556 | 0.534 | 0.517 | 0.503 | 0.492 |\n\n| Metric    | D=2   | D=3   | D=4   | D=5   | D=6   | D=7   |\n|--------|------:|------:|------:|------:|------:|------:|\n| sc-TMScore | 0.838 | 0.849 | 0.852 | 0.859 | 0.858 | 0.859 |\n| Novelty  | 0.598 | 0.577 | 0.561 | 0.556 | 0.545 | 0.528 |\n\n> **W3:** “Quantify the test‑time compute vs. accuracy trade‑off.”\n\n **Reply:** We provide a detailed analysis of the compute–performance trade-off. Specifically, for each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as follows:\n\n| Metric                     | N=2   | N=3   | N=4   | N=5   | N=6   |\n|----------------------------|------:|------:|------:|------:|------:|\n| sc-TMScore                 | 0.859 | 0.865 | 0.868 | 0.872 | 0.878 |\n| Inference Time / design (s)| 6.72  | 11.43 | 21.20 | 32.29 | 43.92 |\n\n> **W4:** There is no experimental or functional validation\n\n **Reply:** Wet‑lab assays are beyond scope. In protein engineering, function is overwhelmingly constrained by 3‑D structure—hence the maxim “structure dictates function.” A design that reproduces the target fold with higher scTMScore is therefore more likely to preserve (or enable) the desired biochemical activity.\n\n> **Q1 & Q2 & Q3**: Intermediate Feedback & Uncertainty. Ablation of Planning Features.\n\n **Reply:**  Starting from the full ProtInvTree, we conducted an ablation study by disabling each key mechanism in isolation to assess its contribution:\n\n| Variant        | Intermed. feedback | Uncertainty (UCT term) | Backtracking |  scTMscore (↑) | Novelty (↑) | Diversity (↑) |\n| ----------------------------- | ------------------ | ---------------------- | ------------- | ---------------: | --------: | ----------: |\n| **Full ProtInvTree**          | ✓                  | ✓                      | ✓             |        0.881 |       0.498 |   0.159 |\n| – backtracking (no path revision) | ✓                  | ✓                     | ✗            | 0.865 |       0.479 |         0.138 |\n| – UCT (greedy selection) | ✓                  | ✗                     | ✓            |         0.874 |       0.461 |         0.127 |\n| Beam Search | ✓                 | ✗                      | ✗             |       0.853 | 0.457 | 0.118 |\n| ESM‑3 (no search)      | ✗                  | ✗                      | ✗             |            0.816 | 0.449 | 0.107 |\n\nWe also evaluated the impact of jumpy denoising on runtime performance. Specifically, for each given backbone, we generate 10 designs and compute the average generation time for each design. \n\n| Variant           | N = 2 | N = 3 | N = 4 | N = 5 | N = 6 |\n| ----------------- | ----: | ----: | ----: | ----: | ----: |\n| ProtInvTree       |  6.72 | 11.43 | 21.20 | 32.29 | 43.92 |\n| – jumpy denoising |  6.78 | 11.54 | 21.38 | 32.61 | 44.66 |\n\n\n\n> **Q4:** Uncertainty Quantification\n\n **Reply:** ProtInvTree follows the classic UCT rule (Eq. 1 in the paper):\n $\\text{UCT}(s)=V(s)+\\omega\\sqrt{\\frac{\\ln N(\\text{parent}(s))}{N(s)}} .$\n We treat this visit‑count–based bonus as an implicit measure of epistemic uncertainty—lower $N(s)$ ≈ higher uncertainty. No additional statistics are stored or tuned. We provice more results by setting $w\\!=\\!0$ (greedy value search) as follows:\n\n| Variant                                      | scTM‑score (↑) | RMSD (↓)  | Novelty (↑) |\n| -------- | ----- | ---- | ----- |\n| ProtInvTree (full, $\\omega=0.01$)             | **0.881**      | **1.513** | **0.498**   |\n| ProtInvTree w/o uncertainty term ($\\omega=0$) | 0.874          | 1.562     | 0.461       |\n\n Removing the uncertainty‑driven exploration degrades structural quality and shrinks the explored sequence space, demonstrating that the built‑in visit‑count heuristic already captures useful uncertainty information. \n\n\n\n> **Q6:**  Failure Mode Characterization\n\n**Reply:** We attempted to explore higher values (as shown in the following) as further extreme cases. \n\n| Expansion Number (N) | Planning Depth (D) | Novelty (↑) |\n| ---- | ------ | ----- |\n| 10 | 10 | 0.485       |\n| 20 | 10  | 0.482       |\n| 20 | 20                 | 0.476       |\n| 10 | 50                 | 0.475       |\n\nHowever, we regret that when both the expansion number and planning depth exceed this level, the memory consumption of the model exceeds the capacity of a single A100 GPU (80 GB). Despite this, our current scaling experiments already reveal a clear saturation point: although novelty decreases slightly as both expansion number and planning depth increase, the decline is gradual and does not indicate a full collapse to native-like sequences. \n\n\n> **Q7:** Parameter Sensitivity Study\n\n **Reply:** To systematically characterize the diversity–novelty–consistency landscape, beyond the scaling analysis we have already conducted on planning depth and expansion number, we conducted a controlled sweep over several key planning hyperparameters: the UCT exploration weight $\\omega$, the sampling temperature $T$, the reward threshold used for termination, and selection number schedules.\n\n| $\\omega$ | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.01 | 0.881 | 0.498 | 0.159 |\n| 0.05 | 0.871 | 0.519 | 0.175 |\n| 0.10 | 0.860 | 0.538 | 0.194 |\n\n| $T$ | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.1 | 0.882 | 0.468 | 0.109 |\n| 0.3 | 0.881 | 0.498 | 0.159 |\n| 0.5 | 0.856 | 0.564 | 0.378 |\n| 0.7 | 0.824 | 0.611 | 0.607 |\n\n| Threshold | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.0 | 0.859 | 0.556 | 0.224 |\n| 0.7 | 0.881 | 0.498 | 0.159 |\n| 0.9 | 0.887 | 0.496 | 0.146 |\n\n| Schedule | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| cosine | 0.881 | 0.498 | 0.159 |\n| linear | 0.879 | 0.474 | 0.127 |\n\n> **Q8:**  Recovery-Oriented Trade-off\n\n **Reply:** We agree that introducing an explicit recovery-based reward would bias the search toward the native target.  But we do not perform this ablation because adding a recovery term would require revealing the ground‑truth sequence during generation.\n\n> **Q9:** Structure Complexity Effects.\n\n **Reply:** We thank the reviewer for this valuable question. As partially reflected in Table 1, our evaluation already includes a breakdown of model performance across different protein lengths (i.e., \"Short\" proteins with length ≤ 100, \"Single-chain\" proteins, and \"All\" proteins).\n\nThe fold classes results are shown below: \n\n| Fold Class   | scTMscore (↑) | RMSD(↓)| Novelty (↑) |\n| ----------------- |  ------------: |------: | ----------: |\n| Mainly Alpha      | 0.855 | 1.548 | 0.616 |\n| Mainly Beta       | 0.830 | 1.710 | 0.503 |\n| Alpha-Beta    | 0.908 | 1.488 |0.448 |\n| Few Secondary | 0.764 | 1.349 | 0.553 |"}, {"review_id": "j9xGv8ac18", "reviewer": "Reviewer_PyE2", "summary": "The paper proposes ProtInvTree, a training‑free inference framework that frames protein inverse folding as a reward‑guided Monte‑Carlo Tree Search (MCTS) problem. At each step, a residue position is first chosen to modify and then residues are sampled from a frozen protein language model (e.g., ESM‑3). Intermediate states are evaluated with a jumpy denoising shortcut that avoids full rollouts, using ESMFold to estimate a TM‑score‑based reward. The rewards are then backpropagated normally as in MCTS.", "questions": "- What is J(.) in Equation 10, and how does it save computation compared to standard decoding?\n- What’s DDIM in line 214?\n- Line 135: MPD → MDP", "limitations": "Yes, but I suggest the author also address the computational cost in the limitations section.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "- Strengths\n    - The integration of MCTS into the inverse folding problem is intuitive and executed reasonably.\n    - Results in Table 1-3 demonstrate the method’s effectiveness across multiple benchmarks, achieving SoTA performance.\n    - Figure 3 shows the method’s effectiveness in balancing diversity and consistency.\n- Weaknesses\n    - Comparisons to other test-time scaling methods are lacking. Specifically, the author should compare MCTS to simpler methods like beam search and best-of-N to demonstrate the need for a more complex MCTS approach.\n    - The explanations for the Jumpy Denoising strategy are unclear.\n    - MCTS also brings additional computational costs, which should be noted and discussed.", "was_revised": true, "final_justification": "The authors conducted additional experiments to demonstrate the effectiveness of using MCTS decoding, which addressed my concerns. As a result, I have raised my rating to positive.", "rebuttal": "Thank you for your detailed and constructive feedback on our work. We appreciate your insights into both the strengths and weaknesses of our approach, and we address each of your points below:\n> **W1:** Comparisons to other test-time scaling methods are lacking. Specifically, the author should compare MCTS to simpler methods like beam search and best-of-N to demonstrate the need for a more complex MCTS approach.\n\n**Reply:** We compare our MCTS-based planner (ProtInvTree) against two commonly used test-time strategies: Beam Search and Best-of-N sampling. To ensure a fair comparison in computational cost, all methods are restricted to approximately the same number of model calls per design.\n\n| Models      | scTM-score (↑) | RMSD (↓) | Intermediate Feedback | Backtracking |\n| ----------- | -------------- | -------- | --------------------- | ------------ |\n| ESM-3       | 0.816          | 2.135    | ×                     | ×            |\n| Best-of-N   | 0.839          | 1.974    | ×                     | ×            |\n| Beam Search | 0.853          | 1.724    | √                     | ×            |\n| ProtInvTree | 0.881          | 1.513    | √                     | √            |\n\nOur experiments show that ProtInvTree consistently outperforms these baselines, which we attribute to its ability to leverage intermediate structural feedback and to perform both lookahead planning and backtracking-based revision.\n\n> **W2:** The explanations for the Jumpy Denoising strategy are unclear.\n\n**Reply:** We clarify that the Jumpy Denoising strategy is designed to efficiently estimate the final reward in MCTS without simulating full denoising trajectories. Specifically, instead of performing step-by-step denoising from noise to the final sequence, we adopt a single-step DDIM-based reverse sampling method that directly samples a denoised sequence Sample $\\tilde{\\mathbf{x_{T}}}$ from an intermediate state $\\mathbf{x_{t+1}}$, conditioned on $\\mathbf{c}$. Notably, the jumpy denoiser is not separately trained by us. It leverages the pretrained ESM-3 model, which is capable of filling in arbitrary mask ratios through its masked denoising objective.\n\n\n\n> **W3:**  MCTS also brings additional computational costs, which should be noted and discussed.\n\n**Reply:** Thank you for raising this important concern. We agree that test-time computational efficiency is critical, particularly for methods that involve large pretrained models and structure prediction. We provide a detailed analysis of the compute–performance trade-off. Specifically, for each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as follows:\n\n| Expand Number                      |   2 |   3 |   4 |   5 |   6 |\n| --------------------------- | ----: | ----: | ----: | ----: | ----: |\n| sc-TMScore                  | 0.859 | 0.865 | 0.868 | 0.872 | 0.878 |\n| Inference Time / design (s) |  6.72 | 11.43 | 21.20 | 32.29 | 43.92 |\n\nWe also scaled the number of sampling iterations for ESM-3 to assess its performance–efficiency trade-off. The resulting sc-TMScore and average inference time per design are summarized in the table below:\n\n| Iteration Number            |     5 |    10 |    50 |    80 |   100 |\n| --------------------------- | ----: | ----: | ----: | ----: | ----: |\n| sc-TMScore                  | 0.816 | 0.822 | 0.825 | 0.824 | 0.826 |\n| Inference Time / design (s) | 0.438 | 0.706 | 3.397 | 5.481 | 6.897 |\n\nWe also evaluate the method of Best of N, which generates 10 designs and finds the best one with 58.19, with an average sc-TMScore of 0.839. \n\n\n\n\n> **Q1:** What is J(.) in Equation 10, and how does it save computation compared to standard decoding?\n\n**Reply:** J(·) approximates the single-step reverse denoising $p(\\mathbf{x_T} \\mid \\mathbf{x_{t+1}},\\mathbf{c})$, This contrasts with standard diffusion decoding $\\prod_{s=t+1}^{T-1} p_{\\theta}(\\mathbf{x}_{s+1} \\mid \\mathbf{x}_s, \\mathbf{c})$, which requires iterative denoising steps. We bypass this iterative process and generate the final sample in one step, significantly reducing the computational cost for each node evaluation in the MCTS procedure.\n\n\n\n> **Q2:** What’s DDIM in line 214?\n\n**Reply:** DDIM refers to Denoising Diffusion Implicit Models [1], a sampling method used in diffusion models that accelerates the generation by jumpy denoising. In our method, we apply a single-step DDIM sampling to approximate the final denoised sequence, substantially reducing computational cost during MCTS rollout. We will add the citation [1] in the final version for clarity.\n\n\n\n> **Q3:** Line 135: MPD → MDP\n\n**Reply:** Thank you for pointing this out. We will correct the typo in the revised version of the manuscript. \n\n> **Q4:** Address the computational cost in the limitations section.\n\n**Reply:** Yes, we discuss the computational cost in reply of W3, and we will add the limitations in our revised version.\n\n[1] Jiaming Song et al, Denoising Diffusion Implicit Models, ICLR 2021"}, {"review_id": "EUhISEjIpA", "reviewer": "Reviewer_z7LH", "summary": "The authors proposed ProtInvTree, a test-time framework using MCTS to optimize sequences generated for a target structure. In the framework, ESM-3 is used as a policy for generating candidate mutations in a focus and grounding step-wise methodology, and ESMFold is used to calculate the reward function. Given the step-wise sequence generation, a jumpy denoiser is also proposed to allow the reward calculation in intermediate steps. The proposed methodology is evaluated against other state-of-the-art inverse folding methods, showing better performance, especially in refoldability metrics such as sc-TMScore and RMSD.", "questions": "Comments:\n\n1. It would be helpful to compare the differences between the proposed method with Evoplay [1] and other works using MCTS for protein design in the Related Work section. \n\n[1] Wang et al, “Self-play reinforcement learning guides protein engineering”, Nature Communications, 2023.\n\n2. The term “suboptimal” in Tables 1/2/3 seems not appropriate in this case. It implies that the model with the best result is optimal. This term should be rewritten.\n\n3. (Lines 257-258) The sentence “Compared to ESM-3 alone, when both methods set the same number of iterative steps” is unclear to me. Does it mean trying to optimize iteratively the sentences generated by ESM-3 without using the MCTS framework?\n\n4. Figure 3: Why are there not the same number of points in both graphs for ESM-3 and ProtinvTree?\n\n5. (Lines 259-260) “While the improvement in scTMscore is expected due to its use as the reward function during search”. Does this sentence mean that ESMFold is both used to calculate the reward function and used to calculate the sc-TMscore? This would be a leakage. In the reviewer’s understanding, the more robust way would be to use another folding model, like AF2 or RF2, to calculate the sc-TMscore.\n\n6. (Line 269-270) Can you clarify the sentence “Notably, when at comparable sc-TMScore levels, the baselines of AlphaDesign, PiFold, and KW-Design exhibit progressively higher diversity and lower novelty”? Should I check this pattern in Fig. 3?\n\n7. (Lines 291-292) “Although the average time consumed also rises to some extent”. To what extent? One of the most critical parts for test-time scaling is computational efficiency, but there are no ablations or numbers regarding this in the manuscript. This is crucial for the reader so that it can be evaluated in which situations the proposed model can be applied.\n\n8. The example in Fig. 7 would be more informative if it showcased an example in which the sc-TMScore is increased by applying the proposed method when compared to baseline methods (even if it is a cherry-picked example).\n\n9. Is the code available? There is no mention of the code availability throughout the manuscript.\n\n10. For the reviewer, it is still not clear if the sequence in a state s_t contains all the amino acid identities and these are mutated depending on the positions sampled, or if there are positions masked that are being filled. From Fig. 2(b) it seems that there are masked positions that are being filled, but it is not clear in the writing. Also, this affects the MCTS termination conditions, as I expected the MCTS to be terminated when the full sequence is generated (no need of the denoiser to calculate the reward function).\n\n11. Is the jumpy denoiser described in section 4.4 trained by the authors? There is no mention of that.\n\n12. In the manuscript, the authors used ESM-3 as their inverse folding method, but any other protein inverse folding could be combined with the proposed MCTS and jumpy denoiser framework. Did the authors test other models as the inverse folding method?\n\nMinor Comments:\n\n1. Figure 1: The ground-truth sequence should have the highest sc-TMScore value from my understanding.\n\n2. Acronyms like PLMs and MCTs are defined multiple times throughout the manuscript.\n\n3. (lines 175-176) Is equation 11 the right equation for V(s)?\n\n4. Writing: “Following the previous work [10]”: maybe explicitly mention the reference [10].\n\n5. Figure 4: There is a typo for the word “Noverty”.", "limitations": "The authors have discussed the positive impacts of their work in Appendix D; however, it would be important to also add the potential negative societal impact of their work.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. A test-time methodology for optimizing the sequence candidates generated for a target backbone is proposed, applying a structure-informed protein language model and tree search.\n2. For evaluating intermediate steps during the generation step, a jumpy denoising strategy is proposed.\n3. The proposed methodology improves sc-TMScore when compared to other baseline inverse folding methods.\n\nWeaknesses:\n\n1. The main concern is regarding the fairness of the evaluation in the manuscript: (i) it is not clear if the same folding model is used both as the reward function and to calculate the scTMScore for evaluation; (ii) it would be more fair to evaluate multiple sequences generated also from baseline methods.\n2. There is no information about computational efficiency in the manuscript. For applying test-time methods, computational efficiency and performance are crucial to evaluate which applications are worthy of using the proposed methodology.\n3. There is not enough information for the reader to reproduce the work. For example, there is no information about the training of the jumpy denoiser in section 4.4. The code is also not available.", "was_revised": true, "final_justification": "The authors addressed my concerns regarding the fairness of evaluation and information regarding the computational efficiency of the proposed method. Considering the rebuttal, I increased my score from 3 to 4.", "rebuttal": "Thank you for your detailed and insightful feedback. We appreciate your recognition of the strengths of our approach, and your constructive suggestions highlight important areas for further improvement. Below, we address each of your comments and questions:\n\n> **W1:** The fairness of the evaluation.\n\n **Reply:**  During search we predict structures with ESMFold and compute TM‑score against the target backbone. For all tables/figures we report sc‑TMScore computed with TM‑align between the backbone and the structure returned by AlphaFold2 given the designed sequence. Thus the evaluator is different from the reward model, eliminating information leakage. We sample 10 sequences per backbone for every baseline, and the results are \n\n| Models      | sc-TMscore (↑) | RMSD (↓) |\n| ----------- | -------------- | -------- |\n| ESM-3       | 0.816          | 2.135    |\n| Best-of-N   | 0.839          | 1.974    |\n| Beam Search | 0.853          | 1.724    |\n| ProtInvTree | 0.881          | 1.513    |\n\n> **W2 & Q7:**  Computational efficiency.\n\n **Reply:** For each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as follows:\n\n| Metric                      |   N=2 |   N=3 |   N=4 |   N=5 |   N=6 |\n| --------------------------- | ----: | ----: | ----: | ----: | ----: |\n| sc-TMScore                  | 0.859 | 0.865 | 0.868 | 0.872 | 0.878 |\n| Inference Time / design (s) |  6.72 | 11.43 | 21.20 | 32.29 | 43.92 |\n\n> **W3 & Q9 & Q11:** Reproducibility. The details of the jumpy denoiser.\n\n **Reply:** We clarify that the jumpy denoiser is not separately trained by us. It leverages the pretrained ESM-3 model, which is capable of filling in arbitrary mask ratios through its masked denoising objective. We will release the code upon publication to facilitate reproducibility and further research.\n\n> **Q1:** Related work\n\n **Reply:**  While both ProtInvTree and EvoPlay adopt Monte Carlo Tree Search (MCTS) to guide sequence generation, they differ significantly in motivation, problem formulation, and detailed methodology: \n\n - Motivation and Problem Formulation: ProtInvTree focuses on protein inverse folding that aims at designing **diverse** sequences while preserving s**tructural consistency**. In contrast, EvoPlay focuses on function-oriented protein engineering, where the objective is to optimize **protein functionality** (e.g., fluorescence, binding affinity) \n - Methodology: ProtInvTree is a **test-time scaling** framework that proposed a ***focus-and-grounding*** mechanism and a ***jumpy denoising*** strategy. In contrast, EvoPlay relies on AlphaZero-style self-play with **training** of policy-value networks and uses full simulations to evaluate each move via surrogate scoring functions.\n\n We will revise the Related Work section to explicitly compare ProtInvTree with EvoPlay and other MCTS-based methods in protein design. \n\n> **Q2, Q3, Q5, Q13-17:** Terminology & clarity issues\n\n**Reply:** Thank you for your careful reading and thoughtful suggestions regarding terminology and clarity. We have carefully revised the manuscript to address all noted issues.\n\n| Reviewer line                           | Action in revision                                           |\n| --------------------------------------- | ------------------------------------------------------------ |\n| “Suboptimal” tag in Tables              | replaced by “second‑best”                                    |\n| Lines 257–258 sentence                  | yes, it means: “Compared to *plain* ESM‑3 run for the *same* number of denoising steps (no tree search) ” |\n| Lines 259–260 “expected”                | clarified that *using TM‑score as reward* leads to higher scTM‑score there are highly correlated. We use ESMFold as reward function while using AF2 for evaluation |\n| Fig. 1 misleading sc-TMScore value from | it should be $e^{-scTM}$, which illustrate the energy landscape in terms of structural consistency. We will fix it in revised version. |\n| Repeated acronym definitions            | We will remove repeated acronym definitions.                 |\n| Equation 11, V(s)                       | The reward function is not the same as the value function V(s). Specifically, once a reward r is obtained for a newly expanded node, it is propagated bottom-up to update the value estimates V(s) of all ancestor nodes, as described in Equation (6). |\n| “Following the previous work [10]”      | We will revise the sentence to explicitly mention the reference: \"Following the previous work ProtInvBench [10]\". |\n| “Noverty” typo                          | We will correct the typo in the revised version of the manuscript. |\n\n>**Q4:** Figure 3: Why are there not the same number of points in both graphs for ESM-3 and ProtinvTree?\n\n**Reply:** Thank you for your careful observation. This is because we included an additional run in the left plot to make the performance trend more visually distinguishable. We will revise the right plot to include the same number of data points for both methods to ensure a fair and consistent comparison across the two subplots.\n\n| Metric\\Model   | ESM‑3 (1) | ESM‑3 (2) | ESM‑3 (3) | ProtInvTree (1) | ProtInvTree(2) | ProtInvTree(3) |\n| -------------- | --------- | --------- | --------- | --------------- | -------------- | -------------- |\n| **sc‑TMScore** | 0.816     | 0.796     | 0.761     | 0.857           | 0.841          | 0.824          |\n| **Novelty**    | 0.566     | 0.623     | 0.664     | 0.556           | 0.594          | 0.611          |\n\n\n\n>**Q6:** (Line 269-270) Can you clarify the sentence “Notably, when at comparable sc-TMScore levels, the baselines of AlphaDesign, PiFold, and KW-Design exhibit progressively higher diversity and lower novelty”? Should I check this pattern in Fig. 3?\n\n**Reply:** Yes, as shown in Figure 3, when fixing the sc-TMScore (i.e., drawing a vertical line at a specific value), you can observe that AlphaDesign exhibits the lowest diversity (left panel) and the highest novelty (right panel) compared to PiFold and KW-Design.\n\n\n\n>**Q8:** The example in Fig. 7 would be more informative if it showcased an example in which the sc-TMScore is increased by applying the proposed method when compared to baseline methods (even if it is a cherry-picked example).\n\n**Reply:** In the revision, we will update the figure to showcase an example where our method achieves a higher sc-TMScore compared to baseline methods. We note that such improvements are consistently observed across the majority of test cases, as reflected in our quantitative results.\n\n\n\n>**Q10:** For the reviewer, it is still not clear if the sequence in a state s\\_t contains all the amino acid identities and these are mutated depending on the positions sampled, or if there are positions masked that are being filled. From Fig. 2(b), it seems that there are masked positions that are being filled, but it is not clear in the writing. Also, this affects the MCTS termination conditions, as I expected the MCTS to be terminated when the full sequence is generated (no need of the denoiser to calculate the reward function).\n\n**Reply:** In our framework, the sequence in a state s\\_t is a partially generated sequence, which means there are positions masked that are being filled. And the MCTS terminated when the full sequence was generated and also the reward exceeded the predefined threshold. Importantly, to enable **intermediate feedback** during MCTS, we must evaluate partially generated sequences before reaching the final state. This is why we propose **a jumpy denoising strategy**, which completes the partially filled sequence via a fast approximation.\n\n\n\n> **Q12:** In the manuscript, the authors used ESM-3 as their inverse folding method, but any other protein inverse folding could be combined with the proposed MCTS and jumpy denoiser framework. Did the authors test other models as the inverse folding method?\n\n**Reply:** To the best of our knowledge, ESM-3 is the first structure-sequence unified model that supports arbitrary masking ratios for sequence completion, which makes it particularly suitable for our planning-based inverse folding framework. Other models, such as ProteinMPNN and KWDesign (which relies on ESM-2), do not support arbitrary masking ratios and typically require retraining or finetuning to enable structure-conditioned generation. This conflicts with several core design principles of ProtInvTree:\n\n1. **Stepwise generation**: Our method incrementally constructs sequences, with each decision depending on the prior t−1 steps—requiring the model to flexibly accept partially completed sequences.\n2. **Test-time reward-guided search**: ProtInvTree performs planning by querying the foundation model at test time, without retraining or gradient-based updates.\n3. **Focus-and-grounding with jumpy denoising design**, which requires flexible infilling under arbitrary masking ratios."}, {"review_id": "TV7lqDu9RQ", "reviewer": "Reviewer_mMYi", "summary": "The paper proposes ProtInvTree, a framework for inverse protein folding which generates diverse and structurally consistent designs for a given backbone using reward-guided tree-search applied to existing structure-conditioned design models. The framework is comprised of four steps; selection, expansion, evaluation, and backpropagation. The selection step uses UCT to select the node with the highest potential for exploration. In the expansion step, the pre-trained ESM-3 model is used to predict the amino acid identities at selected positions in the backbone. This yields a number of child nodes. In the evaluation step, ESM-3 is used to predict the full sequence as a \"look-ahead\" for the current designs. These are fed to ESMFold to predict the three-dimensional structures which in turn are used to compute the reward of the current designs. In the backpropagation step, the computed rewards are used to update the visited nodes. These steps repeat until a termination criteria is met. ProtInvTree is comprehensively evaluated on popular benchmarks where it achieves state-of-the-art performance in multiple metrics simultaneously.", "questions": "1. L118: Shouldn’t $n$ be $L$?\n2. L214: What is DDIM? \n3. More of a comment than a question, but I find it curious and partly non-satisfactory that equation 10 essentially implies that using some different model for inverse folding is part of the proposed inverse folding model.\n4. In equation 8, how are the tokens chosen? Are they sampled or do you apply argmax to the distribution over amino acids?\n5. L197 and L201: Why is $N$ used? Shouldn’t it be $K_t$ after the top-$K_t$ positions have been selected?\n6. L201: Curious that random ends up being optimal. Have you considered other approaches than the ones included in the supplementaries, or do you believe that “random” is optimal?\n7. L205: If the positions are randomly sampled, then calling it “precise localization of modifications” is somewhat misleading. I suppose that the approach does *enable* it, but in actuality it’s “random localization of modifications”, which I acknowledge does not sound as convincing.\n8. Section 5.1: \n    1. Did you explore other hyperparameter configurations? E.g., different values of $M$, different schedules for $K_t$, different values for the balancing parameter $w$? An ablation study or sweep over various configurations would be a valuable addition to the paper or the supplementaries.\n    2. Did you explore other PLMs or folding models? Is ESMFold accurate enough, or would a higher-fidelity folding model improve performance? \n    3. Why is it not possible to use a different structure-conditioned model than ESM-3? This model essentially plays the role of inverse folding in that a partially masked sequence and a structure is used to design a sequence. Something like MIF-ST or SaProt might work as well - or even just models like KWDesign or ProteinMPNN. The relative performance gap between base models and the ProtInvTree-version of them would be interesting to observe and would support the framework's utility.\n9. The termination number is set to 50. How many iterations are typically required before the algorithm terminates? Is it due to reaching this number, or is the structural consistency goal often met? An analysis of this would be very interesting. \n10. In the same vein, how many nodes end up being generated? How many structures are predicted to arrive at a given design? This feeds back into my earlier questions regarding the compute cost. Are we talking a handful of structures or hundreds/thousands?\n11. Figure 4: Noverty→Novelty", "limitations": "I do not think that the model limitations have been adequately addressed. \n\nIn the conclusion it is mentioned that a potential limitation is the lack of experimental validation. While this is true, I’d be very curious to hear about modeling limitations. E.g., the computational cost of relying on a 1.4B model which is extensively used is arguably a limitation, as is the computational burden of relying on online protein folding and the quality of the predicted structures. Similarly, the Jumpy Denoising process is, as far as I can tell, an inverse folding process in and of itself. Having both protein folding and inverse folding as often-repeated operations by other pre-trained models necessarily means that these models do most of the heavy lifting. However, I believe this can be ameliorated by ablation studies as mentioned in both the weaknesses and questions sections.\n\nThere must also be other limitations that I am not aware of and I believe it would be highly valuable to the paper to address these properly.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 2, "strengths_and_weaknesses": "__Strengths__:\n\n1. Well-written and well-structured paper - it was a pleasure to read and easy to follow.\n2. Impressive performance across diverse metrics, comfortably beating state-of-the-art inverse folding models.\n3. Comprehensive and succinct related works. \n4. Conceptually simple yet effective ideas.\n5. Comprehensive benchmarking which goes beyond simply maximizing sequence recovery but considers pareto-optimal solutions regarding structural consistency, novelty, and diversity.\n\n__Weaknesses__:\n\n1. No mention of computational cost at inference time which to me is significant omission. I think this is an important detail, particularly since protein folding is an active part of the pipeline as well as extensive use of a billion+ parameter model. An analysis of the cost of creating, e.g., 10 designs for a given backbone for ProtInvTree vs. ESM-3 and other models would be particularly beneficial. If the model is expensive at inference, that can perhaps be excused by the absence of model training. Experiments or at least discussions of the computational cost would be a valuable if not necessary addition to an otherwise great paper which would, potentially, further support the model’s utility. \n2. Few ablation studies to support modeling choices. Only a single model configuration is presented despite relying on two pre-trained models; ESM-3 and ESMFold. The inclusion of alternatives and their effect on downstream performance would shine light on where the performance is coming from. See related questions.\n3. This also applies to hyperparameter configurations, where it would be interesting to see model behavior using, e.g., different schedules for selection numbers, different balancing parameter in the UCT algorithm, different termination strategies. Without experiments supporting the chosen hyperparameters, they seem arbitrary. I appreciate the study in section 5.4 and would appreciate seeing something similar for the remaining parameters. Presumably, increasing both depth and expansions numbers leads to increased computational costs. I think this should be addressed as well.\n4. No code in the supplementaries.\n5. No mention of statistical significance, despite the checklist saying so.\n6. Very limited discussion on model limitations.", "was_revised": true, "final_justification": "I had highlighted a number of questions and limitations in my initial review and I believe that the majority of these have been adequately addressed. Given the additional and more comprehensive ablation study as well as the authors' comprehensive rebuttal to the reviewers, I believe that the new methods introduced for inverse protein folding would be of interest to the broader community and I therefore support the acceptance of the paper at this year's NeurIPS conference.", "rebuttal": "> **W1:** No mention of computational cost at inference time which to me is significant omission. An analysis of the cost of creating, e.g., 10 designs for a given backbone for ProtInvTree vs. ESM-3 and other models would be particularly beneficial. \n\n**Reply:**  We agree that test-time computational efficiency is critical, particularly for methods that involve large pretrained models and structure prediction. We provide a detailed analysis of the compute–performance trade-off. Specifically, for each given backbone, we generate 10 designs and compute the average generation time for each design. We fix the depth and scale the expand number from 2 to 6, as follows:\n\n| Expand Number|2 | 3 | 4 | 5 | 6 |\n| ----- | ---: | ---: | ---: | ---: | ---: |\n| sc-TMScore| 0.859 | 0.865 | 0.868 | 0.872 | 0.878 |\n| Inference Time / design (s) |  6.724 | 11.433 | 21.201 | 32.294 | 43.922 |\n\nWe also scaled the number of sampling iterations for ESM-3 to assess its performance–efficiency trade-off. The resulting sc-TMScore and average inference time per design are summarized in the table below:\n\n| Iteration Number|5| 10| 50| 80 | 100 |\n| ----- | ----: | ----: | ----: | ----: | ----: |\n| sc-TMScore | 0.816  | 0.822 | 0.825 | 0.824 | 0.826 |\n| Inference Time / design (s) | 0.438  | 0.706 |  3.397 | 5.481 | 6.897|\n\n> **W2:** Few ablation studies to support modeling choices. \n\n**Reply:** We ran an ablation study. Starting from the full ProtInvTree, we conducted an ablation study by disabling each key mechanism in isolation to assess its contribution:\n\n| Variant| Intermed. feedback | Uncertainty (UCT term) | Backtracking |  scTMscore (↑) | Novelty (↑) | Diversity (↑) |\n| -------- | ---- | ------- | ------- | --------: | -----: | ----: |\n| **Full ProtInvTree**  | ✓    | ✓  | ✓  |0.881 |0.498 |0.159 |\n| – backtracking (no path revision) | ✓ | ✓  | ✗ | 0.865 |0.479 | 0.138 |\n| – UCT (greedy selection) | ✓   | ✗  | ✓ |0.874 |0.461 |0.127 |\n| Beam Search | ✓  | ✗ | ✗|0.853 | 0.457 | 0.118 |\n| ESM‑3 (no search)| ✗| ✗ | ✗|0.816 | 0.449 | 0.107 |\n\n> **W3 & Q8-1:** Hyperparameter Ablation. \n\n**Reply:** We conducted a controlled sweep over several key planning hyperparameters: the UCT exploration weight $\\omega$, the sampling temperature $T$, the reward threshold used for termination and selection number schedules.\n\n| $\\omega$ | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.01 | 0.881 | 0.498 | 0.159 |\n| 0.05 | 0.871 | 0.519 | 0.175 |\n| 0.10 | 0.860 | 0.538 | 0.194 |\n\n| $T$ | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.1 | 0.882 | 0.468 | 0.109 |\n| 0.3 | 0.881 | 0.498 | 0.159 |\n| 0.5 | 0.856 | 0.564 | 0.378 |\n| 0.7 | 0.824 | 0.611 | 0.607 |\n\n| Threshold | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| 0.0 | 0.859 | 0.556 | 0.224 |\n| 0.7 | 0.881 | 0.498 | 0.159 |\n| 0.9 | 0.887 | 0.496 | 0.146 |\n\n| Schedule | Consistency (↑) | Novelty (↑) | Diversity (↑) |\n| --- | --- | --- | --- |\n| cosine | 0.881 | 0.498 | 0.159 |\n| linear | 0.879 | 0.474 | 0.127 |\n\n> **W4:** No code in the supplementaries.\n\n**Reply:**  We will release the code upon publication to facilitate reproducibility and further research.\n\n> **W5:** No mention of statistical significance, despite the checklist saying so.\n\n**Reply:** All reported results are the average over three independent runs, and we will update the standard deviation to reflect variability. Below, we present a subset of results with standard deviation values:\n\n| Method      | sc-TMScore (↑)    | RMSD (↓)          |\n| ----------- | ------- | -------- |\n| PiFold      | 0.842 ± 0.012     | 1.723 ± 0.007     |\n| KW-Design   | 0.858 ± 0.010     | 1.566 ± 0.009     |\n| ESM-3       | 0.816 ± 0.011     | 2.135 ± 0.007     |\n| ProtInvTree | **0.881 ± 0.008** | **1.513 ± 0.008** |\n\n> **W6:** Very limited discussion on model limitations.\n\n**Reply:** In the revised manuscript, we will discuss more imitations:\n(1) the reliance on large pretrained models such as ESM-3 and ESMFold, which introduces non-negligible inference cost,\n(2) the assumption that structural consistency alone is sufficient for functional accuracy, which may not hold in all biological contexts.\n\n\n> **Q1:** L118: Shouldn’t $n$ be $L$?\n\n**Reply:**  Thank you for catching this typo. It should be $L$ to properly denote the sequence length. We will fix this in the revised version.\n\n> **Q2:** L214: What is DDIM?\n\n**Reply:** DDIM refers to Denoising Diffusion Implicit Models [1], a sampling method used in diffusion models that accelerates the generation by jumpy denoising. In our method, we apply a single-step DDIM sampling to approximate the final denoised sequence, substantially reducing computational cost during MCTS rollout. We will add the citation [1] in the final version.\n\n> **Q3:**  equation 10 essentially implies that using some different model for inverse folding is part of the proposed inverse folding model.\n\n**Reply:** No, it is the same inverse folding model. The jumpy denoising mechanism simply takes advantage of ESM-3’s ability to perform flexible infilling under arbitrary masking ratios.\n\n> **Q4:** In equation 8, how are the tokens chosen? Are they sampled or do you apply argmax to the distribution over amino acids?\n\n**Reply:** Concretely, we first soften the model’s logits with a temperature T (T = 0.3 in all experiments) and then sample a residue from the resulting categorical distribution.\n\n> **Q5:** L197 and L201: Why is $N$ used? Shouldn’t it be $K_t$ after the top-$K_t$ positions have been selected?\n\n**Reply:**  Yes, it should be $K_t$. We will fix this in the revised version.\n\n> **Q6 & Q7:** L201: Curious that random ends up being optimal. \n\n**Reply:** We were also initially surprised that the random position selection strategy outperformed some more \"informed\" heuristics. However, our analysis suggests that random selection introduces useful exploration into the MCTS process and avoids biasing the search toward fixed or overconfident regions of the sequence. We do not claim that random selection is inherently optimal. Instead, we view it as a strong and surprisingly effective baseline. In future work, we plan to explore hybrid strategies that incorporate biologically or structurally informed priors—e.g., conservation profiles, solvent accessibility, or functional annotations—to guide the modification positions more precisely.\n\n> **Q8-2&3:**  Did you explore other PLMs or folding models? Why is it not possible to use a different structure-conditioned model than ESM-3? \n\n**Reply:** ESM-3 is the first unified structure–sequence model that supports arbitrary masking ratios, making it particularly well-suited for our planning-based inverse folding framework. In contrast, models like ProteinMPNN and KWDesign (based on ESM-2) lack this flexibility and typically require retraining to support structure-conditioned generation—conflicting with the core design of ProtInvTree, which relies on: 1. Stepwise sequence construction; 2. Test-time reward-guided planning without finetuning, and 3. Flexible infilling for focus-and-grounding with jumpy denoising.\nIn addition, we use ESMFold for structure prediction due to its favorable trade-off between accuracy and computational efficiency, which is crucial for iterative structure evaluations during MCTS.\n\n> **Q9:** The termination number is set to 50. How many iterations are typically required before the algorithm terminates? Is it due to reaching this number, or is the structural consistency goal often met? An analysis of this would be very interesting.\n\n**Reply:** The actual number of iterations is dynamically determined by the expand N, depths, and predefined structural consistency threshold. We analyzed the average number of iterations required under different thresholds:\n\n|     Threshold  |  0   |0.7 | 0.9 |\n| --------- | ---------| ------- | --------- |\n|Iterations (expand Number=3, depth=4) | 5.133 |         8.466 | 9.066 |\n|Iterations (expand Number=4, depth=5) | 10.466 | 14.266 | 15.2   |\n|Iterations (expand Number=5, depth=5) | 14.066 | 18.642 | 20.722 |\n|Iterations (expand Number=6, depth=5) | 17.266 | 21.461 | 25.5   |\n|Iterations (expand Number=10, depth=10) | 50     | 50     | 50     |\n\nThese results show that early termination frequently occurs, especially under lower thresholds or smaller planning budgets. When both the expand number and depth are large (e.g., N=10, depth=10), the planner often reaches the iteration cap (50).\n\n> **Q10:** In the same vein, how many nodes end up being generated? How many structures are predicted to arrive at a given design? This feeds back into my earlier questions regarding the compute cost. Are we talking a handful of structures or hundreds/thousands?\n\n**Reply:** The table below reports the average number of nodes explored under different configurations:\n\n|  Threshold  |  0   |0.7 | 0.9 |\n| ----- | ----| ---- | ----- |\n|Nodes (expand Number=3, depth=4) | 22.4  | 31.6 | 33.4 |\n|Nodes (expand Number=4, depth=5) | 62.866 | 65.8    | 75.66  |\n|Nodes (expand Number=5, depth=5) | 97.333 | 101.333 | 116.0  |\n|Nodes (expand Number=6, depth=5) | 151.8  | 154.0   | 157.66 |\n|Nodes (expand Number=10, depth=10) | 611    | 611     | 611    |\n\nEach node, except for the root node, requires a structure prediction call (ESMFold). Moreover, a single MCTS tree can yield multiple high-scoring, diverse candidates from the final pool; accordingly, we report the **amortized inference time per design** by dividing the total runtime by the number of extracted outputs, shown in reply to W1.\n\n> **Q11:** Figure 4: Noverty→Novelty\n\n**Reply:** Thank you for pointing this out. We will correct the typo in the revised version of the manuscript."}]

Author rebuttal:

Meta-review: After the review, rebuttal and discussion all reviewers recommend acceptance. The AC agrees.
The reviewers appreciated the novelty (MCTS) and found the paper well executed. Most questions have been resolved satisfactory.
Decision: Accept (spotlight)