论文检索

Applications · Chemistry and Drug Discovery

Zhiyu Wang, Bingxin Zhou, Weishu Zhao, Yang Tan, Jing Wang, Pietro Lio, liang hong

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

Applications · Chemistry and Drug Discovery

Yanke Li, Tianyu Cui, Tommaso Mansi, Mangal Prakash, Rui Liao

Efficient design of genomic perturbation experiments is crucial for accelerating drug discovery and therapeutic target identification, yet exhaustive perturbation of the human genome remains infeasible due to the vast search space of potential genetic interactions and experimental constraints. Bayesian optimization (BO) has emerged as a powerful framework for selecting informative interventions, but existing approaches often fail to exploit domain-specific biological prior knowledge. We propose Biology-Informed Bayesian Optimization (BioBO), a method that integrates Bayesian optimization with multimodal gene embeddings and enrichment analysis, a widely used tool for gene prioritization in biology, to enhance surrogate modeling and acquisition strategies. BioBO combines biologically grounded priors with acquisition functions in a principled framework, which biases the search toward promising genes while maintaining the ability to explore uncertain regions. Through experiments on established public benchmarks and datasets, we demonstrate that BioBO improves labeling efficiency by 25-40\%, and consistently outperforms conventional BO by identifying top-performing perturbations more effectively. Moreover, by incorporating enrichment analysis, BioBO yields pathway-level explanations for selected perturbations, offering mechanistic interpretability that links designs to biologically coherent regulatory circuits.

Applications · Chemistry and Drug Discovery

Yuanchang Zhou, Siyu Hu, Xiangyu Zhang, Hongyu Wang, Guangming Tan, Weile Jia

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (\textbf{Mat}erials \textbf{R}epresentation and \textbf{I}nteraction \textbf{S}imulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity $O(N)$, enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.

Applications · Chemistry and Drug Discovery

Pavel Strashnov, Andrey Shevtsov, Viacheslav Meshchaninov, Olga Kardymon, Dmitry P. Vetrov

Motif scaffolding in protein design involves generating complete protein structures while preserving the 3D geometry of designated structural fragments, analogous to image outpainting in computer vision. Current benchmarks focus on functional motifs, leaving general geometric preservation capabilities largely untested. We introduce GeomMotif, a systematic benchmark that evaluates arbitrary structural fragment preservation without requiring functional specificity. We construct 57 benchmark tasks, each containing one or two motifs with up to 7 continuous fragments, by sampling from the Protein Data Bank (PDB) to ensure a ground-truth, solvable conformation for every problem. The tasks are characterized by comprehensive structural and physicochemical properties: size, geometric context, secondary structure, hydrophobicity, charge, and degree of burial. These features enable detailed performance analysis beyond simple success rates, revealing model-specific strengths and limitations. We evaluate models using scRMSD and pLDDT for geometric fidelity and clustering for structural diversity and novelty. Our results show that sequence-based and structure-based approaches find different tasks challenging, and that geometric preservation varies significantly with structural and physicochemical context. GeomMotif provides insights complementary to function-focused benchmarks and establishes a foundation for improving protein generative models.

Applications · Chemistry and Drug Discovery

James Bowden, Sergey Levine, Jennifer Listgarten

In the era of AI-driven science and engineering, we often want to design discrete objects (e.g., circuits, proteins, materials) in silico according to user-specified properties (e.g., that a protein binds its target). Given a property predictive model, in silico design typically involves training a generative model over the design space (e.g., over the set of all length-L proteins) to concentrate on designs with the desired properties. Distributional optimization, formalized as an estimation of distribution algorithm or as reinforcement learning policy optimization, maximizes an objective function in expectation over samples. Optimizing a distribution over discrete-valued designs is in general challenging due to the combinatorial nature of the design space. However, many property predictors in scientific applications are decomposable in the sense that they can be factorized over design variables in a way that will prove useful. For example, the active site amino acids in a catalytic protein may need to only loosely interact with the rest of the protein for maximal catalytic activity. Current distributional optimization algorithms are unable to make use of such structure, which could dramatically improve the optimization. Herein, we propose and demonstrate use of a new distributional optimization algorithm, Decomposition-Aware Distributional Optimization (DADO), that can leverage any decomposability defined by a junction tree on the design variables. At its core, DADO employs a factorized “search distribution”—a learned generative model—for efficient navigation of the search space, and invokes graph message passing to coordinate optimization across all variables.

Applications · Chemistry and Drug Discovery

Alvaro Prat, Leo Zhang, Charlotte Deane, Yee Whye Teh, Garrett Morris

Determining the binding pose of a ligand to a protein, known as molecular docking, is a fundamental task in drug discovery. Generative approaches promise faster, improved, and more diverse pose sampling than physics-based methods, but are often hindered by chemically implausible outputs, poor generalisability, and high computational cost. To address these challenges, we introduce a novel fragmentation scheme, leveraging inductive biases from structural chemistry, to decompose ligands into rigid-body fragments. Building on this decomposition, we present SigmaDock, an SE(3) Riemannian diffusion model that generates poses by learning to reassemble these rigid bodies within the binding pocket. By operating at the level of fragments in SE(3), SigmaDock exploits well-established geometric priors while avoiding overly complex diffusion processes and unstable training dynamics. Experimentally, we show SigmaDock achieves state-of-the-art performance, reaching Top-1 success rates (RMSD $<2$ \& PB-valid) above 79.9\% on the PoseBusters set, compared to 12.7-32.8\% reported by recent deep learning approaches, whilst demonstrating consistent generalisation to unseen proteins. SigmaDock is the first deep learning approach to surpass classical physics-based docking under the PB train-test split, marking a significant leap forward in the reliability and feasibility of deep learning for molecular modelling.

Applications · Chemistry and Drug Discovery

Jianwei Zhu, Yu Shi, Ran Bi, Peiran Jin, Chang Liu, Zhe Zhang, Haitao Huang, Zekun Guo, Pipi Hu, Fusong Ju 等

Protein foundation models have advanced rapidly, with most approaches falling into two dominant paradigms. Sequence-based language models (e.g., ESM-2) capture sequence semantics at scale, and a number of recent works incorporate structural signals into sequence encoders. MSA-based predictors (e.g., AlphaFold 2/3) achieve accurate folding by exploiting evolutionary couplings, but their reliance on homologous sequences makes them less reliable in highly mutated or alignment-sparse regimes. We present FlexRibbon, a pretrained protein model that jointly learns from amino acid sequences and three-dimensional structures. Our pretraining strategy combines masked language modeling with diffusion-based denoising, enabling bidirectional sequence-structure learning without requiring MSAs. Trained on both experimentally resolved structures and AlphaFold 2 predictions, FlexRibbon captures global folds as well as flexible conformations critical for biological function. Evaluated across diverse tasks spanning interface design, intermolecular interaction prediction, and protein function prediction, FlexRibbon establishes new state-of-the-art performance on 12 different tasks, with particularly strong gains in mutation-rich settings where MSA-based methods often struggle.

Applications · Chemistry and Drug Discovery

Lars Holdijk, Nithishwer Mouroug Anand, Michael Bronstein, Max Welling

Estimating relative free energy differences between multiple thermodynamic states lies at the core of numerous problems in computational biochemistry. Traditional estimators, such as Free Energy Perturbation and its non-equilibrium counterpart based on the Jarzynski equality, rely on defining a switching protocol between thermodynamic states and computing the free energy difference from the work performed during this process. In this work, we present a method for learning such switching protocols within the class of escorted protocols that combine deterministic and stochastic steps. For this purpose, we use Conditional Flow Matching, and introduce Conditional Density Matching (CDM) for the purpose of estimating the change in Free-Energy. We further reduce the variance in the multistate setting by coupling multiple flows between thermodynamic states into a Flow Graph, enforcing estimator consistency across different transition paths.

Applications · Chemistry and Drug Discovery

Jeffrey Ouyang-Zhang, Pranav Murugan, Daniel Diaz, Gianluca Scarpellini, Richard Bowen, Nate Gruver, Adam Klivans, Philipp Krähenbühl, Aleksandra Faust, Maruan Al-Shedivat

AlphaFold has transformed protein structure prediction, but emerging applications such as virtual ligand screening, proteome-wide folding, and de novo binder design demand predictions at a massive scale, where runtime and memory costs become prohibitive. A major bottleneck lies in the Pairformer backbone of AlphaFold3-style models, which relies on computationally expensive triangular primitives—especially triangle attention—for pairwise reasoning. We introduce Pairmixer, a streamlined alternative that eliminates triangle attention while preserving higher-order geometric reasoning capabilities that are critical for structure prediction. Pairmixer substantially improves computational efficiency, matching state-of-the-art structure predictors across folding and docking benchmarks, delivering up to 4x faster inference on long sequences while reducing training cost by 34%. Its efficiency alleviates the computational burden of downstream applications such as modeling large protein complexes, high-throughput ligand and binder screening, and hallucination-based design. Within BoltzDesign, for example, Pairmixer delivers over 2x faster sampling and scales to sequences 30% longer than the memory limits of Pairformer. Code is available at https://github.com/genesistherapeutics/pairmixer.

Applications · Chemistry and Drug Discovery

Christoph Bartmann, Johannes Schimunek, Mykyta Ielanskyi, Philipp Seidl, Günter Klambauer, Sohvi Luukkonen

A molecule’s properties are fundamentally determined by its composition and structure encoded in its molecular graph. Thus, reasoning about molecular properties requires the ability to parse and understand the molecular graph. Large Language Models (LLMs) are increasingly applied to chemistry, tackling tasks such as molecular name conversion, captioning, text-guided generation, and property or reaction prediction. Most existing benchmarks emphasize general chemical knowledge, rely on literature or surrogate labels that risk leakage or bias, or reduce evaluation to multiple-choice questions. We introduce MolecularIQ, a molecular structure reasoning benchmark focused exclusively on symbolically verifiable tasks. MolecularIQ enables fine-grained evaluation of reasoning over molecular graphs and reveals capability patterns that localize model failures to specific tasks and molecular structures. This provides actionable insights into the strengths and limitations of current chemistry LLMs and guides the development of models that reason faithfully over molecular structure.

Applications · Chemistry and Drug Discovery

Max Shen

While data augmentation is widely used to train symmetry-agnostic models, it remains unclear how quickly and effectively they learn to respect symmetries. We investigate this by deriving a principled measure of equivariance error that, for convex losses, calculates the percent of total loss attributable to imperfections in learned symmetry. We focus our empirical investigation to 3D-rotation equivariance on high-dimensional molecular tasks (flow matching, force field prediction, denoising voxels) and find that models reduce equivariance error quickly to $\leq$2\% held-out loss within 1k-10k training steps, a result robust to model and dataset size. This happens because learning 3D-rotational equivariance is an easier learning task, with a smoother and better-conditioned loss landscape, than the main prediction task. For 3D rotations, the loss penalty for non-equivariant models is small throughout training, so they may achieve lower test loss than equivariant models per GPU-hour unless the equivariant ``efficiency gap'' is narrowed. We also experimentally and theoretically investigate the relationships between relative equivariance error, learning gradients, and model parameters.

Applications · Chemistry and Drug Discovery

Danyal Rehman, Oscar Davis, Jiarui Lu, Jian Tang, Michael Bronstein, Yoshua Bengio, Alexander Tong, Joey Bose

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from expensive inference, inhibiting their use in numerous scientific applications like Boltzmann Generators (BGs) for molecular conformations that require fast likelihood evaluation. In this paper, we revisit classical normalizing flows in the context of BGs that offer efficient sampling and likelihoods, but whose training via maximum likelihood is often unstable and computationally challenging. We propose Regression Training of Normalizing Flows (RegFlow), a novel and scalable regression-based training objective that bypasses the numerical instability and computational challenge of conventional maximum likelihood training in favour of a simple $\ell_2$-regression objective. Specifically, RegFlow maps prior samples under our flow to targets computed using optimal transport couplings or a pre-trained continuous normalizing flow (CNF). To enhance numerical stability, RegFlow employs effective regularization strategies such as a new forward-backward self-consistency loss that enjoys painless implementation. Empirically, we demonstrate that RegFlow unlocks a broader class of architectures that were previously intractable to train for BGs with maximum likelihood. We also show RegFlow exceeds the performance, computational cost, and stability of maximum likelihood training in equilibrium sampling in Cartesian coordinates of alanine dipeptide, tripeptide, and tetrapeptide, showcasing its potential in molecular systems. Code available at: https://github.com/danyalrehman/RegFlow.

Applications · Chemistry and Drug Discovery

Joongwon Lee, Seonghwan Kim, Seokhyun Moon, Hyunwoo Kim, Woo Youn Kim

We introduce FragFM, a novel hierarchical framework via fragment-level discrete flow matching for efficient molecular graph generation. FragFM generates molecules at the fragment level, leveraging a coarse-to-fine autoencoder to reconstruct details at the atom level. Together with a stochastic fragment bag strategy to effectively handle a large fragment space, our framework enables more efficient, scalable molecular generation. We demonstrate that our fragment-based approach achieves better property control than the atom-based method and additional flexibility through conditioning the fragment bag. We also propose a Natural Product Generation benchmark (NPGen) to evaluate the ability of modern molecular graph generative models to generate natural product-like molecules. Since natural products are biologically prevalidated and differ from typical drug-like molecules, our benchmark provides a more challenging yet meaningful evaluation relevant to drug discovery. We conduct a comparative study of FragFM against various models on diverse molecular generation benchmarks, including NPGen, demonstrating superior performance. The results highlight the potential of fragment-based generative modeling for large-scale, property-aware molecular design, paving the way for more efficient exploration of chemical space.

Applications · Chemistry and Drug Discovery

Robert Calef, Arthur Liang, Manolis Kellis, Marinka Zitnik

Protein representation learning has achieved major advances using large sequence and structure datasets, yet current models primarily operate at the level of individual residues or entire proteins. This overlooks a critical aspect of protein biology: proteins are composed of recurrent, evolutionarily conserved substructures that mediate core molecular functions. Despite decades of curated biological knowledge, these substructures remain largely unexploited in modern protein models. We introduce Magneton, an integrated environment for developing substructure-aware protein models. Magneton provides (1) a large-scale dataset of 530,601 proteins annotated with over 1.7 million substructures spanning 13,075 types, (2) a training framework for incorporating substructures into existing models, and (3) a benchmark suite of 13 tasks probing residue-, substructure-, and protein-level representations. Using Magneton, we develop substructure-tuning, a supervised fine-tuning method that distills substructural knowledge into pretrained protein models. Across state-of-the-art sequence- and structure-based models, substructure-tuning improves function-related tasks while revealing that substructural signals are complementary to global structural information. The Magneton environment, datasets, and substructure-tuned models are all openly available.

Applications · Chemistry and Drug Discovery

Nhat Khang Ngo, Siamak Ravanbakhsh

We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute with “architecture-dependent exponents”. In particular, we observe that equivariant architectures, which leverage task symmetry, scale better than non-equivariant models. Moreover, among equivariant architectures, higher-order representations translate to better scaling exponents. Our analysis also suggests that for computeoptimal training, the data and model sizes should scale in tandem regardless of the architecture. At a high level, these results suggest that, contrary to common belief, we should not leave it to the model to discover fundamental inductive biases such as symmetry, especially as we scale, because they change the inherent difficulty of the task and its scaling laws.

Applications · Chemistry and Drug Discovery

Manasa Kaniselvan, Benjamin Miller, Meng Gao, Juno Nam, Daniel Levine

Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of accompanying data in the Hamiltonian matrix $\mathbf{H}$ behind these datasets has so far gone unused for this purpose. Here, we provide a recipe for integrating the orbital interaction data within $\mathbf{H}$ towards training pipelines for atomic-level properties. We first introduce HELM ('Hamiltonian-trained Electronic-structure Learning for Molecules'), a state-of-the-art Hamiltonian prediction model which bridges the gap between Hamiltonian prediction and universal MLIPs by scaling to $\mathbf{H}$ of structures with 100+ atoms, high elemental diversity, and large basis sets including diffuse functions. To accompany HELM, we release a curated Hamiltonian matrix dataset, 'OMol\_CSH\_58k', with unprecedented elemental diversity (58 elements), molecular size (up to 150 atoms), and basis set (def2-TZVPD). Finally, we introduce 'Hamiltonian pretraining' as a method to extract meaningful descriptors of atomic environments even from a limited number atomic structures, and repurpose this shared embedding space to improve performance on energy-prediction in low-data regimes. Our results highlight the use of electronic interactions as a rich and transferable data source for representing chemical space.

Applications · Chemistry and Drug Discovery

Zhanghan Ni, Yanjing Li, Zeju Qiu, Bernhard Schölkopf, Hongyu Guo, Weiyang Liu, Shengchao Liu

Generative models have recently advanced $\textit{de novo}$ protein design by learning the statistical regularities of natural structures. However, current approaches face three key limitations: (1) Existing methods cannot jointly learn protein geometry and design tasks, where pretraining can be a solution; (2) Current pretraining methods mostly rely on local, non-rigid atomic representations for property prediction downstream tasks, limiting global geometric understanding for protein generation tasks; and (3) Existing approaches have yet to effectively model the rich dynamic and conformational information of protein structures. To overcome these issues, we introduce $\textbf{RigidSSL}$ ($\textit{Rigidity-Aware Self-Supervised Learning}$), a geometric pretraining framework that front-loads geometry learning prior to generative finetuning. Phase I (RigidSSL-Perturb) learns geometric priors from 432K structures from the AlphaFold Protein Structure Database with simulated perturbations. Phase II (RigidSSL-MD) refines these representations on 1.3K molecular dynamics trajectories to capture physically realistic transitions. Underpinning both phases is a bi-directional, rigidity-aware flow matching objective that jointly optimizes translational and rotational dynamics to maximize mutual information between conformations. Empirically, RigidSSL variants improve designability by up to 43\% while enhancing novelty and diversity in unconditional generation. Furthermore, RigidSSL-Perturb improves the success rate by 5.8\% in zero-shot motif scaffolding and RigidSSL-MD captures more biophysically realistic conformational ensembles in G protein-coupled receptor modeling. The code is available at: https://github.com/ZhanghanNi/RigidSSL.git.

Applications · Chemistry and Drug Discovery

Gen Zhou, Sugitha Janarthanan, Lianghong Chen, Pingzhao Hu

To address the global health threat of antimicrobial resistance, antimicrobial peptides (AMP) are being explored for their potent and promising ability to fight resistant pathogens. While artificial intelligence (AI) is being employed to advance AMP discovery and design, most AMP design models struggle to balance key goals like activity, toxicity, and novelty, using rigid or unclear scoring methods that make results hard to interpret and optimize. As the capabilities of Large Language Models (LLM) advance and evolve swiftly, we turn to AI multi-agent collaboration based on such models (multi-agent LLMs), which show rapidly rising potential in complex scientific design scenarios. Based on this, we introduce $\textbf{MAC-AMP}$, a closed-loop multi-agent collaboration (MAC) system for multi-objective AMP design. The system implements a fully autonomous simulated peer review-adaptive reinforcement learning framework that requires only a task description and example dataset to design novel AMPs. The novelty of our work lies in introducing a closed-loop multi-agent system for AMP design, with cross-domain transferability, that supports multi-objective optimization while remaining explainable rather than a 'black box'. Experiments show that MAC-AMP outperforms other AMP generative models by effectively optimizing AMP generation for multiple key molecular properties, demonstrating exceptional results in antibacterial activity, AMP likeliness, toxicity compliance, and structural reliability.

Applications · Chemistry and Drug Discovery

Yang Tan, Wenrui Gou, Bozitao Zhong, Huiqun Yu, liang hong, Bingxin Zhou

Deep learning models have driven significant progress in predicting protein function and interactions at the protein level. While these advancements have been invaluable for many biological applications such as enzyme engineering and function annotation, a more detailed perspective is essential for understanding protein functional mechanisms and evaluating the biological knowledge captured by models. This study introduces VenusX, the first benchmark designed to assess protein representation learning with a focus on fine-grained intra-protein functional understanding. VenusX comprises three major task categories across six types of annotations, including residue-level binary classification, fragment-level multi-class classification, and pairwise functional similarity scoring for identifying critical active sites, binding sites, conserved sites, motifs, domains, and epitopes. The benchmark features over 878,000 samples curated from major open-source databases such as InterPro, BioLiP, and SAbDab. By providing mixed-family and cross-family splits at three sequence identity thresholds, our benchmark enables a comprehensive assessment of model performance on both in-distribution and out-of-distribution scenarios. For baseline evaluation, we assess a diverse set of popular and open-source models, including pre-trained protein language models, sequence-structure hybrids, structure-based methods, and alignment-based techniques. Their performance is reported across all benchmark datasets and evaluation settings using multiple metrics, offering a thorough comparison and a strong foundation for future research. Our code (https://github.com/ai4protein/VenusX), data (https://huggingface.co/collections/AI4Protein/venusx-dataset), and a leaderboard (https://ai4protein.github.io/venusx/) are provided as open-source resources.

Applications · Chemistry and Drug Discovery

Xuan Li, (Andrew) Zhanke Zhou, Zongze Li, Jiangchao Yao, Yu Rong, Lu Zhang, Bo Han

Large language models (LLMs) benefit substantially from supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR) in reasoning tasks. However, these recipes perform poorly in instruction-based molecular optimization, where each data point typically provides only a single optimized reference molecule and no step-by-step optimization trajectory. We reveal that answer-only SFT on the reference molecules collapses reasoning, and RLVR provides sparse feedback under similarity constraints due to the model's lack of effective exploration, which slows learning and limits optimization. To encourage the exploration of new molecules while balancing the exploitation of the reference molecules, we introduce **Re**ference-guided **P**olicy **O**ptimization (RePO), an optimization approach that learns from reference molecules without requiring trajectory data. At each update, RePO samples candidate molecules with their intermediate reasoning trajectories from the model and trains the model using verifiable rewards that measure property satisfaction under similarity constraints in an RL manner. Meanwhile, it applies reference guidance by keeping the policy’s intermediate reasoning trajectory as context and training only the answer in a supervised manner. Together, the RL term promotes exploration, while the guidance term mitigates reward sparsity and stabilizes training by grounding outputs to references when many valid molecular edits exist. Across molecular optimization benchmarks, RePO consistently outperforms SFT and RLVR baselines (e.g., GRPO), achieving improvements on the optimization metric (Success Rate $\times$ Similarity), improving balance across competing objectives, and generalizing better to unseen instruction styles. Our code is publicly available at https://github.com/tmlr-group/RePO.