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Xiangxin Zhou

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19 papers
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19

ICML Conference 2025 Conference Paper

An All-Atom Generative Model for Designing Protein Complexes

  • Ruizhe Chen
  • Dongyu Xue
  • Xiangxin Zhou
  • Zaixiang Zheng
  • Xiangxiang Zeng
  • Quanquan Gu

Proteins typically exist in complexes, interacting with other proteins or biomolecules to perform their specific biological roles. Research on single-chain protein modeling has been extensively and deeply explored, with advancements seen in models like the series of ESM and AlphaFold2. Despite these developments, the study and modeling of multi-chain proteins remain largely uncharted, though they are vital for understanding biological functions. Recognizing the importance of these interactions, we introduce APM (all-Atom Protein generative Model), a model specifically designed for modeling multi-chain proteins. By integrating atom-level information and leveraging data on multi-chain proteins, APM is capable of precisely modeling inter-chain interactions and designing protein complexes with binding capabilities from scratch. It also performs folding and inverse-folding tasks for multi-chain proteins. Moreover, APM demonstrates versatility in downstream applications: it achieves enhanced performance through supervised fine-tuning (SFT) while also supporting zero-shot sampling in certain tasks, achieving state-of-the-art results. We released our code at https: //github. com/bytedance/apm.

TMLR Journal 2025 Journal Article

Decomposed Direct Preference Optimization for Structure-Based Drug Design

  • Xiwei Cheng
  • Xiangxin Zhou
  • Yuwei Yang
  • Yu Bao
  • Quanquan Gu

Diffusion models have achieved promising results for Structure-Based Drug Design (SBDD). Nevertheless, high-quality protein subpocket and ligand data are relatively scarce, which hinders the models’ generation capabilities. Recently, Direct Preference Optimization (DPO) has emerged as a pivotal tool for aligning generative models with human preferences. In this paper, we propose DecompDpo, a structure-based optimization method aligns diffusion models with pharmaceutical needs using multi-granularity preference pairs. DecompDpo introduces decomposition into the optimization objectives and obtains preference pairs at the molecule or decomposed substructure level based on each objective’s decomposability. Additionally, DecompDpo introduces a physics-informed energy term to ensure reasonable molecular conformations in the optimization results. Notably, DecompDpo can be effectively used for two main purposes: (1) fine-tuning pretrained diffusion models for molecule generation across various protein families, and (2) molecular optimization given a specific protein subpocket after generation. Extensive experiments on the CrossDocked2020 benchmark show that DecompDpo significantly improves model performance, achieving up to 98.5% Med. High Affinity and a 43.9% success rate for molecule generation, and 100% Med. High Affinity and a 52.1% success rate for targeted molecule optimization.

ICML Conference 2025 Conference Paper

Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling

  • Xiangxin Zhou
  • Mingyu Li
  • Yi Xiao
  • Jiahan Li
  • Dongyu Xue
  • Zaixiang Zheng
  • Jianzhu Ma
  • Quanquan Gu

Cyclic peptides offer inherent advantages in pharmaceuticals. For example, cyclic peptides are more resistant to enzymatic hydrolysis compared to linear peptides and usually exhibit excellent stability and affinity. Although deep generative models have achieved great success in linear peptide design, several challenges prevent the development of computational methods for designing diverse types of cyclic peptides. These challenges include the scarcity of 3D structural data on target proteins and associated cyclic peptide ligands, the geometric constraints that cyclization imposes, and the involvement of non-canonical amino acids in cyclization. To address the above challenges, we introduce CpSDE, which consists of two key components: AtomSDE, a generative structure prediction model based on harmonic SDE, and ResRouter, a residue type predictor. Utilizing a routed sampling algorithm that alternates between these two models to iteratively update sequences and structures, CpSDE facilitates the generation of cyclic peptides. By employing explicit all-atom and bond modeling, CpSDE overcomes existing data limitations and is proficient in designing a wide variety of cyclic peptides. Our experimental results demonstrate that the cyclic peptides designed by our method exhibit reliable stability and affinity.

ICLR Conference 2025 Conference Paper

Group Ligands Docking to Protein Pockets

  • Jiaqi Guan
  • Jiahan Li
  • Xiangxin Zhou
  • Xingang Peng
  • Sheng Wang 0001
  • Yunan Luo
  • Jian Peng 0001
  • Jianzhu Ma

Molecular docking is a key task in computational biology that has attracted increasing interest from the machine learning community. While existing methods have achieved success, they generally treat each protein-ligand pair in isolation. Inspired by the biochemical observation that ligands binding to the same target protein tend to adopt similar poses, we propose \textsc{GroupBind}, a novel molecular docking framework that simultaneously considers multiple ligands docking to a protein. This is achieved by introducing an interaction layer for the group of ligands and a triangle attention module for embedding protein-ligand and group-ligand pairs. By integrating our approach with diffusion based docking model, we set a new state-of-the-art performance on the PDBBind blind docking benchmark, demonstrating the effectiveness of our paradigm in enhancing molecular docking accuracy.

ICLR Conference 2025 Conference Paper

Integrating Protein Dynamics into Structure-Based Drug Design via Full-Atom Stochastic Flows

  • Xiangxin Zhou
  • Yi Xiao
  • Haowei Lin
  • Xinheng He
  • Jiaqi Guan
  • Yang Wang 0103
  • Qiang Liu 0006
  • Feng Zhou

The dynamic nature of proteins, influenced by ligand interactions, is essential for comprehending protein function and progressing drug discovery. Traditional structure-based drug design (SBDD) approaches typically target binding sites with rigid structures, limiting their practical application in drug development. While molecular dynamics simulation can theoretically capture all the biologically relevant conformations, the transition rate is dictated by the intrinsic energy barrier between them, making the sampling process computationally expensive. To overcome the aforementioned challenges, we propose to use generative modeling for SBDD considering conformational changes of protein pockets. We curate a dataset of apo and multiple holo states of protein-ligand complexes, simulated by molecular dynamics, and propose a full-atom flow model (and a stochastic version), named DynamicFlow, that learns to transform apo pockets and noisy ligands into holo pockets and corresponding 3D ligand molecules. Our method uncovers promising ligand molecules and corresponding holo conformations of pockets. Additionally, the resultant holo-like states provide superior inputs for traditional SBDD approaches, playing a significant role in practical drug discovery.

ICML Conference 2025 Conference Paper

Modeling All-Atom Glycan Structures via Hierarchical Message Passing and Multi-Scale Pre-training

  • Minghao Xu
  • Jiaze Song
  • Keming Wu
  • Xiangxin Zhou
  • Bin Cui 0001
  • Wentao Zhang 0001

Understanding the various properties of glycans with machine learning has shown some preliminary promise. However, previous methods mainly focused on modeling the backbone structure of glycans as graphs of monosaccharides (i. e. , sugar units), while they neglected the atomic structures underlying each monosaccharide, which are actually important indicators of glycan properties. We fill this blank by introducing the GlycanAA model for All-Atom-wise Glycan modeling. GlycanAA models a glycan as a heterogeneous graph with monosaccharide nodes representing its global backbone structure and atom nodes representing its local atomic-level structures. Based on such a graph, GlycanAA performs hierarchical message passing to capture from local atomic-level interactions to global monosaccharide-level interactions. To further enhance model capability, we pre-train GlycanAA on a high-quality unlabeled glycan dataset, deriving the PreGlycanAA model. We design a multi-scale mask prediction algorithm to endow the model about different levels of dependencies in a glycan. Extensive benchmark results show the superiority of GlycanAA over existing glycan encoders and verify the further improvements achieved by PreGlycanAA. We maintain all resources at https: //github. com/kasawa1234/GlycanAA.

ICLR Conference 2025 Conference Paper

ProteinBench: A Holistic Evaluation of Protein Foundation Models

  • Fei Ye
  • Zaixiang Zheng
  • Dongyu Xue
  • Yuning Shen
  • Lihao Wang
  • Yiming Ma
  • Yan Wang
  • Xinyou Wang

Recent years have witnessed a surge in the development of protein foundation models, significantly improving performance in protein prediction and generative tasks ranging from 3D structure prediction and protein design to conformational dynamics. However, the capabilities and limitations associated with these models remain poorly understood due to the absence of a unified evaluation framework. To fill this gap, we introduce ProteinBench, a holistic evaluation framework designed to enhance the transparency of protein foundation models. Our approach consists of three key components: (i) A taxonomic classification of tasks that broadly encompass the main challenges in the protein domain, based on the relationships between different protein modalities; (ii) A multi-metric evaluation approach that assesses performance across four key dimensions: quality, novelty, diversity, and robustness; and (iii) In-depth analyses from various user objectives, providing a holistic view of model performance. Our comprehensive evaluation of protein foundation models reveals several key findings that shed light on their current capabilities and limitations. To promote transparency and facilitate further research, we release the evaluation dataset, code, and a public leaderboard publicly for further analysis and a general modular toolkit. We intend for ProteinBench to be a living benchmark for establishing a standardized, in-depth evaluation framework for protein foundation models, driving their development and application while fostering collaboration within the field.

NeurIPS Conference 2025 Conference Paper

Riemannian Consistency Model

  • Chaoran Cheng
  • Yusong Wang
  • Yuxin Chen
  • Xiangxin Zhou
  • Nanning Zheng
  • Ge Liu

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to Riemannian manifolds remain challenging due to the curved geometry. In this work, we propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling while respecting the intrinsic manifold constraint imposed by the Riemannian geometry. Leveraging the covariant derivative and exponential-map-based parameterization, we derive the closed-form solutions for both discrete- and continuous-time training objectives for RCM. We then demonstrate theoretical equivalence between the two variants of RCM: Riemannian consistency distillation (RCD) that relies on a teacher model to approximate the marginal vector field, and Riemannian consistency training (RCT) that utilizes the conditional vector field for training. We further propose a simplified training objective that eliminates the need for the complicated differential calculation. Finally, we provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles. Through extensive experiments, we manifest the superior generative quality of RCM in few-step generation on various non-Euclidean manifolds, including flat-tori, spheres, and the 3D rotation group SO(3), spanning a variety of crucial real-world applications such as RNA and protein generation.

ICLR Conference 2025 Conference Paper

UniMatch: Universal Matching from Atom to Task for Few-Shot Drug Discovery

  • Ruifeng Li
  • Mingqian Li
  • Wei Liu
  • Yuhua Zhou
  • Xiangxin Zhou
  • Yuan Yao
  • Qiang Zhang 0026
  • Hongyang Chen 0001

Drug discovery is crucial for identifying candidate drugs for various diseases. However, its low success rate often results in a scarcity of annotations, posing a few-shot learning problem. Existing methods primarily focus on single-scale features, overlooking the hierarchical molecular structures that determine different molecular properties. To address these issues, we introduce Universal Matching Networks (UniMatch), a dual matching framework that integrates explicit hierarchical molecular matching with implicit task-level matching via meta- learning, bridging multi-level molecular representations and task-level generalization. Specifically, our approach explicitly captures structural features across multiple levels—atoms, substructures, and molecules—via hierarchical pooling and matching, facilitating precise molecular representation and comparison. Additionally, we employ a meta-learning strategy for implicit task-level matching, allowing the model to capture shared patterns across tasks and quickly adapt to new ones. This unified matching framework ensures effective molecular alignment while leveraging shared meta-knowledge for fast adaptation. Our experimental results demonstrate that UniMatch outperforms state-of-the-art methods on the MoleculeNet and FS-Mol benchmarks, achieving improvements of 2.87% in AUROC and 6.52% in ∆AUPRC. UniMatch also shows excellent generalization ability on the Meta-MolNet benchmark.

NeurIPS Conference 2024 Conference Paper

Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization

  • Xiangxin Zhou
  • Dongyu Xue
  • Ruizhe Chen
  • Zaixiang Zheng
  • Liang Wang
  • Quanquan Gu

Antibody design, a crucial task with significant implications across various disciplines such as therapeutics and biology, presents considerable challenges due to its intricate nature. In this paper, we tackle antigen-specific antibody sequence-structure co-design as an optimization problem towards specific preferences, considering both rationality and functionality. Leveraging a pre-trained conditional diffusion model that jointly models sequences and structures of antibodies with equivariant neural networks, we propose direct energy-based preference optimization to guide the generation of antibodies with both rational structures and considerable binding affinities to given antigens. Our method involves fine-tuning the pre-trained diffusion model using a residue-level decomposed energy preference. Additionally, we employ gradient surgery to address conflicts between various types of energy, such as attraction and repulsion. Experiments on RAbD benchmark show that our approach effectively optimizes the energy of generated antibodies and achieves state-of-the-art performance in designing high-quality antibodies with low total energy and high binding affinity simultaneously, demonstrating the superiority of our approach.

AAAI Conference 2024 Conference Paper

Binding-Adaptive Diffusion Models for Structure-Based Drug Design

  • Zhilin Huang
  • Ling Yang
  • Zaixi Zhang
  • Xiangxin Zhou
  • Yu Bao
  • Xiawu Zheng
  • Yuwei Yang
  • Yu Wang

Structure-based drug design (SBDD) aims to generate 3D ligand molecules that bind to specific protein targets. Existing 3D deep generative models including diffusion models have shown great promise for SBDD. However, it is complex to capture the essential protein-ligand interactions exactly in 3D space for molecular generation. To address this problem, we propose a novel framework, namely Binding-Adaptive Diffusion Models (BindDM). In BindDM, we adaptively extract subcomplex, the essential part of binding sites responsible for protein-ligand interactions. Then the selected protein-ligand subcomplex is processed with SE(3)-equivariant neural networks, and transmitted back to each atom of the complex for augmenting the target-aware 3D molecule diffusion generation with binding interaction information. We iterate this hierarchical complex-subcomplex process with cross-hierarchy interaction node for adequately fusing global binding context between the complex and its corresponding subcomplex. Empirical studies on the CrossDocked2020 dataset show BindDM can generate molecules with more realistic 3D structures and higher binding affinities towards the protein targets, with up to -5.92 Avg. Vina Score, while maintaining proper molecular properties. Our code is available at https://github.com/YangLing0818/BindDM

ICLR Conference 2024 Conference Paper

DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization

  • Xiangxin Zhou
  • Xiwei Cheng
  • Yuwei Yang
  • Yu Bao
  • Liang Wang 0001
  • Quanquan Gu

Recently, 3D generative models have shown promising performances in structure-based drug design by learning to generate ligands given target binding sites. However, only modeling the target-ligand distribution can hardly fulfill one of the main goals in drug discovery -- designing novel ligands with desired properties, e.g., high binding affinity, easily synthesizable, etc. This challenge becomes particularly pronounced when the target-ligand pairs used for training do not align with these desired properties. Moreover, most existing methods aim at solving de novo design task, while many generative scenarios requiring flexible controllability, such as R-group optimization and scaffold hopping, have received little attention. In this work, we propose DecompOpt, a structure-based molecular optimization method based on a controllable and decomposed diffusion model. DecompOpt presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering to the molecular grammar. Additionally, DecompOpt offers a unified framework covering both de novo design and controllable generation. To achieve so, ligands are decomposed into substructures which allows fine-grained control and local optimization. Experiments show that DecompOpt can efficiently generate molecules with improved properties than strong de novo baselines, and demonstrate great potential in controllable generation tasks.

ICML Conference 2024 Conference Paper

Interaction-based Retrieval-augmented Diffusion Models for Protein-specific 3D Molecule Generation

  • Zhilin Huang
  • Ling Yang 0006
  • Xiangxin Zhou
  • Chujun Qin
  • Yijie Yu 0001
  • Xiawu Zheng
  • Zikun Zhou
  • Wentao Zhang 0001

Generating ligand molecules that bind to specific protein targets via generative models holds substantial promise for advancing structure-based drug design. Existing methods generate molecules from scratch without reference or template ligands, which poses challenges in model optimization and may yield suboptimal outcomes. To address this problem, we propose an innovative interaction-based retrieval-augmented diffusion model named IRDiff to facilitate target-aware molecule generation. IRDiff leverages a curated set of ligand references, i. e. , those with desired properties such as high binding affinity, to steer the diffusion model towards synthesizing ligands that satisfy design criteria. Specifically, we utilize a protein-molecule interaction network (PMINet), which is pretrained with binding affinity signals to: (i) retrieve target-aware ligand molecules with high binding affinity to serve as references, and (ii) incorporate essential protein-ligand binding structures for steering molecular diffusion generation with two effective augmentation mechanisms, i. e. , retrieval augmentation and self augmentation. Empirical studies on CrossDocked2020 dataset show IRDiff can generate molecules with more realistic 3D structures and achieve state-of-the-art binding affinities towards the protein targets, while maintaining proper molecular properties. The codes and models are available at https: //github. com/YangLing0818/IRDiff

ICLR Conference 2024 Conference Paper

Protein-Ligand Interaction Prior for Binding-aware 3D Molecule Diffusion Models

  • Zhilin Huang
  • Ling Yang 0006
  • Xiangxin Zhou
  • Zhilong Zhang
  • Wentao Zhang 0001
  • Xiawu Zheng
  • Jie Chen 0001
  • Yu Wang 0027

Generating 3D ligand molecules that bind to specific protein targets via diffusion models has shown great promise for structure-based drug design. The key idea is to disrupt molecules into noise through a fixed forward process and learn its reverse process to generate molecules from noise in a denoising way. However, existing diffusion models primarily focus on incorporating protein-ligand interaction information solely in the reverse process, and neglect the interactions in the forward process. The inconsistency between forward and reverse processes may impair the binding affinity of generated molecules towards target protein. In this paper, we propose a novel Interaction Prior-guided Diffusion model (IPDiff) for the protein-specific 3D molecular generation by introducing geometric protein-ligand interactions into both diffusion and sampling process. Specifically, we begin by pretraining a protein-ligand interaction prior network (IPNet) by utilizing the binding affinity signals as supervision. Subsequently, we leverage the pretrained prior network to (1) integrate interactions between the target protein and the molecular ligand into the forward process for adapting the molecule diffusion trajectories (prior-shifting), and (2) enhance the binding-aware molecule sampling process (prior-conditioning). Empirical studies on CrossDocked2020 dataset show IPDiff can generate molecules with more realistic 3D structures and state-of-the-art binding affinities towards the protein targets, with up to -6.42 Avg. Vina Score, while maintaining proper molecular properties. https://github.com/YangLing0818/IPDiff

NeurIPS Conference 2024 Conference Paper

Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Design

  • Xiangxin Zhou
  • Jiaqi Guan
  • Yijia Zhang
  • Xingang Peng
  • Liang Wang
  • Jianzhu Ma

Dual-target therapeutic strategies have become a compelling approach and attracted significant attention due to various benefits, such as their potential in overcoming drug resistance in cancer therapy. Considering the tremendous success that deep generative models have achieved in structure-based drug design in recent years, we formulate dual-target drug design as a generative task and curate a novel dataset of potential target pairs based on synergistic drug combinations. We propose to design dual-target drugs with diffusion models that are trained on single-target protein-ligand complex pairs. Specifically, we align two pockets in 3D space with protein-ligand binding priors and build two complex graphs with shared ligand nodes for SE(3)-equivariant composed message passing, based on which we derive a composed drift in both 3D and categorical probability space in the generative process. Our algorithm can well transfer the knowledge gained in single-target pretraining to dual-target scenarios in a zero-shot manner. We also repurpose linker design methods as strong baselines for this task. Extensive experiments demonstrate the effectiveness of our method compared with various baselines.

ICML Conference 2024 Conference Paper

Stabilizing Policy Gradients for Stochastic Differential Equations via Consistency with Perturbation Process

  • Xiangxin Zhou
  • Liang Wang 0001
  • Yichi Zhou

Considering generating samples with high rewards, we focus on optimizing deep neural networks parameterized stochastic differential equations (SDEs), the advanced generative models with high expressiveness, with policy gradient, the leading algorithm in reinforcement learning. Nevertheless, when applying policy gradients to SDEs, since the policy gradient is estimated on a finite set of trajectories, it can be ill-defined, and the policy behavior in data-scarce regions may be uncontrolled. This challenge compromises the stability of policy gradients and negatively impacts sample complexity. To address these issues, we propose constraining the SDE to be consistent with its associated perturbation process. Since the perturbation process covers the entire space and is easy to sample, we can mitigate the aforementioned problems. Our framework offers a general approach allowing for a versatile selection of policy gradient methods to effectively and efficiently train SDEs. We evaluate our algorithm on the task of structure-based drug design and optimize the binding affinity of generated ligand molecules. Our method achieves the best Vina score (-9. 07) on the CrossDocked2020 dataset.

ICML Conference 2023 Conference Paper

DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design

  • Jiaqi Guan
  • Xiangxin Zhou
  • Yuwei Yang
  • Yu Bao
  • Jian Peng 0001
  • Jianzhu Ma
  • Qiang Liu 0006
  • Liang Wang 0001

Designing 3D ligands within a target binding site is a fundamental task in drug discovery. Existing structured-based drug design methods treat all ligand atoms equally, which ignores different roles of atoms in the ligand for drug design and can be less efficient for exploring the large drug-like molecule space. In this paper, inspired by the convention in pharmaceutical practice, we decompose the ligand molecule into two parts, namely arms and scaffold, and propose a new diffusion model, DecompDiff, with decomposed priors over arms and scaffold. In order to facilitate the decomposed generation and improve the properties of the generated molecules, we incorporate both bond diffusion in the model and additional validity guidance in the sampling phase. Extensive experiments on CrossDocked2020 show that our approach achieves state-of-the-art performance in generating high-affinity molecules while maintaining proper molecular properties and conformational stability, with up to $-8. 39$ Avg. Vina Dock score and $24. 5%$ Success Rate. The code is provided at https: //github. com/bytedance/DecompDiff

NeurIPS Conference 2023 Conference Paper

GSLB: The Graph Structure Learning Benchmark

  • Zhixun Li
  • Xin Sun
  • Yifan Luo
  • Yanqiao Zhu
  • Dingshuo Chen
  • Yingtao Luo
  • Xiangxin Zhou
  • Qiang Liu

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https: //github. com/GSL-Benchmark/GSLB.

NeurIPS Conference 2019 Conference Paper

Global Sparse Momentum SGD for Pruning Very Deep Neural Networks

  • Xiaohan Ding
  • Guiguang Ding
  • Xiangxin Zhou
  • Yuchen Guo
  • Jungong Han
  • Ji Liu

Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at eliminating some parameters with tolerable performance degradation. In this paper, we propose a novel momentum-SGD-based optimization method to reduce the network complexity by on-the-fly pruning. Concretely, given a global compression ratio, we categorize all the parameters into two parts at each training iteration which are updated using different rules. In this way, we gradually zero out the redundant parameters, as we update them using only the ordinary weight decay but no gradients derived from the objective function. As a departure from prior methods that require heavy human works to tune the layer-wise sparsity ratios, prune by solving complicated non-differentiable problems or finetune the model after pruning, our method is characterized by 1) global compression that automatically finds the appropriate per-layer sparsity ratios; 2) end-to-end training; 3) no need for a time-consuming re-training process after pruning; and 4) superior capability to find better winning tickets which have won the initialization lottery.

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