CVOct 26, 2023Code
ControlLLM: Augment Language Models with Tools by Searching on GraphsZhaoyang Liu, Zeqiang Lai, Zhangwei Gao et al.
We present ControlLLM, a novel framework that enables large language models (LLMs) to utilize multi-modal tools for solving complex real-world tasks. Despite the remarkable performance of LLMs, they still struggle with tool invocation due to ambiguous user prompts, inaccurate tool selection and parameterization, and inefficient tool scheduling. To overcome these challenges, our framework comprises three key components: (1) a \textit{task decomposer} that breaks down a complex task into clear subtasks with well-defined inputs and outputs; (2) a \textit{Thoughts-on-Graph (ToG) paradigm} that searches the optimal solution path on a pre-built tool graph, which specifies the parameter and dependency relations among different tools; and (3) an \textit{execution engine with a rich toolbox} that interprets the solution path and runs the tools efficiently on different computational devices. We evaluate our framework on diverse tasks involving image, audio, and video processing, demonstrating its superior accuracy, efficiency, and versatility compared to existing methods. The code is at https://github.com/OpenGVLab/ControlLLM.
CVJun 8, 2023Code
ADDP: Learning General Representations for Image Recognition and Generation with Alternating Denoising Diffusion ProcessChangyao Tian, Chenxin Tao, Jifeng Dai et al.
Image recognition and generation have long been developed independently of each other. With the recent trend towards general-purpose representation learning, the development of general representations for both recognition and generation tasks is also promoted. However, preliminary attempts mainly focus on generation performance, but are still inferior on recognition tasks. These methods are modeled in the vector-quantized (VQ) space, whereas leading recognition methods use pixels as inputs. Our key insights are twofold: (1) pixels as inputs are crucial for recognition tasks; (2) VQ tokens as reconstruction targets are beneficial for generation tasks. These observations motivate us to propose an Alternating Denoising Diffusion Process (ADDP) that integrates these two spaces within a single representation learning framework. In each denoising step, our method first decodes pixels from previous VQ tokens, then generates new VQ tokens from the decoded pixels. The diffusion process gradually masks out a portion of VQ tokens to construct the training samples. The learned representations can be used to generate diverse high-fidelity images and also demonstrate excellent transfer performance on recognition tasks. Extensive experiments show that our method achieves competitive performance on unconditional generation, ImageNet classification, COCO detection, and ADE20k segmentation. Importantly, our method represents the first successful development of general representations applicable to both generation and dense recognition tasks. Code is released at \url{https://github.com/ChangyaoTian/ADDP}.
CLJun 2
MemTrain: Self-Supervised Context Memory TrainingZiheng Li, Xingrun Xing, Haoqing Wang et al.
Memory is an indispensable capability for long-horizon LLM agents, enabling them to preserve and utilize information accumulated across extended interactions. Existing memory-agent approaches are typically trained end-to-end with reinforcement learning on downstream tasks. However, collecting high-quality annotated problems for memory-intensive scenarios is costly, and the resulting training data often lack sufficient diversity to cover general memory behaviors. In this work, we propose MemTrain, a self-supervised training framework for generally enhancing the context-memory capability of LLM agents for more effective downstream post-training. MemTrain introduces two coupled proxy tasks over unlabeled Wikipedia corpora: (1) an end-to-end masked reconstruction objective, which requires the model to recover masked entities after multiple rounds of memory updates, thereby encouraging memory maintenance from the final outcome perspective; and (2) an intermediate memory recall objective, which requires the model to reconstruct masked historical information using intermediate memory states, encouraging faithful compression and memory completeness throughout the interaction process. The two objectives are jointly optimized using GRPO. Extensive experiments on long-text QA and search-based QA benchmarks demonstrate that MemTrain consistently improves downstream memory-intensive reasoning performance across different models, achieving gains of up to 17.67 points over direct task-specific post-training.
CVJun 2, 2023
Denoising Diffusion Semantic Segmentation with Mask Prior ModelingZeqiang Lai, Yuchen Duan, Jifeng Dai et al.
The evolution of semantic segmentation has long been dominated by learning more discriminative image representations for classifying each pixel. Despite the prominent advancements, the priors of segmentation masks themselves, e.g., geometric and semantic constraints, are still under-explored. In this paper, we propose to ameliorate the semantic segmentation quality of existing discriminative approaches with a mask prior modeled by a recently-developed denoising diffusion generative model. Beginning with a unified architecture that adapts diffusion models for mask prior modeling, we focus this work on a specific instantiation with discrete diffusion and identify a variety of key design choices for its successful application. Our exploratory analysis revealed several important findings, including: (1) a simple integration of diffusion models into semantic segmentation is not sufficient, and a poorly-designed diffusion process might lead to degradation in segmentation performance; (2) during the training, the object to which noise is added is more important than the type of noise; (3) during the inference, the strict diffusion denoising scheme may not be essential and can be relaxed to a simpler scheme that even works better. We evaluate the proposed prior modeling with several off-the-shelf segmentors, and our experimental results on ADE20K and Cityscapes demonstrate that our approach could achieve competitively quantitative performance and more appealing visual quality.
LGMay 31
Trust Region On-Policy DistillationXingrun Xing, Haoqing Wang, Boyan Gao et al.
On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.
CLMar 20Code
LiveClawBench: Benchmarking LLM Agents on Complex, Real-World Assistant TasksXiang Long, Li Du, Yilong Xu et al.
LLM-based agents are increasingly expected to handle real-world assistant tasks, yet existing benchmarks typically evaluate them under isolated sources of difficulty, such as a single environment or fully specified instructions. This leaves a substantial gap between current evaluation settings and the compositional challenges that arise in practical deployment. To address this gap, we introduce LiveClawBench, a benchmark to evaluate LLM agents on real-world assistant tasks. Based on an analysis of various real OpenClaw usage cases, we derive a Triple-Axis Complexity Framework that characterizes task difficulty along three dimensions: Environment Complexity, Cognitive Demand, and Runtime Adaptability. Guided by this framework, we construct a pilot benchmark with explicit complexity-factor annotations, covering real-world assistant tasks with compositional difficulty. Together, the framework and benchmark provide a principled foundation for evaluating LLM agents in realistic assistant settings, and establish a basis for future expansion across task domains and complexity axes. We are continuing to enrich our case collections to achieve more comprehensive domain and complexity coverage. The project page is at https://github.com/Mosi-AI/LiveClawBench.
CVApr 22, 2022
Alleviating Representational Shift for Continual Fine-tuningShibo Jie, Zhi-Hong Deng, Ziheng Li · pku
We study a practical setting of continual learning: fine-tuning on a pre-trained model continually. Previous work has found that, when training on new tasks, the features (penultimate layer representations) of previous data will change, called representational shift. Besides the shift of features, we reveal that the intermediate layers' representational shift (IRS) also matters since it disrupts batch normalization, which is another crucial cause of catastrophic forgetting. Motivated by this, we propose ConFiT, a fine-tuning method incorporating two components, cross-convolution batch normalization (Xconv BN) and hierarchical fine-tuning. Xconv BN maintains pre-convolution running means instead of post-convolution, and recovers post-convolution ones before testing, which corrects the inaccurate estimates of means under IRS. Hierarchical fine-tuning leverages a multi-stage strategy to fine-tune the pre-trained network, preventing massive changes in Conv layers and thus alleviating IRS. Experimental results on four datasets show that our method remarkably outperforms several state-of-the-art methods with lower storage overhead.
AIFeb 13Code
To Mix or To Merge: Toward Multi-Domain Reinforcement Learning for Large Language ModelsHaoqing Wang, Xiang Long, Ziheng Li et al.
Reinforcement Learning with Verifiable Rewards (RLVR) plays a key role in stimulating the explicit reasoning capability of Large Language Models (LLMs). We can achieve expert-level performance in some specific domains via RLVR, such as coding or math. When a general multi-domain expert-level model is required, we need to carefully consider the collaboration of RLVR across different domains. The current state-of-the-art models mainly employ two different training paradigms for multi-domain RLVR: mixed multi-task RLVR and separate RLVR followed by model merging. However, most of the works did not provide a detailed comparison and analysis about these paradigms. To this end, we choose multiple commonly used high-level tasks (e.g., math, coding, science, and instruction following) as our target domains and design extensive qualitative and quantitative experiments using open-source datasets. We find the RLVR across domains exhibits few mutual interferences, and reasoning-intensive domains demonstrate mutually synergistic effects. Furthermore, we analyze the internal mechanisms of mutual gains from the perspectives of weight space geometry, model prediction behavior, and information constraints. This project is named as M2RL that means Mixed multi-task training or separate training followed by model Merging for Reinforcement Learning, and the homepage is at https://github.com/mosAI25/M2RL
LGMay 19, 2022
Bypassing Logits Bias in Online Class-Incremental Learning with a Generative FrameworkGehui Shen, Shibo Jie, Ziheng Li et al. · pku
Continual learning requires the model to maintain the learned knowledge while learning from a non-i.i.d data stream continually. Due to the single-pass training setting, online continual learning is very challenging, but it is closer to the real-world scenarios where quick adaptation to new data is appealing. In this paper, we focus on online class-incremental learning setting in which new classes emerge over time. Almost all existing methods are replay-based with a softmax classifier. However, the inherent logits bias problem in the softmax classifier is a main cause of catastrophic forgetting while existing solutions are not applicable for online settings. To bypass this problem, we abandon the softmax classifier and propose a novel generative framework based on the feature space. In our framework, a generative classifier which utilizes replay memory is used for inference, and the training objective is a pair-based metric learning loss which is proven theoretically to optimize the feature space in a generative way. In order to improve the ability to learn new data, we further propose a hybrid of generative and discriminative loss to train the model. Extensive experiments on several benchmarks, including newly introduced task-free datasets, show that our method beats a series of state-of-the-art replay-based methods with discriminative classifiers, and reduces catastrophic forgetting consistently with a remarkable margin.
LGFeb 23, 2023
Detachedly Learn a Classifier for Class-Incremental LearningZiheng Li, Shibo Jie, Zhi-Hong Deng · pku
In continual learning, model needs to continually learn a feature extractor and classifier on a sequence of tasks. This paper focuses on how to learn a classifier based on a pretrained feature extractor under continual learning setting. We present an probabilistic analysis that the failure of vanilla experience replay (ER) comes from unnecessary re-learning of previous tasks and incompetence to distinguish current task from the previous ones, which is the cause of knowledge degradation and prediction bias. To overcome these weaknesses, we propose a novel replay strategy task-aware experience replay. It rebalances the replay loss and detaches classifier weight for the old tasks from the update process, by which the previous knowledge is kept intact and the overfitting on episodic memory is alleviated. Experimental results show our method outperforms current state-of-the-art methods.
AINov 13, 2025
Efficient Thought Space Exploration through Strategic InterventionZiheng Li, Hengyi Cai, Xiaochi Wei et al.
While large language models (LLMs) demonstrate emerging reasoning capabilities, current inference-time expansion methods incur prohibitive computational costs by exhaustive sampling. Through analyzing decoding trajectories, we observe that most next-token predictions align well with the golden output, except for a few critical tokens that lead to deviations. Inspired by this phenomenon, we propose a novel Hint-Practice Reasoning (HPR) framework that operationalizes this insight through two synergistic components: 1) a hinter (powerful LLM) that provides probabilistic guidance at critical decision points, and 2) a practitioner (efficient smaller model) that executes major reasoning steps. The framework's core innovation lies in Distributional Inconsistency Reduction (DIR), a theoretically-grounded metric that dynamically identifies intervention points by quantifying the divergence between practitioner's reasoning trajectory and hinter's expected distribution in a tree-structured probabilistic space. Through iterative tree updates guided by DIR, HPR reweights promising reasoning paths while deprioritizing low-probability branches. Experiments across arithmetic and commonsense reasoning benchmarks demonstrate HPR's state-of-the-art efficiency-accuracy tradeoffs: it achieves comparable performance to self-consistency and MCTS baselines while decoding only 1/5 tokens, and outperforms existing methods by at most 5.1% absolute accuracy while maintaining similar or lower FLOPs.
CVAug 13, 2024
PathInsight: Instruction Tuning of Multimodal Datasets and Models for Intelligence Assisted Diagnosis in HistopathologyXiaomin Wu, Rui Xu, Pengchen Wei et al.
Pathological diagnosis remains the definitive standard for identifying tumors. The rise of multimodal large models has simplified the process of integrating image analysis with textual descriptions. Despite this advancement, the substantial costs associated with training and deploying these complex multimodal models, together with a scarcity of high-quality training datasets, create a significant divide between cutting-edge technology and its application in the clinical setting. We had meticulously compiled a dataset of approximately 45,000 cases, covering over 6 different tasks, including the classification of organ tissues, generating pathology report descriptions, and addressing pathology-related questions and answers. We have fine-tuned multimodal large models, specifically LLaVA, Qwen-VL, InternLM, with this dataset to enhance instruction-based performance. We conducted a qualitative assessment of the capabilities of the base model and the fine-tuned model in performing image captioning and classification tasks on the specific dataset. The evaluation results demonstrate that the fine-tuned model exhibits proficiency in addressing typical pathological questions. We hope that by making both our models and datasets publicly available, they can be valuable to the medical and research communities.
CLApr 1Code
MemFactory: Unified Inference & Training Framework for Agent MemoryZiliang Guo, Ziheng Li, Bo Tang et al.
Memory-augmented Large Language Models (LLMs) are essential for developing capable, long-term AI agents. Recently, applying Reinforcement Learning (RL) to optimize memory operations, such as extraction, updating, and retrieval, has emerged as a highly promising research direction. However, existing implementations remain highly fragmented and task-specific, lacking a unified infrastructure to streamline the integration, training, and evaluation of these complex pipelines. To address this gap, we present MemFactory, the first unified, highly modular training and inference framework specifically designed for memory-augmented agents. Inspired by the success of unified fine-tuning frameworks like LLaMA-Factory, MemFactory abstracts the memory lifecycle into atomic, plug-and-play components, enabling researchers to seamlessly construct custom memory agents via a "Lego-like" architecture. Furthermore, the framework natively integrates Group Relative Policy Optimization (GRPO) to fine-tune internal memory management policies driven by multi-dimensional environmental rewards. MemFactory provides out-of-the-box support for recent cutting-edge paradigms, including Memory-R1, RMM, and MemAgent. We empirically validate MemFactory on the open-source MemAgent architecture using its publicly available training and evaluation data. Across both in-domain and out-of-distribution evaluation sets, MemFactory consistently improves performance over the corresponding base models, with relative gains of up to 14.8%. By providing a standardized, extensible, and easy-to-use infrastructure, MemFactory significantly lowers the barrier to entry, paving the way for future innovations in memory-driven AI agents.
LGJan 2
IRPM: Intergroup Relative Preference Modeling for Pointwise Generative Reward ModelsHaonan Song, Qingchen Xie, Huan Zhu et al.
Generative Reward Models (GRMs) have demonstrated strong performance in reward modeling, due to their interpretability and potential for refinement through reinforcement learning (RL). However, widely used pairwise GRMs create a computational bottleneck in reinforcement learning from human feedback (RLHF), when calibrating or aggregating preference signals over n candidates, often incurring O(n^2) pairwise judgments. To address this issue, we propose Intergroup Relative Preference Modeling (IRPM), an RL-based method that extends the Bradley--Terry preference-learning paradigm via intergroup comparisons to train pointwise GRMs from pairwise preference data. IRPM derives pointwise reward for each response by contrasting groups of chosen vs. rejected samples, enabling pointwise scores comparable across candidate sets and O(n) reward evaluation for a variable number of candidates during RL training, while preserving interpretability and scalability. Experiments show that IRPM achieves state-of-the-art performance among pointwise GRMs on RM-Bench, JudgeBench and RewardBench, and approaches the performance of leading pairwise GRMs. In addition, IRPM achieves substantial gains in post-training evaluations, demonstrating its effectiveness.
CLMay 16, 2023Code
Dual-Alignment Pre-training for Cross-lingual Sentence EmbeddingZiheng Li, Shaohan Huang, Zihan Zhang et al.
Recent studies have shown that dual encoder models trained with the sentence-level translation ranking task are effective methods for cross-lingual sentence embedding. However, our research indicates that token-level alignment is also crucial in multilingual scenarios, which has not been fully explored previously. Based on our findings, we propose a dual-alignment pre-training (DAP) framework for cross-lingual sentence embedding that incorporates both sentence-level and token-level alignment. To achieve this, we introduce a novel representation translation learning (RTL) task, where the model learns to use one-side contextualized token representation to reconstruct its translation counterpart. This reconstruction objective encourages the model to embed translation information into the token representation. Compared to other token-level alignment methods such as translation language modeling, RTL is more suitable for dual encoder architectures and is computationally efficient. Extensive experiments on three sentence-level cross-lingual benchmarks demonstrate that our approach can significantly improve sentence embedding. Our code is available at https://github.com/ChillingDream/DAP.
CLJan 12
Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical ReasoningZiheng Li, Liu Kang, Feng Xiao et al.
Group Relative Policy Optimization (GRPO) has emerged as a promising critic-free reinforcement learning paradigm for reasoning tasks. However, standard GRPO employs a coarse-grained credit assignment mechanism that propagates group-level rewards uniformly to to every token in a sequence, neglecting the varying contribution of individual reasoning steps. We address this limitation by introducing Outcome-grounded Advantage Reshaping (OAR), a fine-grained credit assignment mechanism that redistributes advantages based on how much each token influences the model's final answer. We instantiate OAR via two complementary strategies: (1) OAR-P, which estimates outcome sensitivity through counterfactual token perturbations, serving as a high-fidelity attribution signal; (2) OAR-G, which uses an input-gradient sensitivity proxy to approximate the influence signal with a single backward pass. These importance signals are integrated with a conservative Bi-Level advantage reshaping scheme that suppresses low-impact tokens and boosts pivotal ones while preserving the overall advantage mass. Empirical results on extensive mathematical reasoning benchmarks demonstrate that while OAR-P sets the performance upper bound, OAR-G achieves comparable gains with negligible computational overhead, both significantly outperforming a strong GRPO baseline, pushing the boundaries of critic-free LLM reasoning.
LGSep 8, 2025
Staying in the Sweet Spot: Responsive Reasoning Evolution via Capability-Adaptive Hint ScaffoldingZiheng Li, Zexu Sun, Jinman Zhao et al.
Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to mismatches between the training data's difficulty and the model's capability. LLMs fail to discover viable reasoning paths when problems are overly difficult, while learning little new capability when problems are too simple. In this work, we formalize the impact of problem difficulty by quantifying the relationship between loss descent speed and rollout accuracy. Building on this analysis, we propose SEELE, a novel supervision-aided RLVR framework that dynamically adjusts problem difficulty to stay within the high-efficiency region. SEELE augments each training sample by appending a hint (part of a full solution) after the original problem. Unlike previous hint-based approaches, SEELE deliberately and adaptively adjusts the hint length for each problem to achieve an optimal difficulty. To determine the optimal hint length, SEELE employs a multi-round rollout sampling strategy. In each round, it fits an item response theory model to the accuracy-hint pairs collected in preceding rounds to predict the required hint length for the next round. This instance-level, real-time difficulty adjustment aligns problem difficulty with the evolving model capability, thereby improving exploration efficiency. Experimental results show that SEELE outperforms Group Relative Policy Optimization (GRPO) and Supervised Fine-tuning (SFT) by +11.8 and +10.5 points, respectively, and surpasses the best previous supervision-aided approach by +3.6 points on average across six math reasoning benchmarks.
AIFeb 1
Not All Preferences Are Created Equal: Stability-Aware and Gradient-Efficient Alignment for Reasoning ModelsHui Wu, Hengyi Cai, Jinman Zhao et al.
Preference-based alignment is pivotal for training large reasoning models; however, standard methods like Direct Preference Optimization (DPO) typically treat all preference pairs uniformly, overlooking the evolving utility of training instances. This static approach often leads to inefficient or unstable optimization, as it wastes computation on trivial pairs with negligible gradients and suffers from noise induced by samples near uncertain decision boundaries. Facing these challenges, we propose SAGE (Stability-Aware Gradient Efficiency), a dynamic framework designed to enhance alignment reliability by maximizing the Signal-to-Noise Ratio of policy updates. Concretely, SAGE integrates a coarse-grained curriculum mechanism that refreshes candidate pools based on model competence with a fine-grained, stability-aware scoring function that prioritizes informative, confident errors while filtering out unstable samples. Experiments on multiple mathematical reasoning benchmarks demonstrate that SAGE significantly accelerates convergence and outperforms static baselines, highlighting the critical role of policy-aware, stability-conscious data selection in reasoning alignment.
CLAug 11, 2025
Keyword-Centric Prompting for One-Shot Event Detection with Self-Generated Rationale EnhancementsZiheng Li, Zhi-Hong Deng
Although the LLM-based in-context learning (ICL) paradigm has demonstrated considerable success across various natural language processing tasks, it encounters challenges in event detection. This is because LLMs lack an accurate understanding of event triggers and tend to make over-interpretation, which cannot be effectively corrected through in-context examples alone. In this paper, we focus on the most challenging one-shot setting and propose KeyCP++, a keyword-centric chain-of-thought prompting approach. KeyCP++ addresses the weaknesses of conventional ICL by automatically annotating the logical gaps between input text and detection results for the demonstrations. Specifically, to generate in-depth and meaningful rationale, KeyCP++ constructs a trigger discrimination prompting template. It incorporates the exemplary triggers (a.k.a keywords) into the prompt as the anchor to simply trigger profiling, let LLM propose candidate triggers, and justify each candidate. These propose-and-judge rationales help LLMs mitigate over-reliance on the keywords and promote detection rule learning. Extensive experiments demonstrate the effectiveness of our approach, showcasing significant advancements in one-shot event detection.
SYJun 18, 2017
Generalized-impedance and Stability Criterion for Grid-connected ConvertersHuanhai Xin, Ziheng Li, Wei Dong et al.
The output impedance matrix of a grid-connected converter plays an important role in analyzing system stability. Due to the dynamics of the DC-link control and the phase locked loop (PLL), the output impedance matrices of the converter and grid are difficult to be diagonally decoupled simultaneously, neither in the dq domain nor in the phase domain. It weakens the effectiveness of impedance-based stability criterion (ISC) in system oscillation analysis. To this end, this paper innovatively proposes the generalized-impedance based stability criterion (GISC) to reduce the dimension of the transfer function matrix and simplify system small-signal stability analysis. Firstly, the impedances of the converter and the grid in polar coordinates are formulated, and the concept of generalized-impedance of the converter and the grid is put forward. Secondly, through strict mathematical derivation, the equation that implies the dynamic interaction between the converter and the grid is then extracted from the characteristic equation of the grid-connected converter system. Using the proposed method, the small-signal instability of system can be interpreted as the resonance of the generalized-impedances of the converter and the grid. Besides, the GISC is equivalent to ISC when the dynamics of the outer-loop control and PLL are not considered. Finally, the effectiveness of the proposed method is further verified using the MATLAB based digital simulation and RT-LAB based hardware-in-the-loop (HIL) simulation.
SYApr 1, 2017
A Generalized-Impedance Based Stability Criterion for Three-Phase Grid-Connected Voltage Source ConvertersHuanhai Xin, Ziheng Li, Wei Dong et al.
The output impedance matrices of three-phase grid-connected voltage source converters (VSCs) are widely used in power system stability analysis. Regardless of how the impedance is modeled, there always exist coupling terms in the impedance matrix, which makes the system a multi-input- multi-output (MIMO) system. Some approximation approaches omit the coupling terms so that a three-phase system can be treated like a single-phase one, and the impedance-based stability criterion for a single-input-single-output (SISO) system is applicable. However, such handling may result in analytical errors or even incorrect conclusions in a mirror frequency coupled system. By introducing the concept of generalized- impedances, this letter proposes a new stability criterion based on a virtual SISO system, which can effectively handle the coupling terms. Further, the effects of the phase-locked-loop (PLL) parameters on system stability are studied based on the proposed criterion. The effectiveness of the proposed criterion is verified by a hardware-in-the-loop (HIL) simulation based on RT-LAB.