We introduce a one-step generative policy for offline reinforcement learning that maps *noise* directly to *actions* via a *residual reformulation* of MeanFlow, making it compatible with Q-learning. While one-step Gaussian policies enable fast inference, they struggle to capture complex, multimodal action distributions. Existing flow-based methods improve expressivity but typically rely on distillation and two-stage training when trained with Q-learning. To overcome these limitations, we propose to reformulate MeanFlow to enable *direct noise-to-action generation* by integrating the velocity field and noise-to-action transformation into a single policy network—eliminating the need for separate velocity estimation. We explore several reformulation variants and identify an effective *residual formulation* that supports expressive and stable policy learning. Our method offers three key advantages: 1) efficient one-step noise-to-action generation, 2) expressive modelling of multimodal action distributions, and 3) efficient and stable policy learning via Q-learning in a single-stage training setup. Extensive experiments on 73 tasks across the OGBench and D4RL benchmarks demonstrate that our method achieves strong performance in both offline and offline-to-online reinforcement learning settings.

The emergence of vision-language foundation models, such as CLIP, has revolutionized image-text representation, enabling a broad range of applications via prompt learning. Despite its promise, real-world datasets often contain noisy labels that can degrade prompt learning performance. In this paper, we demonstrate that using mean absolute error (MAE) loss in prompt learning, named PromptMAE, significantly enhances robustness against noisy labels while maintaining high accuracy. Though MAE is straightforward and recognized for its robustness, it is rarely used in noisy-label learning due to its slow convergence and poor performance outside prompt learning scenarios. To elucidate the robustness of PromptMAE, we leverage feature learning theory to show that MAE can suppress the influence of noisy samples, thereby improving the signal-to-noise ratio and enhancing overall robustness. Additionally, we introduce PromptOT, a prompt-based optimal transport data purification method to enhance the robustness further. PromptOT employs text features in vision-language models as prototypes to construct an optimal transportation matrix. This matrix effectively partitions datasets into clean and noisy subsets, allowing for the application of cross-entropy loss to the clean subset and MAE loss to the noisy subset. Our Noise-Label Prompt Learning method, named NLPrompt, offers a simple and efficient approach that leverages the expressive representations and precise alignment capabilities of vision-language models for robust prompt learning. We validate NLPrompt through extensive experiments across various noise settings, demonstrating significant performance improvements.

Diffusion-based policies have shown impressive performance in robotic manipulation tasks while struggling with out-of-domain distributions. Recent efforts attempted to enhance generalization by improving the visual feature encoding for diffusion policy. However, their generalization is typically limited to the same category with similar appearances. Our key insight is that leveraging affordances—manipulation priors that define "where" and "how" an agent interacts with an object—can substantially enhance generalization to entirely unseen object instances and categories. We introduce the Diffusion Policy with transferable Affordance (AffordDP), designed for generalizable manipulation across novel categories. AffordDP models affordances through 3D contact points and post-contact trajectories, capturing the essential static and dynamic information for complex tasks. The transferable affordance from in-domain data to unseen objects is achieved by estimating a 6D transformation matrix using foundational vision models and point cloud registration techniques. More importantly, we incorporate affordance guidance during diffusion sampling that can refine action sequence generation. This guidance directs the generated action to gradually move towards the desired manipulation for unseen objects while keeping the generated action within the manifold of action space. Experimental results from both simulated and real-world environments demonstrate that AffordDP consistently outperforms previous diffusion-based methods, successfully generalizing to unseen instances and categories where others fail.

3D affordance segmentation aims to link human instructions to touchable regions of 3D objects for embodied manipulations. Existing efforts typically adhere to single-object, single-affordance paradigms, where each affordance type or explicit instruction strictly corresponds to a specific affordance region and are unable to handle long-horizon tasks. Such a paradigm cannot actively reason about complex user intentions that often imply sequential affordances. In this paper, we introduce the Sequential 3D Affordance Reasoning task, which extends the traditional paradigm by reasoning from cumbersome user intentions and then decomposing them into a series of segmentation maps. Toward this, we construct the first instruction-based affordance segmentation benchmark that includes reasoning over both single and sequential affordances, comprising 180K instruction-point cloud pairs. Based on the benchmark, we propose our model, SeqAfford, to unlock the 3D multi-modal large language model with additional affordance segmentation abilities, which ensures reasoning with world knowledge and fine-grained affordance grounding in a cohesive framework. We further introduce a multi-granular language-point integration module to endow 3D dense prediction. Extensive experimental evaluations show that our model excels over well-established methods and exhibits open-world generalization with sequential reasoning abilities. Project page: https://seq-afford.github.io/.

Real-time synthesis of physically plausible human interactions remains a critical challenge for immersive VR/AR systems and humanoid robotics. While existing methods demonstrate progress in kinematic motion generation, they often fail to address the fundamental tension between real-time responsiveness, physical feasibility, and safety requirements in dynamic human-machine interactions. We introduce Human-X, a novel framework designed to enable immersive and physically plausible human interactions across diverse entities, including human-avatar, human-humanoid, and human-robot systems. Unlike existing approaches that focus on post-hoc alignment or simplified physics, our method jointly predicts actions and reactions in real-time using an auto-regressive reaction diffusion planner, ensuring seamless synchronization and context-aware responses. To enhance physical realism and safety, we integrate an actor-aware motion tracking policy trained with reinforcement learning, which dynamically adapts to interaction partners' movements while avoiding artifacts like foot sliding and penetration. Extensive experiments on the Inter-X and InterHuman datasets demonstrate significant improvements in motion quality, interaction continuity, and physical plausibility over state-of-the-art methods. Our framework is validated in real-world applications, including virtual reality interface for human-robot interaction, showcasing its potential for advancing human-robot collaboration.

This paper addresses the challenging task of generating dynamic Human-Object Interactions from textual descriptions, named Text2HOI. While most existing works assume interactions with limited body parts or static objects, our task involves addressing the variation in human motion, the diversity of object shapes, and the semantic vagueness of object motion simultaneously. To tackle this, we propose a novel Text-guided Human-Object Interaction diffusion model with Relation Intervention (THOR). THOR is a cohesive diffusion model equipped with a relation intervention mechanism. In each diffusion step, we initiate text-guided human and object motion and then leverage human-object relations to intervene in object motion. This intervention enhances the spatial-temporal relations between humans and objects, with human-centric motion providing additional guidance for synthesizing consistent motion from text. To achieve more reasonable and realistic results, relation intervention loss is introduced at different levels of motion granularity.

Recent advances in diffusion bridge models leverage Doob’s $h$-transform to establish fixed endpoints between distributions, demonstrating promising results in image translation and restoration tasks. However, these approaches frequently produce blurred or excessively smoothed image details and lack a comprehensive theoretical foundation to explain these shortcomings. To address these limitations, we propose UniDB, a unified framework for diffusion bridges based on Stochastic Optimal Control (SOC). UniDB formulates the problem through an SOC-based optimization and derives a closed-form solution for the optimal controller, thereby unifying and generalizing existing diffusion bridge models. We demonstrate that existing diffusion bridges employing Doob’s $h$-transform constitute a special case of our framework, emerging when the terminal penalty coefficient in the SOC cost function tends to infinity. By incorporating a tunable terminal penalty coefficient, UniDB achieves an optimal balance between control costs and terminal penalties, substantially improving detail preservation and output quality. Notably, UniDB seamlessly integrates with existing diffusion bridge models, requiring only minimal code modifications. Extensive experiments across diverse image restoration tasks validate the superiority and adaptability of the proposed framework. Our code is available at https://github.com/UniDB-SOC/UniDB/.

Recent advances in reinforcement learning (RL) have demonstrated the powerful exploration capabilities and multimodality of generative diffusion-based policies. While substantial progress has been made in offline RL and off-policy RL settings, integrating diffusion policies into on-policy frameworks like PPO remains underexplored. This gap is particularly significant given the widespread use of large-scale parallel GPU-accelerated simulators, such as IsaacLab, which are optimized for on-policy RL algorithms and enable rapid training of complex robotic tasks. A key challenge lies in computing state-action log-likelihoods under diffusion policies, which is straightforward for Gaussian policies but intractable for flow-based models due to irreversible forward-reverse processes and discretization errors (e.g., Euler-Maruyama approximations). To bridge this gap, we propose GenPO, a generative policy optimization framework that leverages exact diffusion inversion to construct invertible action mappings. GenPO introduces a novel doubled dummy action mechanism that enables invertibility via alternating updates, resolving log-likelihood computation barriers. Furthermore, we also use the action log-likelihood for unbiased entropy and KL divergence estimation, enabling KL-adaptive learning rates and entropy regularization in on-policy updates. Extensive experiments on eight IsaacLab benchmarks, including legged locomotion (Ant, Humanoid, Anymal-D, Unitree H1, Go2), dexterous manipulation (Shadow Hand), aerial control (Quadcopter), and robotic arm tasks (Franka), demonstrate GenPO’s superiority over existing RL baselines. Notably, GenPO is the first method to successfully integrate diffusion policies into on-policy RL, unlocking their potential for large-scale parallelized training and real-world robotic deployment.

Understanding and synthesizing realistic 3D hand-object interactions (HOI) is critical for applications ranging from immersive AR/VR to dexterous robotics. Existing methods struggle with generalization, performing well on closed-set objects and predefined tasks but failing to handle unseen objects or open-vocabulary instructions. We introduce OpenHOI, the first framework for open-world HOI synthesis, capable of generating long-horizon manipulation sequences for novel objects guided by free-form language commands. Our approach integrates a 3D Multimodal Large Language Model (MLLM) fine-tuned for joint affordance grounding and semantic task decomposition, enabling precise localization of interaction regions (e.g., handles, buttons) and breakdown of complex instructions (e.g., “Find a water bottle and take a sip”) into executable sub-tasks. To synthesize physically plausible interactions, we propose an affordance-driven diffusion model paired with a training-free physics refinement stage that minimizes penetration and optimizes affordance alignment. Evaluations across diverse scenarios demonstrate OpenHOI’s superiority over state-of-the-art methods in generalizing to novel object categories, multi-stage tasks, and complex language instructions.

Learning effective visuomotor policies for robotic manipulation is challenging, as it requires generating precise actions while maintaining computational efficiency. Existing methods remain unsatisfactory due to inherent limitations in the essential action representation and the basic network architectures. We observe that representing actions in the frequency domain captures the structured nature of motion more effectively: low-frequency components reflect global movement patterns, while high-frequency components encode fine local details. Additionally, robotic manipulation tasks of varying complexity demand different levels of modeling precision across these frequency bands. Motivated by this, we propose a novel paradigm for visuomotor policy learning that progressively models hierarchical frequency components. To further enhance precision, we introduce continuous latent representations that maintain smoothness and continuity in the action space. Extensive experiments across diverse 2D and 3D robotic manipulation benchmarks demonstrate that our approach outperforms existing methods in both accuracy and efficiency, showcasing the potential of a frequency-domain autoregressive framework with continuous tokens for generalized robotic manipulation.Code is available at https://github.com/4DVLab/Freqpolicy

Existing methods for predicting lithium-ion battery remaining useful lifetime (RUL) rely on complete capacity degradation data or extensive historical profiles. However, such sufficient conditions are usually unavailable in practical battery usage. To cope with this issue, a framework for RUL estimation with fragment data is proposed. The framework utilizes a small amount of prior knowledge as benchmark data to create an empirical model-based predictive method for estimating RUL by fragment historical data during nonlinear degradation stage. A more specified parameter initialization is obtained by trend identification of the fragment. Particle filter (PF) algorithm is utilized for model parameter update with proposed improved resampling strategy. RUL predictions using two different datasets demonstrate the effectiveness of the proposed method. An error margin of less than ten cycles in RUL predictions is consistently achieved in CS2 dataset when employing fragments ranging from 50 to 60 cycles. And an error margin of around 20 cycles is achieved in CX2 dataset by fragments ranging from 60 to 80 cycles. The proposed method renders a more precise and stable predictive result with high confident level.

Existing gait recognition benchmarks mostly include minor clothing variations in the laboratory environments, but lack persistent changes in appearance over time and space. In this paper, we propose the first in-the-wild benchmark CCGait for cloth-changing gait recognition, which incorporates diverse clothing changes, indoor and outdoor scenes, and multi-modal statistics over 92 days. To further address the coupling effect of clothing and viewpoint variations, we propose a hybrid approach HybridGait that exploits both temporal dynamics and the projected 2D information of 3D human meshes. Specifically, we introduce a Canonical Alignment Spatial-Temporal Transformer (CA-STT) module to encode human joint position-aware features, and fully exploit 3D dense priors via a Silhouette-guided Deformation with 3D-2D Appearance Projection (SilD) strategy. Our contributions are twofold: we provide a challenging benchmark CCGait that captures realistic appearance changes over expanded time and space, and we propose a hybrid framework HybridGait that outperforms prior works on CCGait and Gait3D benchmarks. Our project page is available at https://github.com/HCVLab/HybridGait.

Unsupervised cross-domain image retrieval (UCIR) aims to retrieve images sharing the same category across diverse domains without relying on labeled data. Prior approaches have typically decomposed the UCIR problem into two distinct tasks: intra-domain representation learning and cross-domain feature alignment. However, these segregated strategies overlook the potential synergies between these tasks. This paper introduces ProtoOT, a novel Optimal Transport formulation explicitly tailored for UCIR, which integrates intra-domain feature representation learning and cross-domain alignment into a unified framework. ProtoOT leverages the strengths of the K-means clustering method to effectively manage distribution imbalances inherent in UCIR. By utilizing K-means for generating initial prototypes and approximating class marginal distributions, we modify the constraints in Optimal Transport accordingly, significantly enhancing its performance in UCIR scenarios. Furthermore, we incorporate contrastive learning into the ProtoOT framework to further improve representation learning. This encourages local semantic consistency among features with similar semantics, while also explicitly enforcing separation between features and unmatched prototypes, thereby enhancing global discriminativeness. ProtoOT surpasses existing state-of-the-art methods by a notable margin across benchmark datasets. Notably, on DomainNet, ProtoOT achieves an average P@200 enhancement of 24.44%, and on Office-Home, it demonstrates a P@15 improvement of 12.12%. Code is available at https://github.com/HCVLAB/ProtoOT.

Prompt learning in pretrained visual-language mod-els has shown remarkable flexibility across various down-stream tasks. Leveraging its inherent lightweight nature, re-cent research attempted to integrate the powerful pretrained models into federated learning frameworks to simultane-ously reduce communication costs and promote local training on insufficient data. Despite these efforts, current fed-erated prompt learning methods lack specialized designs to systematically address severe data heterogeneities, e.g., data distribution with both label and feature shifts involved. To address this challenge, we present Federated Prompts Cooperation via Optimal Transport (FedOTP), which intro-duces efficient collaborative prompt learning strategies to capture diverse category traits on a per-client basis. Specif-ically, for each client, we learn a global prompt to extract consensus knowledge among clients, and a local prompt to capture client-specific category characteristics. Unbal-anced Optimal Transport is then employed to align local vi-sual features with these prompts, striking a balance between global consensus and local personalization. By relaxing one of the equality constraints, FedOTP enables prompts to focus solely on the core regions of image patches. Exten-sive experiments on datasets with various types of hetero-geneities have demonstrated that our FedOTP outperforms the state-of-the-art methods.

Estimating full-body human motion via sparse tracking signals from head-mounted displays and hand controllers in 3D scenes is crucial to applications in AR/VR. One of the biggest challenges to this task is the one-to-many mapping from sparse observations to dense full-body motions, which endowed inherent ambiguities. To help resolve this ambiguous problem, we introduce a new framework to combine rich contextual information provided by scenes to benefit fullbody motion tracking from sparse observations. To estimate plausible human motions given sparse tracking signals and 3D scenes, we develop S2Fusion, a unified framework fusing Scene and sparse Signals with a conditional difFusion model. S2Fusion first extracts the spatial-temporal relations residing in the sparse signals via a periodic autoencoder, and then produces time-alignment feature embedding as additional inputs. Subsequently, by drawing initial noisy motion from a pre-trained prior, S2Fusion utilizes conditional diffusion to fuse scene geometry and sparse tracking signals to generate full-body scene-aware motions. The sampling procedure of S2Fusion is further guided by a specially designed scene-penetration loss and phase-matching loss, which effectively regularizes the motion of the lower body even in the absence of any tracking signals, making the generated motion much more plausible and coherent. Extensive experimental results have demonstrated that our S2Fusion outperforms the state-of-the-art in terms of estimation quality and smoothness. Code is available at https://github.com/jntang/S2Fusion.

Humans naturally interact with both others and the sur-rounding multiple objects, engaging in various social activi-ties. However, recent advances in modeling human-object interactions mostly focus on perceiving isolated individuals and objects, due to fundamental data scarcity. In this pa-per, we introduce HOI-M3, a novel large-scale dataset for modeling the interactions of Multiple huMans and Multiple objects. Notably, it provides accurate 3D tracking for both humans and objects from dense RGB and object-mounted IMU inputs, covering 199 sequences and 181M frames of diverse humans and objects under rich activities. With the unique HOI-M3dataset, we introduce two novel data-driven tasks with companion strong baselines: monocular capture and unstructured generation of multiple human-object interactions. Extensive experiments demonstrate that our dataset is challenging and worthy of further research about multiple human-object interactions and behavior analysis. Our HOI-M3 dataset, corresponding codes, and pre-trained models will be disseminated to the community for future research, which can be found at https://juzezhang.github.io/HOIM3_ProjectPage/

Federated Learning (FL) has attracted significant attention as an efficient privacy-preserving approach to distributed learning across multiple clients. Despite extensive empirical research and practical applications, a systematic way to theoretically understand the convergence and generalization properties in FL remains limited. This work aims to establish a unified theoretical foundation for understanding FL through feature learning theory. We focus on a scenario where each client employs a two-layer convolutional neural network (CNN) for local training on their own data. Many existing works analyze the convergence of Federated Averaging (FedAvg) under lazy training with linearizing assumptions in weight space. In contrast, our approach tracks the trajectory of signal learning and noise memorization in FL, eliminating the need for these assumptions. We further show that FedAvg can achieve near-zero test error by effectively increasing signal-to-noise ratio (SNR) in feature learning, while local training without communication achieves a large constant test error. This finding highlights the benefits of communication for generalization in FL. Moreover, our theoretical results suggest that a weighted FedAvg method, based on the similarity of input features across clients, can effectively tackle data heterogeneity issues in FL. Experimental results on both synthetic and real-world datasets verify our theoretical conclusions and emphasize the effectiveness of the weighted FedAvg approach.

Federated Prompt Learning (FPL) incorporates large pre-trained Vision-Language models (VLM) into federated learning through prompt tuning. The transferable representations and remarkable generalization capacity of VLM make them highly compatible with the integration of federated learning. Addressing data heterogeneity in federated learning requires personalization, but excessive focus on it across clients could compromise the model’s ability to generalize effectively. To preserve the impressive generalization capability of VLM, it is crucial to strike a balance between personalization and generalization in FPL. To tackle this challenge, we proposed Federated Prompt Learning with CLIP Generalization and low-rank Personalization (FedPGP), which employs pre-trained CLIP to provide knowledge-guidance on the global prompt for improved generalization and incorporates a low-rank adaptation term to personalize the global prompt. Further, FedPGP integrates a prompt-wise contrastive loss to achieve knowledge guidance and personalized adaptation simultaneously, enabling a harmonious balance between personalization and generalization in FPL. We conduct extensive experiments on various datasets to explore base-to-novel generalization in both category-level and domain-level scenarios with heterogeneous data, showing the superiority of FedPGP in balancing generalization and personalization.

Recent advances in diffusion models attempt to handle conditional generative tasks by utilizing a differentiable loss function for guidance without the need for additional training. While these methods achieved certain success, they often compromise on sample quality and require small guidance step sizes, leading to longer sampling processes. This paper reveals that the fundamental issue lies in the manifold deviation during the sampling process when loss guidance is employed. We theoretically show the existence of manifold deviation by establishing a certain lower bound for the estimation error of the loss guidance. To mitigate this problem, we propose Diffusion with Spherical Gaussian constraint (DSG), drawing inspiration from the concentration phenomenon in high-dimensional Gaussian distributions. DSG effectively constrains the guidance step within the intermediate data manifold through optimization and enables the use of larger guidance steps. Furthermore, we present a closed-form solution for DSG denoising with the Spherical Gaussian constraint. Notably, DSG can seamlessly integrate as a plugin module within existing training-free conditional diffusion methods. Implementing DSG merely involves a few lines of additional code with almost no extra computational overhead, yet it leads to significant performance improvements. Comprehensive experimental results in various conditional generation tasks validate the superiority and adaptability of DSG in terms of both sample quality and time efficiency.

Learning the prior knowledge of the 3D human-object spatial relation is crucial for reconstructing human-object interaction from images and understanding how humans interact with objects in 3D space. Previous works learn this prior from datasets collected in controlled environments, but due to the diversity of domains, they struggle to generalize to real-world scenarios. To overcome this limitation, we present a 2D-supervised method that learns the 3D human-object spatial relation prior purely from 2D images in the wild. Our method utilizes a flow-based neural network to learn the prior distribution of the 2D human-object keypoint layout and viewports for each image in the dataset. The effectiveness of the prior learned from 2D images is demonstrated on the human-object reconstruction task by applying the prior to tune the relative pose between the human and the object during the post-optimization stage. To validate and benchmark our method on in-the-wild images, we collect the WildHOI dataset from the YouTube website, which consists of various interactions with 8 objects in real-world scenarios. We conduct the experiments on the indoor BEHAVE dataset and the outdoor WildHOI dataset. The results show that our method achieves almost comparable performance with fully 3D supervised methods on the BEHAVE dataset, even if we have only utilized the 2D layout information, and outperforms previous methods in terms of generality and interaction diversity on in-the-wild images.

Diffusion models have garnered widespread attention in Reinforcement Learning (RL) for their powerful expressiveness and multimodality. It has been verified that utilizing diffusion policies can significantly improve the performance of RL algorithms in continuous control tasks by overcoming the limitations of unimodal policies, such as Gaussian policies. Furthermore, the multimodality of diffusion policies also shows the potential of providing the agent with enhanced exploration capabilities. However, existing works mainly focus on applying diffusion policies in offline RL, while their incorporation into online RL has been less investigated. The diffusion model's training objective, known as the variational lower bound, cannot be applied directly in online RL due to the unavailability of 'good' samples (actions). To harmonize the diffusion model with online RL, we propose a novel model-free diffusion-based online RL algorithm named Q-weighted Variational Policy Optimization (QVPO). Specifically, we introduce the Q-weighted variational loss and its approximate implementation in practice. Notably, this loss is shown to be a tight lower bound of the policy objective. To further enhance the exploration capability of the diffusion policy, we design a special entropy regularization term. Unlike Gaussian policies, the log-likelihood in diffusion policies is inaccessible; thus this entropy term is nontrivial. Moreover, to reduce the large variance of diffusion policies, we also develop an efficient behavior policy through action selection. This can further improve its sample efficiency during online interaction. Consequently, the QVPO algorithm leverages the exploration capabilities and multimodality of diffusion policies, preventing the RL agent from converging to a sub-optimal policy. To verify the effectiveness of QVPO, we conduct comprehensive experiments on MuJoCo continuous control benchmarks. The final results demonstrate that QVPO achieves state-of-the-art performance in terms of both cumulative reward and sample efficiency.

Integrating pretrained vision-language foundation models like CLIP into federated learning has attracted significant attention for enhancing generalization across diverse tasks. Typically, federated learning of vision-language models employs prompt learning to reduce communication and computational costs, i.e., prompt-based federated learning. However, there is limited theoretical analysis to understand the performance of prompt-based federated learning. In this work, we construct a theoretical analysis framework for prompt-based federated learning via feature learning theory. Specifically, we monitor the evolution of signal learning and noise memorization in prompt-based federated learning, demonstrating that performance can be assessed by the ratio of task-relevant to task-irrelevant coefficients. Furthermore, we draw an analogy between income and risk in portfolio optimization and the task-relevant and task-irrelevant terms in feature learning. Leveraging inspiration from portfolio optimization that combining two independent assets will maintain the income while reducing the risk, we introduce two prompts: global prompt and local prompt to construct a prompt portfolio to balance the generalization and personalization. Consequently, we showed the performance advantage of the prompt portfolio and derived the optimal mixing coefficient. These theoretical claims have been further supported by empirical experiments.

Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical analysis on the representation of DEQ. In this paper, we utilize the Neural Collapse ($\mathcal{NC}$) as a tool to systematically analyze the representation of DEQ under both balanced and imbalanced conditions. $\mathcal{NC}$ is an interesting phenomenon in the neural network training process that characterizes the geometry of class features and classifier weights. While extensively studied in traditional explicit neural networks, the $\mathcal{NC}$ phenomenon has not received substantial attention in the context of implicit neural networks. We theoretically show that $\mathcal{NC}$ exists in DEQ under balanced conditions. Moreover, in imbalanced settings, despite the presence of minority collapse, DEQ demonstrated advantages over explicit neural networks. These advantages include the convergence of extracted features to the vertices of a simplex equiangular tight frame and self-duality properties under mild conditions, highlighting DEQ's superiority in handling imbalanced datasets. Finally, we validate our theoretical analyses through experiments in both balanced and imbalanced scenarios.

Fuzzy neural networks (FNNs) have been very successful at handling uncertainty in data using fuzzy mappings and if-then rules. However, they suffer from generalization and dimensionality issues. Although deep neural networks (DNNs) represent a step toward processing high-dimensional data, their capacity to address data uncertainty is limited. Furthermore, deep learning algorithms designed to improve robustness are either time consuming or yield unsatisfactory performance. In this article, we propose a robust fuzzy neural network (RFNN) to overcome these problems. The network contains an adaptive inference engine that is capable of handling samples with high-level uncertainty and high dimensions. Unlike traditional FNNs that use a fuzzy AND operation to calculate the firing strength for each rule, our inference engine is able to learn the firing strength adaptively. It also further processes the uncertainty in membership function values. Taking advantage of the learning ability of neural networks, the acquired fuzzy sets can be learned from training inputs automatically to cover the input space well. Furthermore, the consequent layer uses neural network structures to enhance the reasoning ability of the fuzzy rules when dealing with complex inputs. Experiments on a range of datasets show that RFNN delivers state-of-the-art accuracy even at very high levels of uncertainty. Our code is available online. https://github.com/leijiezhang/RFNN.

Weakly supervised anomaly detection (WSAD) has gained increasing attention due to its core idea of enhancing the performance of unsupervised anomaly detection by leveraging prior knowledge from a limited number of labeled anomalies. In this article, we introduce a novel WSAD framework that surpasses current state-of-the-art methods in terms of accuracy, exhibits greater robustness to data uncertainty, and is more efficient in utilizing limited labeled anomalies. Our method is built upon twin fuzzy networks (TFN) that learn robust fuzzy if–then rules from a pairwise training set. TFN can extract informative prototypes of training instances, exploiting the very few labeled anomalies efficiently. A two-stage sequential training scheme, comprising fuzzy C-means clustering and interpolation consistency regularization, ensures that the fuzzy rules form a solid foundation for anomaly detection while improving TFN's generalization ability. The training process of TFN relies on closed-form optimization rather than gradient-based methods, leading to significantly faster training speeds. Comprehensive experiments conducted on numerous real-world datasets confirm the advantages of the TFN framework over existing alternatives.

Federated learning is an emerging learning paradigm where multiple clients collaboratively train a machine learning model in a privacy-preserving manner. Personalized federated learning extends this paradigm to overcome heterogeneity across clients by learning personalized models. Recently, there have been some initial attempts to apply transformers to federated learning. However, the impacts of federated learning algorithms on self-attention have not yet been studied. In this article, we investigate this relationship and reveal that federated averaging (FedAvg) algorithms actually have a negative impact on self-attention in cases of data heterogeneity, which limits the capabilities of the transformer model in federated learning settings. To address this issue, we propose FedTP, a novel transformer-based federated learning framework that learns personalized self-attention for each client while aggregating the other parameters among the clients. Instead of using a vanilla personalization mechanism that maintains personalized self-attention layers of each client locally, we develop a learn-to-personalize mechanism to further encourage the cooperation among clients and to increase the scalability and generalization of FedTP. Specifically, we achieve this by learning a hypernetwork on the server that outputs the personalized projection matrices of self-attention layers to generate clientwise queries, keys, and values. Furthermore, we present the generalization bound for FedTP with the learn-to-personalize mechanism. Extensive experiments verify that FedTP with the learn-to-personalize mechanism yields state-of-the-art performance in the non-IID scenarios. Our code is available online https://github.com/zhyczy/FedTP.

Lifelong person re-identification (LReID) is in significant demand for real-world development as a large amount of ReID data is captured from diverse locations over time and cannot be accessed at once inherently. However, a key challenge for LReID is how to incrementally preserve old knowledge and gradually add new capabilities to the system. Unlike most existing LReID methods, which mainly focus on dealing with catastrophic forgetting, our focus is on a more challenging problem, which is, not only trying to reduce the forgetting on old tasks but also aiming to improve the model performance on both new and old tasks during the lifelong learning process. Inspired by the biological process of human cognition where the somatosensory neocortex and the hippocampus work together in memory consolidation, we formulated a model called Knowledge Refreshing and Consolidation (KRC) that achieves both positive forward and backward transfer. More specifically, a knowledge refreshing scheme is incorporated with the knowledge rehearsal mechanism to enable bi-directional knowledge transfer by introducing a dynamic memory model and an adaptive working model. Moreover, a knowledge consolidation scheme operating on the dual space further improves model stability over the long-term. Extensive evaluations show KRC’s superiority over the state-of-the-art LReID methods with challenging pedestrian benchmarks. Code is available at https://github.com/cly234/LReID-KRKC.

This paper presents an inverse kinematic optimization layer (IKOL) for 3D human pose and shape estimation that leverages the strength of both optimization- and regression-based methods within an end-to-end framework. IKOL involves a nonconvex optimization that establishes an implicit mapping from an image’s 3D keypoints and body shapes to the relative body-part rotations. The 3D keypoints and the body shapes are the inputs and the relative body-part rotations are the solutions. However, this procedure is implicit and hard to make differentiable. So, to overcome this issue, we designed a Gauss-Newton differentiation (GN-Diff) procedure to differentiate IKOL. GN-Diff iteratively linearizes the nonconvex objective function to obtain Gauss-Newton directions with closed form solutions. Then, an automatic differentiation procedure is directly applied to generate a Jacobian matrix for end-to-end training. Notably, the GN-Diff procedure works fast because it does not rely on a time-consuming implicit differentiation procedure. The twist rotation and shape parameters are learned from the neural networks and, as a result, IKOL has a much lower computational overhead than most existing optimization-based methods. Additionally, compared to existing regression-based methods, IKOL provides a more accurate mesh-image correspondence. This is because it iteratively reduces the distance between the keypoints and also enhances the reliability of the pose structures. Extensive experiments demonstrate the superiority of our proposed framework over a wide range of 3D human pose and shape estimation methods. Code is available at https://github.com/Juzezhang/IKOL

Humans constantly interact with objects in daily life tasks. Capturing such processes and subsequently conducting visual inferences from a fixed viewpoint suffers from occlusions, shape and texture ambiguities, motions, etc. To mitigate the problem, it is essential to build a training dataset that captures free-viewpoint interactions. We construct a dense multi-view dome to acquire a complex human object interaction dataset, named HODome, that consists of ~71 M frames on 10 subjects interacting with 23 objects. To process the HODome dataset, we develop NeuralDome, a layer-wise neural processing pipeline tailored for multi-view video inputs to conduct accurate tracking, geometry reconstruction and free-view rendering, for both human subjects and objects. Extensive experiments on the HODome dataset demonstrate the effectiveness of NeuralDome on a variety of inference, modeling, and rendering tasks. Both the dataset and the NeuralDome tools will be disseminated to the community for further development, which can be found at https://juzezhang.github.io/NeuralDome

Federated learning enables multiple decentralized clients to learn collaboratively without sharing local data. However, the expensive annotation cost on local clients remains an obstacle in utilizing local data. In this paper, we propose a federated active learning paradigm to efficiently learn a global model with a limited annotation budget while protecting data privacy in a decentralized learning manner. The main challenge faced by federated active learning is the mismatch between the active sampling goal of the global model on the server and that of the asynchronous local clients. This becomes even more significant when data is distributed non-IID across local clients. To address the aforementioned challenge, we propose Knowledge-Aware Federated Active Learning (KAFAL), which consists of Knowledge-Specialized Active Sampling (KSAS) and Knowledge-Compensatory Federated Update (KCFU). Specifically, KSAS is a novel active sampling method tailored for the federated active learning problem, aiming to deal with the mismatch challenge by sampling actively based on the discrepancies between local and global models. KSAS intensifies specialized knowledge in local clients, ensuring the sampled data is informative for both the local clients and the global model. Meanwhile, KCFU deals with the client heterogeneity caused by limited data and non-IID data distributions by compensating for each client’s ability in weak classes with the assistance of the global model. Extensive experiments and analyses are conducted to show the superiority of KAFAL over recent state-of-the-art active learning methods. Code is available at https://github.com/ycao5602/KAFAL.

Modeling and capturing the 3D spatial arrangement of the human and the object is the key to perceiving 3D human-object interaction from monocular images. In this work, we propose to use the Human-Object Offset between anchors which are densely sampled from the surface of human mesh and object mesh to represent human-object spatial relation. Compared with previous works which use contact map or implicit distance filed to encode 3D human-object spatial relations, our method is a simple and efficient way to encode the highly detailed spatial correlation between the human and object. Based on this representation, we propose Stacked Normalizing Flow (StackFLOW) to infer the posterior distribution of human-object spatial relations from the image. During the optimization stage, we finetune the human body pose and object 6D pose by maximizing the likelihood of samples based on this posterior distribution and minimizing the 2D-3D corresponding reprojection loss. Extensive experimental results show that our method achieves impressive results on two challenging benchmarks, BEHAVE and InterCap datasets. Our code has been publicly available at https://github.com/MoChen-bop/StackFLOW.

Federated Learning (FL) has emerged as a promising distributed learning paradigm that enables multiple clients to learn a global model collaboratively without sharing their private data. However, the effectiveness of FL is highly dependent on the quality of the data that is being used for training. In particular, data heterogeneity issues, such as label distribution skew and feature skew, can significantly impact the performance of FL. Previous studies in FL have primarily focused on addressing label distribution skew data heterogeneity, while only a few recent works have made initial progress in tackling feature skew issues. Notably, these two forms of data heterogeneity have been studied separately and have not been well explored within a unified FL framework. To address this gap, we propose Fed-CO$_2$, a universal FL framework that handles both label distribution skew and feature skew within a Cooperation mechanism between the Online and Offline models. Specifically, the online model learns general knowledge that is shared among all clients, while the offline model is trained locally to learn the specialized knowledge of each individual client. To further enhance model cooperation in the presence of feature shifts, we design an intra-client knowledge transfer mechanism that reinforces mutual learning between the online and offline models, and an inter-client knowledge transfer mechanism to increase the models’ domain generalization ability. Extensive experiments show that our Fed-CO$_2$ outperforms a wide range of existing personalized federated learning algorithms in terms of handling label distribution skew and feature skew, both individually and collectively. The empirical results are supported by our convergence analyses in a simplified setting.

Learning with noisy labels (LNL) poses a significant challenge in training a well-generalized model while avoiding overfitting to corrupted labels. Recent advances have achieved impressive performance by identifying clean labels and correcting corrupted labels for training. However, the current approaches rely heavily on the model’s predictions and evaluate each sample independently without considering either the global or local structure of the sample distribution. These limitations typically result in a suboptimal solution for the identification and correction processes, which eventually leads to models overfitting to incorrect labels. In this paper, we propose a novel optimal transport (OT) formulation, called Curriculum and Structure-aware Optimal Transport (CSOT). CSOT concurrently considers the inter- and intra-distribution structure of the samples to construct a robust denoising and relabeling allocator. During the training process, the allocator incrementally assigns reliable labels to a fraction of the samples with the highest confidence. These labels have both global discriminability and local coherence. Notably, CSOT is a new OT formulation with a nonconvex objective function and curriculum constraints, so it is not directly compatible with classical OT solvers. Here, we develop a lightspeed computational method that involves a scaling iteration within a generalized conditional gradient framework to solve CSOT efficiently. Extensive experiments demonstrate the superiority of our method over the current state-of-the-arts in LNL.

Deep Equilibrium Models (DEQs) and Neural Ordinary Differential Equations (Neural ODEs) are two branches of implicit models that have achieved remarkable success owing to their superior performance and low memory consumption. While both are implicit models, DEQs and Neural ODEs are derived from different mathematical formulations. Inspired by homotopy continuation, we establish a connection between these two models and illustrate that they are actually two sides of the same coin. Homotopy continuation is a classical method of solving nonlinear equations based on a corresponding ODE. Given this connection, we proposed a new implicit model called HomoODE that inherits the property of high accuracy from DEQs and the property of stability from Neural ODEs. Unlike DEQs, which explicitly solve an equilibrium-point-finding problem via Newton's methods in the forward pass, HomoODE solves the equilibrium-point-finding problem implicitly using a modified Neural ODE via homotopy continuation. Further, we developed an acceleration method for HomoODE with a shared learnable initial point. It is worth noting that our model also provides a better understanding of why Augmented Neural ODEs work as long as the augmented part is regarded as the equilibrium point to find. Comprehensive experiments with several image classification tasks demonstrate that HomoODE surpasses existing implicit models in terms of both accuracy and memory consumption.

Recent advances in constrained reinforcement learning (RL) have endowed reinforcement learning with certain safety guarantees. However, deploying existing constrained RL algorithms in continuous control tasks with general hard constraints remains challenging, particularly in those situations with non-convex hard constraints. Inspired by the generalized reduced gradient (GRG) algorithm, a classical constrained optimization technique, we propose a reduced policy optimization (RPO) algorithm that combines RL with GRG to address general hard constraints. RPO partitions actions into basic actions and nonbasic actions following the GRG method and outputs the basic actions via a policy network. Subsequently, RPO calculates the nonbasic actions by solving equations based on equality constraints using the obtained basic actions. The policy network is then updated by implicitly differentiating nonbasic actions with respect to basic actions. Additionally, we introduce an action projection procedure based on the reduced gradient and apply a modified Lagrangian relaxation technique to ensure inequality constraints are satisfied. To the best of our knowledge, RPO is the first attempt that introduces GRG to RL as a way of efficiently handling both equality and inequality hard constraints. It is worth noting that there is currently a lack of RL environments with complex hard constraints, which motivates us to develop three new benchmarks: two robotics manipulation tasks and a smart grid operation control task. With these benchmarks, RPO achieves better performance than previous constrained RL algorithms in terms of both cumulative reward and constraint violation. We believe RPO, along with the new benchmarks, will open up new opportunities for applying RL to real-world problems with complex constraints.

Previous endeavors in self-supervised learning have enlightened the research of deep clustering from an instance discrimination perspective. Built upon this foundation, recent studies further highlight the importance of grouping semantically similar instances. One effective method to achieve this is by promoting the semantic structure preserved by neighborhood consistency. However, the samples in the local neighborhood may be limited due to their close proximity to each other, which may not provide substantial and diverse supervision signals. Inspired by the versatile re-ranking methods in the context of image retrieval, we propose to employ an efficient online re-ranking process to mine more informative neighbors in a Contextually Affinitive (ConAff) Neighborhood, and then encourage the cross-view neighborhood consistency. To further mitigate the intrinsic neighborhood noises near cluster boundaries, we propose a progressively relaxed boundary filtering strategy to circumvent the issues brought by noisy neighbors. Our method can be easily integrated into the generic self-supervised frameworks and outperforms the state-of-the-art methods on several popular benchmarks.

Distributed fuzzy neural networks (DFNNs) have attracted increasing attention recently due to their learning abilities in handling data uncertainties in distributed scenarios. However, it is challenging for DFNNs to handle cases in which the local data are nonindependent and identically distributed (non-IID). In this article, we propose a federated fuzzy neural network (FedFNN) with evolutionary rule learning (ERL) to cope with non-IID issues as well as data uncertainties. The FedFNN maintains a global set of rules in a server and a personalized subset of these rules for each local client. ERL is inspired by the theory of biological evolution; it encourages rule variations while activating superior rules and deactivating inferior rules for local clients with non-IID data. Specifically, ERL consists of two stages in an iterative procedure: a rule cooperation stage that updates global rules by aggregating local rules based on their activation statuses and a rule evolution stage that evolves the global rules and updates the activation statuses of the local rules. This procedure improves both the generalization and personalization of the FedFNN for dealing with non-IID issues and data uncertainties. Extensive experiments conducted on a range of datasets demonstrate the superiority of the FedFNN over state-of-the-art methods.

Emerging Metaverse applications demand accessible, accurate and easy-to-use tools for 3D digital human creations in order to depict different cultures and societies as if in the physical world. Recent large-scale vision-language advances pave the way for novices to conveniently customize 3D content. However, the generated CG-friendly assets still cannot represent the desired facial traits for human characteristics. In this paper, we present Dream-Face, a progressive scheme to generate personalized 3D faces under text guidance. It enables layman users to naturally customize 3D facial assets that are compatible with CG pipelines, with desired shapes, textures and fine-grained animation capabilities. From a text input to describe the facial traits, we first introduce a coarse-to-fine scheme to generate the neutral facial geometry with a unified topology. We employ a selection strategy in the CLIP embedding space to generate coarse geometry, and subsequently optimize both the detailed displacements and normals using Score Distillation Sampling (SDS) from the generic Latent Diffusion Model (LDM). Then, for neutral appearance generation, we introduce a dual-path mechanism, which combines the generic LDM with a novel texture LDM to ensure both the diversity and textural specification in the UV space. We also employ a two-stage optimization to perform SDS in both the latent and image spaces to significantly provide compact priors for fine-grained synthesis. It also enables learning the mapping from the compact latent space into physically-based textures (diffuse albedo, specular intensity, normal maps, etc.). Our generated neutral assets naturally support blendshapes-based facial animations, thanks to the unified geometric topology. We further improve the animation ability with personalized deformation characteristics. To this end, we learn the universal expression prior in a latent space with neutral asset conditioning using the cross-identity hypernetwork, we subsequently train a neural facial tracker from video input space into the pre-trained expression space for personalized fine-grained animation. Extensive qualitative and quantitative experiments validate the effectiveness and generalizability of DreamFace. Notably, DreamFace can generate realistic 3D facial assets with physically-based rendering quality and rich animation ability from video footage, even for fashion icons or exotic characters in cartoons and fiction movies.

Inter-person occlusion and depth ambiguity make estimating the 3D poses of monocular multiple persons as camera-centric coordinates a challenging problem. Typical top-down frameworks suffer from high computational redundancy with an additional detection stage. By contrast, the bottom-up methods enjoy low computational costs as they are less affected by the number of humans. However, most existing bottom-up methods treat camera-centric 3D human pose estimation as two unrelated subtasks: 2.5D pose estimation and camera-centric depth estimation. In this paper, we propose a unified model that leverages the mutual benefits of both these subtasks. Within the framework, a robust structured 2.5D pose estimation is designed to recognize inter-person occlusion based on depth relationships. Additionally, we develop an end-to-end geometry-aware depth reasoning method that exploits the mutual benefits of both 2.5D pose and camera-centric root depths. This method first uses 2.5D pose and geometry information to infer camera-centric root depths in a forward pass, and then exploits the root depths to further improve representation learning of 2.5D pose estimation in a backward pass. Further, we designed an adaptive fusion scheme that leverages both visual perception and body geometry to alleviate inherent depth ambiguity issues. Extensive experiments demonstrate the superiority of our proposed model over a wide range of bottom-up methods. Our accuracy is even competitive with top-down counterparts. Notably, our model runs much faster than existing bottom-up and top-down methods.

Universal Domain Adaptation (UniDA) aims to transfer knowledge from a source domain to a target domain without any constraints on label sets. Since both domains may hold private classes, identifying target common samples for domain alignment is an essential issue in UniDA. Most existing methods require manually specified or hand-tuned threshold values to detect common samples thus they are hard to extend to more realistic UniDA because of the diverse ratios of common classes. Moreover, they cannot recognize different categories among target-private samples as these private samples are treated as a whole. In this paper, we propose to use Optimal Transport (OT) to handle these issues under a unified framework, namely UniOT. First, an OT-based partial alignment with adaptive filling is designed to detect common classes without any predefined threshold values for realistic UniDA. It can automatically discover the intrinsic difference between common and private classes based on the statistical information of the assignment matrix obtained from OT. Second, we propose an OT-based target representation learning that encourages both global discrimination and local consistency of samples to avoid the over-reliance on the source. Notably, UniOT is the first method with the capability to automatically discover and recognize private categories in the target domain for UniDA. Accordingly, we introduce a new metric H^3-score to evaluate the performance in terms of both accuracy of common samples and clustering performance of private ones. Extensive experiments clearly demonstrate the advantages of UniOT over a wide range of state-of-the-art methods in UniDA.

Abstract In the financial market, the stock price prediction is a challenging task which is influenced by many factors. These factors include economic change, politics and global events that are usually recorded in text format, such as the daily news. Therefore, we assume that real-world text information can be used to forecast stock market activity. However, only a few works considered both text and numerical information to predict or analyse stock trends. These works used preprocessed text features as the model inputs; therefore, latent information in text may be lost because the relationships between the text and stock price are not considered. In this paper, we propose a fusion network, i.e. a spatial-temporal attention-based convolutional network (STACN) that can leverage the advantages of an attention mechanism, a convolutional neural network and long short-term memory to extract text and numerical information for stock price prediction. Benefiting from the utilisation of an attention mechanism, reliable text features that are highly relevant to stock value can be extracted, which improves the overall model performance. The experimental results on real-world stock data demonstrate that our STACN model and training scheme can handle both text and numerical data and achieve high accuracy on stock regression tasks. The STACN is compared with CNNs and LSTMs with different settings, e.g. a CNN with only stock data, a CNN with only news titles and LSTMs with only stock data. CNNs considering only stock data and news titles have mean squared errors of 28.3935 and 0.1814, respectively. The accuracy of LSTMs is 0.0763. The STACN can achieve an accuracy of 0.0304, outperforming CNNs and LSTMs in stock regression tasks.

Recently, distributed semisupervised learning (DSSL) algorithms have shown their effectiveness in leveraging unlabeled samples over interconnected networks, where agents cannot share their original data with each other and can only communicate nonsensitive information with their neighbors. However, existing DSSL algorithms cannot cope with data uncertainties and may suffer from high computation and communication overhead problems. To handle these issues, we propose a distributed semisupervised fuzzy regression (DSFR) model with fuzzy if-then rules and interpolation consistency regularization (ICR). The ICR, which was proposed recently for semisupervised problem, can force decision boundaries to pass through sparse data areas, thus increasing model robustness. However, its application in distributed scenarios has not been considered yet. In this work, we proposed a distributed fuzzy C-means (DFCM) method and a distributed interpolation consistency regularization (DICR) built on the well-known alternating direction method of multipliers to respectively locate parameters in antecedent and consequent components of DSFR. Notably, the DSFR model converges very fast since it does not involve back-propagation procedure and is scalable to large-scale datasets benefiting from the utilization of DFCM and DICR. Experiments results on both artificial and real-world datasets show that the proposed DSFR model can achieve much better performance than the state-of-the-art DSSL algorithm in terms of both loss value and computational cost. Our code is available online.1

Mobile robot navigation is an essential problem in robotics. We propose a method for constructing and training fuzzy logic controllers (FLCs) to coordinate a robotic team performing collision-free navigation and arriving simultaneously at a target location in an unknown environment. Our FLCs are organized in a multilayered architecture to reduce the number of tunable parameters and improve the scalability of the solution. In addition, in contrast to simple traditional switching mechanisms between target seeking and obstacle avoidance, we develop a novel rule-embedded FLC to improve the navigation performance. Moreover, we design a grouping and merging mechanism to obtain transparent fuzzy sets and integrate this mechanism into the training process for all FLCs, thus increasing the interpretability of the fuzzy models. We train the proposed FLCs using a novel multiobjective hybrid approach combining a genetic algorithm and particle swarm optimization. Simulation results demonstrate the effectiveness of our algorithms in reliably solving the proposed navigation problem.

Heterogeneous big data poses many challenges in machine learning. Its enormous scale, high dimensionality, and inherent uncertainty make almost every aspect of machine learning difficult, from providing enough processing power to maintaining model accuracy to protecting privacy. However, perhaps the most imposing problem is that big data is often interspersed with sensitive personal data. Hence, we propose a privacy-preserving hierarchical fuzzy neural network to address these technical challenges while also alleviating privacy concerns. The network is trained with a two-stage optimization algorithm, and the parameters at low levels of the hierarchy are learned with a scheme based on the well-known alternating direction method of multipliers, which does not reveal local data to other agents. Coordination at high levels of the hierarchy is handled by the alternating optimization method, which converges very quickly. The entire training procedure is scalable, fast, and does not suffer from gradient vanishing problems like the methods based on backpropagation. Comprehensive simulations conducted on both regression and classification tasks demonstrate the effectiveness of the proposed model. Our code is available online.

This paper investigates phasor measurement unit (PMU) placement for informative state estimation in smart grid by incorporating various constraints for observability. Observability constitutes an important property for PMU placement to characterize the depth of the buses' reachability by the placed PMUs, but addressing it solely by binary linear programming as in many works still does not guarantee a good estimate for the grid state. Some existing works have considered optimization of some estimation indices by ignoring the observability requirements for computational ease and thus potentially lead to trivial results such as acceptance of the estimate for an unobserved state component as its unconditional mean. In this work, the PMU placement optimization problem is considered by minimizing the mean squared error or maximizing the mutual information between the measurement output and grid state subject to observability constraints, which incorporate operating conditions such as presence of zero injection buses, contingency of measurement loss, and limitation of communication channels per PMU. The proposed design is thus free from the fundamental shortcomings in the existing PMU placement designs. The problems are posed as large scale binary nonlinear optimization problems involving thousands of binary variables, for which this paper develops efficient algorithms for computational solutions. Their performance is analyzed in detail through numerical examples on large scale IEEE power networks. The solution method is also shown to be extendable to AC power flow models, which are formulated by nonlinear equations.