arXiv subjects
Publications and source records attributed to Yuquan Xie.
We prove that the values set of \(S=|A|^2\) attained by closed embedded minimal hypersurfaces in \(\mathbb S^{n+1}(1)\) with constant \(S\) and constant \(f_3=\operatorname{tr}(A^3)\) is locally finite, where \(A\) denotes the shape operator. Neither the topology of the hypersurface nor the value of \(f_3\) is fixed.
We prove that the angle function associated with the canonical product structure is constant for an isoparametric hypersurface in $\mathbb{S}^{n}\times \mathbb{S}^{m}$, $\mathbb{S}^{n}\times \mathbb{H}^{m}$, or $\mathbb{H}^{n}\times \mathbb{H}^{m}$. This rigidity result enables us to provide a complete classification of isoparametric and homogeneous hypersurfaces in $\mathbb{S}^{n}\times \mathbb{S}^{m}$ and $\mathbb{S}^{n}\times \mathbb{H}^{m}$. Furthermore, we establish a geometric characterization in these two spaces: a hypersurface is isoparametric if and only if it has constant principal curvatures and a constant angle function.
We first show that every isoparametric hypersurface in $\mathbb{S}^{n}\times \mathbb{R}^{m}$ or $\mathbb{H}^{n}\times \mathbb{R}^{m}$ possesses a constant angle function with respect to the canonical product structure. Exploiting this rigidity, we achieve a complete classification of isoparametric and homogeneous hypersurfaces in these product spaces. Furthermore, we prove that an isoparametric hypersurface in $\mathbb{S}^{n}\times \mathbb{R}^{m}$ or $\mathbb{H}^{n}\times \mathbb{R}^{m}$ also has constant principal curvatures.
Graphical User Interface (GUI) agents require effective use of historical context to perform sequential navigation tasks. While incorporating past actions and observations can improve decision making, naive use of full history leads to excessive computational overhead and distraction from irrelevant information. To address this, we introduce HiconAgent, a GUI agent trained with History Context-aware Policy Optimization (HCPO) for efficient and effective utilization of historical information. HCPO optimizes history usage in both sampling and policy updates through two complementary components: (1) Dynamic Context Sampling (DCS) presents the agent with variable length histories during sampling, enabling adaptive use of the most relevant context; (2) Anchor-guided History Compression (AHC) refines the policy update phase with a dual branch strategy where the compressed branch removes history observations while keeping history actions as information flow anchors. The compressed and uncompressed branches are coupled through a history-enhanced alignment loss to enforce consistent history usage while maintaining efficiency. Experiments on mainstream GUI navigation benchmarks demonstrate strong performance. Despite being smaller, HiconAgent-3B outperforms GUI-R1-7B by +8.46 percent grounding accuracy and +11.32 percent step success rate on GUI-Odyssey, while achieving comparable results on AndroidControl and AITW with up to 2.47x computational speedup and 60 percent FLOPs reduction.
Developing generalist agents capable of solving open-ended tasks in visually rich, dynamic environments remains a core pursuit of embodied AI. While Minecraft has emerged as a compelling benchmark, existing agents often suffer from fragmented cognitive abilities, lacking the synergy between reflexive execution (System 1) and deliberative reasoning (System 2). In this paper, we introduce Optimus-3, a generalist agent that organically integrates these dual capabilities within a unified framework. To achieve this, we address three fundamental challenges. First, to overcome the scarcity of reasoning data, we propose a Knowledge-Enhanced Automated Data Generation Pipeline. It synthesizes high-quality System 2 reasoning traces from raw System 1 interaction trajectories, effectively mitigating hallucinations via injection of domain knowledge. We release the resulting dataset, \textbf{OptimusM$^{4}$}, to the community. Second, to reconcile the dichotomous computational requirements of the dual systems, we design a Dual-Router Aligned MoE Architecture. It employs a Task Router to prevent task interference via parameter decoupling, and a Layer Router to dynamically modulate reasoning depth, creating a computational ``Fast Path'' for System 1 and a ``Deep Path'' for System 2. Third, to activate the reasoning capabilities of System 2, we propose Dual-Granularity Reasoning-Aware Policy Optimization (DGRPO) algorithm. It enforces Process-Outcome Co-Supervision via dual-granularity dense rewards, ensuring consistency between the thought process and the answer. Extensive evaluations demonstrate that Optimus-3 surpasses existing state-of-the-art methods on both System~2 (21$\%$ on Planning, 66\% on Captioning, 76\% on Embodied QA, 3.4$\times$ on Grounding, and 18\% on Reflection) and System~1 (3\% on Long-Horizon Action) tasks, with a notable 60\% success rate on open-ended tasks.
Recent efforts to leverage the Multi-modal Large Language Model (MLLM) as GUI agents have yielded promising outcomes. However, these agents still struggle with long-horizon tasks in online environments, primarily due to insufficient knowledge and the inherent gap between offline and online domains. In this paper, inspired by how humans generalize knowledge in open-ended environments, we propose a Hierarchical Multimodal Skills (HMS) module to tackle the issue of insufficient knowledge. It progressively abstracts trajectories into execution skills, core skills, and ultimately meta-skills, providing a hierarchical knowledge structure for long-horizon task planning. To bridge the domain gap, we propose the Skill-Augmented Monte Carlo Tree Search (SA-MCTS) algorithm, which efficiently leverages skills acquired in offline environments to reduce the action search space during online tree exploration. Building on HMS, we propose Mirage-1, a multimodal, cross-platform, plug-and-play GUI agent. To validate the performance of Mirage-1 in real-world long-horizon scenarios, we constructed a new benchmark, AndroidLH. Experimental results show that Mirage-1 outperforms previous agents by 32\%, 19\%, 15\%, and 79\% on AndroidWorld, MobileMiniWob++, Mind2Web-Live, and AndroidLH, respectively. Project page: https://cybertronagent.github.io/Mirage-1.github.io/
Knowledge Tracing (KT) is a critical task in online education systems, aiming to monitor students' knowledge states throughout a learning period. Common KT approaches involve predicting the probability of a student correctly answering the next question based on their exercise history. However, these methods often suffer from performance degradation when faced with the scarcity of student interactions in new education systems. To address this, we leverage student interactions from existing education systems to mitigate performance degradation caused by limited training data. Nevertheless, these interactions exhibit significant differences since they are derived from different education systems. To address this issue, we propose a domain generalization approach for knowledge tracing, where existing education systems are considered source domains, and new education systems with limited data are considered target domains. Additionally, we design a domain-generalizable knowledge tracing framework (DGKT) that can be applied to any KT model. Specifically, we present a concept aggregation approach designed to reduce conceptual disparities within sequences of student interactions from diverse domains. To further mitigate domain discrepancies, we introduce a novel normalization module called Sequence Instance Normalization (SeqIN). Moreover, to fully leverage exercise information, we propose a new knowledge tracing model tailored for the domain generalization KT task, named Domain-Generalizable Relation-based Knowledge Tracing (DGRKT). Extensive experiments across five benchmark datasets demonstrate that the proposed method performs well despite limited training data.
Building an agent that can mimic human behavior patterns to accomplish various open-world tasks is a long-term goal. To enable agents to effectively learn behavioral patterns across diverse tasks, a key challenge lies in modeling the intricate relationships among observations, actions, and language. To this end, we propose Optimus-2, a novel Minecraft agent that incorporates a Multimodal Large Language Model (MLLM) for high-level planning, alongside a Goal-Observation-Action Conditioned Policy (GOAP) for low-level control. GOAP contains (1) an Action-guided Behavior Encoder that models causal relationships between observations and actions at each timestep, then dynamically interacts with the historical observation-action sequence, consolidating it into fixed-length behavior tokens, and (2) an MLLM that aligns behavior tokens with open-ended language instructions to predict actions auto-regressively. Moreover, we introduce a high-quality Minecraft Goal-Observation-Action (MGOA)} dataset, which contains 25,000 videos across 8 atomic tasks, providing about 30M goal-observation-action pairs. The automated construction method, along with the MGOA dataset, can contribute to the community's efforts to train Minecraft agents. Extensive experimental results demonstrate that Optimus-2 exhibits superior performance across atomic tasks, long-horizon tasks, and open-ended instruction tasks in Minecraft. Please see the project page at https://cybertronagent.github.io/Optimus-2.github.io/.
In this report, we present our approach for the Natural Language Query track and Goal Step track of the Ego4D Episodic Memory Benchmark at CVPR 2024. Both challenges require the localization of actions within long video sequences using textual queries. To enhance localization accuracy, our method not only processes the temporal information of videos but also identifies fine-grained objects spatially within the frames. To this end, we introduce a novel approach, termed ObjectNLQ, which incorporates an object branch to augment the video representation with detailed object information, thereby improving grounding efficiency. ObjectNLQ achieves a mean R@1 of 23.15, ranking 2nd in the Natural Language Queries Challenge, and gains 33.00 in terms of the metric R@1, IoU=0.3, ranking 3rd in the Goal Step Challenge. Our code will be released at https://github.com/Yisen-Feng/ObjectNLQ.
In this report, we present our champion solution for Ego4D EgoSchema Challenge in CVPR 2024. To deeply integrate the powerful egocentric captioning model and question reasoning model, we propose a novel Hierarchical Comprehension scheme for egocentric video Question Answering, named HCQA. It consists of three stages: Fine-grained Caption Generation, Context-driven Summarization, and Inference-guided Answering. Given a long-form video, HCQA captures local detailed visual information and global summarised visual information via Fine-grained Caption Generation and Context-driven Summarization, respectively. Then in Inference-guided Answering, HCQA utilizes this hierarchical information to reason and answer given question. On the EgoSchema blind test set, HCQA achieves 75% accuracy in answering over 5,000 human curated multiple-choice questions. Our code will be released at https://github.com/Hyu-Zhang/HCQA.
Building a general-purpose agent is a long-standing vision in the field of artificial intelligence. Existing agents have made remarkable progress in many domains, yet they still struggle to complete long-horizon tasks in an open world. We attribute this to the lack of necessary world knowledge and multimodal experience that can guide agents through a variety of long-horizon tasks. In this paper, we propose a Hybrid Multimodal Memory module to address the above challenges. It 1) transforms knowledge into Hierarchical Directed Knowledge Graph that allows agents to explicitly represent and learn world knowledge, and 2) summarises historical information into Abstracted Multimodal Experience Pool that provide agents with rich references for in-context learning. On top of the Hybrid Multimodal Memory module, a multimodal agent, Optimus-1, is constructed with dedicated Knowledge-guided Planner and Experience-Driven Reflector, contributing to a better planning and reflection in the face of long-horizon tasks in Minecraft. Extensive experimental results show that Optimus-1 significantly outperforms all existing agents on challenging long-horizon task benchmarks, and exhibits near human-level performance on many tasks. In addition, we introduce various Multimodal Large Language Models (MLLMs) as the backbone of Optimus-1. Experimental results show that Optimus-1 exhibits strong generalization with the help of the Hybrid Multimodal Memory module, outperforming the GPT-4V baseline on many tasks.
Large Language Models (LLMs) have shown remarkable performance in various emotion recognition tasks, thereby piquing the research community's curiosity for exploring their potential in emotional intelligence. However, several issues in the field of emotional generation tasks remain unresolved, including human preference alignment and emotional generation assessment. In this paper, we propose the Emotional Chain-of-Thought (ECoT), a plug-and-play prompting method that enhances the performance of LLMs on various emotional generation tasks by aligning with human emotional intelligence guidelines. To assess the reliability of ECoT, we propose an automated model-based evaluation method called Emotional Generation Score (EGS). EGS incorporates Goleman's Emotional Intelligence Theory as a consensus of human experts, providing a new perspective on the evaluation of emotional generation tasks. Extensive experimental results demonstrate the effectiveness of ECoT and EGS. Further, we discuss the promise of LLMs in the field of emotional intelligence and present key insights into the LLMs with the ECoT in emotional generation tasks.
This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore.
This is a continuation of Tang and Yan, which investigated the first eigenvalues of minimal isoparametric hypersurfaces with $g=4$ distinct principal curvatures and focal submanifolds in unit spheres. For the focal submanifolds with $g=6$, the present paper obtains estimates on all the eigenvalues, among others, giving an affirmative answer in one case to the problem posed in Tang and Yan, which may be regarded as a generalization of Yau's conjecture. In two of the four unsettled cases in Tang and Yan for focal submanifolds $M_1$ of OT-FKM-type, we prove the first eigenvalues to be their dimensions, respectively.
Motivated by the celebrated Schoen-Yau-Gromov-Lawson surgery theory on metrics of positive scalar curvature, we construct a double manifold associated with a minimal isoparametric hypersurface in the unit sphere. The resulting double manifold carries a metric of positive scalar curvature and an isoparametric foliation as well. To investigate the topology of the double manifolds, we use K-theory and the representation of the Clifford algebra for the FKM-type, and determine completely the isotropy subgroups of singular orbits for homogeneous case.
In this note, we study properties of the gradient map of the isoparametric polynomial. For a given isoparametric hypersurface in sphere, we calculate explicitly the gradient map of its isoparametric polynomial which turns out many interesting phenomenons and applications. We find that it should map not only the focal submanifolds to focal submanifolds, isoparametric hypersurfaces to isoparametric hypersurfaces, but also map isoparametric hypersurfaces to focal submanifolds. In particular, it turns out to be a homogeneous polynomial automorphism on certain isoparametric hypersurface. As an immediate consequence, we get the Brouwer degree of the gradient map which was firstly obtained by Peng and Tang with moving frame method. Following Farina's construction, another immediate consequence is a counter example of the Brézis question about the symmetry for the Ginzburg-Landau system in dimension 6, which gives a partial answer toward the Open problem 2 raised by Farina.