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We prove a criterion of existence of solutions conjectured by C. C. Chen and C. S. Lin [20] for the prescribed scalar curvature problem on the standard n-dimensional sphere.

Interpretability analysis methods for artificial intelligence models, such as LIME and SHAP, are widely used, though they primarily serve as post-model for analyzing model outputs. While it is commonly believed that the transparency and interpretability of AI models diminish as their complexity increases, currently there is no standardized method for assessing the inherent interpretability of the models themselves. This paper uses bond market default prediction as a case study, applying commonly used machine learning algorithms within AI models. First, the classification performance of these algorithms in default prediction is evaluated. Then, leveraging LIME and SHAP to assess the contribution of sample features to prediction outcomes, the paper proposes a novel method for evaluating the interpretability of the models themselves. The results of this analysis are consistent with the intuitive understanding and logical expectations regarding the interpretability of these models., Comment: 12 Pages,9 figures

Recent advancements in large language models (LLMs) have shown remarkable potential in automating machine learning tasks. However, existing LLM-based agents often struggle with low-diversity and suboptimal code generation. While recent work has introduced Monte Carlo Tree Search (MCTS) to address these issues, limitations persist in the quality and diversity of thoughts generated, as well as in the scalar value feedback mechanisms used for node selection. In this study, we introduce Introspective Monte Carlo Tree Search (I-MCTS), a novel approach that iteratively expands tree nodes through an introspective process that meticulously analyzes solutions and results from parent and sibling nodes. This facilitates a continuous refinement of the node in the search tree, thereby enhancing the overall decision-making process. Furthermore, we integrate a Large Language Model (LLM)-based value model to facilitate direct evaluation of each node's solution prior to conducting comprehensive computational rollouts. A hybrid rewarding mechanism is implemented to seamlessly transition the Q-value from LLM-estimated scores to actual performance scores. This allows higher-quality nodes to be traversed earlier. Applied to the various ML tasks, our approach demonstrates a 6% absolute improvement in performance compared to the strong open-source AutoML agents, showcasing its effectiveness in enhancing agentic AutoML systems. Resource available at https://github.com/jokieleung/I-MCTS

Recently, Graph Neural Network based Force Field (GNNFF) models are widely used in Molecular Dynamics (MD) simulation, which is one of the most cost-effective means in semiconductor material research. However, even such models provide high accuracy in energy and force Mean Absolute Error (MAE) over trained (in-distribution) datasets, they often become unstable during long-time MD simulation when used for out-of-distribution datasets. In this paper, we propose a feature correlation based method for GNNFF models to enhance the stability of MD simulation. We reveal the negative relationship between feature correlation and the stability of GNNFF models, and design a loss function with a dynamic loss coefficient scheduler to reduce edge feature correlation that can be applied in general GNNFF training. We also propose an empirical metric to evaluate the stability in MD simulation. Experiments show our method can significantly improve stability for GNNFF models especially in out-of-distribution data with less than 3% computational overhead. For example, we can ensure the stable MD simulation time from 0.03ps to 10ps for Allegro model.

Understanding experienced segregation in urban daily life is crucial for addressing societal inequalities and fostering inclusivity. The abundance of user-generated reviews on social media encapsulates nuanced perceptions and feelings associated with different places, offering rich insights into segregation. However, leveraging this data poses significant challenges due to its vast volume, ambiguity, and confluence of diverse perspectives. To tackle these challenges, we propose using Large Language Models (LLMs) to automate online review mining for segregation prediction. We design a Reflective LLM Coder to digest social media content into insights consistent with real-world feedback, and eventually produce a codebook capturing key dimensions that signal segregation experience, such as cultural resonance and appeal, accessibility and convenience, and community engagement and local involvement. Guided by the codebook, LLMs can generate both informative review summaries and ratings for segregation prediction. Moreover, we design a REasoning-and-EMbedding (RE'EM) framework, which combines the reasoning and embedding capabilities of language models to integrate multi-channel features for segregation prediction. Experiments on real-world data demonstrate that our framework greatly improves prediction accuracy, with a 22.79% elevation in R2 and a 9.33% reduction in MSE. The derived codebook is generalizable across three different cities, consistently improving prediction accuracy.Moreover, our user study confirms that the codebook-guided summaries provide cognitive gains for human participants in perceiving POIs' social inclusiveness.Our study marks an important step toward understanding implicit social barriers and inequalities, demonstrating the great potential of promoting social inclusiveness with AI., Comment: 11 pages, 6 figures

3D Gaussian Splatting (3DGS) has achieved excellent rendering quality with fast training and rendering speed. However, its optimization process lacks explicit geometric constraints, leading to suboptimal geometric reconstruction in regions with sparse or no observational input views. In this work, we try to mitigate the issue by incorporating a pre-trained matching prior to the 3DGS optimization process. We introduce Flow Distillation Sampling (FDS), a technique that leverages pre-trained geometric knowledge to bolster the accuracy of the Gaussian radiance field. Our method employs a strategic sampling technique to target unobserved views adjacent to the input views, utilizing the optical flow calculated from the matching model (Prior Flow) to guide the flow analytically calculated from the 3DGS geometry (Radiance Flow). Comprehensive experiments in depth rendering, mesh reconstruction, and novel view synthesis showcase the significant advantages of FDS over state-of-the-art methods. Additionally, our interpretive experiments and analysis aim to shed light on the effects of FDS on geometric accuracy and rendering quality, potentially providing readers with insights into its performance. Project page: https://nju-3dv.github.io/projects/fds, Comment: Accepted by ICLR 2025

Open-vocabulary semantic segmentation (OVSS) is an open-world task that aims to assign each pixel within an image to a specific class defined by arbitrary text descriptions. Recent advancements in large-scale vision-language models have demonstrated their open-vocabulary understanding capabilities, significantly facilitating the development of OVSS. However, most existing methods suffer from either suboptimal performance or long latency. This study introduces ERR-Seg, a novel framework that effectively reduces redundancy to balance accuracy and efficiency. ERR-Seg incorporates a training-free Channel Reduction Module (CRM) that leverages prior knowledge from vision-language models like CLIP to identify the most relevant classes while discarding others. Moreover, it incorporates Efficient Semantic Context Fusion (ESCF) with spatial-level and class-level sequence reduction strategies. CRM and ESCF result in substantial memory and computational savings without compromising accuracy. Additionally, recognizing the significance of hierarchical semantics extracted from middle-layer features for closed-set semantic segmentation, ERR-Seg introduces the Hierarchical Semantic Module (HSM) to exploit hierarchical semantics in the context of OVSS. Compared to previous state-of-the-art methods under the ADE20K-847 setting, ERR-Seg achieves +$5.6\%$ mIoU improvement and reduces latency by $67.3\%$.

We consider the Partition problem and propose a deterministic FPTAS (Fully Polynomial-Time Approximation Scheme) that runs in $\widetilde{O}(n + 1/\varepsilon)$-time. This is the best possible (up to a polylogarithmic factor) assuming the Strong Exponential Time Hypothesis~[Abboud, Bringmann, Hermelin, and Shabtay'22]. Prior to our work, only a randomized algorithm can achieve a running time of $\widetilde{O}(n + 1/\varepsilon)$~[Chen, Lian, Mao and Zhang '24], while the best deterministic algorithm runs in $\widetilde{O}(n+1/\varepsilon^{5/4})$ time~[Deng, Jin and Mao '23] and [Wu and Chen '22].

Physical AI needs to be trained digitally first. It needs a digital twin of itself, the policy model, and a digital twin of the world, the world model. In this paper, we present the Cosmos World Foundation Model Platform to help developers build customized world models for their Physical AI setups. We position a world foundation model as a general-purpose world model that can be fine-tuned into customized world models for downstream applications. Our platform covers a video curation pipeline, pre-trained world foundation models, examples of post-training of pre-trained world foundation models, and video tokenizers. To help Physical AI builders solve the most critical problems of our society, we make our platform open-source and our models open-weight with permissive licenses available via https://github.com/NVIDIA/Cosmos.

Complex visual reasoning remains a key challenge today. Typically, the challenge is tackled using methodologies such as Chain of Thought (COT) and visual instruction tuning. However, how to organically combine these two methodologies for greater success remains unexplored. Also, issues like hallucinations and high training cost still need to be addressed. In this work, we devise an innovative multi-round training and reasoning framework suitable for lightweight Multimodal Large Language Models (MLLMs). Our self-questioning approach heuristically guides MLLMs to focus on visual clues relevant to the target problem, reducing hallucinations and enhancing the model's ability to describe fine-grained image details. This ultimately enables the model to perform well in complex visual reasoning and question-answering tasks. We have named this framework Socratic Questioning(SQ). To facilitate future research, we create a multimodal mini-dataset named CapQA, which includes 1k images of fine-grained activities, for visual instruction tuning and evaluation, our proposed SQ method leads to a 31.2% improvement in the hallucination score. Our extensive experiments on various benchmarks demonstrate SQ's remarkable capabilities in heuristic self-questioning, zero-shot visual reasoning and hallucination mitigation. Our model and code will be publicly available.

Creating AI systems that can interact with environments over long periods, similar to human cognition, has been a longstanding research goal. Recent advancements in multimodal large language models (MLLMs) have made significant strides in open-world understanding. However, the challenge of continuous and simultaneous streaming perception, memory, and reasoning remains largely unexplored. Current MLLMs are constrained by their sequence-to-sequence architecture, which limits their ability to process inputs and generate responses simultaneously, akin to being unable to think while perceiving. Furthermore, relying on long contexts to store historical data is impractical for long-term interactions, as retaining all information becomes costly and inefficient. Therefore, rather than relying on a single foundation model to perform all functions, this project draws inspiration from the concept of the Specialized Generalist AI and introduces disentangled streaming perception, reasoning, and memory mechanisms, enabling real-time interaction with streaming video and audio input. The proposed framework InternLM-XComposer2.5-OmniLive (IXC2.5-OL) consists of three key modules: (1) Streaming Perception Module: Processes multimodal information in real-time, storing key details in memory and triggering reasoning in response to user queries. (2) Multi-modal Long Memory Module: Integrates short-term and long-term memory, compressing short-term memories into long-term ones for efficient retrieval and improved accuracy. (3) Reasoning Module: Responds to queries and executes reasoning tasks, coordinating with the perception and memory modules. This project simulates human-like cognition, enabling multimodal large language models to provide continuous and adaptive service over time., Comment: Github Repo: https://github.com/InternLM/InternLM-XComposer/tree/main/InternLM-XComposer-2.5-OmniLive

Following the construction in arXiv:2210.12127, we develop a symmetry-preserving renormalization group (RG) flow for 3D symmetric theories. These theories are expressed as boundary conditions of a symTFT, which in our case is a 3+1D Dijkgraaf-Witten topological theory in the bulk. The boundary is geometrically organized into tetrahedra and represented as a tensor network, which we refer to as the "simplex tensor network" state. Each simplex tensor is assigned indices corresponding to its vertices, edges, and faces. We propose a numerical algorithm to implement RG flows for these boundary conditions, and explicitly demonstrate its application to a $\mathbb{Z}_2$ symmetric theory. By linearly interpolating between three topological fixed-point boundaries, we map the phase transitions characterized by local and non-local order parameters, which respectively detects the breaking of a 0-form and a 2-form symmetry. This formalism is readily extendable to other discrete symmetry groups and, in principle, can be generalized to describe 3D symmetric topological orders.

Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the least number of distinct elements. In this paper, we show that such CHMs can only be complex equivalent to two kind of matrices, one is $H_2$-reducible and the other is the Tao matrix. Using our result one can further narrow the range of MUB trio (a set of four MUBs in $\mathbb{C}^6$ consists of an MUB trio and the identity) since we find that the two CHMs neither belong to MUB trios. Our results may lead to the more complete classification of $6\times 6$ CHMs whose elements in the first row are all 1., Comment: 29 pages, 0 figures

Reconfigurable intelligent surfaces (RISs) have shown the potential to improve signal-to-interference-plus-noise ratio (SINR) related coverage, especially at high-frequency communications. However, assessing electromagnetic filed exposure (EMFE) and establishing EMFE regulations in RIS-assisted large-scale networks are still open issues. This paper proposes a framework to characterize SINR and EMFE in such networks for downlink and uplink scenarios. Particularly, we carefully consider the association rule with the presence of RISs, accurate antenna pattern at base stations (BSs), fading model, and power control mechanism at mobile devices in the system model. Under the proposed framework, we derive the marginal and joint distributions of SINR and EMFE in downlink and uplink, respectively. The first moment of EMFE is also provided. Additionally, we design the compliance distance (CD) between a BS/RIS and a user to comply with the EMFE regulations. To facilitate efficient identification, we further provide approximate closed-form expressions for CDs. From numerical results of the marginal distributions, we find that in the downlink scenario, deploying RISs may not always be beneficial, as the improved SINR comes at the cost of increased EMFE. However, in the uplink scenario, RIS deployment is promising to enhance coverage while still maintaining EMFE compliance. By simultaneously evaluating coverage and compliance metrics through joint distributions, we demonstrate the feasibility of RISs in improving uplink and downlink performance. Insights from this framework can contribute to establishing EMFE guidelines and achieving a balance between coverage and compliance when deploying RISs.

We introduce Open-Sora Plan, an open-source project that aims to contribute a large generation model for generating desired high-resolution videos with long durations based on various user inputs. Our project comprises multiple components for the entire video generation process, including a Wavelet-Flow Variational Autoencoder, a Joint Image-Video Skiparse Denoiser, and various condition controllers. Moreover, many assistant strategies for efficient training and inference are designed, and a multi-dimensional data curation pipeline is proposed for obtaining desired high-quality data. Benefiting from efficient thoughts, our Open-Sora Plan achieves impressive video generation results in both qualitative and quantitative evaluations. We hope our careful design and practical experience can inspire the video generation research community. All our codes and model weights are publicly available at \url{https://github.com/PKU-YuanGroup/Open-Sora-Plan}., Comment: v1.3

The Water Cherenkov Detector Array (WCDA) is one of the components of Large High Altitude Air Shower Observatory (LHAASO) and can monitor any sources over two-thirds of the sky for up to 7 hours per day with >98\% duty cycle. In this work, we report the detection of two outbursts of the Fanaroff-Riley I radio galaxy NGC 1275 that were detected by LHAASO-WCDA between November 2022 and January 2023 with statistical significance of 5.2~$\sigma$ and 8.3~$\sigma$. The observed spectral energy distribution in the range from 500 GeV to 3 TeV is fitted by a power-law with a best-fit spectral index of $\alpha=-3.37\pm0.52$ and $-3.35\pm0.29$, respectively. The outburst flux above 0.5~TeV was ($4.55\pm 4.21)\times~10^{-11}~\rm cm^{-2}~s^{-1}$ and ($3.45\pm 1.78)\times~10^{-11}~\rm cm^{-2}~s^{-1}$, corresponding to 60\%, 45\% of Crab Nebula flux. Variation analysis reveals the variability time-scale of days at the TeV energy band. A simple test by one-zone synchrotron self-Compton model reproduces the data in the gamma-ray band well., Comment: 11 pages, 8 figures, 3 tables

Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multi-qubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We further investigate the widely-used multi-qubit gates, for example, the entangling and assisted entangling power of the $n$-qubit Toffoli gate is one ebit. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to $\log_25$ ebits.

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an algebraic approach to constructing input-encoding architectures that properly account for the data's structure, providing a step toward achieving more typeful machine learning., Comment: 25 pages, 6 figures. Keywords: typeful, algebraic data types, tensors, structured data

In this paper, we study a vehicle selection problem for federated learning (FL) over vehicular networks. Specifically, we design a mobility-aware vehicular federated learning (MAVFL) scheme in which vehicles drive through a road segment to perform FL. Some vehicles may drive out of the segment which leads to unsuccessful training. In the proposed scheme, the real-time successful training participation ratio is utilized to implement vehicle selection. We conduct the convergence analysis to indicate the influence of vehicle mobility on training loss. Furthermore, we propose a multi-armed bandit-based vehicle selection algorithm to minimize the utility function considering training loss and delay. The simulation results show that compared with baselines, the proposed algorithm can achieve better training performance with approximately 28\% faster convergence., Comment: Accepted by 2024 IEEE Globecom Workshops (GC Wkshps)

This research aims to comprehensively explore building a multimodal foundation model for egocentric video understanding. To achieve this goal, we work on three fronts. First, as there is a lack of QA data for egocentric video understanding, we develop a data engine that efficiently generates 7M high-quality QA samples for egocentric videos ranging from 30 seconds to one hour long, based on human-annotated data. This is currently the largest egocentric QA dataset. Second, we contribute a challenging egocentric QA benchmark with 629 videos and 7,026 questions to evaluate the models' ability in recognizing and memorizing visual details across videos of varying lengths. We introduce a new de-biasing evaluation method to help mitigate the unavoidable language bias present in the models being evaluated. Third, we propose a specialized multimodal architecture featuring a novel "Memory Pointer Prompting" mechanism. This design includes a global glimpse step to gain an overarching understanding of the entire video and identify key visual information, followed by a fallback step that utilizes the key visual information to generate responses. This enables the model to more effectively comprehend extended video content. With the data, benchmark, and model, we successfully build MM-Ego, an egocentric multimodal LLM that shows powerful performance on egocentric video understanding., Comment: Technical Report

We report the detection of an extended very-high-energy (VHE) gamma-ray source coincident with the location of middle-aged (62.4~\rm kyr) pulsar PSR J0248+6021, by using the LHAASO-WCDA data of live 796 days and LHAASO-KM2A data of live 1216 days. A significant excess of \gray induced showers is observed both by WCDA in energy bands of 1-25~\rm TeV and KM2A in energy bands of $>$ 25~\rm TeV with 7.3 $\sigma$ and 13.5 $\sigma$, respectively. The best-fit position derived through WCDA data is R.A. = 42.06$^\circ \pm$ 0.12$^\circ$ and Dec. = 60.24$^\circ \pm $ 0.13$^\circ$ with an extension of 0.69$^\circ\pm$0.15$^\circ$ and that of the KM2A data is R.A.= 42.29$^\circ \pm $ 0.13$^\circ$ and Dec. = 60.38$^\circ \pm$ 0.07$^\circ$ with an extension of 0.37$^\circ\pm$0.07$^\circ$. No clear extended multiwavelength counterpart of this LHAASO source has been found from the radio band to the GeV band. The most plausible explanation of the VHE \gray emission is the inverse Compton process of highly relativistic electrons and positrons injected by the pulsar. These electrons/positrons are hypothesized to be either confined within the pulsar wind nebula or to have already escaped into the interstellar medium, forming a pulsar halo., Comment: 12 pages, 10 figures, Accepted by Sci. China-Phys. Mech. Astron

We give a new proof of Chen-Lin result with Li-Zhang method.

The absolutely separable (resp. PPT) states remain separable (resp. positive partial transpose) under any global unitary operation. We present a compact form of the extreme points in the sets of absolutely separable states and PPT states in two-qubit and qubit-qudit systems. The results imply that each extreme point has at most three distinct eigenvalues. We establish a necessary and sufficient condition for determining extreme points of the set of absolutely PPT states in two-qutrit and qutrit-qudit systems, expressed as solvable linear equations. We also demonstrate that any extreme point in qutrit-qudit system has at most seven distinct eigenvalues. We introduce the concept of robustness of nonabsolute separability. It quantifies the minimal amount by which a state needs to mix with other states such that the overall state is absolutely separable. We show that the robustness satisfies positivity, invariance under unitary transformation, monotonicity and convexity, so it is a good measure within the resource theory of nonabsolute separability. Analytical expressions for this measure are given for pure states in arbitrary system and rank-two mixed states in two-qubit system., Comment: 22 pages, 1 figure

One type of bond with the most implicit government guarantee is municipal investment bonds. In recent years, there have been an increasing number of downgrades in the credit ratings of municipal bonds, which has led some people to question whether the implicit government guarantee may affect the objectivity of the bond ratings? This paper uses text mining methods to mine relevant policy documents related to municipal investment bond issuance, and calculates the implicit guarantee strength of municipal investment bonds based on the PMC index model. It further analyzes the impact of the implicit guarantee strength of municipal bonds on their credit evaluation. The study found that the implicit government guarantee on municipal investment bonds does indeed help to raise the credit ratings assigned by credit rating agencies. The study found that, moreover, the government's implicit guarantee has a more pronounced effect in boosting credit ratings in less developed western regions., Comment: 16pages,1 figure

The implicit government guarantee hampers the recognition and management of risks by all stakeholders in the bond market, and it has led to excessive debt for local governments or state-owned enterprises. To prevent the risk of local government debt defaults and reduce investors' expectations of implicit government guarantees, various regulatory departments have issued a series of policy documents related to municipal investment bonds. By employing text mining techniques on policy documents related to municipal investment bond, and utilizing the PMC index model to assess the effectiveness of policy documents. This paper proposes a novel method for quantifying the intensity of implicit governmental guarantees based on PMC index model. The intensity of implicit governmental guarantees is inversely correlated with the PMC index of policies aimed at de-implicitizing governmental guarantees. Then as these policies become more effective, the intensity of implicit governmental guarantees diminishes correspondingly. These findings indicate that recent policies related to municipal investment bond have indeed succeeded in reducing implicit governmental guarantee intensity, and these policies have achieved the goal of risk management. Furthermore, it was showed that the intensity of implicit governmental guarantee affected by diverse aspects of these policies such as effectiveness, clarity, and specificity, as well as incentive and assurance mechanisms., Comment: 22 pages,6 figures

The recently proposed Kolmogorov-Arnold Networks (KANs) offer enhanced interpretability and greater model expressiveness. However, KANs also present challenges related to privacy leakage during inference. Homomorphic encryption (HE) facilitates privacy-preserving inference for deep learning models, enabling resource-limited users to benefit from deep learning services while ensuring data security. Yet, the complex structure of KANs, incorporating nonlinear elements like the SiLU activation function and B-spline functions, renders existing privacy-preserving inference techniques inadequate. To address this issue, we propose an accurate and efficient privacy-preserving inference scheme tailored for KANs. Our approach introduces a task-specific polynomial approximation for the SiLU activation function, dynamically adjusting the approximation range to ensure high accuracy on real-world datasets. Additionally, we develop an efficient method for computing B-spline functions within the HE domain, leveraging techniques such as repeat packing, lazy combination, and comparison functions. We evaluate the effectiveness of our privacy-preserving KAN inference scheme on both symbolic formula evaluation and image classification. The experimental results show that our model achieves accuracy comparable to plaintext KANs across various datasets and outperforms plaintext MLPs. Additionally, on the CIFAR-10 dataset, our inference latency achieves over 7 times speedup compared to the naive method.

We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eisenstein-generated subcategories.

Remote patient monitoring (RPM) involves the remote collection and transmission of patient health data, serving as a notable application of data-driven healthcare. This technology facilitates clinical monitoring and decision-making, offering benefits like reduced healthcare costs and improved patient outcomes. However, RPM also introduces challenges common to data-driven healthcare, such as additional data work that can disrupt clinician's workflow. This study explores the daily practices, collaboration mechanisms, and sensemaking processes of nurses in RPM through field observations and interviews with six stakeholders. Preliminary results indicate that RPM's scale-up pushes clinicians toward asynchronous collaboration. Data sensemaking is crucial for this type of collaboration, but existing technologies often create friction rather than support. This work provides empirical insights into clinical workflow in nursing practice, especially RPM. We suggest recognizing data sensemaking as a distinct nursing practice within data work and recommend further investigation into its role in the workflow of nurses in RPM.

Video Moment Retrieval (VMR) aims to retrieve relevant moments of an untrimmed video corresponding to the query. While cross-modal interaction approaches have shown progress in filtering out query-irrelevant information in videos, they assume the precise alignment between the query semantics and the corresponding video moments, potentially overlooking the misunderstanding of the natural language semantics. To address this challenge, we propose a novel model called \textit{QD-VMR}, a query debiasing model with enhanced contextual understanding. Firstly, we leverage a Global Partial Aligner module via video clip and query features alignment and video-query contrastive learning to enhance the cross-modal understanding capabilities of the model. Subsequently, we employ a Query Debiasing Module to obtain debiased query features efficiently, and a Visual Enhancement module to refine the video features related to the query. Finally, we adopt the DETR structure to predict the possible target video moments. Through extensive evaluations of three benchmark datasets, QD-VMR achieves state-of-the-art performance, proving its potential to improve the accuracy of VMR. Further analytical experiments demonstrate the effectiveness of our proposed module. Our code will be released to facilitate future research., Comment: 9 pages, 4 figures, 4 tables

Characterizing the $6\times 6$ complex Hadamard matrices (CHMs) is an open problem in linear algebra and quantum information. In this paper, we investigate the eigenvalues and eigenvectors of CHMs. We show that any $n\times n$ CHM with dephased form has two constant eigenvalues $\pm\sqrt{n}$ and has two constant eigenvectors. We obtain the maximum numbers of identical eigenvalues of $6\times 6$ CHMs with dephased form and we extend this result to arbitrary dimension. We also show that there is no $6\times 6$ CHM with four identical eigenvalues. We conjecture that the eigenvalues and eigenvectors of $6\times 6$ CHMs will lead to the complete classification of $6\times 6$ CHMs., Comment: 15 pages,0 figures

Since the birth of quantum theory, it has been controversial that whether real numbers are adequate to describe its formalism. Recently, the imaginary unit $i$ has been experimentally proven to be indispensable for quantum mechanics. It motivates us to study the differences in detection power between real and complex entanglement witnesses (EWs), and analyze the detection power of real EWs under local equivalences. We show that a real EW must detect a real entangled state, and conversely a real entangled state must be detected by a real EW. We present a necessary and sufficient condition for the entangled states detected by real EWs, and give a specific example which implies the detection limitations of real EWs. Then, we conjecture that all entangled states are detected by the EWs locally equivalent to real ones. We prove the conjecture for all states with non-positive partial transpose. We also derive a necessary and sufficient condition for the complex PPT (positive-partial-transpose) entangled states detected by the EWs locally equivalent to real ones. We further prove the conjecture for a family of two-quqart PPT entangled states. Another way to figure out the conjecture is to check whether a counterexample exists. We propose an equivalent method to examine the existence of a counterexample from a set-theoretic perspective, and provide some supporting evidence of non-existence. Finally, we derive some results on local projections of EWs with product projectors., Comment: 17 pages, 2 figures

Recently emerged as a disruptive networking paradigm, quantum networks rely on the mysterious quantum entanglement to teleport qubits without physically transferring quantum particles. However, the state of quantum systems is extremely fragile due to environment noise. A promising technique to combat against quantum decoherence is entanglement purification. To fully exploit its benefit, two fundamental research questions need to be answered: (1) given an entanglement path, what is the optimal entanglement purification schedule? (2) how to compute min-cost end-to-end entanglement paths subject to fidelity constraint? In this paper, we give algorithmic solutions to both questions. For the first question, we develop an optimal entanglement purification scheduling algorithm for the single-hop case and analyze the \textsc{purify-and-swap} strategy in the multi-hop case by establishing the closed-form condition for its optimality. For the second question, we design a polynomial-time algorithm constructing an $\epsilon$-optimal fidelity-constrained path. The effectiveness of our algorithms are also numerically demonstrated by extensive simulations., Comment: 15 pages, 12 figures

As a fundamental task in long-form video understanding, temporal action detection (TAD) aims to capture inherent temporal relations in untrimmed videos and identify candidate actions with precise boundaries. Over the years, various networks, including convolutions, graphs, and transformers, have been explored for effective temporal modeling for TAD. However, these modules typically treat past and future information equally, overlooking the crucial fact that changes in action boundaries are essentially causal events. Inspired by this insight, we propose leveraging the temporal causality of actions to enhance TAD representation by restricting the model's access to only past or future context. We introduce CausalTAD, which combines causal attention and causal Mamba to achieve state-of-the-art performance on multiple benchmarks. Notably, with CausalTAD, we ranked 1st in the Action Recognition, Action Detection, and Audio-Based Interaction Detection tracks at the EPIC-Kitchens Challenge 2024, as well as 1st in the Moment Queries track at the Ego4D Challenge 2024. Our code is available at https://github.com/sming256/OpenTAD/., Comment: 1st in Moment Queries track at the Ego4D Challenge 2024; 1st in Action Recognition, Action Detection, and Audio-Based Interaction Detection tracks at the EPIC-Kitchens Challenge 2024

We present VLMEvalKit: an open-source toolkit for evaluating large multi-modality models based on PyTorch. The toolkit aims to provide a user-friendly and comprehensive framework for researchers and developers to evaluate existing multi-modality models and publish reproducible evaluation results. In VLMEvalKit, we implement over 70 different large multi-modality models, including both proprietary APIs and open-source models, as well as more than 20 different multi-modal benchmarks. By implementing a single interface, new models can be easily added to the toolkit, while the toolkit automatically handles the remaining workloads, including data preparation, distributed inference, prediction post-processing, and metric calculation. Although the toolkit is currently mainly used for evaluating large vision-language models, its design is compatible with future updates that incorporate additional modalities, such as audio and video. Based on the evaluation results obtained with the toolkit, we host OpenVLM Leaderboard, a comprehensive leaderboard to track the progress of multi-modality learning research. The toolkit is released at https://github.com/open-compass/VLMEvalKit and is actively maintained., Comment: Updated on 2025.03.04

We present InternLM-XComposer-2.5 (IXC-2.5), a versatile large-vision language model that supports long-contextual input and output. IXC-2.5 excels in various text-image comprehension and composition applications, achieving GPT-4V level capabilities with merely 7B LLM backend. Trained with 24K interleaved image-text contexts, it can seamlessly extend to 96K long contexts via RoPE extrapolation. This long-context capability allows IXC-2.5 to excel in tasks requiring extensive input and output contexts. Compared to its previous 2.0 version, InternLM-XComposer-2.5 features three major upgrades in vision-language comprehension: (1) Ultra-High Resolution Understanding, (2) Fine-Grained Video Understanding, and (3) Multi-Turn Multi-Image Dialogue. In addition to comprehension, IXC-2.5 extends to two compelling applications using extra LoRA parameters for text-image composition: (1) Crafting Webpages and (2) Composing High-Quality Text-Image Articles. IXC-2.5 has been evaluated on 28 benchmarks, outperforming existing open-source state-of-the-art models on 16 benchmarks. It also surpasses or competes closely with GPT-4V and Gemini Pro on 16 key tasks. The InternLM-XComposer-2.5 is publicly available at https://github.com/InternLM/InternLM-XComposer., Comment: Technical Report. https://github.com/InternLM/InternLM-XComposer

We give two results about Harnack type inequalities. First, on compact smooth Riemannian surface without boundary, we have an estimate of the type $\sup +\inf$. The second result concerns the solutions of prescribed scalar curvature equation on the unit ball of ${\mathbb R}^n$ with Dirichlet condition. Next, we give an inequality of the type $(\sup_K u)^{2s-1} \times \inf_{\Omega} u \leq c$ for positive solutions of $\Delta u=Vu^5$ on $\Omega \subset {\mathbb R}^3$, where $K$ is a compact set of $\Omega$ and $V$ is $s-$ h\"olderian, $s\in ]-1/2,1]$. For the case $s=1/2$, we prove that if $\min_{\Omega} u>m>0$ and the h\"olderian constant $A$ of $V$ is small enough (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of $\Omega$. ----- Nous donnons quelques estimations des solutions d'equations elliptiques sur les surfaces de Riemann et sur des ouverts en dimension n> 2. Nous traitons le cas holderien pour l'equation de la courbure scalaire prescrite en dimension 3.