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Zheng Yuan

Publications and source records attributed to Zheng Yuan.

At least 127 records · Page 7Linked to original sources
arXiv2023

Minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces

In this article, we consider the minimal $L^2$ integrals for the Hardy spaces and the Bergman spaces, and we present some relations between them, which can be regarded as the solutions of the finite points versions of Saitoh's conjecture for conjugate Hardy kernels. As applications, we give optimal $L^2$ extension theorems for the Hardy spaces, and characterizations for the holding of the equality in the optimal $L^2$ extension theorems.

math.CV↗
arXiv2023

How well do Large Language Models perform in Arithmetic tasks?

Large language models have emerged abilities including chain-of-thought to answer math word problems step by step. Solving math word problems not only requires abilities to disassemble problems via chain-of-thought but also needs to calculate arithmetic expressions correctly for each step. To the best of our knowledge, there is no work to focus on evaluating the arithmetic ability of large language models. In this work, we propose an arithmetic dataset MATH 401 to test the latest large language models including GPT-4, ChatGPT, InstrctGPT, Galactica, and LLaMA with various arithmetic expressions and provide a detailed analysis of the ability of large language models. MATH 401 and evaluation codes are released at \url{https://github.com/GanjinZero/math401-llm}.

cs.CL↗
arXiv2023

Optimal $L^2$ extension for holomorphic vector bundles with singular hermitian metrics

In the present paper, we study the properties of singular Nakano positivity of singular hermitian metrics on holomorphic vector bundles, and establish an optimal $L^2$ extension theorem for holomorphic vector bundles with singular hermitian metrics on weakly pseudoconvex Kähler manifolds. As applications, we give a necessary condition for the holding of the equality in optimal $L^2$ extension theorem, and present singular hermitian holomorphic vector bundle versions of some $L^2$ extension theorems with optimal estimate.

math.CV↗
arXiv2023

RAMM: Retrieval-augmented Biomedical Visual Question Answering with Multi-modal Pre-training

Vision-and-language multi-modal pretraining and fine-tuning have shown great success in visual question answering (VQA). Compared to general domain VQA, the performance of biomedical VQA suffers from limited data. In this paper, we propose a retrieval-augmented pretrain-and-finetune paradigm named RAMM for biomedical VQA to overcome the data limitation issue. Specifically, we collect a new biomedical dataset named PMCPM which offers patient-based image-text pairs containing diverse patient situations from PubMed. Then, we pretrain the biomedical multi-modal model to learn visual and textual representation for image-text pairs and align these representations with image-text contrastive objective (ITC). Finally, we propose a retrieval-augmented method to better use the limited data. We propose to retrieve similar image-text pairs based on ITC from pretraining datasets and introduce a novel retrieval-attention module to fuse the representation of the image and the question with the retrieved images and texts. Experiments demonstrate that our retrieval-augmented pretrain-and-finetune paradigm obtains state-of-the-art performance on Med-VQA2019, Med-VQA2021, VQARAD, and SLAKE datasets. Further analysis shows that the proposed RAMM and PMCPM can enhance biomedical VQA performance compared with previous resources and methods. We will open-source our dataset, codes, and pretrained model.

cs.CV↗
arXiv2023

An Extended Sequence Tagging Vocabulary for Grammatical Error Correction

We extend a current sequence-tagging approach to Grammatical Error Correction (GEC) by introducing specialised tags for spelling correction and morphological inflection using the SymSpell and LemmInflect algorithms. Our approach improves generalisation: the proposed new tagset allows a smaller number of tags to correct a larger range of errors. Our results show a performance improvement both overall and in the targeted error categories. We further show that ensembles trained with our new tagset outperform those trained with the baseline tagset on the public BEA benchmark.

cs.CL↗
arXiv2023

Molecular Geometry-aware Transformer for accurate 3D Atomic System modeling

Molecular dynamic simulations are important in computational physics, chemistry, material, and biology. Machine learning-based methods have shown strong abilities in predicting molecular energy and properties and are much faster than DFT calculations. Molecular energy is at least related to atoms, bonds, bond angles, torsion angles, and nonbonding atom pairs. Previous Transformer models only use atoms as inputs which lack explicit modeling of the aforementioned factors. To alleviate this limitation, we propose Moleformer, a novel Transformer architecture that takes nodes (atoms) and edges (bonds and nonbonding atom pairs) as inputs and models the interactions among them using rotational and translational invariant geometry-aware spatial encoding. Proposed spatial encoding calculates relative position information including distances and angles among nodes and edges. We benchmark Moleformer on OC20 and QM9 datasets, and our model achieves state-of-the-art on the initial state to relaxed energy prediction of OC20 and is very competitive in QM9 on predicting quantum chemical properties compared to other Transformer and Graph Neural Network (GNN) methods which proves the effectiveness of the proposed geometry-aware spatial encoding in Moleformer.

q-bio.MN↗
arXiv2023

Concavity property of minimal $L^{2}$ integrals with Lebesgue measurable gain VII -- Negligible weights

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals with negligible weights degenerating to linearity on the fibrations over open Riemann surfaces and the fibrations over products of open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets $L^2$ extension problem with negligible weights on the fibrations over open Riemann surfaces and the fibrations over products of open Riemann surfaces.

math.CV↗
arXiv2022

A remark on a weighted version of Suita conjecture for higher derivatives

In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic functions (maybe multi-valued). For planar domains bounded by finite analytic closed curves, we give relations between the set and Dirichlet problem.

math.CV↗
arXiv2022

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain VI: fibrations over products of open Riemann surfaces

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over products of open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets $L^2$ extension problem from fibers over products of analytic subsets to fibrations over products of open Riemann surfaces, which implies characterizations of the equality parts of Suita conjecture and extended Suita conjecture for fibrations over products of open Riemann surfaces.

math.CV↗
arXiv2022

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain IV: product of open Riemann surfaces

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of products of analytic subsets on products of open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets $L^2$ extension problem from products of analytic subsets to products of open Riemann surfaces, which implies characterizations of the product versions of the equality parts of Suita conjecture and extended Suita conjecture, and the equality holding of a conjecture of Ohsawa for products of open Riemann surfaces.

math.CV↗
arXiv2022

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets $L^2$ extension problem from fibers over analytic subsets to fibrations over open Riemann surfaces, which implies characterizations of the fibration versions of the equality parts of Suita conjecture and extended Suita conjecture.

math.CV↗
arXiv2022

An Opponent-Aware Reinforcement Learning Method for Team-to-Team Multi-Vehicle Pursuit via Maximizing Mutual Information Indicator

The pursuit-evasion game in Smart City brings a profound impact on the Multi-vehicle Pursuit (MVP) problem, when police cars cooperatively pursue suspected vehicles. Existing studies on the MVP problems tend to set evading vehicles to move randomly or in a fixed prescribed route. The opponent modeling method has proven considerable promise in tackling the non-stationary caused by the adversary agent. However, most of them focus on two-player competitive games and easy scenarios without the interference of environments. This paper considers a Team-to-Team Multi-vehicle Pursuit (T2TMVP) problem in the complicated urban traffic scene where the evading vehicles adopt the pre-trained dynamic strategies to execute decisions intelligently. To solve this problem, we propose an opponent-aware reinforcement learning via maximizing mutual information indicator (OARLM2I2) method to improve pursuit efficiency in the complicated environment. First, a sequential encoding-based opponents joint strategy modeling (SEOJSM) mechanism is proposed to generate evading vehicles' joint strategy model, which assists the multi-agent decision-making process based on deep Q-network (DQN). Then, we design a mutual information-united loss, simultaneously considering the reward fed back from the environment and the effectiveness of opponents' joint strategy model, to update pursuing vehicles' decision-making process. Extensive experiments based on SUMO demonstrate our method outperforms other baselines by 21.48% on average in reducing pursuit time. The code is available at \url{https://github.com/ANT-ITS/OARLM2I2}.

cs.MA↗
arXiv2022

Graded-Q Reinforcement Learning with Information-Enhanced State Encoder for Hierarchical Collaborative Multi-Vehicle Pursuit

The multi-vehicle pursuit (MVP), as a problem abstracted from various real-world scenarios, is becoming a hot research topic in Intelligent Transportation System (ITS). The combination of Artificial Intelligence (AI) and connected vehicles has greatly promoted the research development of MVP. However, existing works on MVP pay little attention to the importance of information exchange and cooperation among pursuing vehicles under the complex urban traffic environment. This paper proposed a graded-Q reinforcement learning with information-enhanced state encoder (GQRL-IESE) framework to address this hierarchical collaborative multi-vehicle pursuit (HCMVP) problem. In the GQRL-IESE, a cooperative graded Q scheme is proposed to facilitate the decision-making of pursuing vehicles to improve pursuing efficiency. Each pursuing vehicle further uses a deep Q network (DQN) to make decisions based on its encoded state. A coordinated Q optimizing network adjusts the individual decisions based on the current environment traffic information to obtain the global optimal action set. In addition, an information-enhanced state encoder is designed to extract critical information from multiple perspectives and uses the attention mechanism to assist each pursuing vehicle in effectively determining the target. Extensive experimental results based on SUMO indicate that the total timestep of the proposed GQRL-IESE is less than other methods on average by 47.64%, which demonstrates the excellent pursuing efficiency of the GQRL-IESE. Codes are outsourced in https://github.com/ANT-ITS/GQRL-IESE.

cs.LG↗
arXiv2022

Adaptive Image Transformations for Transfer-based Adversarial Attack

Adversarial attacks provide a good way to study the robustness of deep learning models. One category of methods in transfer-based black-box attack utilizes several image transformation operations to improve the transferability of adversarial examples, which is effective, but fails to take the specific characteristic of the input image into consideration. In this work, we propose a novel architecture, called Adaptive Image Transformation Learner (AITL), which incorporates different image transformation operations into a unified framework to further improve the transferability of adversarial examples. Unlike the fixed combinational transformations used in existing works, our elaborately designed transformation learner adaptively selects the most effective combination of image transformations specific to the input image. Extensive experiments on ImageNet demonstrate that our method significantly improves the attack success rates on both normally trained models and defense models under various settings.

cs.CV↗
arXiv2022

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain

In this article, we present a concavity property of the minimal $L^2$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with weights may not be subharmonic.

math.CV↗
arXiv2022

Customizable Laguerre-Gaussian Perfect Vortex Beams

The recognition in the 1990s that vortex beams (VBs), paraxial light beams with optical vortices, carry orbital angular momentum (OAM), has benefited applications ranging from optical manipulation to high-dimensional classical and quantum information communications. The transverse profiles of common VBs, e.g., Laguerre-Gaussian beam and high-order Bessel beam, are hollow donuts whose radii grow up with OAM inevitably. The inherently unperfect character of the VBs that the radius is always positively correlated with OAM, restricts the application of the VBs in many scenarios like fiber optic data transmission, spatial OAM mode (de)multiplexing communication, and particle manipulation, which call for VBs to have the same scale with distinct OAM or even the small vortex ring for large OAM. Here, we derived a theory based on the most widely used Laguerre-Gaussian beam to generate a brand new type of VB with OAM-independent radii that moves away from the common unperfect constraint, called Laguerre-Gaussian Perfect Vortex Beam (LGPVB). LGPVBs have the self-similar property like common Laguerre-Gaussian beams but can self-heal after suffering disturbance and always remain 'perfection' when propagating. Our Fourier-space design not only allows us to shape the LGPVB's propagating intensity at will, but it also gives LGPVB the fascinating potential to arbitrarily self-accelerate while still perfectly propagating, self-similar, and self-healing. This customizable self-healing LGPVB, whose properties inform our most expectations of VBs, offers a better alternative for application scenarios of common VBs in a wide range of areas.

physics.optics↗