arXiv subjects
Publications and source records attributed to Jian Song.
In this note, we give a new proof for Perelman's scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds. The proof relies on a new Harnack estimate for a special family of functions in space-time. Our new approach initiates the work in \cite{JST23a} for general finite time solutions of the Kähler-Ricci flow.
We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in time in both Gromov-Hausdorff and Gromov-$W_1$ distance. In particular, the singular sets of each time slice and its tangent cones are close and of codimension no less than $4$.
In recent research, non-orthogonal artificial noise (NORAN) has been proposed as an alternative to orthogonal artificial noise (AN). However, NORAN introduces additional noise into the channel, which reduces the capacity of the legitimate channel (LC). At the same time, selecting a NORAN design with ideal security performance from a large number of design options is also a challenging problem. To address these two issues, a novel NORAN based on a pilot information codebook is proposed in this letter. The codebook associates different suboptimal NORANs with pilot information as the key under different channel state information (CSI). The receiver interrogates the codebook using the pilot information to obtain the NORAN that the transmitter will transmit in the next moment, in order to eliminate the NORAN when receiving information. Therefore, NORAN based on pilot information codebooks can improve the secrecy capacity (SC) of the communication system by directly using suboptimal NORAN design schemes without increasing the noise in the LC. Numerical simulations and analyses show that the introduction of NORAN with a novel design using pilot information codebooks significantly enhances the security and improves the SC of the communication system.
Change detection (CD) is a critical task in studying the dynamics of ecosystems and human activities using multi-temporal remote sensing images. While deep learning has shown promising results in CD tasks, it requires a large number of labeled and paired multi-temporal images to achieve high performance. Pairing and annotating large-scale multi-temporal remote sensing images is both expensive and time-consuming. To make deep learning-based CD techniques more practical and cost-effective, we propose an unsupervised single-temporal CD framework based on intra- and inter-image patch exchange (I3PE). The I3PE framework allows for training deep change detectors on unpaired and unlabeled single-temporal remote sensing images that are readily available in real-world applications. The I3PE framework comprises four steps: 1) intra-image patch exchange method is based on an object-based image analysis method and adaptive clustering algorithm, which generates pseudo-bi-temporal image pairs and corresponding change labels from single-temporal images by exchanging patches within the image; 2) inter-image patch exchange method can generate more types of land-cover changes by exchanging patches between images; 3) a simulation pipeline consisting of several image enhancement methods is proposed to simulate the radiometric difference between pre- and post-event images caused by different imaging conditions in real situations; 4) self-supervised learning based on pseudo-labels is applied to further improve the performance of the change detectors in both unsupervised and semi-supervised cases. Extensive experiments on two large-scale datasets demonstrate that I3PE outperforms representative unsupervised approaches and achieves F1 value improvements of 10.65% and 6.99% to the SOTA method. Moreover, I3PE can improve the performance of the ... (see the original article for full abstract)
Synthetic datasets, recognized for their cost effectiveness, play a pivotal role in advancing computer vision tasks and techniques. However, when it comes to remote sensing image processing, the creation of synthetic datasets becomes challenging due to the demand for larger-scale and more diverse 3D models. This complexity is compounded by the difficulties associated with real remote sensing datasets, including limited data acquisition and high annotation costs, which amplifies the need for high-quality synthetic alternatives. To address this, we present SyntheWorld, a synthetic dataset unparalleled in quality, diversity, and scale. It includes 40,000 images with submeter-level pixels and fine-grained land cover annotations of eight categories, and it also provides 40,000 pairs of bitemporal image pairs with building change annotations for building change detection task. We conduct experiments on multiple benchmark remote sensing datasets to verify the effectiveness of SyntheWorld and to investigate the conditions under which our synthetic data yield advantages. We will release SyntheWorld to facilitate remote sensing image processing research.
Transformer-based pre-trained models like BERT have achieved great progress on Semantic Sentence Matching. Meanwhile, dependency prior knowledge has also shown general benefits in multiple NLP tasks. However, how to efficiently integrate dependency prior structure into pre-trained models to better model complex semantic matching relations is still unsettled. In this paper, we propose the \textbf{D}ependency-Enhanced \textbf{A}daptive \textbf{F}usion \textbf{A}ttention (\textbf{DAFA}), which explicitly introduces dependency structure into pre-trained models and adaptively fuses it with semantic information. Specifically, \textbf{\emph{(i)}} DAFA first proposes a structure-sensitive paradigm to construct a dependency matrix for calibrating attention weights. It adopts an adaptive fusion module to integrate the obtained dependency information and the original semantic signals. Moreover, DAFA reconstructs the attention calculation flow and provides better interpretability. By applying it on BERT, our method achieves state-of-the-art or competitive performance on 10 public datasets, demonstrating the benefits of adaptively fusing dependency structure in semantic matching task.
Extremely large-scale multiple-input multiple-output (XL-MIMO) promises to provide ultrahigh data rates in millimeter-wave (mmWave) and Terahertz (THz) spectrum. However, the spherical-wavefront wireless transmission caused by large aperture array presents huge challenges for channel state information (CSI) acquisition and beamforming. Two independent parameters (physical angles and transmission distance) should be simultaneously considered in XL-MIMO beamforming, which brings severe overhead consumption and beamforming degradation. To address this problem, we exploit the near-field channel characteristic and propose two low-overhead hierarchical beam training schemes for near-field XL-MIMO system. Firstly, we project near-field channel into spatial-angular domain and slope-intercept domain to capture detailed representations. Then we point out three critical criteria for XL-MIMO hierarchical beam training. Secondly, a novel spatial-chirp beam-aided codebook and corresponding hierarchical update policy are proposed. Thirdly, given the imperfect coverage and overlapping of spatial-chirp beams, we further design an enhanced hierarchical training codebook via manifold optimization and alternative minimization. Theoretical analyses and numerical simulations are also displayed to verify the superior performances on beamforming and training overhead.
Many operations in workflow systems are dependent on database tables. The classical workflow net and its extensions (e.g., worflow net with data) cannot model these operations so that some related errors cannot be found by them. Recently, workflow nets with tables (WFT-nets) were proposed to remedy such a flaw. However, when the reachability graph of a WFT-net is constructed by their method, some pseudo states are possibly generated since it does not consider the guards that constrain the enabling and firing of transitions. Additionally, they only considered the soundness property that just represents a single design requirement, so that many other requirements, especially those related to tables, cannot be analyzed. In this paper, therefore, we re-define the WFT-net by augmenting constraints of guards to it and re-name it as workflow net with tables and constraints (WFTC-net). We propose a new method to generate the state reachability graphs (SRG) of WFTC-nets such that SRG can avoid pseudo states, due to the consideration of the guards in it. To represent design requirements related to database operations, we define database-oriented computation tree logic (DCTL), to represent more design requirements. We design the model checking algorithms of DCTL based on the SRG of WFTC-nets and develop a tool. Experiments on a number of public benchmarks show the usefulness of our methods.
Deep learning-based super-resolution models have the potential to revolutionize biomedical imaging and diagnoses by effectively tackling various challenges associated with early detection, personalized medicine, and clinical automation. However, the requirement of an extensive collection of high-resolution images presents limitations for widespread adoption in clinical practice. In our experiment, we proposed an approach to effectively train the deep learning-based super-resolution models using only one real image by leveraging self-generated high-resolution images. We employed a mixed metric of image screening to automatically select images with a distribution similar to ground truth, creating an incrementally curated training data set that encourages the model to generate improved images over time. After five training iterations, the proposed deep learning-based super-resolution model experienced a 7.5\% and 5.49\% improvement in structural similarity and peak-signal-to-noise ratio, respectively. Significantly, the model consistently produces visually enhanced results for training, improving its performance while preserving the characteristics of original biomedical images. These findings indicate a potential way to train a deep neural network in a self-revolution manner independent of real-world human data.
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at \url{https://github.com/thu-ml/GNOT}.
Transformer-based pre-trained language models such as BERT have achieved remarkable results in Semantic Sentence Matching. However, existing models still suffer from insufficient ability to capture subtle differences. Minor noise like word addition, deletion, and modification of sentences may cause flipped predictions. To alleviate this problem, we propose a novel Dual Attention Enhanced BERT (DABERT) to enhance the ability of BERT to capture fine-grained differences in sentence pairs. DABERT comprises (1) Dual Attention module, which measures soft word matches by introducing a new dual channel alignment mechanism to model affinity and difference attention. (2) Adaptive Fusion module, this module uses attention to learn the aggregation of difference and affinity features, and generates a vector describing the matching details of sentence pairs. We conduct extensive experiments on well-studied semantic matching and robustness test datasets, and the experimental results show the effectiveness of our proposed method.
Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE constraints that have a complicated or nonlinear dependency on optimization targets. In this paper, we present a novel bi-level optimization framework to resolve the challenge by decoupling the optimization of the targets and constraints. For the inner loop optimization, we adopt PINNs to solve the PDE constraints only. For the outer loop, we design a novel method by using Broyden's method based on the Implicit Function Theorem (IFT), which is efficient and accurate for approximating hypergradients. We further present theoretical explanations and error analysis of the hypergradients computation. Extensive experiments on multiple large-scale and nonlinear PDE constrained optimization problems demonstrate that our method achieves state-of-the-art results compared with strong baselines.
In this article, we consider the following stochastic fractional diffusion equation \begin{equation*} \left(\partial^β+\dfracν{2}\left(-Δ\right)^{α/ 2}\right) u(t, x)= λ\: I_{0_+}^γ\left[u(t, x) \dot{W}(t, x)\right] ,\quad t>0,\: x \in \mathbb{R}, \end{equation*} where $α>0$, $β\in(0,2]$, $γ\ge 0$, $λ\neq0$, $ν>0$, and $\dot{W}$ is a Gaussian noise which is white or fractional in time and rough in space. We prove the existence and uniqueness of the solution in the Itô-Skorohod sense and obtain the lower and upper bounds for the $p$-th moment. The Hölder regularity of the solution is also studied.
Extensive work has demonstrated the excellent performance of orthogonal time frequency space (OTFS) modulation in high-mobility scenarios. Time-variant wideband channel estimation serves as one of the key compositions of OTFS receivers since the data detection requires accurate channel state information (CSI). In practical wideband OTFS systems, the Doppler shift brought by the high mobility is frequency-dependent, which is referred to as the Doppler Squint Effect (DSE). Unfortunately, DSE was ignored in overall prior estimation schemes employed in OTFS systems, which leads to severe performance loss in channel estimation and the consequent data detection. In this paper, we investigate DSE of wideband time-variant channel in delay-Doppler domain and concentrate on the characterization of OTFS channel coefficients considering DSE. The formulation and evaluation of OTFS input-output relationship are provided for both ideal and rectangular waveforms considering DSE. The channel estimation is therefore formulated as a sparse signal recovery problem and an orthogonal matching pursuit (OMP)-based scheme is adopted to solve it. Simulation results confirm the significance of DSE and the performance superiority compared with traditional channel estimation approaches ignoring DSE.
Although the multi-antenna or so-called multiple-input multiple-output (MIMO) transmission has been the enabling technology for the past generations of radio-frequency (RF)-based wireless communication systems, its application to the visible light communication (VLC) still faces a critical challenge as the MIMO spatial multiplexing gain can be hardly attained in VLC channels due to their strong spatial correlation. In this paper, we tackle this problem by deploying the optical intelligent reflecting surface (OIRS) in the environment to boost the capacity of MIMO VLC. Firstly, based on the extremely near-field channel condition in VLC, we propose a new channel model for OIRS-assisted MIMO VLC and reveal its peculiar ``no crosstalk'' property, where the OIRS reflecting elements can be respectively configured to align with one pair of transmitter and receiver antennas without causing crosstalk to each other. Next, we characterize the OIRS-assisted MIMO VLC capacities under different practical power constraints and then proceed to maximize them by jointly optimizing the OIRS element alignment and transmitter emission power. In particular, for optimizing the OIRS element alignment, we propose two algorithms, namely, location-aided interior-point algorithm and log-det-based alternating optimization algorithm, to balance the performance versus complexity trade-off; while the optimal transmitter emission power is derived in closed form. Numerical results are provided, which validate the capacity improvement of OIRS-assisted MIMO VLC against the VLC without OIRS and demonstrate the superior performance of the proposed algorithms compared to baseline schemes.
XL-MIMO promises to provide ultrahigh data rates in Terahertz (THz) spectrum. However, the spherical-wavefront wireless transmission caused by large aperture array presents huge challenges for channel state information (CSI) acquisition. Two independent parameters (physical angles and transmission distance) should be simultaneously considered in XL-MIMO beamforming, which brings severe overhead consumption and beamforming degradation. To address this problem, we exploit the near-field channel characteristic and propose one low-overhead hierarchical beam training scheme for near-field XL-MIMO system. Firstly, we project near-field channel into spatial-angular domain and slope-intercept domain to capture detailed representations. Secondly, a novel spatial-chirp beam-aided codebook and corresponding hierarchical update policy are proposed. Theoretical analyses and numerical simulations are also displayed to verify the superior performances on beamforming and training overhead.
This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two logics, namely the direct inversion and physics-informed neural networks (PINNs), are explored. The direct inversion entails three steps: (i) spectral denoising and differentiation of the full-field data, (ii) building appropriate neural maps to approximate the profile of unknown physical and regularization parameters on their respective domains, and (iii) simultaneous training of the neural networks by minimizing the Tikhonov-regularized PDE loss using data from (i). PINNs furnish efficient surrogate models of complex systems with predictive capabilities via multitask learning where the field variables are modeled by neural maps endowed with (scaler or distributed) auxiliary parameters such as physical unknowns and loss function weights. PINNs are then trained by minimizing a measure of data misfit subject to the underlying physical laws as constraints. In this study, to facilitate learning from ultrasonic data, the PINNs loss adopts (a) wavenumber-dependent Sobolev norms to compute the data misfit, and (b) non-adaptive weights in a specific scaling framework to naturally balance the loss objectives by leveraging the form of PDEs germane to elastic-wave propagation. Both paradigms are examined via synthetic and laboratory test data. In the latter case, the reconstructions are performed at multiple frequencies and the results are verified by a set of complementary experiments highlighting the importance of verification and validation in data-driven modeling.
We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable. In complex dimension 2, we show that any complete Kahler-Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to one of the model metrics constructed by Kobayashi and Nakamura arising from hyperbolic geometry.