arXiv subjects

Hao Zhang

Publications and source records attributed to Hao Zhang.

At least 613 records · Page 34Linked to original sources

arXiv2024

Quantum K Whitney relations for partial flag varieties

In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by proving a Nakayama type result for quantum K theory: if the conjectured set of relations deforms a complete set of relations of the classical K theory ring, then they must form a complete set of relations for the quantum K ring. We prove the conjectured presentation in the case of the incidence varieties, and we show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety. Finally, we briefly revisit the change of variables relating the mathematics and physics presentations.

math.AG↗

arXiv2024

Multipolar Skyrmion Crystals in Non-Kramers Doublet Systems

We study the Kondo lattice model of multipolar magnetic moments interacting with conduction electrons on a triangular lattice. Bond-dependent electron hoppings induce a compass-like anisotropy in the effective Ruderman-Kittel-Kasuya-Yosida interaction between multipolar moments. This unique anisotropy stabilizes multipolar skyrmion crystals at zero magnetic field. In a unit cell, the skyrmion fractionalizes into meron composites subject to the conservation of total topological charge. Diverse multipolar phases in the phase diagram give rise to novel spontaneous Hall response of conduction electrons.

cond-mat.str-el↗

arXiv2024

Boundedness of operator-valued commutators involving martingale paraproducts

Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[π_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $π_a$ is the $d$-adic martingale paraproduct with symbol $a\in BMO^d(\mathbb{R})$ and $M_b$ is the noncommutative left multiplication operator with $b\in BMO^d_\mathcal{M}(\mathbb{R})$. Besides, we consider the extrapolation property of semicommutative $d$-adic martingale paraproducts in terms of the $BMO^d_\mathcal{M}(\mathbb{R})$ space.

math.OA↗

arXiv2024

On the best constants of the noncommutative Littlewood-Paley-Stein inequalities

Let $1 0}$ be a noncommutative symmetric diffusion semigroup on a semifinite von Neumann algebra $\mathcal{M}$, and let $\{P_t\}_{t>0}$ be its associated subordinated Poisson semigroup. The celebrated noncommutative Littlewood-Paley-Stein inequality asserts that for any $x\in L_p(\mathcal{M})$, \begin{equation*} α_p^{-1}\|x\|_{p}\le \|x\|_{p,P}\le β_p \|x\|_{p}, \end{equation*} where $\|\cdot\|_{p,P}$ is the $L_p(\mathcal{M})$-norm of square functions associated with $\{P_t\}_{t>0}$, and $α_p, β_p$ are the best constants only depending on $p$. We show that as $p\to \infty$, $$ β_p\lesssim p, $$ and $p$ is the optimal possible order of $β_p$ as well. We also obtain some lower and upper bounds of $α_p$ and $β_p$ in the other cases.

math.OA↗

arXiv2024

Complex median method and Schatten class membership of commutators

This article is devoted to the study of the Schatten class membership of commutators involving singular integral operators. We utilize martingale paraproducts and Hytönen's dyadic martingale technique to obtain sufficient conditions on the weak-type and strong-type Schatten class membership of commutators in terms of Sobolev spaces and Besov spaces respectively. We also establish the complex median method, which is applicable to complex-valued functions. We apply it to get the optimal necessary conditions on the weak-type and strong-type Schatten class membership of commutators associated with non-degenerate kernels. This resolves the problem on the characterization of the weak-type and strong-type Schatten class membership of commutators. Our new approach is built on Hytönen's dyadic martingale technique and the complex median method. Compared with all the previous ones, this new one is more powerful in several aspects: $(a)$ it permits us to deal with more general singular integral operators with little smoothness; $(b)$ it allows us to deal with commutators with complex-valued kernels; $(c)$ it turns out to be powerful enough to deal with the weak-type and strong-type Schatten class of commutators in a universal way.

math.FA↗

arXiv2024

When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System

Artificial intelligence (AI) has significantly advanced Earth sciences, yet its full potential in to comprehensively modeling Earth's complex dynamics remains unrealized. Geoscience foundation models (GFMs) emerge as a paradigm-shifting solution, integrating extensive cross-disciplinary data to enhance the simulation and understanding of Earth system dynamics. These data-centric AI models extract insights from petabytes of structured and unstructured data, effectively addressing the complexities of Earth systems that traditional models struggle to capture. The unique strengths of GFMs include flexible task specification, diverse input-output capabilities, and multi-modal knowledge representation, enabling analyses that surpass those of individual data sources or traditional AI methods. This review not only highlights the key advantages of GFMs, but also presents essential techniques for their construction, with a focus on transformers, pre-training, and adaptation strategies. Subsequently, we examine recent advancements in GFMs, including large language models, vision models, and vision-language models, particularly emphasizing the potential applications in remote sensing. Additionally, the review concludes with a comprehensive analysis of the challenges and future trends in GFMs, addressing five critical aspects: data integration, model complexity, uncertainty quantification, interdisciplinary collaboration, and concerns related to privacy, trust, and security. This review offers a comprehensive overview of emerging geoscientific research paradigms, emphasizing the untapped opportunities at the intersection of advanced AI techniques and geoscience. It examines major methodologies, showcases advances in large-scale models, and discusses the challenges and prospects that will shape the future landscape of GFMs.

cs.AI↗

arXiv2024

Cross-Domain Pre-training with Language Models for Transferable Time Series Representations

Advancements in self-supervised pre-training (SSL) have significantly advanced the field of learning transferable time series representations, which can be very useful in enhancing the downstream task. Despite being effective, most existing works struggle to achieve cross-domain SSL pre-training, missing valuable opportunities to integrate patterns and features from different domains. The main challenge lies in the significant differences in the characteristics of time-series data across different domains, such as variations in the number of channels and temporal resolution scales. To address this challenge, we propose CrossTimeNet, a novel cross-domain SSL learning framework to learn transferable knowledge from various domains to largely benefit the target downstream task. One of the key characteristics of CrossTimeNet is the newly designed time series tokenization module, which could effectively convert the raw time series into a sequence of discrete tokens based on a reconstruction optimization process. Besides, we highlight that predicting a high proportion of corrupted tokens can be very helpful for extracting informative patterns across different domains during SSL pre-training, which has been largely overlooked in past years. Furthermore, unlike previous works, our work treats the pre-training language model (PLM) as the initialization of the encoder network, investigating the feasibility of transferring the knowledge learned by the PLM to the time series area. Through these efforts, the path to cross-domain pre-training of a generic time series model can be effectively paved. We conduct extensive experiments in a real-world scenario across various time series classification domains. The experimental results clearly confirm CrossTimeNet's superior performance.

cs.LG↗

arXiv2024

Linear and Nonlinear Coupling of Light in Twin-Resonators with Kerr Nonlinearity

Nonlinear effects in microresonators are efficient building blocks for all-optical computing and telecom systems. With the latest advances in microfabrication, coupled microresonators are used in a rapidly growing number of applications. In this work, we investigate the coupling between twin-resonators in the presence of Kerr-nonlinearity. We use an experimental setup with controllable coupling between two high-Q resonators and discuss the effects caused by the simultaneous presence of linear and non-linear coupling between the optical fields. Linear-coupling-induced mode splitting is observed at low input powers, with the controllable coupling leading to a tunable mode splitting. At high input powers, the hybridized resonances show spontaneous symmetry breaking (SSB) effects, in which the optical power is unevenly distributed between the resonators. Our experimental results are supported by a detailed theoretical model of nonlinear twin-resonators. With the recent interest in coupled resonator systems for neuromorphic computing, quantum systems, and optical frequency comb generation, our work provides important insights into the behavior of these systems at high circulating powers.

physics.optics↗

arXiv2024

Text-DiFuse: An Interactive Multi-Modal Image Fusion Framework based on Text-modulated Diffusion Model

Existing multi-modal image fusion methods fail to address the compound degradations presented in source images, resulting in fusion images plagued by noise, color bias, improper exposure, \textit{etc}. Additionally, these methods often overlook the specificity of foreground objects, weakening the salience of the objects of interest within the fused images. To address these challenges, this study proposes a novel interactive multi-modal image fusion framework based on the text-modulated diffusion model, called Text-DiFuse. First, this framework integrates feature-level information integration into the diffusion process, allowing adaptive degradation removal and multi-modal information fusion. This is the first attempt to deeply and explicitly embed information fusion within the diffusion process, effectively addressing compound degradation in image fusion. Second, by embedding the combination of the text and zero-shot location model into the diffusion fusion process, a text-controlled fusion re-modulation strategy is developed. This enables user-customized text control to improve fusion performance and highlight foreground objects in the fused images. Extensive experiments on diverse public datasets show that our Text-DiFuse achieves state-of-the-art fusion performance across various scenarios with complex degradation. Moreover, the semantic segmentation experiment validates the significant enhancement in semantic performance achieved by our text-controlled fusion re-modulation strategy. The code is publicly available at https://github.com/Leiii-Cao/Text-DiFuse.

cs.CV↗

arXiv2024

Unsupervised Modality Adaptation with Text-to-Image Diffusion Models for Semantic Segmentation

Despite their success, unsupervised domain adaptation methods for semantic segmentation primarily focus on adaptation between image domains and do not utilize other abundant visual modalities like depth, infrared and event. This limitation hinders their performance and restricts their application in real-world multimodal scenarios. To address this issue, we propose Modality Adaptation with text-to-image Diffusion Models (MADM) for semantic segmentation task which utilizes text-to-image diffusion models pre-trained on extensive image-text pairs to enhance the model's cross-modality capabilities. Specifically, MADM comprises two key complementary components to tackle major challenges. First, due to the large modality gap, using one modal data to generate pseudo labels for another modality suffers from a significant drop in accuracy. To address this, MADM designs diffusion-based pseudo-label generation which adds latent noise to stabilize pseudo-labels and enhance label accuracy. Second, to overcome the limitations of latent low-resolution features in diffusion models, MADM introduces the label palette and latent regression which converts one-hot encoded labels into the RGB form by palette and regresses them in the latent space, thus ensuring the pre-trained decoder for up-sampling to obtain fine-grained features. Extensive experimental results demonstrate that MADM achieves state-of-the-art adaptation performance across various modality tasks, including images to depth, infrared, and event modalities. We open-source our code and models at https://github.com/XiaRho/MADM.

cs.CV↗

arXiv2024

DiffusionVel: Multi-Information Integrated Velocity Inversion Using Generative Diffusion Models

Full waveform inversion (FWI) is capable of reconstructing subsurface properties with high resolution from seismic data. However, conventional FWI faces challenges such as cycle-skipping and high computational costs. Recently, deep learning method has emerged as a promising solution for efficient velocity estimation. We develop DiffusionVel, a data-driven technique based on the state-of-the-art generative diffusion models (GDMs) with integration of multiple information including seismic data, background velocity, geological knowledge, and well logs. We use two separate conditional GDMs, namely the seismic-data GDM and the well-log GDM, and an unconditional GDM, i.e., the geology-oriented GDM, to adapt the generated velocity model to the constraints of seismic data, well logs, and prior geological knowledge, respectively. Besides, the background velocity can be incorporated into the generated velocity model with a low-pass filter. The generation of these GDM are then combined together with a weighted summation in the sampling process. We can flexibly control the constraints from each information by adjusting the weighting factors. We make a comprehensive comparison between the proposed DiffusionVel and three previously-developed methods including conventional FWI, InversionNet, and VelocityGAN by using the OpenFWI datasets and the Hess VTI model example. The test results demonstrate that the proposed DiffusionVel method predicts the velocity model reasonably by integrating multiple information effectively.

physics.geo-ph↗

arXiv2024

LLaVA-OneVision: Easy Visual Task Transfer

We present LLaVA-OneVision, a family of open large multimodal models (LMMs) developed by consolidating our insights into data, models, and visual representations in the LLaVA-NeXT blog series. Our experimental results demonstrate that LLaVA-OneVision is the first single model that can simultaneously push the performance boundaries of open LMMs in three important computer vision scenarios: single-image, multi-image, and video scenarios. Importantly, the design of LLaVA-OneVision allows strong transfer learning across different modalities/scenarios, yielding new emerging capabilities. In particular, strong video understanding and cross-scenario capabilities are demonstrated through task transfer from images to videos.

cs.CV↗

arXiv2024

Cavity dark mode mediated by atom array without atomic scattering loss

We realize a ring cavity strongly interacting with an atom array with configurable spatial structures. By preparing the atom array with a maximized structure factor, we observe the emergence of a cavity dark mode, where the standing-wave nodes are dynamically locked to the positions of the atoms. The dark mode is decoupled from the atoms, protecting the system from dissipation through atomic scattering, but still mediates strong coupling and enables efficient conversion between two optical modes. Moreover, we impart an arbitrary large phase shift on the converted optical fields by translating the atom array. This strongly interacting ring cavity system with single-atom addressability opens ways to quantum optical engineering and the generation of photonic quantum states based on the geometrical structure of atom arrays.

quant-ph↗

arXiv2024

Neuroevolution Neural Architecture Search for Evolving RNNs in Stock Return Prediction and Portfolio Trading

Stock return forecasting is a major component of numerous finance applications. Predicted stock returns can be incorporated into portfolio trading algorithms to make informed buy or sell decisions which can optimize returns. In such portfolio trading applications, the predictive performance of a time series forecasting model is crucial. In this work, we propose the use of the Evolutionary eXploration of Augmenting Memory Models (EXAMM) algorithm to progressively evolve recurrent neural networks (RNNs) for stock return predictions. RNNs are evolved independently for each stocks and portfolio trading decisions are made based on the predicted stock returns. The portfolio used for testing consists of the 30 companies in the Dow-Jones Index (DJI) with each stock have the same weight. Results show that using these evolved RNNs and a simple daily long-short strategy can generate higher returns than both the DJI index and the S&P 500 Index for both 2022 (bear market) and 2023 (bull market).

q-fin.PM↗

arXiv2024

Learning to Generate and Evaluate Fact-checking Explanations with Transformers

In an era increasingly dominated by digital platforms, the spread of misinformation poses a significant challenge, highlighting the need for solutions capable of assessing information veracity. Our research contributes to the field of Explainable Artificial Antelligence (XAI) by developing transformer-based fact-checking models that contextualise and justify their decisions by generating human-accessible explanations. Importantly, we also develop models for automatic evaluation of explanations for fact-checking verdicts across different dimensions such as \texttt{(self)-contradiction}, \texttt{hallucination}, \texttt{convincingness} and \texttt{overall quality}. By introducing human-centred evaluation methods and developing specialised datasets, we emphasise the need for aligning Artificial Intelligence (AI)-generated explanations with human judgements. This approach not only advances theoretical knowledge in XAI but also holds practical implications by enhancing the transparency, reliability and users' trust in AI-driven fact-checking systems. Furthermore, the development of our metric learning models is a first step towards potentially increasing efficiency and reducing reliance on extensive manual assessment. Based on experimental results, our best performing generative model \textsc{ROUGE-1} score of 47.77, demonstrating superior performance in generating fact-checking explanations, particularly when provided with high-quality evidence. Additionally, the best performing metric learning model showed a moderately strong correlation with human judgements on objective dimensions such as \texttt{(self)-contradiction and \texttt{hallucination}, achieving a Matthews Correlation Coefficient (MCC) of around 0.7.}

cs.CL↗

arXiv2024

The Generation of All Regular Rational Orthogonal Matrices

A \emph{rational orthogonal matrix} $Q$ is an orthogonal matrix with rational entries, and $Q$ is called \emph{regular} if each of its row sum equals one, i.e., $Qe = e$ where $e$ is the all-one vector. This paper presents a method for generating all regular rational orthogonal matrices using the classic Cayley transformation. Specifically, we demonstrate that for any regular rational orthogonal matrix $Q$, there exists a permutation matrix $P$ such that $QP$ does not possess an eigenvalue of $-1$. Consequently, $Q$ can be expressed in the form $Q = (I_n + S)^{-1}(I_n - S)P$, where $I_n$ is the identity matrix of order $n$, $S$ is a rational skew-symmetric matrix satisfying $Se = 0$, and $P$ is a permutation matrix. Central to our approach is a pivotal intermediate result, which holds independent interest: given a square matrix $M$, then $MP$ has $-1$ as an eigenvalue for every permutation matrix $P$ if and only if either every row sum of $M$ is $-1$ or every column sum of $M$ is $-1$.

math.CO↗

arXiv2024

AdaMoE: Token-Adaptive Routing with Null Experts for Mixture-of-Experts Language Models

Mixture of experts (MoE) has become the standard for constructing production-level large language models (LLMs) due to its promise to boost model capacity without causing significant overheads. Nevertheless, existing MoE methods usually enforce a constant top-k routing for all tokens, which is arguably restrictive because various tokens (e.g., " " vs. "apple") may require various numbers of experts for feature abstraction. Lifting such a constraint can help make the most of limited resources and unleash the potential of the model for downstream tasks. In this sense, we introduce AdaMoE to realize token-adaptive routing for MoE, where different tokens are permitted to select a various number of experts. AdaMoE makes minimal modifications to the vanilla MoE with top-k routing -- it simply introduces a fixed number of null experts, which do not consume any FLOPs, to the expert set and increases the value of k. AdaMoE does not force each token to occupy a fixed number of null experts but ensures the average usage of the null experts with a load-balancing loss, leading to an adaptive number of null/true experts used by each token. AdaMoE exhibits a strong resemblance to MoEs with expert choice routing while allowing for trivial auto-regressive modeling. AdaMoE is easy to implement and can be effectively applied to pre-trained (MoE-)LLMs. Extensive studies show that AdaMoE can reduce average expert load (FLOPs) while achieving superior performance. For example, on the ARC-C dataset, applying our method to fine-tuning Mixtral-8x7B can reduce FLOPs by 14.5% while increasing accuracy by 1.69%.

cs.AI↗

arXiv2024

Scalable Weibull Graph Attention Autoencoder for Modeling Document Networks

Although existing variational graph autoencoders (VGAEs) have been widely used for modeling and generating graph-structured data, most of them are still not flexible enough to approximate the sparse and skewed latent node representations, especially those of document relational networks (DRNs) with discrete observations. To analyze a collection of interconnected documents, a typical branch of Bayesian models, specifically relational topic models (RTMs), has proven their efficacy in describing both link structures and document contents of DRNs, which motives us to incorporate RTMs with existing VGAEs to alleviate their potential issues when modeling the generation of DRNs. In this paper, moving beyond the sophisticated approximate assumptions of traditional RTMs, we develop a graph Poisson factor analysis (GPFA), which provides analytic conditional posteriors to improve the inference accuracy, and extend GPFA to a multi-stochastic-layer version named graph Poisson gamma belief network (GPGBN) to capture the hierarchical document relationships at multiple semantic levels. Then, taking GPGBN as the decoder, we combine it with various Weibull-based graph inference networks, resulting in two variants of Weibull graph auto-encoder (WGAE), equipped with model inference algorithms. Experimental results demonstrate that our models can extract high-quality hierarchical latent document representations and achieve promising performance on various graph analytic tasks.

cs.LG↗