arXiv subjects
Publications and source records attributed to Cong Yao.
Given $h_o: \mathbb{S} \to \mathbb{S}$, an orientation-preserving homeomorphism of the unit circle, we seek to establish very weak conditions so as to derive a modulus of continuity for $h_o$ and its inverse $h_o^{-1}$, then use these to derive various compactness properties for families of circle homeomorphisms and solutions to Beltrami equations.
We study the hyperbolically weighted distortion energies \[ \mathcal{I}_p(f)=\int_\mathbb{D} \frac{|μ_f|^p}{(1-|μ_f|^2)^{\max\{2,p\}/2}}\,dA_η\] for finite-distortion disk homeomorphisms with prescribed boundary values, together with the associated inverse problem in the monotone Sobolev class. For $1 2$. \
A circle homeomorphism $β:\mathbb{S}\to\mathbb{S}$ is Weil--Petersson if it has a quasiconformal disk extension whose Beltrami coefficient is square integrable for hyperbolic area. We minimise the hyperbolic anti-holomorphic energy \[ E_2(h)=\int_\mathbb{D}η(h)|h_{\bar w}|^2,dA, \quad\text{equivalently}\quad \int_\mathbb{D}\frac{|μ_f|^2}{1-|μ_f|^2},dA_η,\quad f=h^{-1}, \] over all monotone Sobolev maps with boundary values $β$. For Weil--Petersson data, the unique minimiser is a real analytic hyperbolic harmonic diffeomorphism, globally quasiconformal and asymptotically conformal, with an explicit dilatation bound in terms of any admissible barrier's energy. We prove that a circle homeomorphism is Weil--Petersson if and only if it admits a finite-distortion homeomorphic extension satisfying \[ \int_\mathbb{D}(\mathbb{K}_F-1),dA_η<\infty. \] For every $p>1$, the boundary values of a finite-distortion homeomorphism satisfying \[ \int_\mathbb{D}|μ_F|^p(1-|μ_F|^2)^{-p_*/2},dA_η<\infty \] lie in Guo's $p$-integrable Teichm"uller space $T^p$. A capacity estimate for boundary moduli for the quasisymmetric ratio yields a derivative-free characterisation of $T^p$, essentially Bishop's theorem when $p=2$. The minimum defines a M"obius-invariant boundary energy, quantitatively comparable to the weighted square norm of the minimiser's Hopf differential. For arbitrary quasisymmetric data, we prove Markovi'c's theorem (the Schoen conjecture) by approximation with our smooth quadratic minimisers. Mori's theorem and the mean-value property of a logarithm verify the averaged-distance hypothesis in Riestenberg--Smillie's interior comparison, giving explicit displacement, energy-density and dilatation bounds in terms of the quasisymmetry constant. The nonquadratic ($p\neq2$) theory is developed in Part~II.
Cross-material magnetic core loss prediction requires adapting to new material responses with limited measurements. Global feature alignment overlooks differences in source and target excitation coverage. This motivates selecting comparable samples and controlling each source measurement's alignment contribution. This paper proposes T-PCOT, a Transformer transfer method based on condition-supported partial optimal transport. Frequency, flux excursion, temperature, and waveform descriptors define a sparse graph of comparable operating conditions. A capacity-constrained transport plan distributes alignment across source measurements and leaves costly target mass unmatched. The plan is constructed from measured inputs before training and guides local waveform-feature consistency. An importance-weighted sampling scheme preserves both uniform source regression and the transport objective during minibatch optimization. Experiments on three material pairs and three target label budgets show that T-PCOT reduces mean relative error (MRE) and 95th-percentile error (P95) relative to Transformer-based multiple-kernel maximum mean discrepancy (T-MKMMD) in all nine comparisons. Macro MRE decreases from 12.60% to 9.65%, and macro P95 from 30.94% to 25.06%, corresponding to relative reductions of 23.41% and 19.01%. Controlled comparisons and ablations examine the roles of input processing, condition correspondence, and source capacity. The results demonstrate the predictive advantage of organizing cross-material alignment through operating-condition support over the compared global alignment method. The proposed method achieves state-of-the-art predictive performance in magnetic core loss transfer learning.
Power magnetic materials are characterized on the sinusoidal and triangular waveforms that excitation hardware conveniently produces, whereas deployed converters expose cores to trapezoidal, PWM-shaped flux trajectories, so loss models must predict exactly where their training data are thinnest. The final test of the MagNet Challenge embeds a deliberately extreme instance of this characterization-deployment mismatch: for material D, trapezoids form 16.4% of the test set but only 1.4% of the training set. The 95th-percentile relative error, hereafter p95, of the best submission, built on sequential transfer learning, stalled at 15.9%, the worst among the five materials. This paper shows that the obstacle is missing information under covariate shift rather than class imbalance, and that the missing support can be borrowed from sibling materials instead of being extrapolated. Controlled experiments first refute the imbalance reading: four standard remedies fail, and raising the trapezoidal share to the test-set level degrades accuracy further. The proposed material-identity support transfer, MIST, then trains one 2784-parameter predictor jointly on all five challenge materials. Material identity enters through feature-wise linear modulation, or FiLM, the scarce material's true-label loss is reweighted, and material D receives no fine-tuning, so that the bias of its trapezoid-free training set is never re-installed. MIST lowers the five-seed material-D p95 from 20.39+/-2.03% to 12.38+/-0.92% and the trapezoidal-class p95 from 37.4+/-8.8% to 15.16+/-1.69%, surpassing the best submission with one-sixth of its parameters and no fine-tuning stage; removing material identity at matched capacity inflates the error by an order of magnitude. These results argue that scarce materials should be characterized jointly with their siblings.
Magnetic core loss originates in the hysteresis loop: the energy dissipated per excitation cycle equals the loop area, and frequency, temperature, and waveform shape set the loss by reshaping the loop geometry. Most existing models let these conditions act only on a terminal scalar - empirical equations fold them into fitted exponents, and data-driven predictors append them to encoded features - so no intermediate hysteresis representation remains for the conditions to reshape. This paper proposes CAHR-Net, a condition-adaptive hysteresis reconstruction network that injects the operating conditions where they physically act. It preserves the interpretable chain from flux density waveform to magnetic field reconstruction, loop-area integration, and power loss estimation, and uses feature-wise linear modulation to inject frequency, temperature, and waveform statistics into the intermediate reconstruction representation. A matched large-batch training protocol based on AdamW, cosine scheduling, and a staged reconstruction-to-power-loss objective is also reported, because the modulation pathway takes effect only within it. On the MagNet final A-E material protocol, CAHR-Net attains an average p95 relative error of 6.89% with only 1874 parameters, the lowest among all compared methods, together with a lower worst-material p95 than the strongest black-box solution at about 48x fewer parameters; it reduces the average p95 of the physical reconstruction backbone from 7.47% to 6.89% and the p95 of material D, the most difficult material, from 16.40% to 14.87%. Ablation and condition-slice analyses attribute the improvement to the coupling of physical loop reconstruction, structured condition modulation, and the matched optimization trajectory.
We consider minimisers in the homotopy class of a homeomorphism $f_0:R\to S$ between analytically finite Riemann surfaces with minimal $L^p$- conformal energy \[ \mathsf{E}_p(f:R,S)=\int_R \IK^p(z,f)\; dσ_R(z). \] The problem was first raised by Ahlfors in his celebrated proof of Teichmüller's theorem-the case $p=\infty$, but the existence, topological regularity and analytic regularity of these $L^p$ minimisers remained unknown for all $1<p<\infty$. Ahlfors established weak existence for $p\geq 2$. Here we prove that for all p, $1\leq p<\infty$, such minimisers exist, are unique and are diffeomorphisms. They are quasiconformal but not diffeomorphic at $p=\infty$.
We present GLM-5V-Turbo, a step toward native foundation models for multimodal agents. As foundation models are increasingly deployed in real environments, agentic capability depends not only on language reasoning, but also on the ability to perceive, interpret, and act over heterogeneous contexts such as images, videos, webpages, documents, GUIs. GLM-5V-Turbo is built around this objective: multimodal perception is integrated as a core component of reasoning, planning, tool use, and execution, rather than as an auxiliary interface to a language model. This report summarizes the main improvements behind GLM-5V-Turbo across model design, multimodal training, reinforcement learning, toolchain expansion, and integration with agent frameworks. These developments lead to strong performance in multimodal coding, visual tool use, and framework-based agentic tasks, while preserving competitive text-only coding capability. More importantly, our development process offers practical insights for building multimodal agents, highlighting the central role of multimodal perception, hierarchical optimization, and reliable end-to-end verification.
Here we advance the study of boundary the value problem for extremal functions of mean distortion and the associated Teichmüller spaces interpolating between the classical examples of extremal quasiconformal mappings, and the more recent approach through harmonic mappings (of extreme Dirichlet energy). In this paper we focus on the Alhfors-Hopf differential \[ Φ=\mathcal{A}(\mathbb{K}(w,h))h_w\,\overline{h_{\overline{w}}}\, η(h), \] where $h=f^{-1}$ is the pseudo-inverse of an extremal mapping $f$ for the problem \[ \inf_{f:\mathbb{D}\to\mathbb{D}}\int_\mathbb{D} \mathcal{A}(\mathbb{K}(z,f)) \; dz, \quad\quad \mathbb{K}(z,f) = \frac{|f_z|^2+|f_{\overline{z}}|^2}{|f_z|^2-|f_{\overline{z}}|^2}. \] where the infimum is taken over those homeomorphisms of finite distortion $f:\overline{\mathbb{D}}\to\overline{\mathbb{D}}$ with $f|\mathbb{S}=f_0$, typically a quasisymmetric barrier function. The inner-variational equations, an analogue of the Euler-Lagrange equations, show $Φ$ is holomorphic at an extremal. Exploiting this Ahlfors-Hopf differential, we prove that an extreme point $f$ is a local diffeomorphism in $\mathbb{D}$, resolving some conjectures in [16].
Accurate core loss modeling is critical for the design of high-efficiency power electronic systems. Traditional core loss modeling methods have limitations in prediction accuracy. To advance this field, the IEEE Power Electronics Society launched the MagNet Challenge in 2023, the first international competition focused on data-driven power electronics design methods, aiming to uncover complex loss patterns in magnetic components through a data-driven paradigm. Although purely data-driven models demonstrate strong fitting performance, their interpretability and cross-distribution generalization capabilities remain limited. To address these issues, this paper proposes a hybrid model, SEPI-TFPNet, which integrates empirical models with deep learning. The physical-prior submodule employs a spectral entropy discrimination mechanism to select the most suitable empirical model under different excitation waveforms. The data-driven submodule incorporates convolutional neural networks, multi-head attention mechanisms, and bidirectional long short-term memory networks to extract flux-density time-series features. An adaptive feature fusion module is introduced to improve multimodal feature interaction and integration. Using the MagNet dataset containing various magnetic materials, this paper evaluates the proposed method and compares it with 21 representative models from the 2023 challenge and three advanced methods from 2024-2025. The results show that the proposed method achieves improved modeling accuracy and robustness.
We establish that the $p$-conformal energy, $p\geq 1$, defined by the $L^p$-norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller space of Riemann surfaces of a fixed genus. This result is an application of a result herein identifying explicitly both the unique extremal mappings of finite distortion between hyperbolic annuli of given modulus, and their $p$-conformal energy.
Multi-modal document pre-trained models have proven to be very effective in a variety of visually-rich document understanding (VrDU) tasks. Though existing document pre-trained models have achieved excellent performance on standard benchmarks for VrDU, the way they model and exploit the interactions between vision and language on documents has hindered them from better generalization ability and higher accuracy. In this work, we investigate the problem of vision-language joint representation learning for VrDU mainly from the perspective of supervisory signals. Specifically, a pre-training paradigm called Bi-VLDoc is proposed, in which a bidirectional vision-language supervision strategy and a vision-language hybrid-attention mechanism are devised to fully explore and utilize the interactions between these two modalities, to learn stronger cross-modal document representations with richer semantics. Benefiting from the learned informative cross-modal document representations, Bi-VLDoc significantly advances the state-of-the-art performance on three widely-used document understanding benchmarks, including Form Understanding (from 85.14% to 93.44%), Receipt Information Extraction (from 96.01% to 97.84%), and Document Classification (from 96.08% to 97.12%). On Document Visual QA, Bi-VLDoc achieves the state-of-the-art performance compared to previous single model methods.
Visual Information Extraction (VIE), aiming at extracting structured information from visually rich document images, plays a pivotal role in document processing. Considering various layouts, semantic scopes, and languages, VIE encompasses an extensive range of types, potentially numbering in the thousands. However, many of these types suffer from a lack of training data, which poses significant challenges. In this paper, we propose a novel generative model, named Generative Compositor, to address the challenge of few-shot VIE. The Generative Compositor is a hybrid pointer-generator network that emulates the operations of a compositor by retrieving words from the source text and assembling them based on the provided prompts. Furthermore, three pre-training strategies are employed to enhance the model's perception of spatial context information. Besides, a prompt-aware resampler is specially designed to enable efficient matching by leveraging the entity-semantic prior contained in prompts. The introduction of the prompt-based retrieval mechanism and the pre-training strategies enable the model to acquire more effective spatial and semantic clues with limited training samples. Experiments demonstrate that the proposed method achieves highly competitive results in the full-sample training, while notably outperforms the baseline in the 1-shot, 5-shot, and 10-shot settings.
Recently, large language models (LLMs) and multimodal large language models (MLLMs) have demonstrated promising results on document visual question answering (VQA) task, particularly after training on document instruction datasets. An effective evaluation method for document instruction data is crucial in constructing instruction data with high efficacy, which, in turn, facilitates the training of LLMs and MLLMs for document VQA. However, most existing evaluation methods for instruction data are limited to the textual content of the instructions themselves, thereby hindering the effective assessment of document instruction datasets and constraining their construction. In this paper, we propose ProcTag, a data-oriented method that assesses the efficacy of document instruction data. ProcTag innovatively performs tagging on the execution process of instructions rather than the instruction text itself. By leveraging the diversity and complexity of these tags to assess the efficacy of the given dataset, ProcTag enables selective sampling or filtering of document instructions. Furthermore, DocLayPrompt, a novel semi-structured layout-aware document prompting strategy, is proposed for effectively representing documents. Experiments demonstrate that sampling existing open-sourced and generated document VQA/instruction datasets with ProcTag significantly outperforms current methods for evaluating instruction data. Impressively, with ProcTag-based sampling in the generated document datasets, only 30.5\% of the document instructions are required to achieve 100\% efficacy compared to the complete dataset. The code is publicly available at https://github.com/AlibabaResearch/AdvancedLiterateMachinery/tree/main/DocumentUnderstanding/ProcTag.
Recently, with the rapid advancements of generative models, the field of visual text generation has witnessed significant progress. However, it is still challenging to render high-quality text images in real-world scenarios, as three critical criteria should be satisfied: (1) Fidelity: the generated text images should be photo-realistic and the contents are expected to be the same as specified in the given conditions; (2) Reasonability: the regions and contents of the generated text should cohere with the scene; (3) Utility: the generated text images can facilitate related tasks (e.g., text detection and recognition). Upon investigation, we find that existing methods, either rendering-based or diffusion-based, can hardly meet all these aspects simultaneously, limiting their application range. Therefore, we propose in this paper a visual text generator (termed SceneVTG), which can produce high-quality text images in the wild. Following a two-stage paradigm, SceneVTG leverages a Multimodal Large Language Model to recommend reasonable text regions and contents across multiple scales and levels, which are used by a conditional diffusion model as conditions to generate text images. Extensive experiments demonstrate that the proposed SceneVTG significantly outperforms traditional rendering-based methods and recent diffusion-based methods in terms of fidelity and reasonability. Besides, the generated images provide superior utility for tasks involving text detection and text recognition. Code and datasets are available at AdvancedLiterateMachinery.
End-to-end visual information extraction (VIE) aims at integrating the hierarchical subtasks of VIE, including text spotting, word grouping, and entity labeling, into a unified framework. Dealing with the gaps among the three subtasks plays a pivotal role in designing an effective VIE model. OCR-dependent methods heavily rely on offline OCR engines and inevitably suffer from OCR errors, while OCR-free methods, particularly those employing a black-box model, might produce outputs that lack interpretability or contain hallucinated content. Inspired by CenterNet, DeepSolo, and ESP, we propose HIP, which models entities as HIerarchical Points to better conform to the hierarchical nature of the end-to-end VIE task. Specifically, such hierarchical points can be flexibly encoded and subsequently decoded into desired text transcripts, centers of various regions, and categories of entities. Furthermore, we devise corresponding hierarchical pre-training strategies, categorized as image reconstruction, layout learning, and language enhancement, to reinforce the cross-modality representation of the hierarchical encoders. Quantitative experiments on public benchmarks demonstrate that HIP outperforms previous state-of-the-art methods, while qualitative results show its excellent interpretability.
We consider minimisers of the $p$-exponential conformal energy for homeomorphisms $f:R \to S$ of finite distortion $\IK(z,f)$ between analytically finite Riemann surfaces in a fixed homotopy class $[f_0]$,\[ \mE_p(f:R,S)=\int_R \exp(p\IK(z,f))\; dσ(z). \] Homeomorphic minimisers exist should the barrier be a homeomorphism of finite energy, $\mE_p(f_0,R,S)<\infty$. In general this problem is not variational, however the Euler-Lagrange equations show the inverses $h=f^{-1}$ of sufficiently regular stationary solutions have an associated holomorphic quadratic differential -- the Ahlfors-Hopf differential, \[Φ=\exp(p\IK(w,h))\,h_w\overline{h_\wbar}\,dσ_R(h). \] From the Riemann-Roch theorem and an approximation technique, we show the variational equations hold for extremal mappings. We take this as a starting point for higher regularity to show that if $h:Ω\to\tildeΩ$ is a Sobolev homeomorphism between planar domains with holomorphic Ahlfors-Hopf differential, then $h$ is a diffeomorphism. It will follow that $h$ is harmonic in a metric induced by its own (smooth) distortion. We develop equations for the Beltrami coefficient of $h$, establishing a connection between degenerate elliptic non-linear Beltrami equations and these harmonic mappings. On the surface we conclude that minimisers $f_p\in [f_0]$ of $\mE_p(f:R,S)$ are diffeomorphisms and are unique stationary points. This now links two different approaches to Teichmüller theory; the classical theory of extremal quasiconformal maps and the harmonic mapping theory. As $p\to\infty$ we show $f_p\to f_\infty$ to recover the unique extremal quasiconformal mapping . This extremal quasiconformal mapping is not a diffeomorphism (unless it is conformal) and $f_p$ degenerates on a divisor. As $p\to0$ we recover the harmonic diffeomorphism in $[f_0]$ and Shoen-Yau's results.
Text recognition is an inherent integration of vision and language, encompassing the visual texture in stroke patterns and the semantic context among the character sequences. Towards advanced text recognition, there are three key challenges: (1) an encoder capable of representing the visual and semantic distributions; (2) a decoder that ensures the alignment between vision and semantics; and (3) consistency in the framework during pre-training, if it exists, and fine-tuning. Inspired by masked autoencoding, a successful pre-training strategy in both vision and language, we propose an innovative scene text recognition approach, named VL-Reader. The novelty of the VL-Reader lies in the pervasive interplay between vision and language throughout the entire process. Concretely, we first introduce a Masked Visual-Linguistic Reconstruction (MVLR) objective, which aims at simultaneously modeling visual and linguistic information. Then, we design a Masked Visual-Linguistic Decoder (MVLD) to further leverage masked vision-language context and achieve bi-modal feature interaction. The architecture of VL-Reader maintains consistency from pre-training to fine-tuning. In the pre-training stage, VL-Reader reconstructs both masked visual and text tokens, while in the fine-tuning stage, the network degrades to reconstruct all characters from an image without any masked regions. VL-reader achieves an average accuracy of 97.1% on six typical datasets, surpassing the SOTA by 1.1%. The improvement was even more significant on challenging datasets. The results demonstrate that vision and language reconstructor can serve as an effective scene text recognizer.