arXiv subjects

Ming Xiao

Publications and source records attributed to Ming Xiao.

At least 19 recordsLinked to original sources

arXiv2026

Degree-Three Rational Sphere Maps: Sharp Denominator Region and Gram Normal Forms

We study degree-three rational sphere maps in two complex variables. After a standard normalization, the denominator of such a map takes the form \[ g_\sigma(z)=1+\sigma_1 z_1^2+\sigma_2 z_2^2, \qquad \sigma_1,\sigma_2\geq 0. \] A basic question is: which pairs $(\sigma_1,\sigma_2)$ can actually occur as the denominator of a degree-three rational sphere map? The first main result of the paper gives a complete answer: such a denominator occurs if and only if \[ 0\leq \sigma_1,\sigma_2<1, \qquad \sqrt{1-\sigma_1^2}+\sqrt{1-\sigma_2^2}>1. \] Our approach converts the sphere-mapping condition into a finite-dimensional Gram-matrix positivity problem. Furthermore, for each admissible parameter $ \sigma=(\sigma_1,\sigma_2), $ we determine all possible minimal target dimensions in which the corresponding denominator $g_\sigma$ can be realized. We also give a Gram-matrix normal form for maps with a fixed denominator and compute, for each admissible $\sigma$, the dimension of the moduli space of equivalence classes of rational sphere maps realizing $g_\sigma$. Finally, we extend the Gram-matrix method to arbitrary source dimension and obtain a general sufficient condition for the existence of degree-three rational sphere maps.

math.CV↗

arXiv2026

A new strong rigidity phenomenon for the Bergman metric

We establish a new local-to-global rigidity phenomenon for the Bergman metric. Namely, under natural geometric hypotheses, a local conformal identification of Bergman metrics determines the underlying complex manifold globally, up to the unavoidable ambiguity of removing Bergman-negligible subsets. More precisely, let $\Omega\subseteq\mathbb C^n$ be a bounded domain with a complete Bergman metric, and suppose that the Bergman metric of a complex manifold $M$ is locally conformal, via a holomorphic map $f$, to that of $\Omega$. We prove that the given local map $f$ extends to a biholomorphism $F\colon M\to D$ onto a subdomain $D\subseteq\Omega$ in two complementary settings. If $M$ is Stein, then $\Omega\setminus D$ is a closed pluripolar set. If $M$ is a bounded domain and $\Omega$ satisfies a natural symmetry condition expressed in terms of its automorphism orbits, then $\Omega\setminus D$ is Bergman-negligible. In particular, this applies when $\Omega$ is a bounded homogeneous domain and yields a characterization, up to Bergman-negligible sets, of bounded domains with locally symmetric Bergman metrics. The latter answers a question raised by Loi--Palmieri and Zimmer. A key ingredient in the proof is a new Calabi-type extension theorem tailored to Bergman metrics.

math.CV↗

arXiv2026

Resource-efficient Semantic Coding Schemes with Manifold-constrained Hyper-connections

Semantic communication (SemCom) and task-oriented communication (TOC) can reduce wireless resource consumption by focusing on transmitting semantic or task-relevant information instead of raw messages. In practice, a main challenge is to make transmitting information robust to channel noise and fading while keeping it compact. Existing learning-based transceivers often improve reliability by using larger encoders or higher-dimensional channel features, which increase computation complexity and channel uses. Therefore, optimized system design needs explicit rate control to balance performance and transmitting resources e.g., bandwidth and power. For this purpose, we propose a manifold-constrained hyper-connection (mHC) coding scheme with an entropy bottleneck (EB) for resource-efficient SemCom and TOC over wireless channels. Instead of using a single residual path of existing encoders, the proposed mHC-based semantic encoder applies multiple residual streams and constrains their interaction by doubly stochastic (DS) mixing matrices. The new structure improves representation diversity and training stability with negligible parameter and floating-point overhead. The EB quantizes the channel features and estimates the entropy-coded rate, enabling end-to-end rate--distortion/task optimization under bandwidth and transmit-power constraints. We further show that DS-constrained stream mixing does not increase the differential entropy of the transmitted features. This implies no increase in the ideal EB coding length. Experiments on SemCom and TOC under additive white Gaussian noise (AWGN), Rayleigh fading, Rician fading, and imperfect channel state information (CSI) show that the proposed scheme improves semantic/task performance, communication robustness, and convergence stability over residual and unconstrained HC baselines, while requiring no additional channel uses.

cs.IT↗

arXiv2026

The Kalman Evolve: Closing the Gap in Kalman Filtering via Interpretable Algorithm Discovery

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail in realistic sensing settings such as Doppler radar and LiDAR. In these cases, the optimal estimator is inherently nonlinear, which leads to systematic performance degradation. This creates a performance gap that cannot be eliminated by tuning the noise covariance parameters (i.e., the process and measurement noise in the Kalman Filter) alone. To address this limitation, we propose Kalman Evolve, a framework for discovering improved filtering algorithms by jointly optimizing both noise parameters and the update structure. Our approach leverages large language models (LLMs) as a structured prior over program space, enabling the generation of interpretable, non-affine modifications to the classical Kalman filter while preserving its recursive form. We provide analytical results establishing the suboptimality of affine estimators under common nonlinear sensing models, motivating the need for structure-aware updates. Across a range of synthetic and real-world tracking benchmarks, including Doppler radar, LiDAR-based localization, and pedestrian tracking, the discovered algorithms consistently improve over strong baselines such as the Optimized Kalman Filter, achieving up to 12\% reduction in RMSE. These results suggest that optimizing the structure of the Kalman filter, rather than only its parameters, provides a practical and interpretable way to improve state estimation.

cs.LG↗

arXiv2026

Abundance of Bergman metrics with constant positive holomorphic sectional curvature

An outstanding open question, which has attracted renewed attention following the pioneering work of Huang--Li--Treuer, is whether, for a given positive integer $m$, there exists a complex manifold whose Bergman metric is locally isometric to $m$ times the Fubini--Study metric. Previously, this question had only been resolved in the case $m=1$. In this paper, we construct, for any pair of positive integers $(m,n)$ with $n \geq 2$, an $\mathbb{R}$-parameter (hence uncountable) family of Reinhardt domains in $\mathbb{C}^n$ whose Bergman metrics are all locally isometric to $m$ times the Fubini--Study metric. Moreover, we show that the domains in this family are mutually Bergman inequivalent. This not only answers the folklore question, but also suggests that a reasonable classification of the geometry of such complex manifolds is infeasible. We also note such examples cannot exist in dimension one. The results complete the remaining open case in the study of complex manifolds whose Bergman space separates points and whose Bergman metric has constant holomorphic sectional curvature. Our approach differs from existing methods in the literature. We reduce the construction to a mapping problem and apply a Brouwer fixed point argument to establish the existence of the desired domains.

math.CV↗

arXiv2026

ITGPT: Generative Pretraining on Irregular Timeseries

Timeseries regression models often struggle to leverage large volumes of labeled multimodal data, particularly when the data are irregularly sampled or contain missing values. This is common in domains like healthcare and predictive maintenance, where data are collected from unreliable sources, and labeling requires expert knowledge or costly equipments. Transformer-based large language models have proven effective on structured data such as text through self-supervised learning (SSL) and generative pretraining (GPT) frameworks. However, such models lack the flexibility to efficiently process irregularly sampled multimodal timeseries data. In this paper, we introduce ITGPT, an attention-based architecture designed for handling multimodal, irregularly sampled timeseries by allowing training with both SSL losses and GPT-like objectives. We evaluate its performance on a healthcare task with the TIHM dataset, and a predictive maintenance task with the CompX dataset. Our results demonstrate that ITGPT achieves state-of-the-art performance without requiring resampling, feature fusion or explicit data imputation. Furthermore, when labels are scarce, ITGPT effectively leverages unlabeled data through SSL and GPT training, outperforming the purely supervised approach. This represents an important step towards efficiently using large and unstructured timeseries datasets for practical inference tasks.

cs.LG↗

arXiv2026

DriftDecode: One-Step Wireless Image Decoding via Drifting-Inspired Detail Recovery

Generative receivers for wireless image transmission can improve reconstruction quality, but diffusion-based and flow-based decoding relies on iterative inference and therefore incurs substantial latency. In wireless image transmission, however, the received signal already preserves the coarse structure of the source image. Wireless decoding is therefore better viewed as a recovery task than as image generation from scratch, and the main challenge lies in restoring channel-impaired details. Motivated by this recovery-oriented perspective, this paper proposes DriftDecode, a signal-to-noise ratio (SNR)-conditioned one-step decoder for wireless image reconstruction. DriftDecode couples a one-step U-Net decoder with a drift-inspired instance-level texture loss. The loss reformulates the drifting-field mechanism from generative drifting models in perceptual feature space, guiding each reconstructed local feature toward its spatially aligned ground-truth counterpart while suppressing mismatched textures. Experiments on DIV2K and MNIST under additive white Gaussian noise (AWGN) and Rayleigh fading channels show a favorable quality-latency tradeoff. DriftDecode achieves 30~ms decoding latency, providing a 4.8$\times$ speedup over a 10-step flow-matching decoder, while consistently outperforming MSE-only training and yielding up to 1.13~dB PSNR gain on MNIST under Rayleigh fading. These results support recovery-oriented one-step decoding as an effective alternative to iterative generative decoding for low-latency wireless image transmission.

eess.IV↗

arXiv2026

SkillCom: Decomposing LLM-based Semantic Communication into Task and Channel Aware Skills

Large language models (LLMs) are increasingly used as semantic encoders and decoders in semantic communication. However, current LLM based systems mostly remain monolithic: a single prompted model, or a tightly coupled transmitter/receiver pair, must jointly perform semantic encoding, channel adaptation, and semantic decoding. Such coupling makes intermediate decisions difficult to control, diagnose, or replace, and may cause channel corruption to propagate through a compressed source representation. To address the limitations, we propose \textbf{SkillCom}, a modular framework that decomposes LLM-based semantic communication into four explicit skills: semantic abstraction skill, channel-adaptive transmission skill, receiver-side repair skill, and task execution skill. These skills are interconnected through typed semantic-unit interfaces. Thus, transmission operates on structured unit-level representations rather than on one monolithic text block. This design localizes channel impairment, enables targeted repair from successfully received units, and supports stage-wise ablation and single-skill replacement under matched communication constraints. Experiments on multi-hop question answering and dialogue state tracking show that SkillCom consistently outperforms the monolithic LLM baseline, remains more robust under varying channel conditions, and exhibits task-dependent preferences over skill realizations. The results suggest that explicit skill decomposition provides a more robust and diagnosable foundation for LLM-based semantic communication than monolithic methods.

eess.SY↗

arXiv2026

Channel-coded Over-the-Air Computation

This letter studies channel coding for over-the-air computation (AirComp). AirComp enables efficient wireless data aggregation, where computation accuracy is the key performance metric. However, this accuracy is sensitive to channel impairments. As a promising solution, the role of channel coding in AirComp has been largely unexplored, creating a critical gap in achieving reliable AirComp systems. To address this, we propose a novel channel coding scheme tailored for AirComp that preserves the aggregation structure while mitigating channel distortions. We show that the computation error decreases with the coding rate and can asymptotically approach zero. Both theoretical and simulation results demonstrate that the proposed scheme significantly enhances computation performance.

cs.IT↗

arXiv2026

Perfectly Private Over-the-Air Computation

This paper studies a key research question: how to achieve perfect privacy in over-the-air computation (AirComp)? The problem is particularly intriguing due to a dilemma. Real-field operations can ensure invertibility but generally introduce statistical dependence, resulting in inevitable privacy leakage. In contrast, modulo operations can decorrelate the output from the original message, but suffer from the ill-posed invertibility when applied over non-prime groups (e.g., the real field). This raises a subtle yet fundamental question: Does perfect privacy intrinsically conflict with AirComp? We show that the answer is no. By carefully leveraging the interplay between real-field and modulo operations, perfect privacy and accurate computation can, in fact, be achieved simultaneously, enabling perfectly private aggregation.

cs.IT↗

arXiv2026

Pinching Antenna-Aided Spatial Multiplexing: Transceiver Design and Performance Analysis

In this paper, a novel pinching antenna-aided spatial multiplexing (PASM) architecture is conceived, which intrinsically amalgamates the benefits of flexible radiating element placement with radio-frequency (RF) chain transmission. Specifically, we leverage the deterministic phase variation along dielectric waveguides as a zero-power phase-control mechanism, where each waveguide fed by a single RF chain drives multiple pinching antennas (PAs) acquiring position-dependent phase shifts. Then, the PASM propagation environment is characterized by a realistic channel model encompassing Rician small-scale fading, correlated shadowing, and large-scale path loss. Based on this, a low-complexity vector approximate message passing (VAMP) detector is conceived, which exploits a waveguide-structured prior for jointly processing the signals associated with all PAs. Moreover, we derive an analytical upper bound on the bit error rate (BER) for the maximum likelihood (ML) detector to quantify the achievable performance limits. Finally, our simulation results demonstrate that the proposed PASM architecture achieves substantial signal-to-noise ratio (SNR) gain over the conventional phase-shifter-aided spatial multiplexing (PSSM), while the VAMP detector strikes an attractive trade-off between the system performance and computational complexity.

eess.SP↗

arXiv2026

Biased Compression in Gradient Coding for Distributed Learning

Communication bottlenecks and the presence of stragglers pose significant challenges in distributed learning (DL). To deal with these challenges, recent advances leverage unbiased compression functions and gradient coding. However, the significant benefits of biased compression remain largely unexplored. To close this gap, we propose Compressed Gradient Coding with Error Feedback (COCO-EF), a novel DL method that combines gradient coding with biased compression to mitigate straggler effects and reduce communication costs. In each iteration, non-straggler devices encode local gradients from redundantly allocated training data, incorporate prior compression errors, and compress the results using biased compression functions before transmission. The server aggregates these compressed messages from the non-stragglers to approximate the global gradient for model updates. We provide rigorous theoretical convergence guarantees for COCO-EF and validate its superior learning performance over baseline methods through empirical evaluations. As far as we know, we are among the first to rigorously demonstrate that biased compression has substantial benefits in DL, when gradient coding is employed to cope with stragglers.

cs.DC↗

arXiv2026

Byzantine-Robust and Communication-Efficient Distributed Training: Compressive and Cyclic Gradient Coding

In this paper, we study the problem of distributed training (DT) under Byzantine attacks with communication constraints. While prior work has developed various robust aggregation rules at the server to enhance robustness to Byzantine attacks, the existing methods suffer from a critical limitation in that the solution error does not diminish when the local gradients sent by different devices vary considerably, as a result of data heterogeneity among the subsets held by different devices. To overcome this limitation, we propose a novel DT method, cyclic gradient coding-based DT (LAD). In LAD, the server allocates the entire training dataset to the devices before training begins. In each iteration, it assigns computational tasks redundantly to the devices using cyclic gradient coding. Each honest device then computes local gradients on a fixed number of data subsets and encodes the local gradients before transmitting to the server. The server aggregates the coded vectors from the honest devices and the potentially incorrect messages from Byzantine devices using a robust aggregation rule. Leveraging the redundancy of computation across devices, the convergence performance of LAD is analytically characterized, demonstrating improved robustness against Byzantine attacks and significantly lower solution error. Furthermore, we extend LAD to a communication-efficient variant, compressive and cyclic gradient coding-based DT (Com-LAD), which further reduces communication overhead under constrained settings. Numerical results validate the effectiveness of the proposed methods in enhancing both Byzantine resilience and communication efficiency.

cs.DC↗

arXiv2026

Quantization-Aware Collaborative Inference for Large Embodied AI Models

Large artificial intelligence models (LAIMs) are increasingly regarded as a core intelligence engine for embodied AI applications. However, the massive parameter scale and computational demands of LAIMs pose significant challenges for resource-limited embodied agents. To address this issue, we investigate quantization-aware collaborative inference (co-inference) for embodied AI systems. First, we develop a tractable approximation for quantization-induced inference distortion. Based on this approximation, we derive lower and upper bounds on the quantization rate-inference distortion function, characterizing its dependence on LAIM statistics, including the quantization bit-width. Next, we formulate a joint quantization bit-width and computation frequency design problem under delay and energy constraints, aiming to minimize the distortion upper bound while ensuring tightness through the corresponding lower bound. Extensive evaluations validate the proposed distortion approximation, the derived rate-distortion bounds, and the effectiveness of the proposed joint design. Particularly, simulations and real-world testbed experiments demonstrate the effectiveness of the proposed joint design in balancing inference quality, latency, and energy consumption in edge embodied AI systems.

cs.LG↗

arXiv2026

LingxiDiagBench: A Multi-Agent Framework for Benchmarking LLMs in Chinese Psychiatric Consultation and Diagnosis

Mental disorders are highly prevalent worldwide, but the shortage of psychiatrists and the inherent subjectivity of interview-based diagnosis create substantial barriers to timely and consistent mental-health assessment. Progress in AI-assisted psychiatric diagnosis is constrained by the absence of benchmarks that simultaneously provide realistic patient simulation, clinician-verified diagnostic labels, and support for dynamic multi-turn consultation. We present LingxiDiagBench, a large-scale multi-agent benchmark that evaluates LLMs on both static diagnostic inference and dynamic multi-turn psychiatric consultation in Chinese. At its core is LingxiDiag-16K, a dataset of 16,000 EMR-aligned synthetic consultation dialogues designed to reproduce real clinical demographic and diagnostic distributions across 12 ICD-10 psychiatric categories. Through extensive experiments across state-of-the-art LLMs, we establish key findings: (1) although LLMs achieve high accuracy on binary depression--anxiety classification (up to 92.3%), performance deteriorates substantially for depression--anxiety comorbidity recognition (43.0%) and 12-way differential diagnosis (28.5%); (2) dynamic consultation often underperforms static evaluation, indicating that ineffective information-gathering strategies significantly impair downstream diagnostic reasoning; (3) consultation quality assessed by LLM-as-a-Judge shows only moderate correlation with diagnostic accuracy, suggesting that well-structured questioning alone does not ensure correct diagnostic decisions. We release LingxiDiag-16K and the full evaluation framework to support reproducible research at https://github.com/Lingxi-mental-health/LingxiDiagBench.

cs.AI↗

arXiv2026

ComAgent: Multi-LLM based Agentic AI Empowered Intelligent Wireless Networks

Emerging 6G networks rely on complex cross-layer optimization, yet manually translating high-level intents into mathematical formulations remains a bottleneck. While Large Language Models (LLMs) offer promise, monolithic approaches often lack sufficient domain grounding, constraint awareness, and verification capabilities. To address this, we present ComAgent, a multi-LLM agentic AI framework. ComAgent employs a closed-loop Perception-Planning-Action-Reflection cycle, coordinating specialized agents for literature search, coding, and scoring to autonomously generate solver-ready formulations and reproducible simulations. By iteratively decomposing problems and self-correcting errors, the framework effectively bridges the gap between user intent and execution. Evaluations demonstrate that ComAgent achieves expert-comparable performance in complex beamforming optimization and outperforms monolithic LLMs across diverse wireless tasks, highlighting its potential for automating design in emerging wireless networks.

cs.AI↗

arXiv2026

Coding-Enforced Resilient and Secure Aggregation for Hierarchical Federated Learning

Hierarchical federated learning (HFL) has emerged as an effective paradigm to enhance link quality between clients and the server. However, ensuring model accuracy while preserving privacy under unreliable communication remains a key challenge in HFL, as the coordination among privacy noise can be randomly disrupted. To address this limitation, we propose a robust hierarchical secure aggregation scheme, termed H-SecCoGC, which integrates coding strategies to enforce structured aggregation. The proposed scheme not only ensures accurate global model construction under varying levels of privacy, but also avoids the partial participation issue, thereby significantly improving robustness, privacy preservation, and learning efficiency. Both theoretical analyses and experimental results demonstrate the superiority of our scheme under unreliable communication across arbitrarily strong privacy guarantees

cs.LG↗

arXiv2026

On Resilient and Efficient Linear Secure Aggregation in Hierarchical Federated Learning

In this paper, we study the fundamental limits of hierarchical secure aggregation under unreliable communication. We consider a hierarchical network where each client connects to multiple relays, and both client-to-relay and relay-to-server links are intermittent. Under this setting, we characterize the minimum communication and randomness costs required to achieve robust secure aggregation. We then propose an optimal protocol that attains these minimum costs, and establish its optimality through a matching converse proof. In addition, we introduce an improved problem formulation that bridges the gap between existing information-theoretic secure aggregation protocols and practical real-world federated learning problems.

cs.DC↗