arXiv subjects

Zhiyu Zhang

Publications and source records attributed to Zhiyu Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Central values of Asai L-functions and twisted Gan--Gross--Prasad conjecture

We study certain new relative trace formulas on (non-reductive) period integrals involving Weil representations, in the context of the relative Langlands program. We study normal representatives using Galois theory, and establish geometric decompositions of relative trace formulas using normal representatives for good test functions. By comparing global representatives, local distributions and orbital integrals, we prove the twisted Gan--Gross--Prasad (GGP) conjecture on Asai L-functions, in any dimension under some local assumptions, allowing ramifications of number fields.

math.NT↗

arXiv2025

Holographic Transformers for Complex-Valued Signal Processing: Integrating Phase Interference into Self-Attention

Complex-valued signals encode both amplitude and phase, yet most deep models treat attention as real-valued correlation, overlooking interference effects. We introduce the Holographic Transformer, a physics-inspired architecture that incorporates wave interference principles into self-attention. Holographic attention modulates interactions by relative phase and coherently superimposes values, ensuring consistency between amplitude and phase. A dual-headed decoder simultaneously reconstructs the input and predicts task outputs, preventing phase collapse when losses prioritize magnitude over phase. We demonstrate that holographic attention implements a discrete interference operator and maintains phase consistency under linear mixing. Experiments on PolSAR image classification and wireless channel prediction show strong performance, achieving high classification accuracy and F1 scores, low regression error, and increased robustness to phase perturbations. These results highlight that enforcing physical consistency in attention leads to generalizable improvements in complex-valued learning and provides a unified, physics-based framework for coherent signal modeling. The code is available at https://github.com/EonHao/Holographic-Transformers.

eess.SP↗

arXiv2025

Colossal Cryogenic Electro-Optic Response Through Metastability in Strained BaTiO$_{3}$ Thin Films

The search for thin film electro-optic (EO) materials that can retain superior performance under cryogenic conditions has become critical for quantum computing. Barium titanate thin films show large linear EO coefficients in the tetragonal phase at room temperature, which is severely degraded down to ~200 pm V$^{-1}$ in the rhombohedral phase at cryogenic temperatures. There is immense interest in manipulating these phase transformations and retaining superior EO properties down to liquid helium temperature. Utilizing the thermodynamic theory of optical properties, a large low-temperature EO response is designed by engineering the energetic competition between different ferroelectric phases, leading to a low-symmetry monoclinic phase with a massive EO response. The existence of this phase is demonstrated in a strain-tuned BaTiO$_{3}$ thin film that exhibits a linear EO coefficient of 2516 +/- 100 pm V$^{-1}$ at 5 K, which is an order of magnitude higher than the best reported performance thus far. Importantly, the EO coefficient increases by 100x during cooling, unlike the conventional films, where it degrades. Further, at the lowest temperature, significant higher order EO responses also emerge. These results represent a new framework for designing materials with property enhancements by stabilizing highly tunable metastable phases with strain. Copyright 2025 The Author(s). Advanced Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. (A. Suceava, S. Hazra, A. Ross, et al. "Colossal Cryogenic Electro-Optic Response Through Metastability in Strained BaTiO3 Thin Films." Adv. Mater. (2025): e07564. https://doi.org/10.1002/adma.202507564)

cond-mat.mtrl-sci↗

arXiv2025

Widespread Hot Molecular Gas Heated by Shear-induced Turbulence in the Galactic Center

We observed NH3 metastable inversion lines from (3, 3) to (18, 18) toward G0.66-0.13 in the Galactic center with the Shanghai Tianma 65m radio telescope and Yebes 40 m telescope. Highly-excited lines of NH3 (17, 17), (18, 18) were detected in emission for the first time in the interstellar medium, with upper energy levels up to 3100 K. Mapping observations reveal widespread hot molecular gas traced by NH3 (13, 13) toward G0.66-0.13. The rotation temperatures of hot gas traced by NH3 exceed 400 K, which amounts to five percent of the total NH3 in the Galactic Center. Hot gas (>400 K) and warm gas (100-140 K) are found in distinct clumps, with the hot gas located at the interfacing regions between different warm clouds. The theory of intermittency in turbulence reproduces the complex temperature structure in the central molecular zone, especially the hot gas observed here. The results presented here demonstrate that turbulence heating dominates the heating of the molecular gas in the Central Molecular Zone, while the turbulence is induced by the shear-motion of molecular clouds under the gravitational potential of the nuclear star clusters and the supermassive black hole. Our results suggest that shear-induced turbulence heating could be a widespread factor influencing galactic evolution.

astro-ph.GA↗

arXiv2025

Torus feeding and outflow launching in the active nucleus of the Circinus galaxy

Context: Most active galactic nuclei (AGN) are believed to be surrounded by a dusty molecular torus on the parsec scale which is often embedded within a larger circumnuclear disk (CND). AGN are fuelled by the inward transport of material through these structures and can launch multi-phase outflows that influence the host galaxy through AGN feedback. Aims: We use the Circinus Galaxy as a nearby laboratory to investigate the physical mechanisms responsible for feeding the torus and launching a multi-phase outflow in this Seyfert-type AGN, as these mechanisms remain poorly understood. Methods: We analysed observations from the Atacama Large Millimeter/submillimeter Array of the Circinus nucleus at angular resolutions down to 13 mas (0.25 pc). We traced dust and the ionised outflow using 86-665 GHz continuum emission, and studied the morphology and kinematics of the molecular gas. Results: We find that the Circinus CND hosts molecular and dusty spiral arms, two of which connect directly to the torus. We detect inward mass transport along these structures and argue that the non-axisymmetric potential generated by these arms is the mechanism responsible for fuelling the torus. We estimate a feeding rate of 0.3-7.5 M$_{\odot}$yr$^{-1}$, implying that over 88% of the inflowing material is expelled in a multi-phase outflow before reaching the accretion disk. The inferred torus feeding time scale (120 kyr - 2.7 Myr) suggests that variability in AGN activity may be driven by changes in torus feeding. On parsec scales, the ionised outflow is traced by optically thin free-free emission. The outflow is stratified, with a slightly wider opening angle in the molecular phase than in the dusty and ionised components. The ionised outflow is launched or collimated by a warped accretion disk at a radius of r ~ 0.16 pc, and its geometry requires an anisotropic launching mechanism.

astro-ph.GA↗

arXiv2025

Massive Star Formation at Supersolar Metallicities: Constraints on the Initial Mass Function

Metals enhance the cooling efficiency of molecular clouds, promoting fragmentation. Consequently, increasing the metallicity may boost the formation of low-mass stars. Within the integrated galaxy initial mass function (IGIMF) theory, this effect is empirically captured by a linear relation between the slope of the low-mass stellar IMF, $α_1$, and the metal mass fraction, $Z$. This linear $α_1$-$Z$ relation has been calibrated up to $\approx 2 \, Z_{\odot}$, though higher metallicity environments are known to exist. We show that if the linear $α_1$-$Z$ relation extends to higher metallicities ($[Z] \gtrsim 0.5$), massive star formation is suppressed entirely. Alternatively, fragmentation efficiency may saturate beyond some metallicity threshold if gravitational collapse cascades rapidly enough. To model this behavior, we propose a logistic function describing the transition from metallicity-sensitive to metallicity-insensitive fragmentation regimes. We provide a user-friendly public code, pyIGIMF, which enables the instantaneous computation of the IGIMF theory with the logistic $α_1$-$Z$ relation.

astro-ph.GA↗

arXiv2025

Scientific Objectives of the Xue-shan-mu-chang 15-meter Submillimeter Telescope

Submillimeter astronomy is poised to revolutionize our understanding of the Universe by revealing cosmic phenomena hidden from optical and near-infrared observations, particularly those associated with interstellar dust, molecular gas, and star formation. The Xue-shan-mu-chang 15-meter submillimeter telescope (XSMT-15m), to be constructed at a premier high-altitude site (4813 m) in Qinghai, China, marks a major milestone for Chinese astronomy, establishing the China mainland's first independently developed, world-class submillimeter facility. Equipped with state-of-the-art instruments, XSMT-15m will address a diverse range of frontier scientific questions spanning extragalactic astronomy, Galactic structure, time-domain astrophysics, and astrochemistry. In synergy with current and forthcoming observatories, XSMT-15m will illuminate the formation and evolution of galaxies, unravel the physical and chemical processes shaping the interstellar medium, and explore transient phenomena in the submillimeter regime. These capabilities will advance our understanding across extragalactic astronomy, Galactic ecology, astrochemistry, and time-domain astrophysics, inaugurating a new era for submillimeter research in China and the northern hemisphere.

astro-ph.GA↗

arXiv2025

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications

The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\sqrt{T\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\sqrt{T\cdot S(X||d^{-1}I_d)})$, where $X$ is the comparator in the regret, $I_d$ is the identity matrix, and $S(\cdot||\cdot)$ denotes the quantum relative entropy. Furthermore, our algorithm has the same computational complexity as MMWU, indicating that the improvement in the regret bound is ``free''. Technically, we first develop a general potential-based framework for matrix LEA, with MMWU being its special case induced by the standard exponential potential. Then, the crux of our analysis is a new ``one-sided'' Jensen's trace inequality built on a Laplace transform technique, which allows the application of general potential functions beyond exponential to matrix LEA. Our algorithm is finally induced by an optimal potential function from the vector LEA problem, based on the imaginary error function. Complementing the above, we provide a memory lower bound for matrix LEA, and explore the applications of our algorithm in quantum learning theory. We show that it outperforms the state of the art for learning quantum states corrupted by depolarization noise, random quantum states, and Gibbs states. In addition, applying our algorithm to linearized convex losses enables predicting nonlinear quantum properties, such as purity, quantum virtual cooling, and Rényi-$2$ correlation.

cs.LG↗

arXiv2025

Unitary Shimura varieties at ramified primes and arithmetic transfer

We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative local models in this context, which relies on a reformulation of the Eisenstein condition of Rapoport--Zink and Rapoport--Smithling--Zhang. Related to that, we also provide a moduli description for the integral models of RSZ unitary Shimura varieties in new cases. Our second result lifts the comparison of local models to categories of $p$-divisible groups and, as a corollary, to various kinds of Rapoport--Zink spaces. Our third result is a proof of the arithmetic transfer conjecture of the third author in full generality. Using our statements about Rapoport--Zink spaces, we extend the previous proof from the unramified case to that of all $p$-adic local fields ($p$ odd).

math.AG↗

arXiv2025

Overmassive Black holes live in compact galaxies in the early Universe

A significant population of quasars have been found to exist within the first Gyr of cosmic time. Most of them have high black hole (BH) masses ($M_{\rm BH} \sim 10^{8-10} M_{\odot}$) with an elevated BH-to-stellar mass ratio compared to typical local galaxies, posing challenges to our understanding of the formation of supermassive BHs and their coevolution with host galaxies. Here, based on size measurements of [CII] 158$μ$m emission for a statistical sample of $z \sim 6$ quasars, we find that their host galaxies are systematically more compact (with half-light radius $R_{\rm e} \sim 1.6$ kpc) than typical star-forming galaxies at the same redshifts. Specifically, the sizes of the most compact quasar hosts, which also tend to contain less cold gas than their more extended counterparts, are comparable to that of massive quiescent galaxies at $z \sim 4-5$. These findings reveal an intimate connection between the formation of massive BHs and compactness of their host galaxies in the early universe. These compact quasar hosts are promising progenitors of the first population of quiescent galaxies.

astro-ph.GA↗

arXiv2025

Sparsity-Based Interpolation of External, Internal and Swap Regret

Focusing on the expert problem in online learning, this paper studies the interpolation of several performance metrics via $ϕ$-regret minimization, which measures the total loss of an algorithm by its regret with respect to an arbitrary action modification rule $ϕ$. With $d$ experts and $T\gg d$ rounds in total, we present a single algorithm achieving the instance-adaptive $ϕ$-regret bound \begin{equation*} \tilde O\left(\min\left\{\sqrt{d-d^{\mathrm{unif}}_ϕ+1},\sqrt{d-d^{\mathrm{self}}_ϕ}\right\}\cdot\sqrt{T}\right), \end{equation*} where $d^{\mathrm{unif}}_ϕ$ is the maximum amount of experts modified identically by $ϕ$, and $d^{\mathrm{self}}_ϕ$ is the amount of experts that $ϕ$ trivially modifies to themselves. By recovering the optimal $O(\sqrt{T\log d})$ external regret bound when $d^{\mathrm{unif}}_ϕ=d$, the standard $\tilde O(\sqrt{T})$ internal regret bound when $d^{\mathrm{self}}_ϕ=d-1$ and the optimal $\tilde O(\sqrt{dT})$ swap regret bound in the worst case, we improve upon existing algorithms in the intermediate regimes. In addition, the computational complexity of our algorithm matches that of the standard swap-regret minimization algorithm due to (Blum and Mansour, 2007). Technically, building on the well-known reduction from $ϕ$-regret minimization to external regret minimization on stochastic matrices, our main idea is to further convert the latter to online linear regression using Haar-wavelet-inspired matrix features. Then, by associating the complexity of each $ϕ$ instance with its sparsity under the feature representation, we apply techniques from comparator-adaptive online learning to exploit the sparsity in this regression subroutine.

stat.ML↗

arXiv2025

Adapting Prediction Sets to Distribution Shifts Without Labels

Recently there has been a surge of interest to deploy confidence set predictions rather than point predictions in machine learning. Unfortunately, the effectiveness of such prediction sets is frequently impaired by distribution shifts in practice, and the challenge is often compounded by the lack of ground truth labels at test time. Focusing on a standard set-valued prediction framework called conformal prediction (CP), this paper studies how to improve its practical performance using only unlabeled data from the shifted test domain. This is achieved by two new methods called ECP and EACP, whose main idea is to adjust the score function in CP according to its base model's own uncertainty evaluation. Through extensive experiments on a number of large-scale datasets and neural network architectures, we show that our methods provide consistent improvement over existing baselines and nearly match the performance of fully supervised methods.

cs.LG↗

arXiv2025

A Generative Adaptive Replay Continual Learning Model for Temporal Knowledge Graph Reasoning

Recent Continual Learning (CL)-based Temporal Knowledge Graph Reasoning (TKGR) methods focus on significantly reducing computational cost and mitigating catastrophic forgetting caused by fine-tuning models with new data. However, existing CL-based TKGR methods still face two key limitations: (1) They usually one-sidedly reorganize individual historical facts, while overlooking the historical context essential for accurately understanding the historical semantics of these facts; (2) They preserve historical knowledge by simply replaying historical facts, while ignoring the potential conflicts between historical and emerging facts. In this paper, we propose a Deep Generative Adaptive Replay (DGAR) method, which can generate and adaptively replay historical entity distribution representations from the whole historical context. To address the first challenge, historical context prompts as sampling units are built to preserve the whole historical context information. To overcome the second challenge, a pre-trained diffusion model is adopted to generate the historical distribution. During the generation process, the common features between the historical and current distributions are enhanced under the guidance of the TKGR model. In addition, a layer-by-layer adaptive replay mechanism is designed to effectively integrate historical and current distributions. Experimental results demonstrate that DGAR significantly outperforms baselines in reasoning and mitigating forgetting.

cs.IR↗

arXiv2025

The Benefit of Being Bayesian in Online Conformal Prediction

Based on the framework of Conformal Prediction (CP), we study the online construction of confidence sets given a black-box machine learning model. By converting the target confidence levels into quantile levels, the problem can be reduced to predicting the quantiles (in hindsight) of a sequentially revealed data sequence. Two very different approaches have been studied previously: (i) Assuming the data sequence is iid or exchangeable, one could maintain the empirical distribution of the observed data as an algorithmic belief, and directly predict its quantiles. (ii) Due to the fragility of statistical assumptions, a recent trend is to consider the non-distributional, adversarial setting and apply first-order online optimization algorithms to moving quantile losses. However, it requires the oracle knowledge of the target quantile level, and suffers from a previously overlooked monotonicity issue due to the associated loss linearization. This paper presents an adaptive CP algorithm that combines their strengths. Without any statistical assumption, it is able to answer multiple arbitrary confidence level queries with low regret, while also overcoming the monotonicity issue suffered by first-order optimization baselines. Furthermore, if the data sequence is actually iid, then the same algorithm is automatically equipped with the "correct" coverage probability guarantee. To achieve such strengths, our key technical innovation is to regularize the aforementioned algorithmic belief (the empirical distribution) by a Bayesian prior, which robustifies it by simulating a non-linearized Follow the Regularized Leader (FTRL) algorithm on the output. Such a belief update backbone is shared by prediction heads targeting different confidence levels, bringing practical benefits analogous to the recently proposed concept of U-calibration (Kleinberg et al., 2023).

stat.ML↗

arXiv2025

Non-reductive cycles and twisted arithmetic transfers for Shimura curves

In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic analogs of relative Langlands program. We explain related formulations of arithmetic twisted Gan-Gross-Prasad conjecture, the proof of twisted AFL and certain arithmetic transfers.

math.NT↗

arXiv2025

The Tenth NTIRE 2025 Efficient Super-Resolution Challenge Report

This paper presents a comprehensive review of the NTIRE 2025 Challenge on Single-Image Efficient Super-Resolution (ESR). The challenge aimed to advance the development of deep models that optimize key computational metrics, i.e., runtime, parameters, and FLOPs, while achieving a PSNR of at least 26.90 dB on the $\operatorname{DIV2K\_LSDIR\_valid}$ dataset and 26.99 dB on the $\operatorname{DIV2K\_LSDIR\_test}$ dataset. A robust participation saw \textbf{244} registered entrants, with \textbf{43} teams submitting valid entries. This report meticulously analyzes these methods and results, emphasizing groundbreaking advancements in state-of-the-art single-image ESR techniques. The analysis highlights innovative approaches and establishes benchmarks for future research in the field.

cs.CV↗

arXiv2025

Weighted special cycles on Rapoport--Zink spaces with almost self-dual level

We introduce a ``vector valued'' version of special cycles on GSpin Rapoport--Zink spaces with almost self-dual level in the context of the Kudla program, with certain linear invariance and local modularity features. They are local analogs of special cycles on GSpin Shimura varieties with almost self-dual parahoric level (e.g. Siegel threefolds with paramodular level). We establish local arithmetic Siegel--Weil formulas relating arithmetic intersection numbers of these special cycles and derivatives of certain local Whittaker functions in any dimension. The proof is based on a reduction formula for cyclic quadratic lattices.

math.NT↗

arXiv2025

Population Dynamics Control with Partial Observations

We study the problem of controlling population dynamics, a class of linear dynamical systems evolving on the probability simplex, from the perspective of online non-stochastic control. While Golowich et.al. 2024 analyzed the fully observable setting, we focus on the more realistic, partially observable case, where only a low-dimensional representation of the state is accessible. In classical non-stochastic control, inputs are set as linear combinations of past disturbances. However, under partial observations, disturbances cannot be directly computed. To address this, Simchowitz et.al. 2020 proposed to construct oblivious signals, which are counterfactual observations with zero control, as a substitute. This raises several challenges in our setting: (1) how to construct oblivious signals under simplex constraints, where zero control is infeasible; (2) how to design a sufficiently expressive convex controller parameterization tailored to these signals; and (3) how to enforce the simplex constraint on control when projections may break the convexity of cost functions. Our main contribution is a new controller that achieves the optimal $\tilde{O}(\sqrt{T})$ regret with respect to a natural class of mixing linear dynamic controllers. To tackle these challenges, we construct signals based on hypothetical observations under a constant control adapted to the simplex domain, and introduce a new controller parameterization that approximates general control policies linear in non-oblivious observations. Furthermore, we employ a novel convex extension surrogate loss, inspired by Lattimore 2024, to bypass the projection-induced convexity issue.

math.OC↗