arXiv subjects

Song Liu

Publications and source records attributed to Song Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Non-uniqueness for the hyperdissipative Navier-Stokes equations with arbitrarily small subcritical data

In this paper, we consider the hyperdissipative Navier-Stokes equations with fractional dissipation $(-Δ)^β$ with $β>1$. We prove that smooth solutions of the hyperdissipative Navier-Stokes equations are non-unique with arbitrarily small initial data in ${B}^{-β-α}_{\infty,1}(\mathbb{T}^d)$ for any $α>0$. Moreover, we show the existence of a solution with arbitrarily small initial data in ${B}^{-β-α}_{\infty,1}(\mathbb{T}^d)$ ($α>0$) that grows arbitrarily large in $\dot{B}^{-s}_{\infty,\infty}(\mathbb{T}^d)$ for all $s\in\mathbb{R}$ in arbitrarily small time. It is worth pointing out that ${B}^{-β-α}_{\infty,1}(\mathbb{T}^d)$ lies in the subcritical regime when $0<α<β-1$. To the best of our knowledge, this is the first non-uniqueness result of the Navier-Stokes equations with initial data at the subcritical regularity. To show the sharpness of the above results, we establish the local well-posedness of the hyperdissipative Navier-Stokes equations with initial data in $\dot{B}^{-β-α}_{\infty,\infty}(\mathbb{T}^d)$ with $α< 0$.

math.AP↗

arXiv2026

Direct Fisher Score Estimation for Likelihood Maximization

We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based on a local score matching technique which uses simulations from a localized region around each parameter iterate. By employing a linear parameterization to the surrogate score model, our technique admits a closed-form, least-squares solution. This approach yields a fast, flexible, and efficient approximation to the Fisher score, effectively smoothing the likelihood objective and mitigating the challenges posed by complex likelihood landscapes. We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by the smoothing. Empirical results on a range of synthetic and real-world problems demonstrate the superior performance of our method compared to existing benchmarks.

stat.ML↗

arXiv2026

Minimum Distance Summaries for Robust Neural Posterior Estimation

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.

stat.ML↗

arXiv2026

Supermoiré Chern mosaic in helical trilayer WSe2

Helically twisted multilayers offer access to moiré physics beyond the single-superlattice paradigm, yet their correlated and topological transport properties remain largely unexplored in semiconductor moiré materials. Here we report magnetotransport measurements of helical trilayer WSe2, in which two coupled moiré patterns relax into a supermoiré landscape composed of inequivalent local topological domains with distinct electronic structures and unequal spatial areas. By electrostatic tuning, we identify a trilayer-hybridized regime where interactions and real-space reconstruction combine to generate a plethora of magnetic and topological states absent in the twisted bilayers. At moiré filling factor $ν$ = -1, we observe a ferromagnetic insulating state that is robust against magnetic field and accompanied by a non-quantized anomalous Hall response ~-4 kOhms. This behaviour is consistent with a time-reversal-symmetry-breaking supermoiré Chern mosaic, in which the Hall response arises from the non-cancelling contributions of local domains with opposite Chern character arranged by the relaxed structure. Under strong magnetic fields, a symmetry-broken Chern insulating state (C = 1) emerges near $ν$ = -2/3, displaying a much larger positive Hall response together with strongly enhanced longitudinal resistance, suggestive of field-reconstructed topological minibands and domain-boundary scattering. These results establish relaxed supermoiré semiconductor trilayers as a platform for spatially organized magnetism and topology beyond the bilayer limit.

cond-mat.str-el↗

arXiv2026

Zero-Flow Encoders

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at $t=0.5$ if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

stat.ML↗

arXiv2026

DFlare: Scaling Up Draft Capacity for Block Diffusion Speculative Decoding

Block diffusion speculative decoding accelerates LLM inference by predicting all tokens within a block simultaneously for the target model to verify in parallel. Predicting an entire block at once requires a sufficiently capable draft model and effective utilization of the target model's internal knowledge. However, the state-of-the-art method DFlash constrains all draft layers to share a single fused representation derived from only a few target layers, limiting per-layer expressiveness and hindering further scaling of draft capacity. In this paper, we present \modelname, which flares out the narrow conditioning bottleneck of DFlash through a lightweight layer-wise fusion mechanism: each draft layer attends to its own learnable combination of a broad set of target layers at negligible overhead, simultaneously injecting richer target knowledge and providing every draft layer with a distinct input. This enhanced per-layer expressiveness enables scaling the draft model to deeper architectures with consistent gains. We further scale training data from 800K to 2.4M samples to fully exploit the enlarged capacity. On six benchmarks spanning mathematical reasoning, code generation, and conversation, \modelname attains average wall-clock speedups of 5.52x on Qwen3-4B, 5.46x on Qwen3-8B, and 3.91x on GPT-OSS-20B, improving over DFlash by roughly 11\%, 8\%, and 5\% respectively. Our code is available at https://github.com/Tencent/AngelSlim.

cs.CL↗

arXiv2026

Signatures of quantum chaos in phonon-polariton billiards

We use scanning near-field optical microscopy to image hyperbolic phonon polaritons in hexagonal boron nitride (hBN) billiards with integrable and chaotic geometries. In Sinai billiards, we observe irregular mode patterns consistent with quantum scarring, together with an unexpected sensitivity to weak probe perturbations. These random-wave features coexist with non-chaotic one-dimensional boundary modes arising from nontrivial polariton reflection at the billiard edge. As the billiard boundary becomes increasingly complex, the Fourier transforms of the measured signals evolve toward ring-like structures consistent with Berry's random-wave conjecture. We develop a numerical framework based on the Helmholtz equation with generalized boundary conditions that encode angle-dependent reflection phase shifts. The calculated level statistics exhibit a crossover from Poisson-like behavior in integrable billiards to Wigner-Dyson-like behavior in chaotic geometries, with small deviations from the canonical form arising from nonlinear boundary conditions that require self-consistent bulk-boundary analysis. Theoretical analysis based on dissipative Green's functions qualitatively reproduces the near-field data. These results establish mesoscopic van der Waals billiards as a rich platform for studying generalized chaotic dynamics of hybrid light-matter polaritons.

cond-mat.mes-hall↗

arXiv2026

Destructive interference of second harmonic generation in AA stacked MoTe$_2$/WSe$_2$

The stacking configuration of two-dimensional materials critically governs their optical and electronic responses. Monolayer transition-metal dichalcogenides (TMDC) lack inversion symmetry and exhibit exciton-enhanced second-harmonic generation (SHG). In TMDC bilayers, 60° (0°) stacking is conventionally expected to suppress (enhance) SHG owing to destructive (constructive) interference of the layer-resolved nonlinear polarizations. Here, we report an unconventional destructive SHG interference in nearly 0°-stacked (AA-stacked) MoTe2/WSe2 heterobilayers using two independent probes: atomic-resolution imaging and stacking-sensitive exciton hybridization measurements. Supported by ab initio GW and Bethe-Salpeter equation calculations, we show that distinct two-photon resonances associated with the WSe2 C exciton and the MoTe2 D exciton generate a nearly $π$ phase difference ($Δϕ$) in their second-order nonlinear susceptibilities $χ^{(2)}$, leading to the anomalous destructive interference. We further demonstrate that in small-angle twisted MoTe2/WSe2, the SHG polarization state is governed by the interplay between twist angle $α$ and phase difference $Δϕ$, and can be mapped onto trajectories on the Poincaré sphere. At excitation energies satisfying $Δϕ$ + 3$α$ = 180°, the SHG output becomes nearly circularly polarized (ellipticity ~ 0.91) and undergoes an abrupt 90° azimuthal rotation, corresponding to a geometric polarization singularity in the parameter space. Our findings open new routes for exciton-resonance engineered nonlinear photonics and stacking-resolved optical functionality in moiré materials.

cond-mat.mes-hall↗

arXiv2026

Fröhlich-type Polarons in Isotopically Enriched Hexagonal Boron Nitride

Exciton-phonon interactions play a central role in defining the optical response of hexagonal boron nitride (hBN), yet their quantitative determination has remained incomplete. Here, we reveal the Fröhlich-type exciton-phonon coupling in boron-10-enriched hBN using low-temperature cathodoluminescence. We resolve the indirect exciton 5.95$\pm$0.02 eV together with its longitudinal optical (LO) phonon replica detuned by 184$\pm$56 meV, enabling the extraction of a Fröhlich coupling constant $α$=0.159 and a larger exciton binding energy of 161 meV, larger than previously reported values for natural-abundance hBN, which is attributed to isotope enrichment. The inferred polaron radius exceeds the lattice constant, indicating large-polaron behavior. We deduced an exciton scattering time ~of 97 fs, corresponding to a homogeneous linewidth of ~6.76 meV. We further obtain a polaron binding energy of ~48 meV and an effective mass of 1.045 $m_0$. These results provide a direct quantitative characterization of exciton-phonon coupling in isotopically engineered hBN and establish a foundation for tailoring its phonon-polaritonic and quantum-optical properties.

cond-mat.mes-hall↗

arXiv2026

Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR

Missing data imputation, where a model is trained on observed data to estimate unobserved values, is a fundamental problem in machine learning. In this paper, we rigorously formulate imputation model learning as a mean-squared error risk minimisation problem. We show that when the probability of missingness depends on the data, many state-of-the-art methods fail to account for the resulting distribution shift between the observed data used for training and the full data distribution used for evaluation. Consequently, these approaches do not minimise mean-squared error on the full data distribution. Instead, we propose a novel imputation algorithm designed to learn an imputation model from the observed data while explicitly accounting for this distribution shift. Simulation studies show consistent improvements over otherwise identical uncorrected baselines, with average reductions of 3% in RMSE and 7% in Wasserstein distance.

stat.ML↗

arXiv2026

Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

stat.ML↗

arXiv2026

Quantum-Enhanced Dark Matter Search Using Cat States

Quantum metrology has recently emerged as a powerful approach for dark matter (DM) searches, particularly using nonclassical bosonic states in microwave cavities that are sensitive to weak signals. Nonclassical cat states - macroscopic superpositions of coherent states featuring sub-Planck interference structures - offer promising advantages for high-precision measurements. However, their practical utility in DM search remains unexplored. Here, we report the first experimental application of four-component cat states within a high-quality superconducting microwave cavity to search for dark photons, a potential DM candidate. We demonstrate an 8.1-fold enhancement in the signal photon rate and constrain the dark photon kinetic mixing angle to an unprecedented $ε< 7.32 \times 10^{-16}$ near 6.44~GHz (26.6~$μ$eV). By employing a parametric sideband drive to actively tune the cavity frequency, we achieve dark photon searches and background subtraction across multiple frequency bins, yielding a sensitivity at the $10^{-16}$ level within a 100~kHz bandwidth. Our cat-assisted DM (CaD) search and frequency-scanning techniques demonstrate substantial improvements over previous results, promising potential implications in quantum-enhanced searches for new physics.

quant-ph↗

arXiv2026

Real-time Surface-Code Error Correction Using an FPGA-based Neural-Network Decoder

Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and corrected by a classical decoder. To prevent error accumulation, decoding must be performed with both high throughput and low latency to keep pace with the QEC cycle and enable real-time feedback for universal logical operations. Here we report a hardware-integrated control architecture featuring an FPGA-based neural-network (NN) decoder and experimentally demonstrate real-time surface-code (distance-3) QEC on a superconducting quantum processor. The system achieves a deterministic closed-loop latency of 550 ns, including 124 ns for NN decoding, enabling feedback corrections within a 1.25 us QEC cycle. We show that real-time decoding and feedback correction achieve logical performance comparable to offline decoding while maintaining robustness against varying error conditions. We further demonstrate mid-circuit feedback correction in non-Clifford logical circuits, where Pauli-frame updating alone becomes insufficient. Our results establish a low-latency hardware architecture for embedded QEC control and provide a pathway towards scalable fault-tolerant quantum computing systems.

quant-ph↗

arXiv2026

Data-driven Urban Surface Classification Elucidates Global City Heterogeneity

Accurate urban surface characterization is essential for environmental modeling, risk assessment, and climate adaptation. However, existing classifications of urban surfaces lack the global consistency and physical detail to fully represent present-day urban heterogeneity. To address this need, we developed a globally unified, Data-driven Urban Environmental Zone (DUEZ) framework. By applying unsupervised clustering to high-resolution (500-m) datasets of building morphology, vegetation, and surface imperviousness, we classified global urban surfaces into 27 DUEZs, representing the exposure setting for approximately 85% of the global population. Compared to the Local Climate Zone scheme, DUEZ framework provides a more detailed representation of urban form, capturing the fine-scale mixing of built and vegetated surfaces in modern cities. Further aggregation of DUEZ patterns revealed nine predominant urban textures globally with regional differences and socioeconomic relevance. The DUEZ framework enhances physical representation of complex urban surfaces in numerical models and establishes a consistent, data-driven basis for global urban environmental studies.

physics.ao-ph↗

arXiv2026

Experimental observation of exact quantum critical states

Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is challenging, as it typically necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple superconducting qubit quantum system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.

quant-ph↗

arXiv2026

Blow-up phemomenon for the 3-component Degasperis-Procesi equation

In this paper, we consider the Cauchy problem of the 3-component Degasperis-Procesi equation. Firstly, we discuss a local well-posedness result and a blow-up criterion in the low besov space. Secondly, we study the blow-up phenomenon by using the method which does not require any conservation law. Finally, we investigate some persistence properties.

math.AP↗

arXiv2026

AngelSlim: A more accessible, comprehensive, and efficient toolkit for large model compression

This technical report introduces AngelSlim, a comprehensive and versatile toolkit for large model compression developed by the Tencent Hunyuan team. By consolidating cutting-edge algorithms, including quantization, speculative decoding, token pruning, and distillation. AngelSlim provides a unified pipeline that streamlines the transition from model compression to industrial-scale deployment. To facilitate efficient acceleration, we integrate state-of-the-art FP8 and INT8 Post-Training Quantization (PTQ) algorithms alongside pioneering research in ultra-low-bit regimes, featuring HY-1.8B-int2 as the first industrially viable 2-bit large model. Beyond quantization, we propose a training-aligned speculative decoding framework compatible with multimodal architectures and modern inference engines, achieving 1.8x to 2.0x throughput gains without compromising output correctness. Furthermore, we develop a training-free sparse attention framework that reduces Time-to-First-Token (TTFT) in long-context scenarios by decoupling sparse kernels from model architectures through a hybrid of static patterns and dynamic token selection. For multimodal models, AngelSlim incorporates specialized pruning strategies, namely IDPruner for optimizing vision tokens via Maximal Marginal Relevance and Samp for adaptive audio token merging and pruning. By integrating these compression strategies from low-level implementations, AngelSlim enables algorithm-focused research and tool-assisted deployment.

cs.LG↗

arXiv2026

Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data

Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$.

math.AP↗