arXiv subjects

Yin Liu

Publications and source records attributed to Yin Liu.

At least 19 recordsLinked to original sources

arXiv2026

Strict Monotonicity of Numerical Invariants for the Submodules $[(z-w)^k]$ in $H^2(\mathbb D^2)$

For $k\geq1$, let $M_k=[(z-w)^k]\subset H^2(\mathbb D^2)$. We first determine the banded Toeplitz matrices associated with the homogeneous components of $M_k$, together with explicit formulas for their determinants and the relevant algebraic cofactors. These formulas lead to a complete description of the spectrum of the core operator: \[ \sigma(C_{M_k}) = \{0,1\} \cup \left\{ \pm\frac{k}{n+k}:n\geq1 \right\}. \] In particular, the spectral data determine the parameter $k$. The determinant and cofactor formulas further yield a unified finite-sum representation for $\alpha_{n,j}^{(k)} =\langle w^j\phi_n,z^j\psi_n\rangle$, and hence for Yang's higher numerical invariants. We derive an adjacent relation connecting $\alpha_{n,j}^{(k)}$ and $\alpha_{n,j+1}^{(k)}$ by means of an explicit telescoping certificate, and show that the corresponding finite-section transformations are strict contractions. Combining these finite-dimensional estimates with the asymptotic behavior of $\alpha_{n,j}^{(k)}$, we prove the strict monotonicity \[ \Sigma_0(M_k)> \Sigma_1(M_k)> \Sigma_2(M_k)> \cdots . \] The cases $k\geq3$ constitute the new part of the analysis, while the previously known cases $k=1,2$ are recovered within the same framework. Consequently, Yang's monotonicity conjecture holds in strict form for the entire family $\{[(z-w)^k]:k\geq1\}$.

math.FA↗

arXiv2026

Sinkhorn Linearization and the Spectral Proxy: Unifying the Statistical and Algorithmic Theory of Feature-Parameterized Inverse Optimal Transport via a Single Spectral Sandwich

We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j). The core technical contribution is the Sinkhorn linearization -- the implicit-function sensitivity of the entropic OT plan to the cost -- together with its spectral proxy, a formula that is spectrally exact yet geometrically transparent. The restricted Hessian on the tangent space satisfies the spectral sandwich (pi_min/epsilon) I <= H_T^{-1} <= (pi_max/epsilon) I, yielding the single core bound sigma_min >= (pi_min/(a_max epsilon)) sqrt(lambda_min(Sigma)) that drives the entire theory. On this core we establish four theorems and one observation. T1 (identifiability): theta is globally injective on the quotient of the gauge kernel, with dimension bound F <= (K-1)^2. T2 (sparsistency): the l1-penalized estimator recovers the true support under irrepresentability and score concentration, with exponential failure probability. T3 (well-posedness): the feature-moment map M(theta) = Phi^T x_theta is strongly monotone, and the inverse is Lipschitz with constant L <= epsilon ||Phi^T S_a||_op / (pi_min lambda_min(Sigma)). T4 (convergence): local strong convexity with mu >= pi_min^2 lambda_min(Sigma) / epsilon^2 guarantees monotone gradient descent convergence. O5 (misspecification): the estimator converges to the OT-model projection of the truth; the Holder continuity of the projection map is assessed numerically, yielding setting-dependent empirical exponents alpha_eff in (0,1).

stat.ML↗

arXiv2026

Block Repetition of Numerical Invariants for the Submodules $[z^k-w^k]$ in $H^2(\mathbb D^2)$

For $k\ge 2$, let $M_k=[z^k-w^k]$ be the principal homogeneous submodule of the Hardy space over the bidisk. We determine Yang's complete sequence of numerical invariants and prove $$ \Sigma_0(M_k)=\frac{\pi^2}{6},\qquad \Sigma_j(M_k)=\Sigma_{\lceil j/k\rceil}([z-w]),\quad j\ge1. $$ The proof exploits a residue-class decomposition of the Toeplitz matrices associated with the graded wandering spaces. Consequently, Yang's monotonicity conjecture holds for the family $\{M_k:k\ge2\}$. We also show that the nonzero spectral data of the core operator are independent of $k$, whereas the numerical invariant sequence recovers $k$ from the length of its constant blocks. Thus the higher numerical invariants detect module-theoretic information invisible to the core spectrum.

math.FA↗

arXiv2026

Deterministic fabrication of large-area, high-crystallinity oxide moire superlattices

Oxide twistronics extends moire engineering beyond van der Waals materials, offering a promising platform for accessing emergent interfacial phenomena arising from the strong coupling of lattice, charge, and orbital degrees of freedom in complex oxides. However, deterministic fabrication of high-crystallinity oxide moire superlattices over large lateral dimensions remains challenging due to the three-dimensional bonding network of oxides. Here, we demonstrate a scalable, generalized fabrication strategy that enables the formation of high-crystallinity oxide moire superlattices with clean, chemically bonded interfaces and precisely controlled twist angles down to nominal values of 0.1 degree, achieving sub-degree twist-angle accuracy across large contiguous lateral dimensions approaching the millimeter scale. Using NaNbO3 as a model system, we show that the resulting interlayer coupling drives pronounced structural reconstruction that modifies both the phase structure and ferroelectric domain configuration. Synchrotron-based X-ray 3D reciprocal space mapping reveals the emergence of a single-phase state in twisted bilayers, in contrast to the mixed-phase structure observed in single-layer membranes prior to twist assembly. The structural signatures are further consistent with gradual lattice rotation distributed along the thickness direction that may accommodate interfacial shear strain, distinct from reconstruction observed in van der Waals moire systems, which primarily occurs through in-plane stacking rearrangement. This collective lattice response is correlated with twist-dependent nanoscale electromechanical modulations observed by piezoresponse force microscopy. These results establish a scalable materials platform for oxide twistronics and open new pathways towards integrating twist-engineered complex oxides into practical, macroscale device architectures.

cond-mat.mtrl-sci↗

arXiv2026

On numerical invariants for submodules $[(z-w)^2]$ in $H^2(\mathbb{D}^2)$

In this paper, we study numerical invariants associated with a homogeneous submodule of the Hardy module over the bidisk. We focus on the submodule generated by the polynomial $(z-w)^2$ and obtain explicit formulas for the corresponding invariants. As an application, we verify the monotonicity property in this concrete setting. Our results provide a detailed example illustrating the behavior of these invariants beyond the linear case.

math.FA↗

arXiv2025

Non-Asymptotic Global Convergence of PPO-Clip

Reinforcement learning (RL) has gained attention for aligning large language models (LLMs) via reinforcement learning from human feedback (RLHF). The actor-only variants of Proximal Policy Optimization (PPO) are widely applied for their efficiency. These algorithms incorporate a clipping mechanism to improve stability. Besides, a regularization term, such as the reverse KL-divergence or a more general $f$-divergence, is introduced to prevent policy drift. Despite their empirical success, a rigorous theoretical understanding of the problem and the algorithm's properties is limited. This paper advances the theoretical foundations of the PPO-Clip algorithm by analyzing a deterministic actor-only PPO algorithm within the general RL setting with $f$-divergence regularization under the softmax policy parameterization. We derive a non-uniform Lipschitz smoothness condition and a {\L}ojasiewicz inequality for the considered problem. Based on these, a non-asymptotic linear convergence rate to the globally optimal policy is established for the forward KL-regularizer. Furthermore, stationary convergence and local linear convergence are derived for the reverse KL-regularizer.

math.OC↗

arXiv2025

Understanding Overparametrization in Survival Models through Interpolation

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, double-descent, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define interpolation and finite-norm interpolation, two key characteristics of loss-based models to understand double-descent. We then show the existence (or absence) of (finite-norm) interpolation of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of interpolation and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.

stat.ML↗

arXiv2025

GateFuseNet: An Adaptive 3D Multimodal Neuroimaging Fusion Network for Parkinson's Disease Diagnosis

Accurate diagnosis of Parkinson's disease (PD) from MRI remains challenging due to symptom variability and pathological heterogeneity. Most existing methods rely on conventional magnitude-based MRI modalities, such as T1-weighted images (T1w), which are less sensitive to PD pathology than Quantitative Susceptibility Mapping (QSM), a phase-based MRI technique that quantifies iron deposition in deep gray matter nuclei. In this study, we propose GateFuseNet, an adaptive 3D multimodal fusion network that integrates QSM and T1w images for PD diagnosis. The core innovation lies in a gated fusion module that learns modality-specific attention weights and channel-wise gating vectors for selective feature modulation. This hierarchical gating mechanism enhances ROI-aware features while suppressing irrelevant signals. Experimental results show that our method outperforms three existing state-of-the-art approaches, achieving 85.00% accuracy and 92.06% AUC. Ablation studies further validate the contributions of ROI guidance, multimodal integration, and fusion positioning. Grad-CAM visualizations confirm the model's focus on clinically relevant pathological regions. The source codes and pretrained models can be found at https://github.com/YangGaoUQ/GateFuseNet

cs.CV↗

arXiv2025

SUSEP-Net: Simulation-Supervised and Contrastive Learning-based Deep Neural Networks for Susceptibility Source Separation

Quantitative susceptibility mapping (QSM) provides a valuable tool for quantifying susceptibility distributions in human brains; however, two types of opposing susceptibility sources (i.e., paramagnetic and diamagnetic), may coexist in a single voxel, and cancel each other out in net QSM images. Susceptibility source separation techniques enable the extraction of sub-voxel information from QSM maps. This study proposes a novel SUSEP-Net for susceptibility source separation by training a dual-branch U-net with a simulation-supervised training strategy. In addition, a contrastive learning framework is included to explicitly impose similarity-based constraints between the branch-specific guidance features in specially-designed encoders and the latent features in the decoders. Comprehensive experiments were carried out on both simulated and in vivo data, including healthy subjects and patients with pathological conditions, to compare SUSEP-Net with three state-of-the-art susceptibility source separation methods (i.e., APART-QSM, \c{hi}-separation, and \c{hi}-sepnet). SUSEP-Net consistently showed improved results compared with the other three methods, with better numerical metrics, improved high-intensity hemorrhage and calcification lesion contrasts, and reduced artifacts in brains with pathological conditions. In addition, experiments on an agarose gel phantom data were conducted to validate the accuracy and the generalization capability of SUSEP-Net.

eess.IV↗

arXiv2025

Low-loss far-infrared surface phonon polaritons in suspended SrTiO3 nanomembranes

Phonon polaritons (PhPs), excitations arising from the coupling of light with lattice vibrations, enable light confinement and local field enhancement, which is essential for various photonic and thermal applications. To date, PhPs with high confinement and low loss have been mainly observed in the mid-infrared regime and mostly in manually exfoliated flakes of van der Waals (vdW) materials. In this work, we demonstrate the existence of low-loss, thickness-tunable phonon polaritons in the far-infrared regime within transferable free-standing SrTiO3 membranes synthesized through a scalable approach, achieving high figures of merit, which are comparable to the previous record values from the vdW materials. Leveraging atomic precision in thickness control, large dimensions, and compatibility with mature oxide electronics, functional oxide membranes present a promising large-scale two-dimensional (2D) platform alternative to vdW materials for on-chip polaritonic technologies in the far-infrared regime.

physics.optics↗

arXiv2025

A Memory Efficient Randomized Subspace Optimization Method for Training Large Language Models

The memory challenges associated with training Large Language Models (LLMs) have become a critical concern, particularly when using the Adam optimizer. To address this issue, numerous memory-efficient techniques have been proposed, with GaLore standing out as a notable example designed to reduce the memory footprint of optimizer states. However, these approaches do not alleviate the memory burden imposed by activations, rendering them unsuitable for scenarios involving long context sequences or large mini-batches. Moreover, their convergence properties are still not well-understood in the literature. In this work, we introduce a Randomized Subspace Optimization framework for pre-training and fine-tuning LLMs. Our approach decomposes the high-dimensional training problem into a series of lower-dimensional subproblems. At each iteration, a random subspace is selected, and the parameters within that subspace are optimized. This structured reduction in dimensionality allows our method to simultaneously reduce memory usage for both activations and optimizer states. We establish comprehensive convergence guarantees and derive rates for various scenarios, accommodating different optimization strategies to solve the subproblems. Extensive experiments validate the superior memory and communication efficiency of our method, achieving performance comparable to GaLore and Adam.

cs.LG↗

arXiv2024

Nonasymptotic Analysis of Accelerated Methods With Inexact Oracle Under Absolute Error Bound

Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has demonstrated that the performance of accelerated first-order methods is more sensitive to gradient errors compared with non-accelerated ones. This paper investigates the nonasymptotic convergence bound of two accelerated methods with inexact gradients to solve deterministic smooth convex problems. Performance Estimation Problem (PEP) is used as the primary tool to analyze the convergence bounds of the underlying algorithms. By finding an analytical solution to PEP, we derive novel convergence bounds of the Generalized Optimized Gradient Method (GOGM) and Generalized Fast Gradient Method (GFGM) with inexact gradient oracles following the absolute error bound. Next, we analyze the tradeoff between the vanishing term and the accumulated error in the convergence bound that guides finding the optimal stepsize. Furthermore, we determine the optimal strategy to set the gradient inexactness along iterations, ensuring that the accumulated error remains subordinate to the vanishing term. Finally, we establish a lower bound for accumulated error for a subclass of first-order methods satisfying two properties, which then motivated us to develop PEP solutions satisfying this lower bound for GOGM and GFGM methods.

math.OC↗

arXiv2024

A combinatorial view of Holant problems on higher domains

On the Boolean domain, there is a class of symmetric signatures called ``Fibonacci gates'' for which a beautiful P-time combinatorial algorithm has been designed for the corresponding $\operatorname{Holant}$ problems. In this work, I give a combinatorial view for $\operatorname{Holant}(\mathcal{F})$ problems on a domain of size 3 where $\mathcal{F}$ is a set of arity 3 functions with inputs taking values on the domain of size 3 and the functions share some common properties. The combinatorial view can also be extended to the domain of size 4. Specifically, I extend the definition of "Fibonacci gates" to the domain of size 3 and the domain of size 4. Moreover, I give the corresponding combinatorial algorithms.

cs.CC↗

arXiv2024

Highly confined epsilon-near-zero- and surface-phonon polaritons in SrTiO3 membranes

Recent theoretical studies have suggested that transition metal perovskite oxide membranes can enable surface phonon polaritons in the infrared range with low loss and much stronger subwavelength confinement than bulk crystals. Such modes, however, have not been experimentally observed so far. Here, using a combination of far-field Fourier-transform infrared (FTIR) spectroscopy and near-field synchrotron infrared nanospectroscopy (SINS) imaging, we study the phonon-polaritons in a 100 nm thick freestanding crystalline membrane of SrTiO3 transferred on metallic and dielectric substrates. We observe a symmetric-antisymmetric mode splitting giving rise to epsilon-near-zero and Berreman modes as well as highly confined (by a factor of 10) propagating phonon polaritons, both of which result from the deep-subwavelength thickness of the membranes. Theoretical modeling based on the analytical finite-dipole model and numerical finite-difference methods fully corroborate the experimental results. Our work reveals the potential of oxide membranes as a promising platform for infrared photonics and polaritonics.

cond-mat.mtrl-sci↗

arXiv2024

Derivative-Free Optimization for Low-Rank Adaptation in Large Language Models

Parameter-efficient tuning methods such as LoRA could achieve comparable performance to model tuning by tuning a small portion of the parameters. However, substantial computational resources are still required, as this process involves calculating gradients and performing back-propagation throughout the model. Much effort has recently been devoted to utilizing the derivative-free optimization method to eschew the computation of gradients and showcase an augmented level of robustness in few-shot settings. In this paper, we prepend the low-rank modules into each self-attention layer of the model and employ two derivative-free optimization methods to optimize these low-rank modules at each layer alternately. Extensive results on various tasks and language models demonstrate that our proposed method achieves substantial improvement and exhibits clear advantages in memory usage and convergence speed compared to existing gradient-based parameter-efficient tuning and derivative-free optimization methods in few-shot settings.

cs.CL↗

arXiv2023

Plug-and-Play Latent Feature Editing for Orientation-Adaptive Quantitative Susceptibility Mapping Neural Networks

Quantitative susceptibility mapping (QSM) is a post-processing technique for deriving tissue magnetic susceptibility distribution from MRI phase measurements. Deep learning (DL) algorithms hold great potential for solving the ill-posed QSM reconstruction problem. However, a significant challenge facing current DL-QSM approaches is their limited adaptability to magnetic dipole field orientation variations during training and testing. In this work, we propose a novel Orientation-Adaptive Latent Feature Editing (OA-LFE) module to learn the encoding of acquisition orientation vectors and seamlessly integrate them into the latent features of deep networks. Importantly, it can be directly Plug-and-Play (PnP) into various existing DL-QSM architectures, enabling reconstructions of QSM from arbitrary magnetic dipole orientations. Its effectiveness is demonstrated by combining the OA-LFE module into our previously proposed phase-to-susceptibility single-step instant QSM (iQSM) network, which was initially tailored for pure-axial acquisitions. The proposed OA-LFE-empowered iQSM, which we refer to as iQSM+, is trained in a self-supervised manner on a specially-designed simulation brain dataset. Comprehensive experiments are conducted on simulated and in vivo human brain datasets, encompassing subjects ranging from healthy individuals to those with pathological conditions. These experiments involve various MRI platforms (3T and 7T) and aim to compare our proposed iQSM+ against several established QSM reconstruction frameworks, including the original iQSM. The iQSM+ yields QSM images with significantly improved accuracies and mitigates artifacts, surpassing other state-of-the-art DL-QSM algorithms.

eess.IV↗

arXiv2023

TensorMD: Scalable Tensor-Diagram based Machine Learning Interatomic Potential on Heterogeneous Many-Core Processors

Molecular dynamics simulations have emerged as a potent tool for investigating the physical properties and kinetic behaviors of materials at the atomic scale, particularly in extreme conditions. Ab initio accuracy is now achievable with machine learning based interatomic potentials. With recent advancements in high-performance computing, highly accurate and large-scale simulations become feasible. This study introduces TensorMD, a new machine learning interatomic potential (MLIP) model that integrates physical principles and tensor diagrams. The tensor formalism provides a more efficient computation and greater flexibility for use with other scientific codes. Additionally, we proposed several portable optimization strategies and developed a highly optimized version for the new Sunway supercomputer. Our optimized TensorMD can achieve unprecedented performance on the new Sunway, enabling simulations of up to 52 billion atoms with a time-to-solution of 31 ps/step/atom, setting new records for HPC + AI + MD.

physics.comp-ph↗

arXiv2023

Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)

The data-driven approach of supervised learning methods has limited applicability in solving dipole inversion in Quantitative Susceptibility Mapping (QSM) with varying scan parameters across different objects. To address this generalization issue in supervised QSM methods, we propose a novel training-free model-based unsupervised method called MoDIP (Model-based Deep Image Prior). MoDIP comprises a small, untrained network and a Data Fidelity Optimization (DFO) module. The network converges to an interim state, acting as an implicit prior for image regularization, while the optimization process enforces the physical model of QSM dipole inversion. Experimental results demonstrate MoDIP's excellent generalizability in solving QSM dipole inversion across different scan parameters. It exhibits robustness against pathological brain QSM, achieving over 32% accuracy improvement than supervised deep learning and traditional iterative methods. It is also 33% more computationally efficient and runs 4 times faster than conventional DIP-based approaches, enabling 3D high-resolution image reconstruction in under 4.5 minutes.

eess.IV↗