arXiv subjects

Yaru Liu

Publications and source records attributed to Yaru Liu.

At least 19 recordsLinked to original sources

arXiv2026

Kernel Localization and Whole-Trajectory Generalization for Linear Multistep Methods in Deep Learning-Based Discovery of Dynamical Systems

Linear multistep methods (LMMs) combined with neural-network approximation provide a high-order framework for learning governing vector fields of dynamical systems from discrete trajectory data. This paper studies two issues in LMM-based discovery that are not resolved by existing grid-level convergence theory. First, in non-auxiliary Adams--Bashforth (A-B) and Adams--Moulton (A-M) discovery systems, we observe that zero-residual grid solutions are nonunique but consistent along the trajectory, with differences limited to the boundary layer. We explain this phenomenon through a kernel analysis of the non-auxiliary discovery matrices. Under the corresponding discovery-stability conditions, the differences between zero-residual grid solutions are exponentially localized near the initial indices for A-B schemes, whereas they form two-sided boundary layers near the initial and terminal indices for A-M schemes. Second, we derive whole-trajectory generalization estimates for both auxiliary and non-auxiliary formulations. Once the learned vector field is restricted to a fixed observed trajectory, each component of the error becomes a scalar function of time. For the auxiliary formulation, the trajectory error is $O(h^p)$ under the corresponding grid accuracy, approximation, and trace regularity assumptions. For non-auxiliary formulations, the global estimates contain additional boundary-layer terms. On fixed interior subintervals, these terms are exponentially damped. Numerical experiments illustrate the convergence behavior.

math.NA↗

arXiv2026

Streaming of rendered content with adaptive frame rate and resolution

Streaming rendered content is an attractive way to bring high-quality graphics to billions of mobile devices that do not have sufficient rendering power. Existing solutions render content on a server at a fixed frame rate, typically 30 or 60 frames per second, and reduce resolution when bandwidth is restricted. However, this strategy leads to suboptimal rendering quality under the bandwidth constraints. In this work, we exploit the spatio-temporal limits of the human visual system to improve perceived quality while reducing rendering costs by adaptively adjusting both frame rate and resolution based on scene content and motion. Our approach is codec-agnostic and requires only minimal modifications to existing rendering infrastructure. We propose a system in which a lightweight neural network predicts the optimal combination of frame rate and resolution for a given transmission bandwidth, content, and motion velocity. This prediction significantly enhances perceptual quality while minimizing computational cost under bandwidth constraints. The network is trained on a large dataset of rendered content labeled with a perceptual video quality metric. The dataset and further information can be found at the project web page: https://www.cl.cam.ac.uk/research/rainbow/projects/adaptive_streaming/.

eess.IV↗

arXiv2026

A Layer Separation Optimization Framework for Cross-Entropy Training in Deep Learning

This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models with fully connected and convolutional neural networks, we introduce auxiliary variables associated with hidden layer outputs and construct corresponding layer separation models, which decompose the original deeply nested optimization problem into a sequence of more manageable subproblems. We also conduct theoretical analyses, proving that the new layer separation loss provides an upper bound for the original cross-entropy loss. Moreover, we design alternating minimization algorithms and prove that, under appropriate conditions, these algorithms exhibit decreasing properties of the loss function. Numerical experiments validate the effectiveness of the proposed methods and indicate improved optimization behavior, especially for fully connected and convolutional neural networks.

cs.LG↗

arXiv2026

V-CAGE: Vision-Closed-Loop Agentic Generation Engine for Robotic Manipulation

Scaling Vision-Language-Action (VLA) models requires massive datasets that are both semantically coherent and physically feasible. However, existing scene generation methods often lack context-awareness, making it difficult to synthesize high-fidelity environments embedded with rich semantic information, frequently resulting in unreachable target positions that cause tasks to fail prematurely. We present V-CAGE (Vision-Closed-loop Agentic Generation Engine), an agentic framework for autonomous robotic data synthesis. Unlike traditional scripted pipelines, V-CAGE operates as an embodied agentic system, leveraging foundation models to bridge high-level semantic reasoning with low-level physical interaction. Specifically, we introduce Inpainting-Guided Scene Construction to systematically arrange context-aware layouts, ensuring that the generated scenes are both semantically structured and kinematically reachable. To ensure trajectory correctness, we integrate functional metadata with a Vision-Language Model based closed-loop verification mechanism, acting as a visual critic to rigorously filter out silent failures and sever the error propagation chain. Finally, to overcome the storage bottleneck of massive video datasets, we implement a perceptually-driven compression algorithm that achieves over 90\% filesize reduction without compromising downstream VLA training efficacy. By centralizing semantic layout planning and visual self-verification, V-CAGE automates the end-to-end pipeline, enabling the highly scalable synthesis of diverse, high-quality robotic manipulation datasets.

cs.RO↗

arXiv2026

Seeing enough: non-reference perceptual resolution selection for power-efficient client-side rendering

Many client-side applications, especially games, render video at high resolution and frame rate on power-constrained devices, even when users perceive little or no benefit from all those extra pixels. Existing perceptual video quality metrics can indicate when a lower resolution is "good enough", but they are full-reference and computationally expensive, making them impractical for real-world applications and deployment on-device. In this work, we leverage the spatio-temporal limits of the human visual system and propose a non-reference method that predicts, from the rendered video alone, the lowest resolution that remains perceptually indistinguishable from the best available option, enabling power-efficient client-side rendering. Our approach is codec-agnostic and requires only minimal modifications to existing infrastructure. The network is trained on a large dataset of rendered content labeled with a full-reference perceptual video quality metric. The prediction significantly enhances perceptual quality while substantially reducing computational costs, suggesting a practical path toward perception-guided, power-efficient client-side rendering.

cs.GR↗

arXiv2026

A generalized matrix-valued Allen--Cahn model and its numerical solution

This paper introduces a generalized matrix-valued Allen--Cahn model, where the unknown matrix-valued field belongs to $\mathbb{R}^{m_1\times m_2}$ with dimension $m_1\geq m_2$. By taking different values of $m_1$ and $m_2$, this model covers the classical scalar-valued, vector-valued, and square-matrix-valued Allen--Cahn equations. At the continuous level, the proposed model is proven to admit a unique solution satisfying the maximum bound principle (MBP) and the energy dissipation law. At the discrete level, a class of arbitrarily high-order exponential time differencing Runge-Kutta (ETDRK) schemes is investigated that preserve the MBP unconditionally. Moreover, we prove that the first- and second-order ETDRK schemes satisfy the discrete energy dissipation unconditionally, while third- and higher-order schemes preserve the discrete energy dissipation under suitable time-step constraints. The proof of sharp convergence order in time is provided. Numerical experiments are carried out to confirm our theoretical results.

math.NA↗

arXiv2026

V-CAGE: Context-Aware Generation and Verification for Scalable Long-Horizon Embodied Tasks

Learning long-horizon embodied behaviors from synthetic data remains challenging because generated scenes are often physically implausible, language-driven programs frequently "succeed" without satisfying task semantics, and high-level instructions require grounding into executable action sequences. To address these limitations, we introduce V-CAGE, a closed-loop framework for generating robust, semantically aligned manipulation datasets at scale. First, we propose a context-aware instantiation mechanism that enforces geometric consistency during scene synthesis. By dynamically maintaining a map of prohibited spatial areas as objects are placed, our system prevents interpenetration and ensures reachable, conflict-free configurations in cluttered environments. Second, to bridge the gap between abstract intent and low-level control, we employ a hierarchical instruction decomposition module. This decomposes high-level goals (e.g., "get ready for work") into compositional action primitives, facilitating coherent long-horizon planning. Crucially, we enforce semantic correctness through a VLM-based verification loop. Acting as a visual critic, the VLM performs rigorous rejection sampling after each subtask, filtering out "silent failures" where code executes but fails to achieve the visual goal. Experiments demonstrate that V-CAGE yields datasets with superior physical and semantic fidelity, significantly boosting the success rate and generalization of downstream policies compared to non-verified baselines.

cs.RO↗

arXiv2025

A General Strategy for Realizing Mpemba Effects in Open Quantum Systems

The Mpemba effect, where a state farther from equilibrium relaxes faster than one closer to it, is a striking phenomenon in both classical and quantum systems. In open quantum systems, however, the quantum Mpemba effect (QME) typically occurs only for specifically chosen initial states, which limits its universality. Here we present a general and experimentally feasible strategy to realize both QME and anti-QME. By applying a temporary bond-dissipation quench, we selectively suppresses or enhances slow relaxation modes, thereby reshaping relaxation pathways independently of both the system and the initial state. We demonstrate this mechanism in systems with dephasing and boundary dissipation, and outline feasible cold-atom implementations. Our results establish controllable dissipation as a versatile tool for quantum control, accelerated relaxation, and efficient nonequilibrium protocols.

quant-ph↗

arXiv2025

Real-Time Scene Reconstruction using Light Field Probes

Reconstructing photo-realistic large-scale scenes from images, for example at city scale, is a long-standing problem in computer graphics. Neural rendering is an emerging technique that enables photo-realistic image synthesis from previously unobserved viewpoints; however, state-of-the-art neural rendering methods have difficulty efficiently rendering a high complex large-scale scene because these methods typically trade scene size, fidelity, and rendering speed for quality. The other stream of techniques utilizes scene geometries for reconstruction. But the cost of building and maintaining a large set of geometry data increases as scene size grows. Our work explores novel view synthesis methods that efficiently reconstruct complex scenes without explicit use of scene geometries. Specifically, given sparse images of the scene (captured from the real world), we reconstruct intermediate, multi-scale, implicit representations of scene geometries. In this way, our method avoids explicitly relying on scene geometry, significantly reducing the computational cost of maintaining large 3D data. Unlike current methods, we reconstruct the scene using a probe data structure. Probe data hold highly accurate depth information of dense data points, enabling the reconstruction of highly complex scenes. By reconstructing the scene using probe data, the rendering cost is independent of the complexity of the scene. As such, our approach combines geometry reconstruction and novel view synthesis. Moreover, when rendering large-scale scenes, compressing and streaming probe data is more efficient than using explicit scene geometry. Therefore, our neural representation approach can potentially be applied to virtual reality (VR) and augmented reality (AR) applications.

cs.GR↗

arXiv2025

Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations

In this paper, we propose a new optimization framework, the layer separation (LySep) model, to improve the deep learning-based methods in solving partial differential equations. Due to the highly non-convex nature of the loss function in deep learning, existing optimization algorithms often converge to suboptimal local minima or suffer from gradient explosion or vanishing, resulting in poor performance. To address these issues, we introduce auxiliary variables to separate the layers of deep neural networks. Specifically, the output and its derivatives of each layer are represented by auxiliary variables, effectively decomposing the deep architecture into a series of shallow architectures. New loss functions with auxiliary variables are established, in which only variables from two neighboring layers are coupled. Corresponding algorithms based on alternating directions are developed, where many variables can be updated optimally in closed forms. Moreover, we provide theoretical analyses demonstrating the consistency between the LySep model and the original deep model. High-dimensional numerical results validate our theory and demonstrate the advantages of LySep in minimizing loss and reducing solution error.

cs.LG↗

arXiv2025

Deep Learning Optimization Using Self-Adaptive Weighted Auxiliary Variables

In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning because of the high non-convexity of loss functions and the vanishing gradient issue. Our idea is to introduce auxiliary variables to separate the layers of the deep neural networks and reformulate the loss functions for ease of optimization. We design the self-adaptive weights to preserve the consistency between the reformulated loss and the original mean squared loss, which guarantees that optimizing the new loss helps optimize the original problem. Numerical experiments are presented to verify the consistency and show the effectiveness and robustness of our models over gradient descent.

cs.LG↗

arXiv2024

sEMG-based Gesture-Free Hand Intention Recognition: System, Dataset, Toolbox, and Benchmark Results

In sensitive scenarios, such as meetings, negotiations, and team sports, messages must be conveyed without detection by non-collaborators. Previous methods, such as encrypting messages, eye contact, and micro-gestures, had problems with either inaccurate information transmission or leakage of interaction intentions. To this end, a novel gesture-free hand intention recognition scheme was proposed, that adopted surface electromyography(sEMG) and isometric contraction theory to recognize different hand intentions without any gesture. Specifically, this work includes four parts: (1) the experimental system, consisting of the upper computer software, self-conducted myoelectric watch, and sports platform, is built to get sEMG signals and simulate multiple usage scenarios; (2) the paradigm is designed to standard prompt and collect the gesture-free sEMG datasets. Eight-channel signals of ten subjects were recorded twice per subject at about 5-10 days intervals; (3) the toolbox integrates preprocessing methods (data segmentation, filter, normalization, etc.), commonly used sEMG signal decoding methods, and various plotting functions, to facilitate the research of the dataset; (4) the benchmark results of widely used methods are provided. The results involve single-day, cross-day, and cross-subject experiments of 6-class and 12-class gesture-free hand intention when subjects with different sports motions. To help future research, all data, hardware, software, and methods are open-sourced on the following website: click here.

cs.HC↗

arXiv2024

M^3ashy: Multi-Modal Material Synthesis via Hyperdiffusion

High-quality material synthesis is essential for replicating complex surface properties to create realistic scenes. Despite advances in the generation of material appearance based on analytic models, the synthesis of real-world measured BRDFs remains largely unexplored. To address this challenge, we propose M^3ashy, a novel multi-modal material synthesis framework based on hyperdiffusion. M^3ashy enables high-quality reconstruction of complex real-world materials by leveraging neural fields as a compact continuous representation of BRDFs. Furthermore, our multi-modal conditional hyperdiffusion model allows for flexible material synthesis conditioned on material type, natural language descriptions, or reference images, providing greater user control over material generation. To support future research, we contribute two new material datasets and introduce two BRDF distributional metrics for more rigorous evaluation. We demonstrate the effectiveness of Mashy through extensive experiments, including a novel statistics-based constrained synthesis, which enables the generation of materials of desired categories.

cs.GR↗

arXiv2024

Eikonal Approximation for Floquet Scattering

The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians, {\it i.e.}, the Floquet scattering problems. We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential, by comparing the results given by this approximation and the exact ones. The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field, {\it e.g.}, the manipulation of atom, molecule or nuclear collisions or reactions via strong laser fields.

quant-ph↗

arXiv2024

Dissipation induced extended-localized transition

Mobility edge (ME), representing the critical energy that distinguishes between extended and localized states, is a key concept in understanding the transition between extended (metallic) and localized (insulating) states in disordered and quasiperiodic systems. Here we explore the impact of dissipation on a quasiperiodic system featuring MEs by calculating steady-state density matrix and analyzing quench dynamics with sudden introduction of dissipation, and demonstrate that dissipation can lead the system into specific states predominantly characterized by either extended or localized states, irrespective of the initial state. Our results establish the use of dissipation as a new avenue for inducing transitions between extended and localized states, and for manipulating dynamic behaviors of particles.

cond-mat.dis-nn↗

arXiv2023

Maximum bound principle preserving and energy decreasing exponential time differencing schemes for the matrix-valued Allen-Cahn equation

This work delves into the exponential time differencing (ETD) schemes for the matrix-valued Allen-Cahn equation. In fact, the maximum bound principle (MBP) for the first- and second-order ETD schemes is presented in a prior publication [SIAM Review, 63(2), 2021], assuming a symmetric initial matrix field. Noteworthy is our novel contribution, demonstrating that the first- and second-order ETD schemes for the matrix-valued Allen-Cahn equation -- both being linear schemes -- unconditionally preserve the MBP, even in instances of nonsymmetric initial conditions. Additionally, we prove that these two ETD schemes preserve the energy dissipation law unconditionally for the matrix-valued Allen-Cahn equation. Some numerical examples are presented to verify our theoretical results and to simulate the evolution of corresponding matrix fields.

math.NA↗

arXiv2023

Extreme multistability in symmetrically coupled clocks

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyse a model for pendulum clocks coupled by springs and suspended on an oscillating base, and show how EM can be induced in this system by a specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

nlin.AO↗

arXiv2022

Convolutional Neural Networks with A Topographic Representation Module for EEG-Based Brain-Computer Interfaces

Objective: Convolutional Neural Networks (CNNs) have shown great potential in the field of Brain-Computer Interfaces (BCIs). The raw Electroencephalogram (EEG) signal is usually represented as 2-Dimensional (2-D) matrix composed of channels and time points, which ignores the spatial topological information. Our goal is to make the CNN with the raw EEG signal as input have the ability to learn EEG spatial topological features, and improve its performance while essentially maintaining its original structure. Methods:We propose an EEG Topographic Representation Module (TRM). This module consists of (1) a mapping block from the raw EEG signal to a 3-D topographic map and (2) a convolution block from the topographic map to an output of the same size as input. According to the size of the kernel used in the convolution block, we design 2 types of TRMs, namely TRM-(5,5) and TRM-(3,3). We embed the TRM into 3 widely used CNNs, and tested them on 2 publicly available datasets (Emergency Braking During Simulated Driving Dataset (EBDSDD), and High Gamma Dataset (HGD)). Results: The results show that the classification accuracies of all 3 CNNs are improved on both datasets after using the TRM. With TRM-(5,5), the average accuracies of DeepConvNet, EEGNet and ShallowConvNet are improved by 6.54%, 1.72% and 2.07% on EBDSDD, and by 6.05%, 3.02% and 5.14% on HGD, respectively; with TRM-(3,3), they are improved by 7.76%, 1.71% and 2.17% on EBDSDD, and by 7.61%, 5.06% and 6.28% on HGD, respectively. Significance: We improve the classification performance of 3 CNNs on 2 datasets by the use of TRM, indicating that it has the capability to mine the EEG spatial topological information. In addition, since the output of TRM has the same size as the input, CNNs with the raw EEG signal as input can use this module without changing their original structures.

eess.SP↗