arXiv subjects

Kai Xu

Publications and source records attributed to Kai Xu.

At least 163 records · Page 9Linked to original sources

arXiv2025

Enhancement of sensitivity near exceptional points in dissipative qubit-resonator systems

Dissipation usually plays a negative role in quantum metrological technologies, which aim to improve measurement precision by leveraging quantum effects that are vulnerable to environment-induced decoherence. Recently, it has been demonstrated that dissipation can actually be used as a favorable resource for enhancing the susceptibility of signal detection. However, demonstrations of such enhancement for detecting physical quantities in open quantum systems are still lacking. Here we propose and demonstrate a protocol for realizing such non-Hermitian quantum sensors for probing the coupling between a qubit and a resonator subjecting to energy dissipations. The excitation-number conversion associated with the no-jump evolution trajectory enables removal of the noisy outcomes with quantum jumps, implementing the exceptional point (EP), where the Rabi splitting exhibits a divergent behavior in response to a tiny variation of the effective coupling. The sensitivity enhancement near the EP is confirmed by both theoretical calculation and experimental measurement.

quant-ph↗

arXiv2025

Codimension 2 drawstrings with scalar curvature lower bounds

We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are given, primarily on questions concerning the stability of scalar curvature rigidity phenomena, such as Llarull's Theorem and the Positive Mass Theorem.

math.DG↗

arXiv2025

Quantum Avalanches in $\mathbb{Z}_2$-preserving Interacting Ising Majorana Chain

Recent numerical works have revealed the instability of many-body localized (MBL) phase in disordered quantum many-body systems with finite system sizes and over finite timescales. This instability arises from Griffith regions that occur at the thermodynamic limit, which rapidly thermalize and affect the surrounding typical MBL regions, introducing an avalanche mechanism into the system. Here, we consider the $\mathbb{Z}_2$-preserving interacting Ising Majorana chain model, which exhibits a more complex phase diagram, where an ergodic phase emerges between two MBL phases with different long-range order properties. We calculate the dynamic characteristics of the model when coupled to an infinite bath under perturbation, and through scaling behavior of the slowest thermalization rate, we find how critical disorder strengths in finite-size systems are affected by the avalanche mechanism. We also employe the embedded inclusion model and use the time evolution of mutual information between each spin and the artificial Griffith region to probe the diffusion of the thermal bubble. We observe that in finite-sized systems, the critical disorder strength gradually drifts away from the central. Our work demonstrate that both MBL paramagnetic phase and MBL spin-glass phase are unstable at finite sizes.

cond-mat.dis-nn↗

arXiv2025

Layout2Scene: 3D Semantic Layout Guided Scene Generation via Geometry and Appearance Diffusion Priors

3D scene generation conditioned on text prompts has significantly progressed due to the development of 2D diffusion generation models. However, the textual description of 3D scenes is inherently inaccurate and lacks fine-grained control during training, leading to implausible scene generation. As an intuitive and feasible solution, the 3D layout allows for precise specification of object locations within the scene. To this end, we present a text-to-scene generation method (namely, Layout2Scene) using additional semantic layout as the prompt to inject precise control of 3D object positions. Specifically, we first introduce a scene hybrid representation to decouple objects and backgrounds, which is initialized via a pre-trained text-to-3D model. Then, we propose a two-stage scheme to optimize the geometry and appearance of the initialized scene separately. To fully leverage 2D diffusion priors in geometry and appearance generation, we introduce a semantic-guided geometry diffusion model and a semantic-geometry guided diffusion model which are finetuned on a scene dataset. Extensive experiments demonstrate that our method can generate more plausible and realistic scenes as compared to state-of-the-art approaches. Furthermore, the generated scene allows for flexible yet precise editing, thereby facilitating multiple downstream applications.

cs.CV↗

arXiv2024

DAS3R: Dynamics-Aware Gaussian Splatting for Static Scene Reconstruction

We propose a novel framework for scene decomposition and static background reconstruction from everyday videos. By integrating the trained motion masks and modeling the static scene as Gaussian splats with dynamics-aware optimization, our method achieves more accurate background reconstruction results than previous works. Our proposed method is termed DAS3R, an abbreviation for Dynamics-Aware Gaussian Splatting for Static Scene Reconstruction. Compared to existing methods, DAS3R is more robust in complex motion scenarios, capable of handling videos where dynamic objects occupy a significant portion of the scene, and does not require camera pose inputs or point cloud data from SLAM-based methods. We compared DAS3R against recent distractor-free approaches on the DAVIS and Sintel datasets; DAS3R demonstrates enhanced performance and robustness with a margin of more than 2 dB in PSNR. The project's webpage can be accessed via \url{https://kai422.github.io/DAS3R/}

cs.CV↗

arXiv2024

Topological eigenvalues braiding and quantum state transfer near a third-order exceptional point

Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EP). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems, which emerge after encircling the EP either quasistatically or dynamically. However, experimental exploration of EP encirclement in quantum systems, particularly those involving high-order EPs, remains challenging due to the difficulty of coherently controlling more degrees of freedom. In this work, we experimentally investigate the eigenvalues braiding and state transfer arising from the encirclement of EP in a three-dimensional non-Hermitian quantum system using superconducting circuits. We characterize the second- and third-order EPs through the coalescence of eigenvalues. Then we reveal the topological structure near the EP3 by quasistatically encircling it along various paths with three independent parameters, which yields the eigenvalues braiding described by the braid group $B_3$. Additionally, we observe chiral state transfer between three eigenstates under a fast driving scheme when no EPs are enclosed, while time-symmetric behavior occurs when at least one EP is encircled. Our findings offer insights into understanding non-Hermitian topological structures and the manipulation of quantum states through dynamic operations.

quant-ph↗

arXiv2024

A sharp spectral splitting theorem

We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold $M$ of dimension $n\geq 2$ has at least two ends and \[ λ_1(-γΔ+\mathrm{Ric})\geq 0, \] for some $γ<\frac{4}{n-1}$, then $M$ splits isometrically as $\mathbb R\times N$ for some compact manifold $N$ with nonnegative Ricci curvature. We show that the constant $\frac{4}{n-1}$ is sharp, and the multiple-end assumption is necessary for any $γ>0$.

math.DG↗

arXiv2024

Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small LLMs

The rise of large language models (LLMs) has created a significant disparity: industrial research labs with their computational resources, expert teams, and advanced infrastructures, can effectively fine-tune LLMs, while individual developers and small organizations face barriers due to limited resources. In this paper, we aim to bridge this gap by presenting a comprehensive study on supervised fine-tuning of LLMs using instruction-tuning datasets spanning diverse knowledge domains and skills. We focus on small-sized LLMs (3B to 7B parameters) for their cost-efficiency and accessibility. We explore various training configurations and strategies across four open-source pre-trained models. We provide detailed documentation of these configurations, revealing findings that challenge several common training practices, including hyperparameter recommendations from TULU and phased training recommended by Orca. Key insights from our work include: (i) larger batch sizes paired with lower learning rates lead to improved model performance on benchmarks such as MMLU, MTBench, and Open LLM Leaderboard; (ii) early-stage training dynamics, such as lower gradient norms and higher loss values, are strong indicators of better final model performance, enabling early termination of sub-optimal runs and significant computational savings; (iii) through a thorough exploration of hyperparameters like warmup steps and learning rate schedules, we provide guidance for practitioners and find that certain simplifications do not compromise performance; and (iv) we observed no significant difference in performance between phased and stacked training strategies, but stacked training is simpler and more sample efficient. With these findings holding robustly across datasets and models, we hope this study serves as a guide for practitioners fine-tuning small LLMs and promotes a more inclusive environment for LLM research.

cs.LG↗

arXiv2024

Neural Observation Field Guided Hybrid Optimization of Camera Placement

Camera placement is crutial in multi-camera systems such as virtual reality, autonomous driving, and high-quality reconstruction. The camera placement challenge lies in the nonlinear nature of high-dimensional parameters and the unavailability of gradients for target functions like coverage and visibility. Consequently, most existing methods tackle this challenge by leveraging non-gradient-based optimization methods.In this work, we present a hybrid camera placement optimization approach that incorporates both gradient-based and non-gradient-based optimization methods. This design allows our method to enjoy the advantages of smooth optimization convergence and robustness from gradient-based and non-gradient-based optimization, respectively. To bridge the two disparate optimization methods, we propose a neural observation field, which implicitly encodes the coverage and observation quality. The neural observation field provides the measurements of the camera observations and corresponding gradients without the assumption of target scenes, making our method applicable to diverse scenarios, including 2D planar shapes, 3D objects, and room-scale 3D scenes.Extensive experiments on diverse datasets demonstrate that our method achieves state-of-the-art performance, while requiring only a fraction (8x less) of the typical computation time. Furthermore, we conducted a real-world experiment using a custom-built capture system, confirming the resilience of our approach to real-world environmental noise.

cs.CV↗

arXiv2024

Simultaneous Image-to-Zero and Zero-to-Noise: Diffusion Models with Analytical Image Attenuation

Recent studies have demonstrated that the forward diffusion process is crucial for the effectiveness of diffusion models in terms of generative quality and sampling efficiency. We propose incorporating an analytical image attenuation process into the forward diffusion process for high-quality (un)conditioned image generation with significantly fewer denoising steps compared to the vanilla diffusion model requiring thousands of steps. In a nutshell, our method represents the forward image-to-noise mapping as simultaneous \textit{image-to-zero} mapping and \textit{zero-to-noise} mapping. Under this framework, we mathematically derive 1) the training objectives and 2) for the reverse time the sampling formula based on an analytical attenuation function which models image to zero mapping. The former enables our method to learn noise and image components simultaneously which simplifies learning. Importantly, because of the latter's analyticity in the \textit{zero-to-image} sampling function, we can avoid the ordinary differential equation-based accelerators and instead naturally perform sampling with an arbitrary step size. We have conducted extensive experiments on unconditioned image generation, \textit{e.g.}, CIFAR-10 and CelebA-HQ-256, and image-conditioned downstream tasks such as super-resolution, saliency detection, edge detection, and image inpainting. The proposed diffusion models achieve competitive generative quality with much fewer denoising steps compared to the state of the art, thus greatly accelerating the generation speed. In particular, to generate images of comparable quality, our models require only one-twentieth of the denoising steps compared to the baseline denoising diffusion probabilistic models. Moreover, we achieve state-of-the-art performances on the image-conditioned tasks using only no more than 10 steps.

cs.CV↗

arXiv2024

GSEditPro: 3D Gaussian Splatting Editing with Attention-based Progressive Localization

With the emergence of large-scale Text-to-Image(T2I) models and implicit 3D representations like Neural Radiance Fields (NeRF), many text-driven generative editing methods based on NeRF have appeared. However, the implicit encoding of geometric and textural information poses challenges in accurately locating and controlling objects during editing. Recently, significant advancements have been made in the editing methods of 3D Gaussian Splatting, a real-time rendering technology that relies on explicit representation. However, these methods still suffer from issues including inaccurate localization and limited manipulation over editing. To tackle these challenges, we propose GSEditPro, a novel 3D scene editing framework which allows users to perform various creative and precise editing using text prompts only. Leveraging the explicit nature of the 3D Gaussian distribution, we introduce an attention-based progressive localization module to add semantic labels to each Gaussian during rendering. This enables precise localization on editing areas by classifying Gaussians based on their relevance to the editing prompts derived from cross-attention layers of the T2I model. Furthermore, we present an innovative editing optimization method based on 3D Gaussian Splatting, obtaining stable and refined editing results through the guidance of Score Distillation Sampling and pseudo ground truth. We prove the efficacy of our method through extensive experiments.

cs.CV↗

arXiv2024

Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling

Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the (aggregate) posterior to encourage statistical independence of the latent factors. This approach introduces a trade-off between disentangled representation learning and reconstruction quality since the model does not have enough capacity to learn correlated latent variables that capture detail information present in most image data. To overcome this trade-off, we present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method; then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables, adding detail information while maintaining conditioning on the previously learned disentangled factors. Taken together, our multi-stage modelling approach results in a single, coherent probabilistic model that is theoretically justified by the principal of D-separation and can be realized with a variety of model classes including likelihood-based models such as variational autoencoders, implicit models such as generative adversarial networks, and tractable models like normalizing flows or mixtures of Gaussians. We demonstrate that our multi-stage model has higher reconstruction quality than current state-of-the-art methods with equivalent disentanglement performance across multiple standard benchmarks. In addition, we apply the multi-stage model to generate synthetic tabular datasets, showcasing an enhanced performance over benchmark models across a variety of metrics. The interpretability analysis further indicates that the multi-stage model can effectively uncover distinct and meaningful features of variations from which the original distribution can be recovered.

stat.ML↗

arXiv2024

A topological gap theorem for the $π_2$-systole of positive scalar curvature 3-manifolds

Let $M$ be a closed orientable 3-manifold with scalar curvature greater than or equal to 1. If $M$ has nonvanishing second homotopy group, then it is known that the $π_2$-systole of $M$ (i.e. the minimal achievable area of homotopically nontrivial spheres) is at most $8π$. We prove the following gap theorem: if $M$ is further not a quotient of $S^2\times S^1$, then the $π_2$-systole of $M$ is no greater than an improved constant $c\approx 5.44π$. This statement follows as a new topological application of Huisken and Ilmanen's weak inverse mean curvature flow.

math.DG↗

arXiv2024

Privacy without Noisy Gradients: Slicing Mechanism for Generative Model Training

Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure. As a result, such approaches often struggle with hyper-parameter tuning and convergence. We consider the slicing privacy mechanism that injects noise into random low-dimensional projections of the private data, and provide strong privacy guarantees for it. These noisy projections are used for training generative models. To enable optimizing generative models using this DP approach, we introduce the smoothed-sliced $f$-divergence and show it enjoys statistical consistency. Moreover, we present a kernel-based estimator for this divergence, circumventing the need for adversarial training. Extensive numerical experiments demonstrate that our approach can generate synthetic data of higher quality compared with baselines. Beyond performance improvement, our method, by sidestepping the need for noisy gradients, offers data scientists the flexibility to adjust generator architecture and hyper-parameters, run the optimization over any number of epochs, and even restart the optimization process -- all without incurring additional privacy costs.

cs.LG↗

arXiv2024

High-precision pulse calibration of tunable couplers for high-fidelity two-qubit gates in superconducting quantum processors

For superconducting quantum processors, stable high-fidelity two-qubit operations depend on precise flux control of the tunable coupler. However, the pulse distortion poses a significant challenge to the control precision. Current calibration methods, which often rely on microwave crosstalk or additional readout resonators for coupler excitation and readout, tend to be cumbersome and inefficient, especially when couplers only have flux control. Here, we introduce and experimentally validate a novel pulse calibration scheme that exploits the strong coupling between qubits and couplers, eliminating the need for extra coupler readout and excitation. Our method directly measures the short-time and long-time step responses of the coupler flux pulse transient, enabling us to apply predistortion to subsequent signals using fast Fourier transformation and deconvolution. This approach not only simplifies the calibration process but also significantly improves the precision and stability of the flux control. We demonstrate the efficacy of our method through the implementation of diabatic CZ and iSWAP gates with fidelities of $99.61\pm0.04\%$ and $99.82\pm0.02\%$, respectively, as well as a series of diabatic CPhase gates with high fidelities characterized by cross-entropy benchmarking. The consistency and robustness of our technique are further validated by the reduction in pulse distortion and phase error observed across multilayer CZ gates. These results underscore the potential of our calibration and predistortion method to enhance the performance of two-qubit gates in superconducting quantum processors.

quant-ph↗

arXiv2024

PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis

View synthesis using Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) has demonstrated impressive fidelity in rendering real-world scenarios. However, practical methods for accurate and efficient epistemic Uncertainty Quantification (UQ) in view synthesis are lacking. Existing approaches for NeRF either introduce significant computational overhead (e.g., ``10x increase in training time" or ``10x repeated training") or are limited to specific uncertainty conditions or models. Notably, GS models lack any systematic approach for comprehensive epistemic UQ. This capability is crucial for improving the robustness and scalability of neural view synthesis, enabling active model updates, error estimation, and scalable ensemble modeling based on uncertainty. In this paper, we revisit NeRF and GS-based methods from a function approximation perspective, identifying key differences and connections in 3D representation learning. Building on these insights, we introduce PH-Dropout (Post hoc Dropout), the first real-time and accurate method for epistemic uncertainty estimation that operates directly on pre-trained NeRF and GS models. Extensive evaluations validate our theoretical findings and demonstrate the effectiveness of PH-Dropout.

cs.CV↗

arXiv2024

LInK: Learning Joint Representations of Design and Performance Spaces through Contrastive Learning for Mechanism Synthesis

In this paper, we introduce LInK, a novel framework that integrates contrastive learning of performance and design space with optimization techniques for solving complex inverse problems in engineering design with discrete and continuous variables. We focus on the path synthesis problem for planar linkage mechanisms. By leveraging a multimodal and transformation-invariant contrastive learning framework, LInK learns a joint representation that captures complex physics and design representations of mechanisms, enabling rapid retrieval from a vast dataset of over 10 million mechanisms. This approach improves precision through the warm start of a hierarchical unconstrained nonlinear optimization algorithm, combining the robustness of traditional optimization with the speed and adaptability of modern deep learning methods. Our results on an existing benchmark demonstrate that LInK outperforms existing methods with 28 times less error compared to a state of the art approach while taking 20 times less time on an existing benchmark. Moreover, we introduce a significantly more challenging benchmark, named LINK ABC, which involves synthesizing linkages that trace the trajectories of English capital alphabets, an inverse design benchmark task that existing methods struggle with due to large nonlinearities and tiny feasible space. Our results demonstrate that LInK not only advances the field of mechanism design but also broadens the applicability of contrastive learning and optimization to other areas of engineering. The code and data are publicly available at https://github.com/ahnobari/LInK.

cs.LG↗

arXiv2024

Dimension constraints in some problems involving intermediate curvature

In arXiv:2207.08617 [math.DG] Brendle-Hirsch-Johne proved that $T^m\times S^{n-m}$ does not admit metrics with positive $m$-intermediate curvature when $n\leq 7$. Chu-Kwong-Lee showed in arXiv:2208.12240 [math.DG] a corresponding rigidity statement when $n\leq 5$. In this paper, we show the sharpness of the dimension constraints by giving concrete counterexamples in $n\geq 7$ and extending the rigidity result to $n=6$. Concerning uniformly positive intermediate curvature, we show that simply-connected manifolds with dimension $\leq 5$ and bi-Ricci curvature $\geq 1$ have finite Urysohn 1-width. Counterexamples are constructed in dimension $\geq 6$.

math.DG↗