arXiv subjects

Yuxi Cai

Publications and source records attributed to Yuxi Cai.

At least 19 recordsLinked to original sources

arXiv2026

ParaRNN: An Interpretable and Parallelizable Recurrent Neural Network for Time-Dependent Data

The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can be viewed as nonlinear extensions of classical autoregressive moving average models. Despite their flexibility and empirical success in machine learning, RNNs often suffer from limited interpretability and slow training, which hinders their use in statistics. This paper proposes the Parallelized RNN (ParaRNN), a novel model composed of multiple small recurrent units. ParaRNN admits an additive representation that decouples recurrent dynamics into interpretable components, whose behavior can be characterized through recurrence features. This interpretability enables its applications in nonparametric regression for time-dependent data, while the design also allows efficient parallelization. The approximation capacity and non-asymptotic prediction error bounds in a nonparametric regression setting are established for ParaRNN. Empirical results on three sequential modeling tasks further demonstrate that ParaRNN achieves performance comparable to vanilla RNNs while offering improved interpretability and efficiency.

stat.ML↗

arXiv2026

Skyrmions based on optical anisotropy for topological encoding

The observation of skyrmions across diverse physical domains suggests that they are universal features of S$^{2}$-valued fields, reflecting the ubiquity of topology in the study of the natural world. In this paper, we develop an abstract technique of parameter space dimensionality reduction that extends the skyrmion framework to fields taking values in manifolds of dimension greater than 2, thereby broadening the range of systems that can support skyrmions. To prove that this is more than just a mathematical abstraction, we apply our technique to light-matter interactions, directly encoding skyrmionic structures into the optical anisotropy of spatially varying structured matter by selecting a distinguished axis, an approach fundamentally different from the more commonly known skyrmions formed by director fields in liquid crystals. We experimentally realize such skyrmions using a liquid-crystal-based tunable elliptical retarder array as a proof-of-concept platform and demonstrate complex, reconfigurable skyrmionic states exhibiting topological robustness under artificially introduced stochastic perturbations. Exploiting this robustness, we demonstrate a promising application of skyrmions in topologically protected information storage and provide an easily verifiable rule, which we term the 60° rule, that serves as a practical engineering criterion for guaranteeing robustness against noise and measurement errors.

physics.optics↗

arXiv2026

Topologically robust programmable logic arrays using light and matter skyrmions

Photonic computing offers a low-power, high-bandwidth paradigm for information processing; however, the analogue nature of conventional architectures means that intrinsic noise and fabrication imperfections greatly impact performance, thereby severely limiting scalability. Recent work on optical skyrmions offers a route to overcoming these limitations by exploiting perturbation-resilient topological invariants assigned to the optical field for computation. Crucially, owing to its relative novelty, an architectural perspective on integrating individual components that manipulate topological charge into a functional system remains an important open goal. In this paper, we take concrete steps toward system-level design by introducing a platform-independent architecture for skyrmion-based logic, built around a modular library of topologically robust optical primitives, including generators, converters, registers, and adders. This framework enables the synthesis and arithmetic manipulation of topological numbers within a unified programmable architecture. We then experimentally validate this approach using multichannel arrays, demonstrating accurate charge readout and high robustness against alignment errors and environmental noise. These results provide a scalable foundation for topologically robust programmable logic arrays, paving the way for compact and integrated photonic processing circuits.

physics.optics↗

arXiv2026

General in situ feedback control of cascaded liquid crystal spatial light modulators for structured field generation

Cascaded liquid crystal spatial light modulators provide a versatile strategy for the generation of structured light and matter fields, with applications including optical communications, photonic computing, and topological field engineering. However, experimental imperfections, such as temperature-dependent liquid crystal response, variations between individual pixels, and alignment errors, present significant engineering challenges in generating high-quality fields. Moreover, changes in experimental conditions over time mean that calibrating each component once is insufficient for maintaining long-term, high-quality field generation. To address this, we present a general engineering approach based on a bespoke, physically informed, and manifold-constrained gradient-descent scheme that enables in situ feedback control, compensating for such errors in real time without the need to alter the experimental setup. We further demonstrate the correction efficacy of our proposed strategy through experiments in both spatially varying light and matter field generation, including scenarios in which complex vectorial aberrations are artificially introduced into the setup. Together, these demonstrations underscore the practicality of our method and its suitability for deployment in real-world experimental environments, paving the way for robust operation of cascaded architectures for structured field generation.

physics.optics↗

arXiv2026

Resolving topological obstructions to vectorial structured field control

The use of structured matter, such as optical retarders, for vectorial control is a well-established and widely employed technique in modern optics, and has driven continued advances in the manipulation of complex, spatially varying vectorial fields. However, achieving arbitrary field conversion typically requires the use of cascaded elements, as intrinsic physical and fabrication constraints fundamentally limit individual devices to a restricted subset of transformations. This results in an overall continuous transformation potentially failing to be continuous at the level of the parameters of the cascade, leading to detrimental engineering consequences such as the introduction of complex, discontinuous aberrations that disrupt important topological properties of the underlying matter field. In this work, we establish a novel mathematical framework for analyzing the topological difficulties that emerge in the decomposition of an overall transformation into individual layers, and for determining the minimal depth required to overcome them. The strategy introduced provides a general pathway for optimizing designs for vectorial field control and matter field generation, with particular significance for the manipulation of topological phases in optical polarization fields, such as Stokes skyrmions, where continuity is of vital importance.

physics.optics↗

arXiv2025

Rethinking conditioning in polarimetry: a new framework beyond $\ell^2$-based metrics

A standard procedure to achieve accurate, precise, and fast polarization measurement is to choose analyzing and generating polarization states that yield an $\ell^2$-condition number optimized instrument matrix. This strategy works well for rotating-waveplate systems, where the accessible polarization states trace a curve on the Poincaré sphere and the corresponding optimization problem is generally well posed. However, it becomes degenerate for liquid-crystal-based systems, which can generate arbitrary polarization states, and whose additional degrees of freedom allow the optimization of metrics beyond the $\ell^2$-condition number. Leveraging this unique advantage of liquid-crystal polarimeters, we introduce additional performance measures derived from alternative norms and error distributions computed via Monte Carlo simulations to inform the design of measurement schemes. We then experimentally demonstrate their effectiveness in suppressing errors, paving the way for more robust and efficient polarization measurements.

physics.optics↗

arXiv2025

Perturbation-resilient integer arithmetic using optical skyrmions

The decline of Moore's law coupled with the rise of artificial intelligence has recently motivated research into photonic computing as a high-bandwidth, low-power strategy to accelerate digital electronics. However, many modern-day photonic computing strategies are analog, making them susceptible to noise and intrinsically difficult to scale. Optical skyrmions offer a route to overcoming these limitations through digitization in the form of a discrete topological number that can be assigned to the analog optical field. Apart from an intrinsic robustness against perturbations, optical skyrmions represent a new medium that has yet to be fully exploited for photonic computing, namely spatially varying polarization. Here, we propose and experimentally demonstrate a method for performing perturbation-resilient integer arithmetic with optical skyrmions and passive optical components. To the best of our knowledge, this is the first time such discrete mathematical operations have been directly achieved using optical skyrmions without external energy input.

physics.optics↗

arXiv2025

A reconfigurable arbitrary retarder array as complex structured matter

Tuneable retarder arrays, such as spatially patterned liquid crystal devices, have given rise to impressive photonic functionality, fuelling diverse applications ranging from microscopy and holography to encryption and communications. Presently these solutions are limited by the controllable degrees of freedom of structured matter, hindering applications that demand photonic systems with high flexibility and reconfigurable topologies. Here we demonstrate a compound modulator that implements a synthetic tuneable arbitrary retarder array as virtual pixels derived by cascading low functionality tuneable devices, realising full dynamic control of its arbitrary elliptical axis geometry, retardance value, and induced phase. Our approach offers unprecedented functionality that is user-defined and possesses high flexibility, allowing our modulator to act as a new beam generator, analyser, and corrector, opening an exciting path to tuneable topologies of light and matter.

physics.optics↗

arXiv2025

An Efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor order. Conversely, canonical polyadic (CP) decomposition maintains efficiency but lacks a precise statistical interpretation. To attain both interpretability and powerful dimension reduction, this paper proposes a novel approach under the supervised factor modeling paradigm, which first uses CP decomposition to extract response and covariate features separately and then regresses response features on covariate ones. This leads to a new CP-based low-rank structure for the coefficient tensor. Furthermore, to address heterogeneous signals or potential model misspecifications arising from stringent low-rank assumptions, a low-rank plus sparse model is introduced by incorporating an additional sparse coefficient tensor. Nonasymptotic properties are established for the ordinary least squares estimators, and an alternating least squares algorithm is introduced for optimization. Theoretical properties of the proposed methodology are validated by simulation studies, and its enhanced prediction performance and interpretability are demonstrated by the El Ni$\tilde{\text{n}}$o-Southern Oscillation example.

stat.ME↗

arXiv2025

Optical Skyrmions in Waveguides

Optical skyrmions are topologically non-trivial polarization fields which have recently attracted attention due to their potential use in high density data applications such as optical communications, photonic computing and more. An important hurdle in utilizing optical skyrmions for such applications is establishing conditions under which their topological structure remains preserved during propagation: while results of this type already exist for paraxial beams in free-space propagation, the critical case relevant to modern applications involves propagation in confined media, such as waveguide systems. In this paper, we demonstrate for the first time that, within a conducting waveguide, the preservation of the skyrmion number during propagation is determined by the presence of so-called topologically stabilizing modes. If such a mode is present, not only will topological protection hold despite the transverse polarization profile changing due to modal dispersion, but there is also a degree of robustness to variations in the coefficients of TE and TM modes present. Lastly, we demonstrate how a generalized skyrmion number can recover topological protection in situations where the usual skyrmion number is not preserved. Our methods open new avenues for robust high-dimensional information manipulation in waveguiding systems.

physics.optics↗

arXiv2024

Generalized Skyrmions

Skyrmions are important topologically non-trivial fields characteristic of models spanning scales from the microscopic to the cosmological. However, the Skyrmion number can only be defined for fields with specific boundary conditions, limiting its use in broader contexts. Here, we address this issue through a generalized notion of the Skyrmion derived from the De Rham cohomology of compactly supported forms. This allows for the definition of an entirely new $\coprod_{i=1}^\infty \mathbb{Z}^i$-valued topological number that assigns a tuple of integers $(a_1, \ldots, a_k)\in \mathbb{Z}^k$ to a field instead of a single number, with no restrictions to its boundary. The notion of the generalized Skyrmion presented in this paper is completely abstract and can be applied to vector fields in any discipline, not unlike index theory within dynamical systems. To demonstrate the power of our new formalism, we focus on the propagation of optical polarization fields and show that our newly defined generalized Skyrmion number significantly increases the dimension of data that can be stored within the field while also demonstrating strong robustness. Our work represents a fundamental paradigm shift away from the study of fields with natural topological character to engineered fields that can be artificially embedded with topological structures.

physics.optics↗

arXiv2024

Topological Protection of Optical Skyrmions through Complex Media

Optical Skyrmions have many important properties that make them ideal units for high-density data applications, including the ability to carry digital information through a discrete topological number and the independence of spatially varying polarization to other dimensions. More importantly, the topological nature of the optical Skyrmion heuristically suggests a strong degree of robustness to perturbations, which is crucial for reliably carrying information in noisy environments. However, the study of the topological robustness of optical Skyrmions is still in its infancy. Here, we quantify this robustness precisely by proving that the topological nature of the Skyrmion arises from its structure on the boundary and, by duality, is therefore resilient to complex perturbations provided they respect the relevant boundary conditions of the unperturbed Skyrmion. We then present experimental evidence validating this robustness in the context of paraxial Skyrmion beams against different polarization aberrations. Our work provides a framework for handling various perturbations of Skyrmion fields and offers guarantees of robustness in a general sense. This, in turn, has implications for applications of the optical Skyrmion where their topological nature is exploited explicitly, and, in particular, provides an underpinning for the use of Skyrmions in optical communications and photonic computing.

physics.optics↗

arXiv2024

An efficient tensor regression for high-dimensional data

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it to tensor regression such that a nice statistical interpretation can be obtained. The new tensor regression can well match the data with hierarchical structures, and it even can lead to a better interpretation for the data with factorial structures, which are supposed to be better fitted by models with Tucker decomposition. More importantly, the new tensor regression can be easily applied to the case with higher order tensors since TT decomposition can compress the coefficient tensors much more efficiently. The methodology is also extended to tensor autoregression for time series data, and nonasymptotic properties are derived for the ordinary least squares estimations of both tensor regression and autoregression. A new algorithm is introduced to search for estimators, and its theoretical justification is also discussed. Theoretical and computational properties of the proposed methodology are verified by simulation studies, and the advantages over existing methods are illustrated by two real examples.

stat.ME↗

arXiv2023

Cross-Layer Retrospective Retrieving via Layer Attention

More and more evidence has shown that strengthening layer interactions can enhance the representation power of a deep neural network, while self-attention excels at learning interdependencies by retrieving query-activated information. Motivated by this, we devise a cross-layer attention mechanism, called multi-head recurrent layer attention (MRLA), that sends a query representation of the current layer to all previous layers to retrieve query-related information from different levels of receptive fields. A light-weighted version of MRLA is also proposed to reduce the quadratic computation cost. The proposed layer attention mechanism can enrich the representation power of many state-of-the-art vision networks, including CNNs and vision transformers. Its effectiveness has been extensively evaluated in image classification, object detection and instance segmentation tasks, where improvements can be consistently observed. For example, our MRLA can improve 1.6% Top-1 accuracy on ResNet-50, while only introducing 0.16M parameters and 0.07B FLOPs. Surprisingly, it can boost the performances by a large margin of 3-4% box AP and mask AP in dense prediction tasks. Our code is available at https://github.com/joyfang1106/MRLA.

cs.CV↗

arXiv2022

Lightweight Spatial-Channel Adaptive Coordination of Multilevel Refinement Enhancement Network for Image Reconstruction

Benefiting from the vigorous development of deep learning, many CNN-based image super-resolution methods have emerged and achieved better results than traditional algorithms. However, it is difficult for most algorithms to adaptively adjust the spatial region and channel features at the same time, let alone the information exchange between them. In addition, the exchange of information between attention modules is even less visible to researchers. To solve these problems, we put forward a lightweight spatial-channel adaptive coordination of multilevel refinement enhancement networks(MREN). Specifically, we construct a space-channel adaptive coordination block, which enables the network to learn the spatial region and channel feature information of interest under different receptive fields. In addition, the information of the corresponding feature processing level between the spatial part and the channel part is exchanged with the help of jump connection to achieve the coordination between the two. We establish a communication bridge between attention modules through a simple linear combination operation, so as to more accurately and continuously guide the network to pay attention to the information of interest. Extensive experiments on several standard test sets have shown that our MREN achieves superior performance over other advanced algorithms with a very small number of parameters and very low computational complexity.

cs.CV↗

arXiv2022

Image Reconstruction of Multi Branch Feature Multiplexing Fusion Network with Mixed Multi-layer Attention

Image super-resolution reconstruction achieves better results than traditional methods with the help of the powerful nonlinear representation ability of convolution neural network. However, some existing algorithms also have some problems, such as insufficient utilization of phased features, ignoring the importance of early phased feature fusion to improve network performance, and the inability of the network to pay more attention to high-frequency information in the reconstruction process. To solve these problems, we propose a multi-branch feature multiplexing fusion network with mixed multi-layer attention (MBMFN), which realizes the multiple utilization of features and the multistage fusion of different levels of features. To further improve the networks performance, we propose a lightweight enhanced residual channel attention (LERCA), which can not only effectively avoid the loss of channel information but also make the network pay more attention to the key channel information and benefit from it. Finally, the attention mechanism is introduced into the reconstruction process to strengthen the restoration of edge texture and other details. A large number of experiments on several benchmark sets show that, compared with other advanced reconstruction algorithms, our algorithm produces highly competitive objective indicators and restores more image detail texture information.

cs.CV↗

arXiv2021

SigVM: Enabling Event-Driven Execution for Autonomous Smart Contracts

This paper presents SigVM, a novel blockchain virtual machine that supports an event-driven execution model, enabling developers to build autonomous smart contracts. Contracts in SigVM can emit signal events, on which other contracts can listen. Once an event is triggered, corresponding handler functions are automatically executed as signal transactions. We build an end-to-end blockchain platform SigChain and a contract language compiler SigSolid to realize the potential of SigVM. Experimental results show that our benchmark applications can be reimplemented with SigVM in an autonomous way, eliminating the dependency on unreliable mechanisms like off-chain relay servers. The development effort of reimplementing these contracts with SigVM is small, i.e., we modified on average 2.6% of the contract code.

cs.PL↗

arXiv2021

DL-AMP and DBTO: An Automatic Merge Planning and Trajectory Optimization and Its Application in Autonomous Driving

This paper presents an automatic merging algorithm for autonomous driving vehicles, which decouples the specific motion planning problem into a Dual-Layer Automatic Merge Planning (DL_AMP) and a Descent-Based Trajectory Optimization (DBTO). This work leads to great improvements in finding the best merge opportunity, lateral and longitudinal merge planning and control, trajectory postprocessing and driving comfort.

cs.RO↗