arXiv subjects

Beicheng Lou

Publications and source records attributed to Beicheng Lou.

14 recordsLinked to original sources

arXiv2026

CRoPE: Efficient Parametrization of Rotary Positional Embedding

Rotary positional embedding has become the state-of-the-art approach to encode position information in transformer-based models. While it is often succinctly expressed in complex linear algebra, we note that the actual implementation of $Q/K/V$-projections is not equivalent to a complex linear transformation. We argue that complex linear transformation is a more natural parametrization and saves near 50\% parameters within the attention block. We show empirically that removing such redundancy has negligible impact on the model performance. Our modification achieves more efficient parameter usage, as well as a cleaner interpretation of the representation space.

cs.LG↗

arXiv2024

Twist-Induced Beam Steering and Blazing Effects in Photonic Crystal Devices

Twisted bilayer photonic crystals introduce a twist between two stacked photonic crystal slabs, enabling strong modulation of their electromagnetic properties. The change in the twist angle strongly influences the resonant frequencies and available propagating diffraction orders with applications including sensing, lasing, slow light or wavefront engineering. In this work, we design and analyze twisted bilayer crystals capable of steering light in a direction controlled by the twist angle. In order to achieve beam steering, the device efficiently routes input power into a single, twist-dependent, transmitted diffraction order. The outgoing light then follows the orientation of this diffraction order, externally controlled by the twist angle. The optimization is performed using high-efficiency heuristic optimization method which enabled a data-oriented approach to further understand the design operation. The optimized device demonstrates an efficiency above 90% across twist angles ranging from 0 to 30 degrees for both TE and TM polarizations. Extending the optimization to include left- and right-handed polarizations yields overall accuracy nearing 90% when averaged across the entire 0 to 60 degrees control range. Finally, we show how the device resembles blazed gratings by effectively canceling the undesired diffraction orders. The optimized devices exhibit a shared slant dependent on the selected diffraction order. Our analysis is supported by a structural blazing model arising from the data-oriented statistical analysis.

physics.optics↗

arXiv2024

Control of chirality and directionality of nonlinear metasurface light source via twisting

Metasurfaces have revolutionized nonlinear and quantum light manipulation in the past decade, enabling the design of materials that can tune polarization, frequency, and direction of light simultaneously. However, tuning of metasurfaces is traditionally achieved by changing their microscopic structure, which does not allow \emph{in situ} tuning and dynamic optimization of the metasurfaces. In this Letter, we explore the concept of twisted bilayer and tetralayer nonlinear metasurfaces, which offer rich tunability in its effective nonlinear susceptibilities. Using gold-based metasurfaces, we demonstrate that a number of different singularities of nonlinear susceptibilities can exist in the parameter space of twist angle and interlayer gap between different twisted layers. At the singularities, reflected/transmitted light from the nonlinear process (such as second-harmonic generation) can either become circularly polarized (for C points), or entirely vanish (for V points). By further breaking symmetries of the system, we can independently tune all aspects of the reflected and transmitted nonlinear emission, achieving unidirectional emission with full-Poincar\'e polarization tunability, a dark state (V-V point), or any other bidirectional output. Our work paves the way for multidimensional control of polarization and directionality in nonlinear light sources, opening new avenues in ultrafast optics, optical communication, sensing, and quantum optics.

physics.optics↗

arXiv2023

On-Chip Multidimensional Dynamic Control of Twisted Moiré Photonic Crystal for Smart Sensing and Imaging

Reconfigurable optics, optical systems that have a dynamically tunable configuration, are emerging as a new frontier in photonics research. Recently, twisted moiré photonic crystal has become a competitive candidate for implementing reconfigurable optics because of its high degree of tunability. However, despite its great potential as versatile optics components, simultaneous and dynamic modulation of multiple degrees of freedom in twisted moiré photonic crystal has remained out of reach, severely limiting its area of application. In this paper, we present a MEMS-integrated twisted moiré photonic crystal sensor that offers precise control over the interlayer gap and twist angle between two photonic crystal layers, and demonstrate an active twisted moiré photonic crystal-based optical sensor that can simultaneously resolve wavelength and polarization. Leveraging twist- and gap-tuned resonance modes, we achieve high-accuracy spectropolarimetric reconstruction of light using an adaptive sensing algorithm over a broad operational bandwidth in the telecom range and full Poincaré sphere. Our research showcases the remarkable capabilities of multidimensional control over emergent degrees of freedom in reconfigurable nanophotonics platforms and establishes a scalable pathway towards creating comprehensive flat-optics devices suitable for versatile light manipulation and information processing tasks.

physics.optics↗

arXiv2023

Three Dimensional Reconfigurable Optical Singularities in Bilayer Photonic Crystals

Metasurfaces and photonic crystals have revolutionized classical and quantum manipulation of light, and opened the door to studying various optical singularities related to phases and polarization states. However, traditional nanophotonic devices lack reconfigurability, hindering the dynamic switching and optimization of optical singularities. This paper delves into the underexplored concept of tunable bilayer photonic crystals (BPhCs), which offer rich interlayer coupling effects. Utilizing silicon nitride-based BPhCs, we demonstrate tunable bidirectional and unidirectional polarization singularities, along with spatiotemporal phase singularities. Leveraging these tunable singularities, we achieve dynamic modulation of bound-state-in-continuum states, unidirectional guided resonances, and both longitudinal and transverse orbital angular momentum. Our work paves the way for multidimensional control over polarization and phase, inspiring new directions in ultrafast optics, optoelectronics, and quantum optics.

physics.optics↗

arXiv2023

On-chip optical twisted bilayer photonic crystal

Recently, moiré engineering has been extensively employed for creating and studying novel electronic materials in two dimensions. However, its application in nanophotonic systems has not been widely explored so far. Here, we demonstrate that twisted bilayer photonic crystals provide a new photonic platform with twist-angle-tunable optical dispersion. Compared to twisted two-dimensional materials, twisted bilayer photonic crystals host a rich set of physics and provide a much larger number of degrees of freedom choice of material, lattice symmetry, feature size, twist angle, and interlayer gap, which promises an unprecedented toolbox for tailoring optical properties. We directly visualize the dispersion throughout the optical frequency range and show that the measured optical response is in good quantitative agreement with numerical and analytical results. Our results reveal a highly tunable band structure of twisted bilayer photonic crystals due to moiré scattering. This work opens the door to exploring unconventional physics and novel applications in photonics.

physics.optics↗

arXiv2022

Wormhole MAML: Meta-Learning in Glued Parameter Space

In this paper, we introduce a novel variation of model-agnostic meta-learning, where an extra multiplicative parameter is introduced in the inner-loop adaptation. Our variation creates a shortcut in the parameter space for the inner-loop adaptation and increases model expressivity in a highly controllable manner. We show both theoretically and numerically that our variation alleviates the problem of conflicting gradients and improves training dynamics. We conduct experiments on 3 distinctive problems, including a toy classification problem for threshold comparison, a regression problem for wavelet transform, and a classification problem on MNIST. We also discuss ways to generalize our method to a broader class of problems.

cs.LG↗

arXiv2022

Saved You A Click: Automatically Answering Clickbait Titles

Often clickbait articles have a title that is phrased as a question or vague teaser that entices the user to click on the link and read the article to find the explanation. We developed a system that will automatically find the answer or explanation of the clickbait hook from the website text so that the user does not need to read through the text themselves. We fine-tune an extractive question and answering model (RoBERTa) and an abstractive one (T5), using data scraped from the 'StopClickbait' Facebook pages and Reddit's 'SavedYouAClick' subforum. We find that both extractive and abstractive models improve significantly after finetuning. We find that the extractive model performs slightly better according to ROUGE scores, while the abstractive one has a slight edge in terms of BERTscores.

cs.CL↗

arXiv2021

Inverse design of plasma metamaterial devices for optical computing

We apply inverse design methods to produce two-dimensional plasma metamaterial (PMM) devices. Backpropagated finite difference frequency domain (FDFD) simulations are used to design waveguides and demultiplexers operating under both transverse electric (TE) and transverse magnetic (TM) modes. Demultiplexing and waveguiding are demonstrated for devices composed of plasma elements with reasonable plasma densities ~7 GHz, allowing for future in-situ training and experimental realization of these designs. We also explore the possible applicability of PMMs to nonlinear boolean operations for use in optical computing. Functionally complete logical connectives (OR and AND) are achieved in the TM mode.

physics.app-ph↗

arXiv2020

Hyperbolic jigsaws and families of pseudomodular groups II

In our previous paper, we introduced a hyperbolic jigsaw construction and constructed infinitely many non-commensurable, non-uniform, non-arithmetic lattices of $\mathrm{PSL}(2, \mathbb{R})$ with cusp set $\mathbb{Q} \cup \{\infty\}$ (called pseudomodular groups by Long and Reid), thus answering a question posed by Long and Reid. In this paper, we continue with our study of these jigsaw groups exploring questions of arithmeticity, pseudomodularity, and also related pseudo-euclidean and continued fraction algorithms arising from these groups. We also answer another question of Long and Reid by demonstrating a recursive formula for the tessellation of the hyperbolic plane arising from Weierstrass groups which generalizes the well-known "Farey addition" used to generate the Farey tessellation.

math.GT↗

arXiv2020

Compressed imitation learning

In analogy to compressed sensing, which allows sample-efficient signal reconstruction given prior knowledge of its sparsity in frequency domain, we propose to utilize policy simplicity (Occam's Razor) as a prior to enable sample-efficient imitation learning. We first demonstrated the feasibility of this scheme on linear case where state-value function can be sampled directly. We also extended the scheme to scenarios where only actions are visible and scenarios where the policy is obtained from nonlinear network. The method is benchmarked against behavior cloning and results in significantly higher scores with limited expert demonstrations.

cs.LG↗

arXiv2020

Inverse design of photonic crystals through automatic differentiation

Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has played a major role in this success. However, gradient-based optimization has not yet been applied to the mode-expansion methods that are the most common approach to studying periodic optical structures like photonic crystals. This is because, in such simulations, the adjoint variable method cannot be defined as explicitly as in standard finite-difference or finite-element time- or frequency-domain methods. Here, we overcome this through the use of automatic differentiation, which is a generalization of the adjoint variable method to arbitrary computational graphs. We implement the plane-wave expansion and the guided-mode expansion methods using an automatic differentiation library, and show that the gradient of any simulation output can be computed efficiently and in parallel with respect to all input parameters. We then use this implementation to optimize the dispersion of a photonic crystal waveguide, and the quality factor of an ultra-small cavity in a lithium niobate slab. This extends photonic inverse design to a whole new class of simulations, and more broadly highlights the importance that automatic differentiation could play in the future for tracking and optimizing complicated physical models.

physics.optics↗

arXiv2019

TunaGAN: Interpretable GAN for Smart Editing

In this paper, we introduce a tunable generative adversary network (TunaGAN) that uses an auxiliary network on top of existing generator networks (Style-GAN) to modify high-resolution face images according to user's high-level instructions, with good qualitative and quantitative performance. To optimize for feature disentanglement, we also investigate two different latent space that could be traversed for modification. The problem of mode collapse is characterized in detail for model robustness. This work could be easily extended to content-aware image editor based on other GANs and provide insight on mode collapse problems in more general settings.

cs.CV↗

arXiv2017

Hyperbolic jigsaws and families of pseudomodular groups I

We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to the modular group. We do this by introducing a general construction for the fundamental domains of Fuchsian groups obtained by gluing together marked ideal triangular tiles, which we call hyperbolic jigsaw groups.

math.GT↗