arXiv subjects

Yen-Ju Chen

Publications and source records attributed to Yen-Ju Chen.

10 recordsLinked to original sources

arXiv2026

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields

This paper investigates the dynamical properties of the Dickson polynomials $D_n(x, α)$ of the first kind over finite fields, with an emphasis on the periodicity and algebraic structure of their iterated sequences. We consider the sequence $[D_n(x, α) \pmod{x^q - x}]_{n\geq1}$, and determine the exact period of this sequence. We then use the classical functional equation for the Dickson polynomials to relate the dynamics of $D_n(x,α)$ to the power map $u\mapsto u^n$ on a suitable subset of $\mathbb F_{q^2}^\times$. In the permutation case $\gcd(n,q^2-1)=1$, this gives an explicit description of the group of Dickson polynomial functions under composition. We also obtain partial structural result in the non-permutation case. As further applications, we derive several new identities for the Dickson polynomials. Finally, we identify and prove a symmetry property of the Dickson polynomial family.

math.NT↗

arXiv2025

Narrowband Frequency-Entangled Photon Source for Hong-Ou-Mandel Interferometry

Hong-Ou-Mandel (HOM) interferometry with entangled photons exhibits distinctive quantum features. By introducing frequency entanglement (discrete-color entangled states) into HOM interference, the characteristic HOM dip is modulated by sinusoidal fringes, which significantly enhance the sensitivity of HOM sensors. The frequency-entangled photon sources demonstrated to date rely on non-resonant parametric down-conversion (PDC), which limits the photon coherence length and, consequently, restricts the sensing dynamic range to the sub-millimeter scale. In this work, we demonstrate narrowband frequency-entangled photon source based on resonant PDC in a crystalline whispering gallery mode resonator. The MHz-level spectral bandwidth of photons enables a meter-scale dynamic range. With highly nondegenerate frequency-entangled photon pairs featuring a 96 THz frequency detuning, we observe high-contrast quantum beating with sub-picosecond resolution in the HOM experiment. Our WGMR-based frequency-entangled photon source has potential applications in quantum metrology and quantum information processing.

quant-ph↗

arXiv2025

Investigate the Low-level Visual Perception in Vision-Language based Image Quality Assessment

Recent advances in Image Quality Assessment (IQA) have leveraged Multi-modal Large Language Models (MLLMs) to generate descriptive explanations. However, despite their strong visual perception modules, these models often fail to reliably detect basic low-level distortions such as blur, noise, and compression, and may produce inconsistent evaluations across repeated inferences. This raises an essential question: do MLLM-based IQA systems truly perceive the visual features that matter? To examine this issue, we introduce a low-level distortion perception task that requires models to classify specific distortion types. Our component-wise analysis shows that although MLLMs are structurally capable of representing such distortions, they tend to overfit training templates, leading to biases in quality scoring. As a result, critical low-level features are weakened or lost during the vision-language alignment transfer stage. Furthermore, by computing the semantic distance between visual features and corresponding semantic tokens before and after component-wise fine-tuning, we show that improving the alignment of the vision encoder dramatically enhances distortion recognition accuracy, increasing it from 14.92% to 84.43%. Overall, these findings indicate that incorporating dedicated constraints on the vision encoder can strengthen text-explainable visual representations and enable MLLM-based pipelines to produce more coherent and interpretable reasoning in vision-centric tasks.

cs.CV↗

arXiv2025

Observation and Manipulation of Optical Parametric Down-Conversion in the Langevin Regime

Quantum fluctuation plays a key role in the parametric down-conversion in the Langevin regime. In this paper, we report the experimental realization of optical parametric down-conversion in the Langevin regime on a chip. By precisely controlling the loss inherently tied to fluctuation, we observe the asymmetric Hong-Ou-Mandel dip - a hallmark of quantum fluctuation in the fluctuation-driven PDC, and the fluctuation-induced compression of single photons by nearly one order of magnitude. These findings pave the way for the manipulation of quantum fluctuation, quantum states, and system-reservoir interaction.

quant-ph↗

arXiv2025

Machine Learning Modeling for Multi-order Human Visual Motion Processing

Our research aims to develop machines that learn to perceive visual motion as do humans. While recent advances in computer vision (CV) have enabled DNN-based models to accurately estimate optical flow in naturalistic images, a significant disparity remains between CV models and the biological visual system in both architecture and behavior. This disparity includes humans' ability to perceive the motion of higher-order image features (second-order motion), which many CV models fail to capture because of their reliance on the intensity conservation law. Our model architecture mimics the cortical V1-MT motion processing pathway, utilizing a trainable motion energy sensor bank and a recurrent graph network. Supervised learning employing diverse naturalistic videos allows the model to replicate psychophysical and physiological findings about first-order (luminance-based) motion perception. For second-order motion, inspired by neuroscientific findings, the model includes an additional sensing pathway with nonlinear preprocessing before motion energy sensing, implemented using a simple multilayer 3D CNN block. When exploring how the brain acquired the ability to perceive second-order motion in natural environments, in which pure second-order signals are rare, we hypothesized that second-order mechanisms were critical when estimating robust object motion amidst optical fluctuations, such as highlights on glossy surfaces. We trained our dual-pathway model on novel motion datasets with varying material properties of moving objects. We found that training to estimate object motion from non-Lambertian materials naturally endowed the model with the capacity to perceive second-order motion, as can humans. The resulting model effectively aligns with biological systems while generalizing to both first- and second-order motion phenomena in natural scenes.

cs.CV↗

arXiv2024

Accelerated Policy Gradient: On the Convergence Rates of the Nesterov Momentum for Reinforcement Learning

Various acceleration approaches for Policy Gradient (PG) have been analyzed within the realm of Reinforcement Learning (RL). However, the theoretical understanding of the widely used momentum-based acceleration method on PG remains largely open. In response to this gap, we adapt the celebrated Nesterov's accelerated gradient (NAG) method to policy optimization in RL, termed \textit{Accelerated Policy Gradient} (APG). To demonstrate the potential of APG in achieving fast convergence, we formally prove that with the true gradient and under the softmax policy parametrization, APG converges to an optimal policy at rates: (i) $\tilde{O}(1/t^2)$ with constant step sizes; (ii) $O(e^{-ct})$ with exponentially-growing step sizes. To the best of our knowledge, this is the first characterization of the convergence rates of NAG in the context of RL. Notably, our analysis relies on one interesting finding: Regardless of the parameter initialization, APG ends up entering a locally nearly-concave regime, where APG can significantly benefit from the momentum, within finite iterations. Through numerical validation and experiments on the Atari 2600 benchmarks, we confirm that APG exhibits a $\tilde{O}(1/t^2)$ rate with constant step sizes and a linear convergence rate with exponentially-growing step sizes, significantly improving convergence over the standard PG.

cs.LG↗

arXiv2023

Modelling Human Visual Motion Processing with Trainable Motion Energy Sensing and a Self-attention Network

Visual motion processing is essential for humans to perceive and interact with dynamic environments. Despite extensive research in cognitive neuroscience, image-computable models that can extract informative motion flow from natural scenes in a manner consistent with human visual processing have yet to be established. Meanwhile, recent advancements in computer vision (CV), propelled by deep learning, have led to significant progress in optical flow estimation, a task closely related to motion perception. Here we propose an image-computable model of human motion perception by bridging the gap between biological and CV models. Specifically, we introduce a novel two-stages approach that combines trainable motion energy sensing with a recurrent self-attention network for adaptive motion integration and segregation. This model architecture aims to capture the computations in V1-MT, the core structure for motion perception in the biological visual system, while providing the ability to derive informative motion flow for a wide range of stimuli, including complex natural scenes. In silico neurophysiology reveals that our model's unit responses are similar to mammalian neural recordings regarding motion pooling and speed tuning. The proposed model can also replicate human responses to a range of stimuli examined in past psychophysical studies. The experimental results on the Sintel benchmark demonstrate that our model predicts human responses better than the ground truth, whereas the state-of-the-art CV models show the opposite. Our study provides a computational architecture consistent with human visual motion processing, although the physiological correspondence may not be exact.

cs.AI↗

arXiv2022

Coordinate Ascent for Off-Policy RL with Global Convergence Guarantees

We revisit the domain of off-policy policy optimization in RL from the perspective of coordinate ascent. One commonly-used approach is to leverage the off-policy policy gradient to optimize a surrogate objective -- the total discounted in expectation return of the target policy with respect to the state distribution of the behavior policy. However, this approach has been shown to suffer from the distribution mismatch issue, and therefore significant efforts are needed for correcting this mismatch either via state distribution correction or a counterfactual method. In this paper, we rethink off-policy learning via Coordinate Ascent Policy Optimization (CAPO), an off-policy actor-critic algorithm that decouples policy improvement from the state distribution of the behavior policy without using the policy gradient. This design obviates the need for distribution correction or importance sampling in the policy improvement step of off-policy policy gradient. We establish the global convergence of CAPO with general coordinate selection and then further quantify the convergence rates of several instances of CAPO with popular coordinate selection rules, including the cyclic and the randomized variants of CAPO. We then extend CAPO to neural policies for a more practical implementation. Through experiments, we demonstrate that CAPO provides a competitive approach to RL in practice.

cs.LG↗

arXiv2021

Manipulation of Multipartite Entanglement in an Array of Quantum Dots

Multipartite entanglement is indispensable in the implementation of quantum technologies and the fundamental test of quantum mechanics. Here we study how the W state and W-like state may be generated in a quantum-dot array by controlling the coupling between an incident photon and the quantum dots on a waveguide. We also discuss how the coupling may be controlled to observe the sudden death of entanglement. Our work can find potential applications in quantum information processing.

quant-ph↗

arXiv2020

Time-Resolved Detection of Photon-Surface-Plasmon Coupling at the Single-Quanta Level

The interplay of nonclassical light and surface plasmons has attracted considerable attention due to fundamental interests and potential applications. To gain more insight into the quantum nature of the photon-surface-plasmon coupling, time-resolved detection of the interaction is invaluable. Here we demonstrate the time-resolved detection of photon-surface-plasmon coupling by exploiting single and entangled photons with long coherence time to excite single optical plasmons. We examine the nonclassical correlation between the single photons and single optical plasmons in such systems using the time-resolved Cauchy-Schwarz inequality. We also realize single optical plasmons with programmable temporal wavepacket by manipulating the waveform of incident single photons. The time-resolved detection and coherent control of single optical plasmons offer new opportunities to study and control the light-matter interaction at the nanoscale.

quant-ph↗