arXiv subjects

Chen Jia

Publications and source records attributed to Chen Jia.

At least 37 records · Page 2Linked to original sources

arXiv2025

Feedforward Cancellation of High-Frequency Phase Noise in Frequency-Doubled Lasers

The cancellation of high-frequency laser phase noise using feedforward techniques, as opposed to feedback methods, has achieved significant advancements in recent years. However, directly applying existing feedforward techniques to laser systems based on nonlinear conversion still faces substantial challenges. Here, we propose and demonstrate a feedforward scheme that suppresses phase noise in frequency-doubled light by utilizing phase noise information of its fundamental pump. This scheme is enabled by the fact that the phase jitter of the frequency-doubled light is simply twice that of the pump, except for a first-order low-pass filtering effect introduced by the SHG enhancement cavity. Testing this method on a 420-nm frequency-doubled laser system, we realize a 25-dB suppression of the servo noise bump near 1 MHz on the 420-nm light, and an average suppression of 30 dB for strong injected noise ranging from 100 kHz to 20 MHz. This scheme shows promising potential for applications requiring blue or ultraviolet light with minimal high-frequency phase noise, such as precision control of atoms and molecules.

physics.optics↗

arXiv2024

Robust High-frequency Laser Phase Noise Suppression by Adaptive Pound-Drever-Hall Feedforward

Suppressing high-frequency laser phase noise, particularly at frequencies near and beyond typical feedback bandwidths of a few MHz, is a critical yet challenging task in many advanced applications. Feedforward-based methods generally outperform feedback in high-frequency range, but their performances are more susceptible to perturbations. In this work, we focus on the Pound-Drever-Hall (PDH)-feedforward method we demonstrated recently [Yu-Xin Chao et al., Optica 11(7), 945-950 (2024)] and analyze the factors that affect its long-term stability. By constructing a simple circuit allowing for adaptive control of the feedforward gain in response to power fluctuations of cavity transmission, we demonstrate a robust $\geq 40$ dB suppression of laser phase noise around 2 MHz and a noise suppression bandwidth up to 50 MHz. In comparison, when using normal PDH feedback, robust noise suppression of over 40 dB can only occur for frequencies below tens of kHz in most setups. Our findings may pave the way for general usage of PDH feedforward and allow for simple construction of low-noise lasers for precise quantum controls and precision metrology.

physics.optics↗

arXiv2024

Parameter inference and nonequilibrium identification for Markovian systems based on coarse-grained observations

Most experiments can only detect a set of coarse-grained clusters of a molecular system, while the internal microstates are often inaccessible. Here, based on an infinitely long coarse-grained trajectory, we obtain a set of sufficient statistics which extracts all statistic information of coarse-grained observations. Based on these sufficient statistics, we set up a theoretical framework of parameter inference and nonequilibrium identification for a general Markovian system with an arbitrary number of microstates and arbitrary coarse-grained partitioning. Our framework can identify whether the sufficient statistics are enough for empirical estimation of all unknown parameters and we can also provide a quantitative criterion that reveals nonequilibrium. Our nonequilibrium criterion generalizes the one obtained [J. Chem. Phys. 132:041102 (2010)] for a three-state system with two coarse-grained clusters, and is capable of detecting a larger nonequilibrium region compared to the classical criterion based on autocorrelation functions.

cond-mat.stat-mech↗

arXiv2024

Generalizing Reward Modeling for Out-of-Distribution Preference Learning

Preference learning (PL) with large language models (LLMs) aims to align the LLMs' generations with human preferences. Previous work on reinforcement learning from human feedback (RLHF) has demonstrated promising results in in-distribution PL. However, due to the difficulty of obtaining human feedback, discretely training reward models for every encountered distribution is challenging. Thus, out-of-distribution (OOD) PL is practically useful for enhancing the generalization ability of LLMs with limited preference feedback. This work addresses OOD PL by optimizing a general reward model through a meta-learning approach. During meta-training, a bilevel optimization algorithm is utilized to learn a reward model capable of guiding policy learning to align with human preferences across various distributions. When encountering a test distribution, the meta-test procedure conducts regularized policy optimization using the learned reward model for PL. We theoretically demonstrate the convergence rate of the bilevel optimization algorithm under reasonable assumptions. Additionally, we conduct experiments on two text generation tasks across 20 held-out domains and outperform a variety of strong baselines across various evaluation metrics.

cs.LG↗

arXiv2024

Adversarial Moment-Matching Distillation of Large Language Models

Knowledge distillation (KD) has been shown to be highly effective in guiding a student model with a larger teacher model and achieving practical benefits in improving the computational and memory efficiency for large language models (LLMs). State-of-the-art KD methods for LLMs mostly rely on minimizing explicit distribution distance between teacher and student probability predictions. Instead of optimizing these mandatory behaviour cloning objectives, we explore an imitation learning strategy for KD of LLMs. In particular, we minimize the imitation gap by matching the action-value moments of the teacher's behavior from both on- and off-policy perspectives. To achieve this action-value moment-matching goal, we propose an adversarial training algorithm to jointly estimate the moment-matching distance and optimize the student policy to minimize it. Results from both task-agnostic instruction-following experiments and task-specific experiments demonstrate the effectiveness of our method and achieve new state-of-the-art performance.

cs.CL↗

arXiv2024

Gender Bias in Large Language Models across Multiple Languages

With the growing deployment of large language models (LLMs) across various applications, assessing the influence of gender biases embedded in LLMs becomes crucial. The topic of gender bias within the realm of natural language processing (NLP) has gained considerable focus, particularly in the context of English. Nonetheless, the investigation of gender bias in languages other than English is still relatively under-explored and insufficiently analyzed. In this work, We examine gender bias in LLMs-generated outputs for different languages. We use three measurements: 1) gender bias in selecting descriptive words given the gender-related context. 2) gender bias in selecting gender-related pronouns (she/he) given the descriptive words. 3) gender bias in the topics of LLM-generated dialogues. We investigate the outputs of the GPT series of LLMs in various languages using our three measurement methods. Our findings revealed significant gender biases across all the languages we examined.

cs.CL↗

arXiv2024

Exact power spectrum in a minimal hybrid model of stochastic gene expression oscillations

Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid model of stochastic gene expression including promoter state switching, protein synthesis and degradation, as well as a genetic feedback loop. The oscillations observed in our model are noise-induced since the deterministic theory predicts stable fixed points. The autocorrelated function, power spectrum, and steady-state distribution of protein concentration fluctuations are computed in closed form without making any approximations. Using the exactly solvable model, we illustrate sustained oscillations as a circular motion along a stochastic hysteresis loop induced by gene state switching. A triphasic stochastic bifurcation upon the increasing strength of negative feedback is observed, which reveals how stochastic bursts evolve into stochastic oscillations. In our model, oscillations tend to occur when the protein is relatively stable and when gene switching is relatively slow. Translational bursting is found to enhance the robustness and broaden the region of stochastic oscillations. These results provide deeper insights into R. Thomas' two conjectures for single-cell gene expression kinetics.

q-bio.MN↗

arXiv2022

Large deviations for the empirical measure and empirical flow of Markov renewal processes with a countable state space

Here we propose the Donsker-Varadhan-type compactness conditions and prove the joint large deviation principle for the empirical measure and empirical flow of Markov renewal processes (semi-Markov processes) with a countable state space, generalizing the relevant results for continuous-time Markov chains with a countable state space obtained in [Ann. Inst. H. Poincaré Probab. Statist. 51, 867-900 (2015)] and [Stoch. Proc. Appl. 125, 2786-2819 (2015)], as well as the relevant results for Markov renewal processes with a finite state space obtained in [Adv. Appl. Probab. 48, 648-671 (2016)]. In particular, our results hold when the flow space is endowed with either the bounded weak* topology or the strong $L^1$ topology. Even for continuous-time Markov chains, our compactness conditions are weaker than the ones proposed in previous papers. Furthermore, under some stronger conditions, we obtain the explicit expression of the marginal rate function of the empirical flow.

math.PR↗

arXiv2022

Large deviations and fluctuation theorems for cycle currents defined in the loop-erased and spanning tree manners: a comparative study

The cycle current is a crucial quantity in stochastic thermodynamics. The absolute and net cycle currents of a Markovian system can be defined in the loop-erased (LE) or spanning tree (ST) manner. Here we make a comparative study between the large deviations and fluctuation theorems for LE and ST currents, i.e. cycle currents defined in the LE and ST manners. First, we derive the exact joint distribution and large deviation rate function for the LE currents of a system with a cyclic topology and also obtain the exact rate function for the ST currents of a general system. The relationship between the rate functions for LE and ST currents is clarified and the analytical results are applied to examine the fluctuations in the product rate of a three-step reversible enzyme reaction. Furthermore, we examine various types of fluctuation theorems satisfied by LE and ST currents and clarify their ranges of applicability. We show that both the absolute and net LE currents satisfy the strong form of all types of fluctuation theorems. In contrast, the absolute ST currents do not satisfy fluctuation theorems, while the net ST currents only satisfy the weak form of fluctuation theorems under the periodic boundary condition.

cond-mat.stat-mech↗

arXiv2022

Some mathematical aspects of Anderson localization: boundary effect, multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.

math-ph↗

arXiv2021

Steady-state joint distribution for first-order stochastic reaction kinetics

While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much less attention. Here we develop a novel method of computing the exact joint distributions of a wide class of first-order stochastic reaction systems in steady-state conditions. The effectiveness of our method is validated by applying it to four gene expression models of biological significance, including models with 2A peptides, nascent mRNA, gene regulation, translational bursting, and alternative splicing.

q-bio.MN↗

arXiv2021

Moderate and $L^p$ maximal inequalities for diffusion processes and conformal martingales

The $L^p$ maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the $L^p$ maximal inequalities as special cases. Moreover, we apply our theory to many specific examples, including the Ornstein-Uhlenbeck (OU) process, Brownian motion with drift, reflected Brownian motion with drift, Cox-Ingersoll-Ross process, radial OU process, and Bessel process. The results are further applied to establish the moderate maximal inequalities for some high-dimensional processes, including the complex OU process and general conformal local martingales.

math.PR↗

arXiv2021

Sparsely Overlapped Speech Training in the Time Domain: Joint Learning of Target Speech Separation and Personal VAD Benefits

Target speech separation is the process of filtering a certain speaker's voice out of speech mixtures according to the additional speaker identity information provided. Recent works have made considerable improvement by processing signals in the time domain directly. The majority of them take fully overlapped speech mixtures for training. However, since most real-life conversations occur randomly and are sparsely overlapped, we argue that training with different overlap ratio data benefits. To do so, an unavoidable problem is that the popularly used SI-SNR loss has no definition for silent sources. This paper proposes the weighted SI-SNR loss, together with the joint learning of target speech separation and personal VAD. The weighted SI-SNR loss imposes a weight factor that is proportional to the target speaker's duration and returns zero when the target speaker is absent. Meanwhile, the personal VAD generates masks and sets non-target speech to silence. Experiments show that our proposed method outperforms the baseline by 1.73 dB in terms of SDR on fully overlapped speech, as well as by 4.17 dB and 0.9 dB on sparsely overlapped speech of clean and noisy conditions. Besides, with slight degradation in performance, our model could reduce the time costs in inference.

cs.SD↗

arXiv2021

Detailed balance, local detailed balance, and global potential for stochastic chemical reaction networks

Detailed balance of a chemical reaction network can be defined in several different ways. Here we investigate the relationship among four types of detailed balance conditions: deterministic, stochastic, local, and zero-order local detailed balance. We show that the four types of detailed balance are equivalent when different reactions lead to different species changes and are not equivalent when some different reactions lead to the same species change. Under the condition of local detailed balance, we further show that the system has a global potential defined over the whole space, which plays the central role in the large deviation theory and the Freidlin-Wentzell-type metastability theory of chemical reaction networks. Finally, we provide a new sufficient condition for stochastic detailed balance, which is applied to construct a class of high-dimensional chemical reaction networks that both satisfies stochastic detailed balance and displays multistability.

math.PR↗

arXiv2020

Martingale structure for general thermodynamic functionals of diffusion processes under second-order averaging

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional of inhomogeneous singularly perturbed diffusion processes under second-order averaging, where a general thermodynamic functional is defined as the logarithmic Radon-Nykodim derivative between the laws of the original process and a comparable process (forward case) or its time reversal (backward case). In the forward case, we prove that the regular and anomalous parts of a thermodynamic functional are orthogonal martingales. In the backward case, while the regular part may not be a martingale, we prove that the anomalous part is still a martingale. With the aid of the martingale structure, we prove the integral fluctuation theorem satisfied by the regular and anomalous parts of a general thermodynamic functional. Further extensions and applications to stochastic thermodynamics are also discussed, including the martingale structure and fluctuation theorems for the regular and anomalous parts of entropy production and housekeeping heat in the absence or presence of odd variables.

math-ph↗

arXiv2020

Small protein number effects in stochastic models of autoregulated bursty gene expression

A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here we derive an alternative model that takes into account these fluctuations and hence can be used to study low protein number effects. The exact steady-state protein number distributions is derived as a sum of Gaussian hypergeometric functions. We use the theory to study how promoter switching rates and the type of feedback influence the size of protein noise and noise-induced bistability. Furthermore we show that our model predictions for the protein number distribution are significantly different from those of Kumar et al. when the protein mean is small, gene switching is fast, and protein binding is faster than unbinding.

q-bio.SC↗

arXiv2019

Kinetic foundation of the zero-inflated negative binomial model for single-cell RNA sequencing data

Single-cell RNA sequencing data have complex features such as dropout events, over-dispersion, and high-magnitude outliers, resulting in complicated probability distributions of mRNA abundances that are statistically characterized in terms of a zero-inflated negative binomial (ZINB) model. Here we provide a mesoscopic kinetic foundation of the widely used ZINB model based on the biochemical reaction kinetics underlying transcription. Using multiscale modeling and simplification techniques, we show that the ZINB distribution of mRNA abundance and the phenomenon of transcriptional bursting naturally emerge from a three-state stochastic transcription model. We further reveal a nontrivial quantitative relation between dropout events and transcriptional bursting, which provides novel insights into how and to what extent the burst size and burst frequency could reduce the dropout rate. Three different biophysical origins of over-dispersion are also clarified at the single-cell level.

q-bio.MN↗

arXiv2019

Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback

Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback strengths is observed, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the Lévy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained in [Chaos 26:043108, 2016]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model proposed in [Phys. Rev. Lett. 97:168302, 2006]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit and a complete decomposition of noise in terms of five different biophysical origins is provided.

q-bio.MN↗