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Xiaotian Jiang

Publications and source records attributed to Xiaotian Jiang.

13 recordsLinked to original sources
arXiv2026

Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\geq 4$

Barzilai--Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method (BB1) converges but cannot converge root-superlinearly. More precisely, with the explicit constants $ρ_{\min}=10^{-6},ρ_{\max}=0.61$, every spectral component of the gradient is bounded above and below by the corresponding geometric sequence. Consequently, the gradient norm and the energy norm of the error satisfy two-sided geometric estimates with the same rates, while the objective gap satisfies the corresponding estimates with squared rates. In particular, all three quantities are bounded below by geometric sequences, ruling out superlinear convergence. The construction is highly nontrivial, based on a computer-assisted proof of a nonresonant, attracting seven-cycle of the projectivized BB dynamics in dimension four.

math.OC↗
arXiv2026

On the Nature of Regularity Assumptions in Bilevel Optimization with Constrained Lower-level Problem

In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and the second-order sufficient condition. These conditions are typically required to hold for the lower-level problem at every upper-level variable $x$. We first show that the requirement that these conditions hold at every upper-level variable $x$ is strong, in the sense that it is non-prevalent: there exist problems for which no sufficiently small perturbation of the lower-level objective and constraints can make the conditions hold at every $x$. To establish the result, we prove rigidity theorems showing that certain structural quantities of the lower-level problem must remain invariant across all $x$ whenever these conditions hold everywhere. We then construct explicit counterexamples in which these invariants differ between two values of $x$. In contrast, we show that the weaker requirement, that these conditions hold at almost every $x$, is a weak assumption, in the sense that it is prevalent: with probability one over a random perturbation of the lower-level objective and constraints, each condition holds at almost every $x$. We further analyze the gap between the two requirements. Although the ``every $x$'' and ``almost every $x$'' versions differ only on a measure-zero set, we show that this difference introduces fundamental difficulties in both theory and computation for bilevel optimization.

math.OC↗
arXiv2026

A Correspondence-Driven Approach for Bilevel Decision-making with Nonconvex Lower-Level Problems

We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global minimizer of the lower-level problem is generally unattainable. To address this issue, we propose a correspondence-driven hyperfunction $ϕ^{\text{cd}}$. In this formulation, the follower is modeled not as a rational agent always attaining a global minimizer, but as an algorithm-based bounded rational agent whose decisions are produced by a fixed algorithm with initialization and step size. Since $ϕ^{\text{cd}}$ is generally discontinuous, we apply Gaussian smoothing to obtain a smooth approximation $ϕ^{\text{cd}}_ξ$, then show that its value and gradient converge to those of $ϕ^{\text{cd}}$. In the nonconvex setting, we identify that bifurcation phenomena, which arise when $g(x,\cdot)$ has a degenerate stationary point, pose a key challenge for hyperfunction-based methods. This is especially the case when $ϕ^{\text{cd}}_ξ$ is solved using gradient methods. To overcome this challenge, we analyze the geometric structure of the bifurcation set under some weak assumptions. Building on these results, we design a biased projected SGD-based algorithm SCiNBiO to solve $ϕ^{\text{cd}}_ξ$ with a cubic-regularized Newton lower-level solver. We also provide convergence guarantees and oracle complexity bounds for the upper level. Finally, we connect bifurcation theory from dynamical systems to the bilevel setting and define the notion of fold bifurcation points in this setting. Under the assumption that all degenerate stationary points are fold bifurcation points, we establish the oracle complexity of SCiNBiO for the lower-level problem.

math.OC↗
arXiv2026

Mathematical Reasoning Enhanced LLM for Formula Derivation: A Case Study on Fiber NLI Modellin

Recent advances in large language models (LLMs) have demonstrated strong capabilities in code generation and text synthesis, yet their potential for symbolic physical reasoning in domain-specific scientific problems remains underexplored. We present a mathematical reasoning enhanced generative AI approach for optical communication formula derivation, focusing on the fiber nonlinear interference modelling. By guiding an LLM with structured prompts, we successfully reconstructed the known closed-form ISRS GN expressions and further derived a novel approximation tailored for multi-span C and C+L band transmissions. Numerical validations show that the LLM-derived model produces central-channel GSNRs nearly identical to baseline models, with mean absolute error across all channels and spans below 0.109 dB, demonstrating both physical consistency and practical accuracy.

cs.CL↗
arXiv2026

Large language models for optical network O&M: Agent-embedded workflow for automation

With the continuous expansion of optical networks and the increasing diversity of services, existing operation and maintenance (O&M) approaches are increasingly challenged to meet the rising demands for intelligence and efficiency. Large language models (LLMs), endowed with advanced semantic understanding and contextual analysis capabilities, are emerging as a promising enabler for intelligent optical network O&M. Recent studies have demonstrated the feasibility of applying LLMs to optical network management, marking an important step toward intelligent automation. However, systematic investigations into how LLMs can be effectively integrated into existing O&M workflows remain limited. This paper addresses this gap by drawing inspiration from best practices in real-world O&M workflows and systematically identifying scenarios that are well suited for LLM integration. We highlight that agent-based design is key to improving the executability of tasks, and we propose a multi-Agent collaborative O&M architecture that integrates LLM capabilities with existing O&M tools. The proposed architecture leverages core LLM-related technologies including prompt engineering and tool invocation, to build Agent solutions targeting key tasks such as optical channel management, performance optimization, and fault management. This work presents a conceptual framework for embedding LLM-based Agents into optical network O&M workflows, forming agentized processes that demonstrate the feasibility of LLM-assisted task execution and lay the groundwork for future autonomous O&M systems featuring closed-loop perception, decision-making, and action.

physics.optics↗
arXiv2025

A Discretization Approach for Bilevel Optimization with Low-Dimensional and Non-Convex Lower-Level

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many first-order algorithms have been developed for solving bilevel problems with strongly convex and/or unconstrained lower-level problems; this special structure of the lower-level problem is needed to ensure the tractability of gradient computation (among other reasons). In this work, we deal with a class of more challenging BLO problems where the lower-level problem is non-convex and constrained. We propose a novel approach that approximates the value function of the lower-level problem by first sampling a set of feasible solutions and then constructing an equivalent convex optimization problem. This convexified value function is then used to construct a penalty function for the original BLO problem. We analyze the properties of the original BLO problem and the newly constructed penalized problem by characterizing the relation between their KKT points, as well as the local and global minima of the two problems. We then develop a gradient descent-based algorithm to solve the reformulated problem, and establish its finite-time convergence guarantees. Finally, we conduct numerical experiments to corroborate the theoretical performance of the proposed algorithm.

math.OC↗
arXiv2025

FiberKAN: Kolmogorov-Arnold Networks for Nonlinear Fiber Optics

Scientific discovery and dynamic characterization of the physical system play a critical role in understanding, learning, and modeling the physical phenomena and behaviors in various fields. Although theories and laws of many system dynamics have been derived from rigorous first principles, there are still a considerable number of complex dynamics that have not yet been discovered and characterized, which hinders the progress of science in corresponding fields. To address these challenges, artificial intelligence for science (AI4S) has emerged as a burgeoning research field. In this paper, a Kolmogorov-Arnold Network (KAN)-based AI4S framework named FiberKAN is proposed for scientific discovery and dynamic characterization of nonlinear fiber optics. Unlike the classic multi-layer perceptron (MLP) structure, the trainable and transparent activation functions in KAN make the network have stronger physical interpretability and nonlinear characterization abilities. Multiple KANs are established for fiber-optic system dynamics under various physical effects. Results show that KANs can well discover and characterize the explicit, implicit, and non-analytical solutions under different effects, and achieve better performance than MLPs with the equivalent scale of trainable parameters. Moreover, the effectiveness, computational cost, interactivity, noise resistance, transfer learning ability, and comparison between related algorithms in fiber-optic systems are also studied and analyzed. This work highlights the transformative potential of KAN, establishing it as a pioneering paradigm in AI4S that propels advancements in nonlinear fiber optics, and fosters groundbreaking innovations across a broad spectrum of scientific and engineering disciplines.

physics.optics↗
arXiv2025

A Barrier Function Approach for Bilevel Optimization with Coupled Lower-Level Constraints: Formulation, Approximation and Algorithms

In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level problem. The first is when the objective is strongly convex and the constraints are convex with respect to the lower-level variable; The second is when the lower-level is a linear program. We propose to utilize a barrier function reformulation to translate the problem into an unconstrained problem. By developing a series of new techniques, we proved that both the hyperfunction value and hypergradient of the barrier reformulated problem (uniformly) converge to those of the original problem under minimal assumptions. Further, to overcome the non-Lipschitz smoothness of hyperfunction and lower-level problem for barrier reformulated problems, we design an adaptive algorithm that ensures a non-asymptotic convergence guarantee. We also design an algorithm that converges to the stationary point of the original problem asymptotically under certain assumptions. The proposed algorithms require minimal assumptions, and to our knowledge, they are the first with convergence guarantees when the lower-level problem is a linear program. Numerical experiments are conducted to show the effectiveness of the proposed method.

math.OC↗
arXiv2025

Physics-Informed Machine Learning for EDFA: Parameter Identification and Gain Estimation

As the key component that facilitates long-haul transmission in optical fiber communications by increasing capacity and reducing costs, accurate characterization and gain settings of erbium-doped fiber amplifiers (EDFAs) are essential for quality of transmission estimation and system configuration optimization. However, it is difficult to construct accurate and reliable EDFA models due to complex physical mechanisms and dynamic loading conditions. Although some mathematical and data-driven models have been proposed, their practical applications will face limitations of intricate parameter measurements and high data requirements, respectively. To overcome limitations of both methods, a physics-informed machine learning (PIML) method for parameter identification and gain estimation of EDFA is proposed, which greatly reduces the data requirements by embedding physical prior knowledge in the neural network. In this approach, the gain of EDFA can be accurately estimated by a physics-informed neural network (PINN)-based forward model when parameters including absorption, gain, saturation, and background loss are known. For practical scenarios where parameters are unknown, PINN-based inverse models are established first to identify actual values of parameters from only several sets of input-output data pairs, and PINN-based forward models are accordingly established for gain estimation with identified values. Moreover, an experimental system is constructed to verify the feasibility and performance of proposed method in practical scenarios. Results show that PIML-based method can effectively identify physical parameters from measured data, and better gain estimation results are achieved with mean absolute error of 0.127 dB and standard deviation of 0.065 dB using identified values than typical values of parameters.

physics.optics↗
arXiv2024

When Large Language Models Meet Optical Networks: Paving the Way for Automation

Since the advent of GPT, large language models (LLMs) have brought about revolutionary advancements in all walks of life. As a superior natural language processing (NLP) technology, LLMs have consistently achieved state-of-the-art performance on numerous areas. However, LLMs are considered to be general-purpose models for NLP tasks, which may encounter challenges when applied to complex tasks in specialized fields such as optical networks. In this study, we propose a framework of LLM-empowered optical networks, facilitating intelligent control of the physical layer and efficient interaction with the application layer through an LLM-driven agent (AI-Agent) deployed in the control layer. The AI-Agent can leverage external tools and extract domain knowledge from a comprehensive resource library specifically established for optical networks. This is achieved through user input and well-crafted prompts, enabling the generation of control instructions and result representations for autonomous operation and maintenance in optical networks. To improve LLM's capability in professional fields and stimulate its potential on complex tasks, the details of performing prompt engineering, establishing domain knowledge library, and implementing complex tasks are illustrated in this study. Moreover, the proposed framework is verified on two typical tasks: network alarm analysis and network performance optimization. The good response accuracies and sematic similarities of 2,400 test situations exhibit the great potential of LLM in optical networks.

cs.NI↗
arXiv2023

SPM: Structured Pretraining and Matching Architectures for Relevance Modeling in Meituan Search

In e-commerce search, relevance between query and documents is an essential requirement for satisfying user experience. Different from traditional e-commerce platforms that offer products, users search on life service platforms such as Meituan mainly for product providers, which usually have abundant structured information, e.g. name, address, category, thousands of products. Modeling search relevance with these rich structured contents is challenging due to the following issues: (1) there is language distribution discrepancy among different fields of structured document, making it difficult to directly adopt off-the-shelf pretrained language model based methods like BERT. (2) different fields usually have different importance and their length vary greatly, making it difficult to extract document information helpful for relevance matching. To tackle these issues, in this paper we propose a novel two-stage pretraining and matching architecture for relevance matching with rich structured documents. At pretraining stage, we propose an effective pretraining method that employs both query and multiple fields of document as inputs, including an effective information compression method for lengthy fields. At relevance matching stage, a novel matching method is proposed by leveraging domain knowledge in search query to generate more effective document representations for relevance scoring. Extensive offline experiments and online A/B tests on millions of users verify that the proposed architectures effectively improve the performance of relevance modeling. The model has already been deployed online, serving the search traffic of Meituan for over a year.

cs.IR↗
arXiv2021

Physics-informed Neural Network for Nonlinear Dynamics in Fiber Optics

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schrödinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and comprehensive verification on PINN for multiple physical effects in optical fibers, including dispersion, self-phase modulation, and higher-order nonlinear effects. Moreover, both special case (soliton propagation) and general case (multi-pulse propagation) are investigated and realized with PINN. In the previous studies, the PINN was mainly effective for single scenario. To overcome this problem, the physical parameters (pulse peak power and amplitudes of sub-pulses) are hereby embedded as additional input parameter controllers, which allow PINN to learn the physical constraints of different scenarios and perform good generalizability. Furthermore, PINN exhibits better performance than the data-driven neural network using much less data, and its computational complexity (in terms of number of multiplications) is much lower than that of the split-step Fourier method. The results report here show that the PINN is not only an effective partial differential equation solver, but also a prospective technique to advance the scientific computing and automatic modeling in fiber optics.

physics.optics↗