arXiv subjects

Ziang Chen

Publications and source records attributed to Ziang Chen.

At least 37 records · Page 2Linked to original sources

arXiv2025

Gaia DR3 Open Cluster Cepheids: A Unified Catalog with Calibrated Period-Age and Period-Wesenheit Relations

Classical Cepheids (CCs) in Galactic open clusters (OCs) provide essential observational constraints for calibrating the period-age relation (PAR) and the period-Wesenheit relation (PWR) of CCs. However, distant and long-period OC Cepheids remain limited, while the confirmed samples still require more precise determinations of their physical properties, such as ages and extinctions. In this work, we present a comprehensive census of OC Cepheids based on an extensive sample of distant OCs from Gaia Data Release 3 (DR3). By combining astrometric and photometric membership analyses, we identified 110 CCs associated with 102 OCs, of which 41 CCs across 37 OCs were classified as OC Cepheids, while the remaining cases were considered candidate or rejected associations. Our results are consistent with previous studies, while 4 of the 41 OC Cepheids are newly reported here. Using updated cluster parameters derived from manual isochrone fitting, we primarily refined the PAR to log Age = (-0.595 $\pm$ 0.044) log P + (8.430 $\pm$ 0.042) and recalibrated the PWR to WG = (-3.615 $\pm$ 0.083) log P + (-2.379 $\pm$ 0.096). This study expands the sample of confirmed and candidate OC Cepheids. The newly longest-period confirmed OC Cepheid is BM Per (CWNU 3123) with log P = 1.36, and two newly discovered OC Cepheid candidates have distances exceeding 6 kpc. Moreover, the PAR and PWR are improved by incorporating refined OC ages and updated parallaxes, respectively.

astro-ph.SR↗

arXiv2025

ToMPO: Training LLM Strategic Decision Making from a Multi-Agent Perspective

Large Language Models (LLMs) have been used to make decisions in complex scenarios, where they need models to think deeply, reason logically, and decide wisely. Many existing studies focus solely on multi-round conversations in social tasks or simulated environments, neglecting the various types of decisions and their interdependence. Current reinforcement learning methods struggle to consider the strategies of others during training. To address these issues, we first define a strategic decision-making problem that includes two types of decisions and their temporal dependencies. Furthermore, we propose **T**heory **o**f **M**ind **P**olicy **O**ptimization **(ToMPO)** algorithm to optimize the perception of other individual strategies and the game situation trends. Compared to the Group Relative Policy Optimization (GRPO) algorithm, ToMPO enhances the LLM's strategic decision-making mainly by: 1) generating rollouts based on reasoning the strategies of other individuals, 2) estimating advantages at both the graph-level and sample-level, and 3) balancing global and partial rewards. The ToMPO algorithm outperforms the GRPO method by 35% in terms of model output compliance and cooperative outcomes. Additionally, when compared to models with parameter sizes 100 times larger, it shows an 18% improvement. This demonstrates the effectiveness of the ToMPO algorithm in enhancing the model's strategic decision-making capabilities.

cs.AI↗

arXiv2025

Langevin Unlearning: A New Perspective of Noisy Gradient Descent for Machine Unlearning

Machine unlearning has raised significant interest with the adoption of laws ensuring the ``right to be forgotten''. Researchers have provided a probabilistic notion of approximate unlearning under a similar definition of Differential Privacy (DP), where privacy is defined as statistical indistinguishability to retraining from scratch. We propose Langevin unlearning, an unlearning framework based on noisy gradient descent with privacy guarantees for approximate unlearning problems. Langevin unlearning unifies the DP learning process and the privacy-certified unlearning process with many algorithmic benefits. These include approximate certified unlearning for non-convex problems, complexity saving compared to retraining, sequential and batch unlearning for multiple unlearning requests.

cs.LG↗

arXiv2025

RationAnomaly: Log Anomaly Detection with Rationality via Chain-of-Thought and Reinforcement Learning

Logs constitute a form of evidence signaling the operational status of software systems. Automated log anomaly detection is crucial for ensuring the reliability of modern software systems. However, existing approaches face significant limitations: traditional deep learning models lack interpretability and generalization, while methods leveraging Large Language Models are often hindered by unreliability and factual inaccuracies. To address these issues, we propose RationAnomaly, a novel framework that enhances log anomaly detection by synergizing Chain-of-Thought (CoT) fine-tuning with reinforcement learning. Our approach first instills expert-like reasoning patterns using CoT-guided supervised fine-tuning, grounded in a high-quality dataset corrected through a rigorous expert-driven process. Subsequently, a reinforcement learning phase with a multi-faceted reward function optimizes for accuracy and logical consistency, effectively mitigating hallucinations. Experimentally, RationAnomaly outperforms state-of-the-art baselines, achieving superior F1-scores on key benchmarks while providing transparent, step-by-step analytical outputs. We have released the corresponding resources, including code and datasets.

cs.AI↗

arXiv2025

Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs

Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix decomposition or use the preconditioned conjugate gradient method. For relatively large instances, these methods cannot achieve the real-time requirement unless there is an effective preconditioner. Recently, graph neural networks (GNNs) opened new possibilities for QP. Some promising empirical studies of applying GNNs for QP tasks show that GNNs can capture key characteristics of an optimization instance and provide adaptive guidance accordingly to crucial configurations during the solving process, or directly provide an approximate solution. However, the theoretical understanding of GNNs in this context remains limited. Specifically, it is unclear what GNNs can and cannot achieve for QP tasks in theory. This work addresses this gap in the context of linearly constrained QP tasks. In the continuous setting, we prove that message-passing GNNs can universally represent fundamental properties of convex quadratic programs, including feasibility, optimal objective values, and optimal solutions. In the more challenging mixed-integer setting, while GNNs are not universal approximators, we identify a subclass of QP problems that GNNs can reliably represent.

cs.LG↗

arXiv2025

Randomized coordinate gradient descent almost surely escapes strict saddle points

We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem.

math.OC↗

arXiv2025

Mixed-Mode In-Memory Computing: Towards High-Performance Logic Processing In A Memristive Crossbar Array

In-memory computing is a promising alternative to traditional computer designs, as it helps overcome performance limits caused by the separation of memory and processing units. However, many current approaches struggle with unreliable device behavior, which affects data accuracy and efficiency. In this work, the authors present a new computing method that combines two types of operations,those based on electrical resistance and those based on voltage, within each memory cell. This design improves reliability and avoids the need for expensive current measurements. A new software tool also helps automate the design process, supporting highly parallel operations in dense two-dimensional memory arrays. The approach balances speed and space, making it practical for advanced computing tasks. Demonstrations include a digital adder and a key part of the encryption module, showing both strong performance and accuracy. This work offers a new direction for reliable and efficient in-memory computing systems with real-world applications.

physics.app-ph↗

arXiv2025

SCFormer: Structured Channel-wise Transformer with Cumulative Historical State for Multivariate Time Series Forecasting

The Transformer model has shown strong performance in multivariate time series forecasting by leveraging channel-wise self-attention. However, this approach lacks temporal constraints when computing temporal features and does not utilize cumulative historical series effectively.To address these limitations, we propose the Structured Channel-wise Transformer with Cumulative Historical state (SCFormer). SCFormer introduces temporal constraints to all linear transformations, including the query, key, and value matrices, as well as the fully connected layers within the Transformer. Additionally, SCFormer employs High-order Polynomial Projection Operators (HiPPO) to deal with cumulative historical time series, allowing the model to incorporate information beyond the look-back window during prediction. Extensive experiments on multiple real-world datasets demonstrate that SCFormer significantly outperforms mainstream baselines, highlighting its effectiveness in enhancing time series forecasting. The code is publicly available at https://github.com/ShiweiGuo1995/SCFormer

cs.LG↗

arXiv2025

ValuePilot: A Two-Phase Framework for Value-Driven Decision-Making

Despite recent advances in artificial intelligence (AI), it poses challenges to ensure personalized decision-making in tasks that are not considered in training datasets. To address this issue, we propose ValuePilot, a two-phase value-driven decision-making framework comprising a dataset generation toolkit DGT and a decision-making module DMM trained on the generated data. DGT is capable of generating scenarios based on value dimensions and closely mirroring real-world tasks, with automated filtering techniques and human curation to ensure the validity of the dataset. In the generated dataset, DMM learns to recognize the inherent values of scenarios, computes action feasibility and navigates the trade-offs between multiple value dimensions to make personalized decisions. Extensive experiments demonstrate that, given human value preferences, our DMM most closely aligns with human decisions, outperforming Claude-3.5-Sonnet, Gemini-2-flash, Llama-3.1-405b and GPT-4o. This research is a preliminary exploration of value-driven decision-making. We hope it will stimulate interest in value-driven decision-making and personalized decision-making within the community.

cs.AI↗

arXiv2025

On the Expressive Power of Subgraph Graph Neural Networks for Graphs with Bounded Cycles

Graph neural networks (GNNs) have been widely used in graph-related contexts. It is known that the separation power of GNNs is equivalent to that of the Weisfeiler-Lehman (WL) test; hence, GNNs are imperfect at identifying all non-isomorphic graphs, which severely limits their expressive power. This work investigates $k$-hop subgraph GNNs that aggregate information from neighbors with distances up to $k$ and incorporate the subgraph structure. We prove that under appropriate assumptions, the $k$-hop subgraph GNNs can approximate any permutation-invariant/equivariant continuous function over graphs without cycles of length greater than $2k+1$ within any error tolerance. We also provide an extension to $k$-hop GNNs without incorporating the subgraph structure. Our numerical experiments on established benchmarks and novel architectures validate our theory on the relationship between the information aggregation distance and the cycle size.

cs.LG↗

arXiv2025

Certified Machine Unlearning via Noisy Stochastic Gradient Descent

``The right to be forgotten'' ensured by laws for user data privacy becomes increasingly important. Machine unlearning aims to efficiently remove the effect of certain data points on the trained model parameters so that it can be approximately the same as if one retrains the model from scratch. We propose to leverage projected noisy stochastic gradient descent for unlearning and establish its first approximate unlearning guarantee under the convexity assumption. Our approach exhibits several benefits, including provable complexity saving compared to retraining, and supporting sequential and batch unlearning. Both of these benefits are closely related to our new results on the infinite Wasserstein distance tracking of the adjacent (un)learning processes. Extensive experiments show that our approach achieves a similar utility under the same privacy constraint while using $2\%$ and $10\%$ of the gradient computations compared with the state-of-the-art gradient-based approximate unlearning methods for mini-batch and full-batch settings, respectively.

cs.LG↗

arXiv2025

Mean-Field Analysis for Learning Subspace-Sparse Polynomials with Gaussian Input

In this work, we study the mean-field flow for learning subspace-sparse polynomials using stochastic gradient descent and two-layer neural networks, where the input distribution is standard Gaussian and the output only depends on the projection of the input onto a low-dimensional subspace. We establish a necessary condition for SGD-learnability, involving both the characteristics of the target function and the expressiveness of the activation function. In addition, we prove that the condition is almost sufficient, in the sense that a condition slightly stronger than the necessary condition can guarantee the exponential decay of the loss functional to zero.

cs.LG↗

arXiv2025

Rethinking the Capacity of Graph Neural Networks for Branching Strategy

Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching (SB), the most effective yet computationally expensive heuristic employed in the branch-and-bound algorithm. In the literature, message-passing GNN (MP-GNN), as the simplest GNN structure, is frequently used as a fast approximation of SB and we find that not all MILPs's SB can be represented with MP-GNN. We precisely define a class of "MP-tractable" MILPs for which MP-GNNs can accurately approximate SB scores. Particularly, we establish a universal approximation theorem: for any data distribution over the MP-tractable class, there always exists an MP-GNN that can approximate the SB score with arbitrarily high accuracy and arbitrarily high probability, which lays a theoretical foundation of the existing works on imitating SB with MP-GNN. For MILPs without the MP-tractability, unfortunately, a similar result is impossible, which can be illustrated by two MILP instances with different SB scores that cannot be distinguished by any MP-GNN, regardless of the number of parameters. Recognizing this, we explore another GNN structure called the second-order folklore GNN (2-FGNN) that overcomes this limitation, and the aforementioned universal approximation theorem can be extended to the entire MILP space using 2-FGNN, regardless of the MP-tractability. A small-scale numerical experiment is conducted to directly validate our theoretical findings.

cs.LG↗

arXiv2025

Residual connections provably mitigate oversmoothing in graph neural networks

Graph neural networks (GNNs) have achieved remarkable empirical success in processing and representing graph-structured data across various domains. However, a significant challenge known as "oversmoothing" persists, where vertex features become nearly indistinguishable in deep GNNs, severely restricting their expressive power and practical utility. In this work, we analyze the asymptotic oversmoothing rates of deep GNNs with and without residual connections by deriving explicit convergence rates for a normalized vertex similarity measure. Our analytical framework is grounded in the multiplicative ergodic theorem. Furthermore, we demonstrate that adding residual connections effectively mitigates or prevents oversmoothing across several broad families of parameter distributions. The theoretical findings are strongly supported by numerical experiments.

cs.LG↗

arXiv2024

Representation Theorem for Multivariable Totally Symmetric Functions

In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric polynomials. We then study the singularity and geometry of the generators, and show that the regularity may become worse after applying the decomposition.

math.CA↗

arXiv2024

Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem

This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the $H^1$ norm. For the spatial discretization, we consider the finite element method with quadrature using $P^k$ basis on a simplicial mesh and $Q^k$ basis on a rectangular mesh. We prove the global convergence to a critical point of the discrete GP energy, and establish a local exponential convergence to the ground state under the assumption that the linearized discrete Schrödinger operator has a positive spectral gap. We also show that for the $P^1$ finite element discretization with quadrature on an unstructured shape regular simplicial mesh, the eigengap satisfies a mesh-independent lower bound, which implies a mesh-independent local convergence rate for the proposed discrete gradient flow. Numerical experiments with discretization by high order $Q^k$ spectral element methods in two and three dimensions are provided to validate the efficiency of the proposed method.

math.NA↗

arXiv2024

LogEval: A Comprehensive Benchmark Suite for Large Language Models In Log Analysis

Log analysis is crucial for ensuring the orderly and stable operation of information systems, particularly in the field of Artificial Intelligence for IT Operations (AIOps). Large Language Models (LLMs) have demonstrated significant potential in natural language processing tasks. In the AIOps domain, they excel in tasks such as anomaly detection, root cause analysis of faults, operations and maintenance script generation, and alert information summarization. However, the performance of current LLMs in log analysis tasks remains inadequately validated. To address this gap, we introduce LogEval, a comprehensive benchmark suite designed to evaluate the capabilities of LLMs in various log analysis tasks for the first time. This benchmark covers tasks such as log parsing, log anomaly detection, log fault diagnosis, and log summarization. LogEval evaluates each task using 4,000 publicly available log data entries and employs 15 different prompts for each task to ensure a thorough and fair assessment. By rigorously evaluating leading LLMs, we demonstrate the impact of various LLM technologies on log analysis performance, focusing on aspects such as self-consistency and few-shot contextual learning. We also discuss findings related to model quantification, Chinese-English question-answering evaluation, and prompt engineering. These findings provide insights into the strengths and weaknesses of LLMs in multilingual environments and the effectiveness of different prompt strategies. Various evaluation methods are employed for different tasks to accurately measure the performance of LLMs in log analysis, ensuring a comprehensive assessment. The insights gained from LogEvals evaluation reveal the strengths and limitations of LLMs in log analysis tasks, providing valuable guidance for researchers and practitioners.

cs.CL↗

arXiv2024

Efficient Algorithms for Sum-of-Minimum Optimization

In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a predefined sub-function with respect to the $k$ parameters. This universal framework encompasses numerous clustering applications in machine learning and related fields. We develop efficient algorithms for solving sum-of-minimum optimization problems, inspired by a randomized initialization algorithm for the classic $k$-means (Arthur & Vassilvitskii, 2007) and Lloyd's algorithm (Lloyd, 1982). We establish a new tight bound for the generalized initialization algorithm and prove a gradient-descent-like convergence rate for generalized Lloyd's algorithm. The efficiency of our algorithms is numerically examined on multiple tasks, including generalized principal component analysis, mixed linear regression, and small-scale neural network training. Our approach compares favorably to previous ones based on simpler-but-less-precise optimization reformulations.

math.OC↗