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Jian Luo

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9 papers

1 author row

TMLR Journal 2025 Journal Article

Dynamic Schwartz-Fourier Neural Operator for Enhanced Expressive Power

Wenhan Gao
Jian Luo
Ruichen Xu
Yi Liu

Recently, neural operators have emerged as a prevailing approach for learning discretization-invariant mappings between function spaces. A particular example is the Fourier Neural Operator (FNO), which constrains integral kernels to be convolutions and learns the kernel directly in the frequency domain. Due to the capacity of Fourier transforms to effectively reduce the dimensionality and preserve information, FNOs demonstrate superior performance in terms of both efficiency and accuracy. In FNOs, the convolution kernel is fixed as a point-wise multiplication in the frequency domain; however, these translation-invariant kernels might limit the expressiveness of FNOs. For instance, if the underlying system lacks translational symmetries, the kernels learned by the FNO will still exhibit translational invariance, thereby limiting the model's expressive power. We propose a dynamic Schwartz operator that induces interactions between modes to enhance the expressiveness of FNOs. In this work, we introduce a novel approach that equips FNOs with Schwartz operators to learn dynamic kernels, termed Dynamic Kernel Fourier Neural Operators (DSFNOs). By incorporating this dynamic mechanism, our model gains the ability to capture relevant frequency information patterns, facilitating a better understanding and representation of complex physical phenomena. Through experiments, we demonstrate that DSFNOs can improve FNOs on a range of tasks, highlighting the effectiveness of our proposed approach. The code is available at https://github.com/wenhangao21/TMLR25_DSFNO.

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NeurIPS Conference 2025 Conference Paper

STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem

Hong Wang
Yixuan Jiang
Jie Wang
Xinyi Li
Jian Luo
huanshuo dong

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to address this challenge by iteratively updating neural networks. These methods' performance relies heavily on the spectral distribution of the given operator: larger gaps between the operator's eigenvalues will improve precision, thus tailored spectral transformations that leverage the spectral distribution can enhance their performance. Based on this observation, we propose the S pectral T ransformation Net work ( STNet ). During each iteration, STNet uses approximate eigenvalues and eigenfunctions to perform spectral transformations on the original operator, turning it into an equivalent but easier problem. Specifically, we employ deflation projection to exclude the subspace corresponding to already solved eigenfunctions, thereby reducing the search space and avoiding converging to existing eigenfunctions. Additionally, our filter transform magnifies eigenvalues in the desired region and suppresses those outside, further improving performance. Extensive experiments demonstrate that STNet consistently outperforms existing learning-based methods, achieving state-of-the-art performance in accuracy.

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NeurIPS Conference 2024 Conference Paper

Neural Krylov Iteration for Accelerating Linear System Solving

Jian Luo
Jie Wang
Hong Wang
huanshuo dong
Zijie Geng
Hanzhu Chen
Yufei Kuang

Solving large-scale sparse linear systems is essential in fields like mathematics, science, and engineering. Traditional numerical solvers, mainly based on the Krylov subspace iteration algorithm, suffer from the low-efficiency problem, which primarily arises from the less-than-ideal iteration. To tackle this problem, we propose a novel method, namely Neur al K rylov It era t ion ( NeurKItt ), for accelerating linear system solving. Specifically, NeurKItt employs a neural operator to predict the invariant subspace of the linear system and then leverages the predicted subspace to accelerate linear system solving. To enhance the subspace prediction accuracy, we utilize QR decomposition for the neural operator outputs and introduce a novel projection loss function for training. NeurKItt benefits the solving by using the predicted subspace to guide the iteration process, significantly reducing the number of iterations. We provide extensive experiments and comprehensive theoretical analyses to demonstrate the feasibility and efficiency of NeurKItt. In our main experiments, NeurKItt accelerates the solving of linear systems across various settings and datasets, achieving up to a 5. 5× speedup in computation time and a 16. 1× speedup in the number of iterations.

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IJCAI Conference 2022 Conference Paper

Towards Robust Dense Retrieval via Local Ranking Alignment

Xuanang Chen
Jian Luo
Ben He
Le Sun
Yingfei Sun

Dense retrieval (DR) has extended the employment of pre-trained language models, like BERT, for text ranking. However, recent studies have raised the robustness issue of DR model against query variations, like query with typos, along with non-trivial performance losses. Herein, we argue that it would be beneficial to allow the DR model to learn to align the relative positions of query-passage pairs in the representation space, as query variations cause the query vector to drift away from its original position, affecting the subsequent DR effectiveness. To this end, we propose RoDR, a novel robust DR model that learns to calibrate the in-batch local ranking of query variation to that of original query for the DR space alignment. Extensive experiments on MS MARCO and ANTIQUE datasets show that RoDR significantly improves the retrieval results on both the original queries and different types of query variations. Meanwhile, RoDR provides a general query noise-tolerate learning framework that boosts the robustness and effectiveness of various existing DR models. Our code and models are openly available at https: //github. com/cxa-unique/RoDR.

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AAAI Conference 2016 Conference Paper

Counter-Transitivity in Argument Ranking Semantics

Fuan Pu
Jian Luo
Guiming Luo

The principle of counter-transitivity plays a vital role in argumentation. It states that an argument is strong when its attackers are weak, but weak when its attackers are strong. In this work, we develop a formal theory about the argument ranking semantics based on this principle. Three approaches, i. e. , quantity-based, quality-based and the unity of them, are de- ﬁned to implement the principle. Then, we show an iterative reﬁnement algorithm for capturing the ranking on arguments based on the recursive nature of the principle.

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IS Journal 2016 Journal Article

Satisfiability Degree Analysis and Deductive Reasoning

Kueiming Lo
Chongyuan Yin
Jian Luo

There are many situations that common logic models aren't capable of representing, so nonclassical logic systems have emerged to compensate for their inability to express uncertainty. This article introduces the satisfiability degree for propositional logic. It's a new means of describing the extent to which a proposition is satisfied, and it employs deterministic logic rather than probabilistic or fuzzy logic. The independent formula-pair and incompatible formula-pair of the propositions are discussed. Some properties of the satisfiability degree are given with a conditional satisfiability degree. The weighted satisfiability degree is defined and the properties are proven. Deductive reasoning methods based on the satisfiability degree are established. The formula reasoning and semantic checking are given by the conditional satisfiability degree. Finally, calculations of the satisfiability degree for the circuit logic diagram and Bayesian attack graphs are given.

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AAAI Conference 2014 Conference Paper

Computing Preferences Based on Agents’ Beliefs

Jian Luo
Fuan Pu
Yulai Zhang
Guiming Luo

The knowledgebase uncertainty and the argument preferences are considered in this paper. The uncertainty is captured by weighted satisfiability degree, while a preference relation over arguments is derived by the beliefs of an agent.

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AAMAS Conference 2012 Conference Paper

Improved Use of Partial Policies for Identifying Behavioral Equivalence

Yifeng Zeng
Yinghui Pan
Hua Mao
Jian Luo

Interactive multiagent decision making often requires to predict actions of other agents by solving their behavioral models from the perspective of the modeling agent. Unfortunately, the general space of models in the absence of constraining assumptions tends to be very large thereby making multiagent decision making intractable. One approach that can reduce the model space is to cluster \emph{behaviorally equivalent models} that exhibit identical policies for the whole planning horizon. Currently, the state-of-the art on identifying equivalence of behavioral models compares partial policy trees instead of entire trees. In this paper, we further improve the use of partial trees for the identification purpose and develop an incremental comparison strategy in order to efficiently ascertain the model equivalence. We investigate the improved approach in a well-defined probabilistic graphical model for sequential multiagent decision making - interactive dynamic influence diagrams, and evaluate its performance over multiple problem domains.

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AAAI Conference 2011 Conference Paper

Utilizing Partial Policies for Identifying Equivalence of Behavioral Models

Yifeng Zeng
Prashant Doshi
Yinghui Pan
Hua Mao
Muthukumaran Chandrasekaran
Jian Luo

We present a novel approach for identifying exact and approximate behavioral equivalence between models of agents. This is signiﬁcant because both decision making and game play in multiagent settings must contend with behavioral models of other agents in order to predict their actions. One approach that reduces the complexity of the model space is to group models that are behaviorally equivalent. Identifying equivalence between models requires solving them and comparing entire policy trees. Because the trees grow exponentially with the horizon, our approach is to focus on partial policy trees for comparison and determining the distance between updated beliefs at the leaves of the trees. We propose a principled way to determine how much of the policy trees to consider, which trades off solution quality for efﬁciency. We investigate this approach in the context of the interactive dynamic inﬂuence diagram and evaluate its performance.

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