Liheng Ma

SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting

Boris Oreshkin

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a sp… (see more)ace of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.

2025-10-06

Proceedings of the 42nd International Conference on Machine Learning (published)

proceedings.mlr.press

SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting

Boris Oreshkin

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a sp… (see more)ace of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.

2025-10-06

Proceedings of the 42nd International Conference on Machine Learning (published)

doi.org

openreview.net

Enhancing Logical Reasoning in Large Language Models through Graph-based Synthetic Data

Jiaming Zhou

Abbas Ghaddar

Ge Zhang

Liheng Ma

Yaochen Hu

Soumyasundar Pal

B. Wang

Jianye HAO

Mark Coates

Yingxue Zhang

Despite recent advances in training and prompt- ing strategies for Large Language Models (LLMs), these models continue to face chal- lenges … (see more)with complex logical reasoning tasks that involve long reasoning chains. In this work, we explore the potential and limitations of using graph-based synthetic reasoning data as training signals to enhance LLMs’ reasoning capabilities. Our extensive experiments, con- ducted on two established natural language rea- soning tasks—inductive reasoning and spatial reasoning—demonstrate that supervised fine- tuning (SFT) with synthetic graph-based rea- soning data effectively enhances LLMs’ rea- soning performance, without compromising their effectiveness on other standard evaluation benchmarks.

2025-07-24

colmweb.org/COLM/2025/Workshop/XLLM-Reason-Plan (published)

openreview.net

Enhancing Logical Reasoning in Large Language Models through Graph-based Synthetic Data

Jiaming Zhou

Abbas Ghaddar

Ge Zhang

Liheng Ma

Yaochen Hu

Soumyasundar Pal

Mark Coates

Jianye HAO

B. Wang

Yingxue Zhang

2025-07-24

colmweb.org/COLM/2025/Workshop/XLLM-Reason-Plan (published)

doi.org

openreview.net

SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting

Boris Oreshkin

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a sp… (see more)ace of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance.

2025-06-17

ArXiv (preprint)

doi.org

arxiv.org

Sparse Decomposition of Graph Neural Networks

Yaochen Hu

Mai Zeng

Ge Zhang

Pavel Rumiantsev

Liheng Ma

Yingxue Zhang

Mark Coates

2025-03-17

TMLR (accepted)

doi.org

openreview.net

Enhancing Logical Reasoning in Large Language Models through Graph-based Synthetic Data

Jiaming Zhou

Abbas Ghaddar

Ge Zhang

Liheng Ma

Yaochen Hu

Soumyasundar Pal

Mark Coates

Bin Wang

Yingxue Zhang

Jianye HAO

Despite recent advances in training and prompting strategies for Large Language Models (LLMs), these models continue to face challenges with… (see more) complex logical reasoning tasks that involve long reasoning chains. In this work, we explore the potential and limitations of using graph-based synthetic reasoning data as training signals to enhance LLMs' reasoning capabilities. Our extensive experiments, conducted on two established natural language reasoning tasks -- inductive reasoning and spatial reasoning -- demonstrate that supervised fine-tuning (SFT) with synthetic graph-based reasoning data effectively enhances LLMs' reasoning performance without compromising their effectiveness on other standard evaluation benchmarks.

2024-09-19

ArXiv (preprint)

doi.org

arxiv.org

The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges

Sitao Luan

Chenqing Hua

Qincheng Lu

Liheng Ma

Lirong Wu

Xinyu Wang

Minkai Xu

Xiao-Wen Chang

Doina Precup

Rex Ying

Stan Z. Li

Jian Tang

Guy Wolf

Stefanie Jegelka

Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to b… (see more)e the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning.

2024-07-12

ArXiv (preprint)

doi.org

arxiv.org

The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges

Sitao Luan

Chenqing Hua

Qincheng Lu

Liheng Ma

Lirong Wu

Xinyu Wang

Minkai Xu

Xiao-Wen Chang

Doina Precup

Rex Ying

Stan Z. Li

Jian Tang

Guy Wolf

Stefanie Jegelka

Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to b… (see more)e the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning.

2024-07-12

ArXiv (preprint)

doi.org

arxiv.org

CKGConv: General Graph Convolution with Continuous Kernels

Liheng Ma

Soumyasundar Pal

Yitian Zhang

Jiaming Zhou

Yingxue Zhang

Mark Coates

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a gene… (see more)ral convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.

2024-07-08

Proceedings of the 41st International Conference on Machine Learning (published)

doi.org

openreview.net

CKGConv: General Graph Convolution with Continuous Kernels

Liheng Ma

Soumyasundar Pal

Yitian Zhang

Jiaming Zhou

Yingxue Zhang

Mark Coates

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a gene… (see more)ral convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits the same expressiveness as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets.

2024-05-01

ICML.cc/2024/Conference (poster)

doi.org

openreview.net

Multi-resolution Time-Series Transformer for Long-term Forecasting

Yitian Zhang

Liheng Ma

Soumyasundar Pal

Yingxue Zhang

Mark Coates

2024-04-18

Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (published)