Lequan Lin

Luke Thompson, Dai Shi, Lequan Lin et al.

Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method. This efficiency rests on the shuffle algebra, the algebraic counterpart of Stratonovich calculus. This reliance means NRDEs cannot expose the quadratic-variation terms Itô dynamics require, nor the ordered covariant derivatives that govern Itô flows on connection-equipped manifolds. Ameliorating this, we introduce Branched Neural Rough Differential Equations (B-NRDEs), a Hopf-algebraic framework that recasts the NRDE log-ODE step as geometric numerical integration on the state-space manifold, matching the driving algebra to the governing calculus: Grossman--Larson rooted trees for Euclidean Itô dynamics, Munthe-Kaas--Wright planar rooted trees for ordered covariant derivatives on manifolds, and the shuffle algebra in the classical Stratonovich case. This yields intrinsic coarse-step dynamics that exactly preserve manifold constraints. Finally, we introduce a branched signature-kernel objective to enable Itô-consistent law matching by making quadratic-variation terms visible during training. On rough Bergomi volatility, sim-to-real $\mathrm{SO}(3)$ dynamics forecasting, and SPD covariance dynamics, B-NRDEs offer a unified, effective approach to stochastic and manifold-valued dynamics beyond the Euclidean--Stratonovich setting.

Dai Shi, Luke Thompson, Linhan Luo et al.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We revisit these conclusions and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50\% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Lequan Lin, Junbin Gao

Spectral Graph Convolutional Networks (spectral GCNNs), a powerful tool for analyzing and processing graph data, typically apply frequency filtering via Fourier transform to obtain representations with selective information. Although research shows that spectral GCNNs can be enhanced by framelet-based filtering, the massive majority of such research only considers undirected graphs. In this paper, we introduce Framelet-MagNet, a magnetic framelet-based spectral GCNN for directed graphs (digraphs). The model applies the framelet transform to digraph signals to form a more sophisticated representation for filtering. Digraph framelets are constructed with the complex-valued magnetic Laplacian, simultaneously leading to signal processing in both real and complex domains. We empirically validate the predictive power of Framelet-MagNet over a range of state-of-the-art models in node classification, link prediction, and denoising.

Chunya Zou, Andi Han, Lequan Lin et al.

In this paper, we propose a simple yet effective graph neural network for directed graphs (digraph) based on the classic Singular Value Decomposition (SVD), named SVD-GCN. The new graph neural network is built upon the graph SVD-framelet to better decompose graph signals on the SVD ``frequency'' bands. Further the new framelet SVD-GCN is also scaled up for larger scale graphs via using Chebyshev polynomial approximation. Through empirical experiments conducted on several node classification datasets, we have found that SVD-GCN has remarkable improvements in a variety of graph node learning tasks and it outperforms GCN and many other state-of-the-art graph neural networks for digraphs. Moreover, we empirically demonstate that the SVD-GCN has great denoising capability and robustness to high level graph data attacks. The theoretical and experimental results prove that the SVD-GCN is effective on a variant of graph datasets, meanwhile maintaining stable and even better performance than the state-of-the-arts.

Dai Shi, Andi Han, Lequan Lin et al.

Graph-based message-passing neural networks (MPNNs) have achieved remarkable success in both node and graph-level learning tasks. However, several identified problems, including over-smoothing (OSM), limited expressive power, and over-squashing (OSQ), still limit the performance of MPNNs. In particular, OSQ serves as the latest identified problem, where MPNNs gradually lose their learning accuracy when long-range dependencies between graph nodes are required. In this work, we provide an exposition on the OSQ problem by summarizing different formulations of OSQ from current literature, as well as the three different categories of approaches for addressing the OSQ problem. In addition, we also discuss the alignment between OSQ and expressive power and the trade-off between OSQ and OSM. Furthermore, we summarize the empirical methods leveraged from existing works to verify the efficiency of OSQ mitigation approaches, with illustrations of their computational complexities. Lastly, we list some open questions that are of interest for further exploration of the OSQ problem along with potential directions from the best of our knowledge.

Andi Han, Dai Shi, Lequan Lin et al.

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is being iteratively aggregated to central nodes from their neighbourhood. Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density. Analogizing the process of message passing to the heat dynamics allows to fundamentally understand the power and pitfalls of GNNs and consequently informs better model design. Recently, there emerges a plethora of works that proposes GNNs inspired from the continuous dynamics formulation, in an attempt to mitigate the known limitations of GNNs, such as oversmoothing and oversquashing. In this survey, we provide the first systematic and comprehensive review of studies that leverage the continuous perspective of GNNs. To this end, we introduce foundational ingredients for adapting continuous dynamics to GNNs, along with a general framework for the design of graph neural dynamics. We then review and categorize existing works based on their driven mechanisms and underlying dynamics. We also summarize how the limitations of classic GNNs can be addressed under the continuous framework. We conclude by identifying multiple open research directions.

Jiayu Zhai, Lequan Lin, Dai Shi et al.

Numerous recent research on graph neural networks (GNNs) has focused on formulating GNN architectures as an optimization problem with the smoothness assumption. However, in node classification tasks, the smoothing effect induced by GNNs tends to assimilate representations and over-homogenize labels of connected nodes, leading to adverse effects such as over-smoothing and misclassification. In this paper, we propose a novel bilevel optimization framework for GNNs inspired by the notion of Bregman distance. We demonstrate that the GNN layer proposed accordingly can effectively mitigate the over-smoothing issue by introducing a mechanism reminiscent of the "skip connection". We validate our theoretical results through comprehensive empirical studies in which Bregman-enhanced GNNs outperform their original counterparts in both homophilic and heterophilic graphs. Furthermore, our experiments also show that Bregman GNNs can produce more robust learning accuracy even when the number of layers is high, suggesting the effectiveness of the proposed method in alleviating the over-smoothing issue.

Lequan Lin, Dai Shi, Andi Han et al.

Supervised learning relies on high-quality labeled data, but obtaining such data through human annotation is both expensive and time-consuming. Recent work explores using large language models (LLMs) for annotation, but LLM-generated labels still fall short of human-level quality. To address this problem, we propose the Annotation with Critical Thinking (ACT) data pipeline, where LLMs serve not only as annotators but also as judges to critically identify potential errors. Human effort is then directed towards reviewing only the most "suspicious" cases, significantly improving the human annotation efficiency. Our major contributions are as follows: (1) ACT is applicable to a wide range of domains, including natural language processing (NLP), computer vision (CV), and multimodal understanding, by leveraging multimodal-LLMs (MLLMs). (2) Through empirical studies, we derive 7 insights on how to enhance annotation quality while efficiently reducing the human cost, and then translate these findings into user-friendly guidelines. (3) We theoretically analyze how to modify the loss function so that models trained on ACT data achieve similar performance to those trained on fully human-annotated data. Our experiments show that the performance gap can be reduced to less than 2% on most benchmark datasets while saving up to 90% of human costs.

Feng Chen, Yefei He, Shaoxuan He et al.

Existing sparse attention methods primarily target inference-time acceleration by selecting critical tokens under predefined sparsity patterns. However, they often fail to bridge the training-inference gap and lack the capacity for fine-grained token selection across multiple dimensions such as queries, key-values (KV), and heads, leading to suboptimal performance and limited acceleration gains. In this paper, we introduce OmniSparse, a training-aware fine-grained sparse attention framework for long-video MLLMs, which operates in both training and inference with dynamic token budget allocation. Specifically, OmniSparse contains three adaptive and complementary mechanisms: (1) query selection via lazy-active classification, retaining active queries that capture broad semantic similarity while discarding most lazy ones that focus on limited local context and exhibit high functional redundancy; (2) KV selection with head-level dynamic budget allocation, where a shared budget is determined based on the flattest head and applied uniformly across all heads to ensure attention recall; and (3) KV cache slimming to reduce head-level redundancy by selectively fetching visual KV cache according to the head-level decoding query pattern. Experimental results show that OmniSparse matches the performance of full attention while achieving up to 2.7x speedup during prefill and 2.4x memory reduction during decoding.

Lanxin Zhao, Bamdev Mishra, Pratik Jawanpuria et al.

Orthogonal parameter-efficient fine-tuning (PEFT) adapts pretrained weights through structure-preserving multiplicative transformations, but existing methods often conflate two distinct design choices: the subspace in which adaptation occurs and the transformation applied within that subspace. This paper introduces LOFT, a low-rank orthogonal fine-tuning framework that explicitly separates these two components. By viewing orthogonal adaptation as a multiplicative subspace rotation, LOFT provides a unified formulation that recovers representative orthogonal PEFT methods, including coordinate-, butterfly-, Householder-, and principal-subspace-based variants. More importantly, this perspective exposes support selection as a central design axis rather than a byproduct of a particular parameterization. We develop a first-order analysis showing that useful adaptation supports should be informed by the downstream training signal, motivating practical task-aware support selection strategies. Across language understanding, visual transfer, mathematical reasoning, and multilingual out-of-distribution adaptation, LOFT recovers principal-subspace orthogonal adaptation while gradient-informed supports improve the efficiency-performance trade-off under matched parameter, memory, and compute budgets. These results suggest that principled support selection is an important direction for improving orthogonal PEFT.

Lequan Lin, Dai Shi, Andi Han et al.

Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data, requires comprehensive hyperparameter tuning and meticulous training. Unfortunately, these processes come with high computational costs and significant human effort. Additionally, conventional searching algorithms such as grid search may result in overfitting on validation data, diminishing generalization accuracy. To tackle these challenges, we propose a graph conditional latent diffusion framework (GNN-Diff) to generate high-performing GNNs directly by learning from checkpoints saved during a light-tuning coarse search. Our method: (1) unleashes GNN training from heavy tuning and complex search space design; (2) produces GNN parameters that outperform those obtained through comprehensive grid search; and (3) establishes higher-quality generation for GNNs compared to diffusion frameworks designed for general neural networks.

Feng Chen, Yefei He, Lequan Lin et al.

Sparse attention mechanisms aim to reduce computational overhead with minimal accuracy loss by selectively processing salient tokens. Despite their effectiveness, most methods merely exploit a model's inherent sparsity and thus plateau at moderate budgets (about 50\% token reduction), with little headroom to push budget lower without hurting accuracy. Other approaches attempt to enforce sparsity through trainable sparse attention or sharpness-inducing regularizers, but these either fix rigid patterns that ignore input and layer dynamics, or optimize proxy objectives without direct control over token budgets. In this paper, we explicitly reinforce token sparsity in well-posed multimodal large language models (MLLMs) through a simple RL-based post-training framework named \textit{Sparsity Forcing}. Our method explores the efficiency-accuracy trade-off by running multiple rollouts with different token budgets, where both efficiency (token reduction ratio) and performance (answer correctness) are formulated as joint rewards. By contrasting rollouts within each group, the more efficient and correct answer is rewarded while less efficient or incorrect ones are penalized, thereby turning token saving into an end-to-end, inference-consistent optimization objective. Across thirteen image and video benchmarks, Sparsity Forcing raises token reduction ratio on Qwen2-VL/Qwen2.5-VL from 20\% to 75\% with minimal accuracy decline, significantly reducing long-context inference memory by up to 3$\times$ while speeding up decoding by up to 3.3$\times$.

Dai Shi, Kuan Yan, Lequan Lin et al.

Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by developing a biologically informed graph-forming method to efficiently construct pathway graphs for subjects from our newly curated JR5558 mouse transcriptomics dataset. We then develop Graph-level Pseudotime Analysis (GPA) to infer graph-level trajectories that reveal how disease progresses at the population level, rather than in individual subjects. Based on the trajectories estimated by GPA, we identify the most sensitive pathways that drive disease stage transitions. In addition, we measure changes in pathway features using neural stochastic differential equations (SDEs), which enables us to formally define and compute pathway stability and disease bifurcation points (points of no return), two fundamental problems in disease progression research. We further extend our theory to the case when pathways can interact with each other, enabling a more comprehensive and multi-faceted characterization of disease phenotypes. The comprehensive experimental results demonstrate the effectiveness of our framework in reconstructing the dynamics of the pathway, identifying critical transitions, and providing novel insights into the mechanistic understanding of disease evolution.

Dai Shi, Andi Han, Lequan Lin et al.

Physics-informed Graph Neural Networks have achieved remarkable performance in learning through graph-structured data by mitigating common GNN challenges such as over-smoothing, over-squashing, and heterophily adaption. Despite these advancements, the development of a simple yet effective paradigm that appropriately integrates previous methods for handling all these challenges is still underway. In this paper, we draw an analogy between the propagation of GNNs and particle systems in physics, proposing a model-agnostic enhancement framework. This framework enriches the graph structure by introducing additional nodes and rewiring connections with both positive and negative weights, guided by node labeling information. We theoretically verify that GNNs enhanced through our approach can effectively circumvent the over-smoothing issue and exhibit robustness against over-squashing. Moreover, we conduct a spectral analysis on the rewired graph to demonstrate that the corresponding GNNs can fit both homophilic and heterophilic graphs. Empirical validations on benchmarks for homophilic, heterophilic graphs, and long-term graph datasets show that GNNs enhanced by our method significantly outperform their original counterparts.

Lequan Lin, Dai Shi, Andi Han et al.

Traffic forecasting, a crucial application of spatio-temporal graph (STG) learning, has traditionally relied on deterministic models for accurate point estimations. Yet, these models fall short of quantifying future uncertainties. Recently, many probabilistic methods, especially variants of diffusion models, have been proposed to fill this gap. However, existing diffusion methods typically deal with individual sensors separately when generating future time series, resulting in limited usage of spatial information in the probabilistic learning process. In this work, we propose SpecSTG, a novel spectral diffusion framework, to better leverage spatial dependencies and systematic patterns inherent in traffic data. More specifically, our method generates the Fourier representation of future time series, transforming the learning process into the spectral domain enriched with spatial information. Additionally, our approach incorporates a fast spectral graph convolution designed for Fourier input, alleviating the computational burden associated with existing models. Compared with state-of-the-arts, SpecSTG achieves up to 8% improvements on point estimations and up to 0.78% improvements on quantifying future uncertainties. Furthermore, SpecSTG's training and validation speed is 3.33X of the most efficient existing diffusion method for STG forecasting. The source code for SpecSTG is available at https://anonymous.4open.science/r/SpecSTG.

Lequan Lin, Zhengkun Li, Ruikun Li et al.

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. In recent years, the concept of diffusion has been extended to time series applications, and many powerful models have been developed. Considering the deficiency of a methodical summary and discourse on these models, we provide this survey as an elementary resource for new researchers in this area and also an inspiration to motivate future research. For better understanding, we include an introduction about the basics of diffusion models. Except for this, we primarily focus on diffusion-based methods for time series forecasting, imputation, and generation, and present them respectively in three individual sections. We also compare different methods for the same application and highlight their connections if applicable. Lastly, we conclude the common limitation of diffusion-based methods and highlight potential future research directions.