Catastrophic forgetting is a longstanding challenge in continual learning, where models lose knowledge from earlier tasks when learning new ones. While various mitigation strategies have been proposed for Multi-Layer Perceptrons (MLPs), recent architectural advances like Kolmogorov-Arnold Networks (KANs) have been suggested to offer intrinsic resistance to forgetting by leveraging localized spline-based activations. However, the practical behavior of KANs under continual learning remains unclear, and their limitations are not well understood. To address this, we present a comprehensive study of catastrophic forgetting in KANs and develop a theoretical framework that links forgetting to activation support overlap and intrinsic data dimension. We validate these analyses through systematic experiments on synthetic and vision tasks, measuring forgetting dynamics under varying model configurations and data complexity. Further, we introduce KAN-LoRA, a novel adapter design for parameter-efficient continual fine-tuning of language models, and evaluate its effectiveness in knowledge editing tasks. Our findings reveal that while KANs exhibit promising retention in low-dimensional algorithmic settings, they remain vulnerable to forgetting in high-dimensional domains such as image classification and language modeling. These results advance the understanding of KANs’ strengths and limitations, offering practical insights for continual learning system design.

Biological oscillations are periodic changes in various signaling processes crucial for the proper functioning of living organisms. These oscillations are modeled by ordinary differential equations, with coefficient variations leading to diverse periodic behaviors, typically measured by oscillatory frequencies. This paper explores sampling techniques for neural networks to model the relationship between system coefficients and oscillatory frequency. However, the scarcity of oscillations in the vast coefficient space results in many samples exhibiting non-periodic behaviors, and small coefficient changes near oscillation boundaries can significantly alter oscillatory properties. This leads to non-oscillatory bias and boundary sensitivity, making accurate predictions difficult. While existing importance and uncertainty sampling approaches partially mitigate these challenges, they either fail to resolve the sensitivity problem or result in redundant sampling. To address these limitations, we propose the Hierarchical Gradient-based Genetic Sampling (HGGS) framework, which improves the accuracy of neural network predictions for biological oscillations. The first layer, Gradient-based Filtering, extracts sensitive oscillation boundaries and removes redundant non-oscillatory samples, creating a balanced coarse dataset. The second layer, Multi-grid Genetic Sampling, utilizes residual information to refine these boundaries and explore new high-residual regions, increasing data diversity for model training. Experimental results demonstrate that HGGS outperforms seven comparative sampling methods across four biological systems, highlighting its effectiveness in enhancing sampling and prediction accuracy.

Abstract This study presents a new machine learning algorithm, named Chemical Environment Graph Neural Network (ChemGNN), designed to accelerate materials property prediction and advance new materials discovery. Graphitic carbon nitride (g-C3N4) and its doped variants have gained significant interest for their potential as optical materials. Accurate prediction of their band gaps is crucial for practical applications; however, traditional quantum simulation methods are computationally expensive and challenging to explore the vast space of possible doped molecular structures. The proposed ChemGNN leverages the learning ability of current graph neural networks (GNNs) to satisfactorily capture the characteristics of atoms' chemical environment underlying complex molecular structures. Our experimental results demonstrate more than 100% improvement in band gap prediction accuracy over existing GNNs on g-C3N4. Furthermore, the general ChemGNN model can precisely foresee band gaps of various doped g-C3N4 structures, making it a valuable tool for performing high-throughput prediction in materials design and development.

Mounting evidence has revealed that functional brain networks are intrinsically dynamic, undergoing changes over time, even in the resting-state environment. Notably, recent studies have highlighted the existence of a small number of critical brain regions within each functional brain network that exhibit a flexible role in adapting the geometric pattern of brain connectivity over time, referred to as "temporal hub" regions. Therefore, the identification of these temporal hubs becomes pivotal for comprehending the mechanisms that underlie the dynamic evolution of brain connectivity. However, existing spatio-temporal hub identification methods rely on static network-based approaches, wherein each temporal hub region is independently inferred from individual time-segmented networks without considering their temporal consistency and consequently fails to align the evolution of hubs with the dynamic changes in brain states. To address this limitation, we propose a novel spatio-temporal hub identification method that fully leverages dynamic graph embedding to distinguish temporal hubs from peripheral nodes, in which dynamic graph embeddings are learned from both spatial and temporal dimensions. Specifically, to preserve the temporal consistency of evolving networks, we model the dynamic graph embedding as a physical model of time, where the network-to-network transition is mathematically expressed as a total variation of dynamic graph embedding with respect to time. Furthermore, a Grassmannian manifold optimization scheme is introduced to enhance graph embedding learning and capture the time-varying topology of brain networks. Experimental results on both synthetic and real fMRI data demonstrate superior temporal consistency in hub identification, surpassing conventional approaches.

In biochemical modeling, some foundational systems can exhibit sudden and profound behavioral shifts, such as the cellular signaling pathway models, in which the physiological responses promptly react to environmental changes, resulting in steep changes in their dynamic model trajectories. These steep changes are one of the major challenges in biochemical modeling governed by nonlinear differential equations. One promising way to tackle this challenge is converting the input data from the time domain to the frequency domain through Fourier Neural Operators, which enhances the ability to analyze data periodicity and regularity. However, the effectiveness of these Fourier based methods diminishes in scenarios with complex abrupt switches. To address this limitation, an innovative Multiscale Attention Wavelet Neural Operator (MAWNO) method is proposed in this paper, which comprehensively combines the attention mechanism with the versatile wavelet transforms to effectively capture these abrupt switches. Specifically, the wavelet transform scrutinizes data across multiple scales to extract the characteristics of abrupt signals into wavelet coefficients, while the self-attention mechanism is adeptly introduced to enhance the wavelet coefficients in high-frequency signals that can better characterize the abrupt switches. Experimental results substantiate MAWNO’s supremacy in terms of accuracy on three classical biochemical models featuring periodic and steep trajectories. https://github.com/SUDERS/MAWNO.

Alzheimer's disease (AD) is the most common neurodegenerative disease, and it consumes considerable medical resources with increasing number of patients every year. Mounting evidence show that the regulatory disruptions altering the intrinsic activity of genes in brain cells contribute to AD pathogenesis. To gain insights into the underlying gene regulation in AD, we proposed a graph learning method, Single-Cell based Regulatory Network (SCRN), to identify the regulatory mechanisms based on single-cell data. SCRN implements the γ-decaying heuristic link prediction based on graph neural networks and can identify reliable gene regulatory networks using locally closed subgraphs. In this work, we first performed UMAP dimension reduction analysis on single-cell RNA sequencing (scRNA-seq) data of AD and normal samples. Then we used SCRN to construct the gene regulatory network based on three well-recognized AD genes (APOE, CX3CR1, and P2RY12). Enrichment analysis of the regulatory network revealed significant pathways including NGF signaling, ERBB2 signaling, and hemostasis. These findings demonstrate the feasibility of using SCRN to uncover potential biomarkers and therapeutic targets related to AD.

AMP-activated protein kinase (AMPK), a cellular energy sensor in response to changes in the ADP/ATP ratio, has been proven to not only play roles in metabolic actions but also holds pivotal roles in neurodegenerative diseases such as Alzheimer’s disease (AD), Parkinson’s disease, and Lewy body dementia. However, the downstream effectors regulated by AMPK and its specific contributions to the pathology of these diseases remain elusive. In this study, we combine the power of systems biology and neuroscience to understand the dynamics and regulatory effects of AMPK under the progression of AD. Particularly, our study develops a regulatory protein network that seeks to demystify this intricate protein-protein interaction, placing particular emphasis on the role of AMPK in the pathology of AD. By focusing on two important cellular activities, mRNA translation and autophagy, our model explores the underlying effects of the central governance of a change in AMPK activity and concludes that eEF2-controlled translation is more sensitive to the perturbation. Additionally, we adjust various kinetic parameters to restore proteins affected by the disease to their baseline levels, with the goal of identifying potential new drug targets. The model accurately captures the regulatory effect of AMPK, provides the temporal dynamics of key regulators in AD progression, contributes to the understanding of the disease’s pathophysiology, and potentially generalizes the function of AMPK into other neurodegenerative diseases.

Recently, the fast development of single-cell RNA-seq (scRNA-seq) techniques has enabled high-resolution transcriptomic statistical analysis of individual cells in heterogeneous tissues, which can help researchers to explore the relationship between genes and human diseases. The emerging scRNA-seq data results in new analysis methods aiming to identify cell-level clustering and annotations. However, there are few methods developed to gain insights into the gene-level clusters with biological significance. This study proposes a new deep learning-based framework, scENT (single cell gENe clusTer), to identify significant gene clusters from single-cell RNA-seq data. We started with clustering the scRNA-seq data into multiple optimal groups, followed by a gene set enrichment analysis to identify classes of over-represented genes. Considering high-dimensional data with extensive zeros and dropout issues, scENT integrates perturbation in the learning process of clustering scRNA-seq data to improve its robustness and performance. Experimental results show that scENT outperformed other benchmarking methods on simulation data. To validate the biological insights of scENT, we applied it to the public experimental scRNA-seq data profiled from patients with Alzheimer's disease and brain metastasis. scENT successfully identified novel functional gene clusters and associated functions, facilitating the discovery of prospective mechanisms and the understanding of related diseases.

Patient similarity learning aims to use patient information such as electronic medical records and genetic data as input to calculate the pairwise similarity between patients, and it is becoming increasingly important in healthcare applications. However, in many cases, patient similarity learning models also need to forget some patient data. From the perspective of privacy, patients desire a tool to erase the impacts of their sensitive data from the trained patient similarity models. From the perspective of utility, if a patient similarity model’s utility is damaged by some bad patient data, the patient similarity model needs to forget such patient data to regain utility. Although some researchers have studied the problem of machine unlearning, existing methods cannot be directly applied to patient similarity learning as they fail to consider the comparative relationships among patients. In addition, they also fail to identify the optimal conditions of the local objective functions. In this paper, we fill in this gap by studying the unlearning problem in patient similarity learning. To unlearn the knowledge of a specific patient, we propose a novel erasable patient similarity learning framework, which enjoys the provable data removal guarantee and achieves high unlearning efficiency while keeping high model utility in patient similarity learning. We also conduct extensive experiments on real-world patient disease datasets to verify the desired properties of the proposed erasable framework.

The cell cycle of Caulobacter crescentus involves the polar morphogenesis and an asymmetric cell division driven by precise interactions and regulations of proteins, which makes Caulobacter an ideal model organism for investigating bacterial cell development and differentiation. The abundance of molecular data accumulated on Caulobacter motivates system biologists to analyze the complex regulatory network of cell cycle via quantitative modeling. In this paper, We propose a comprehensive model to accurately characterize the underlying mechanisms of cell cycle regulation based on the study of: a) chromosome replication and methylation; b) interactive pathways of five master regulatory proteins including DnaA, GcrA, CcrM, CtrA, and SciP, as well as novel consideration of their corresponding mRNAs; c) cell cycle-dependent proteolysis of CtrA through hierarchical protease complexes. The temporal dynamics of our simulation results are able to closely replicate an extensive set of experimental observations and capture the main phenotype of seven mutant strains of Caulobacter crescentus. Collectively, the proposed model can be used to predict phenotypes of other mutant cases, especially for nonviable strains which are hard to cultivate and observe. Moreover, the module of cyclic proteolysis is an efficient tool to study the metabolism of proteins with similar mechanisms.

Currently, many studies of Alzheimer's disease (AD) are investigating the neurobiological factors behind the acquisition of beta-amyloid (A), pathologic tau (T), and neurodegeneration ([N]) biomarkers from neuroimages. However, a system-level mechanism of how these neuropathological burdens promote neurodegeneration and why AD exhibits characteristic progression is largely elusive. In this study, we combined the power of systems biology and network neuroscience to understand the dynamic interaction and diffusion process of AT[N] biomarkers from an unprecedented amount of longitudinal Amyloid PET scan, MRI imaging, and DTI data. Specifically, we developed a network-guided biochemical model to jointly (1) model the interaction of AT[N] biomarkers at each brain region and (2) characterize their propagation pattern across the fiber pathways in the structural brain network, where the brain resilience is also considered as a moderator of cognitive decline. Our biochemical model offers a greater mathematical insight to understand the physiopathological mechanism of AD progression by studying the system dynamics and stability. Thus, an in-depth system-level analysis allows us to gain a new understanding of how AT[N] biomarkers spread throughout the brain, capture the early sign of cognitive decline, and predict the AD progression from the preclinical stage.

BACKGROUND: The hybrid stochastic simulation algorithm, proposed by Haseltine and Rawlings (HR), is a combination of differential equations for traditional deterministic models and Gillespie's algorithm (SSA) for stochastic models. The HR hybrid method can significantly improve the efficiency of stochastic simulations for multiscale biochemical networks. Previous studies on the accuracy analysis for a linear chain reaction system showed that the HR hybrid method is accurate if the scale difference between fast and slow reactions is above a certain threshold, regardless of population scales. However, the population of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems. RESULTS: This work investigates the negativity problem of the HR hybrid method, analyzes and tests it with several models including a linear chain system, a nonlinear reaction system, and a realistic biological cell cycle system. As a benchmark, the second slow reaction firing time is used to measure the effect of negative populations on the accuracy of the HR hybrid method. Our analysis demonstrates that usually the error caused by negative populations is negligible compared with approximation errors of the HR hybrid method itself, and sometimes negativity phenomena may even improve the accuracy. But for systems where negative species are involved in nonlinear reactions or some species are highly sensitive to negative species, the system stability will be influenced and may lead to system failure when using the HR hybrid method. In those circumstances, three remedies are studied for the negativity problem. CONCLUSION: The results of different models and examples suggest that the Zero-Reaction rule is a good remedy for nonlinear and sensitive systems considering its efficiency and simplicity.

Parameter estimation in discrete or continuous deterministic cell cycle models is challenging for several reasons, including the nature of what can be observed, and the accuracy and quantity of those observations. The challenge is even greater for stochastic models, where the number of simulations and amount of empirical data must be even larger to obtain statistically valid parameter estimates. The two main contributions of this work are (1) stochastic model parameter estimation based on directly matching multivariate probability distributions, and (2) a new quasi-Newton algorithm class QNSTOP for stochastic optimization problems. QNSTOP directly uses the random objective function value samples rather than creating ensemble statistics. QNSTOP is used here to directly match empirical and simulated joint probability distributions rather than matching summary statistics. Results are given for a current state-of-the-art stochastic cell cycle model of budding yeast, whose predictions match well some summary statistics and one-dimensional distributions from empirical data, but do not match well the empirical joint distributions. The nature of the mismatch provides insight into the weakness in the stochastic model.