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Integer-order calculus fails to capture the long-range dependence (LRD) and memory effects found in many complex systems. Fractional calculus addresses these gaps through fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control tasks. In this paper, we theoretically derive the optimal control via linear quadratic regulator (LQR) for fractional-order linear time-invariant (FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing a novel method for system identification and optimal control strategy in FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, Fractional-Order Learning for Optimal Control (FOLOC), that learns control policies from observed trajectories, and (iii) deriving theoretical bounds on the sample complexity for learning accurate control policies under fractional-order dynamics. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control. 

Today’s generative models can synthesize magnetic resonance images (MRIs) of the brain at specific ages. However, such models can neither map the aging process longitudinally within subjects, nor accommodate its variability across subjects. Such approaches also cannot predict anatomic features of aging in ways that can be validated retrospectively or trusted prospectively. We introduce a three-dimensional hybrid ControlNet + diffusion model that uses the baseline T1-weighted MRIs of healthy adults to predict individual neuroanatomic aging trajectories, as reflected by follow-up MRIs. The approach captures individual anatomical changes with an average predicted voxelwise intensity error of 15% and structural similarity index of 93%. Unlike methods relying on qualitative validation, our approach quantifies the fidelity of prospective MRI synthesis using FreeSurfer volumetrics. Because brain atrophy reflects risk for Alzheimer’s disease (AD), our model’s ability to generate individual-specific prospective MRIs suggests its clinical potential to assist AD risk estimation. 

This study investigated the generalizability of Arabidopsis thaliana immune responses across diverse pathogens, including Botrytis cinerea, Sclerotinia sclerotiorum, and Pseudomonas syringae, using a data-driven, machine learning approach. Machine learning models were trained to predict disease development from early transcriptional responses. Feature selection techniques based on network science and topology were used to train models employing only a fraction of the transcriptome. Machine learning models trained on one pathosystem where then validated by predicting disease development in new pathosystems. The identified feature selection gene sets were enriched for pathways related to biotic, abiotic, and stress responses, though the specific genes involved differed between feature sets. This suggests common immune responses to diverse pathogens that operate via different gene sets.The study demonstrates that machine learning can uncover both established and novel components of the plant's immune response, offering insights into disease resistance mechanisms. These predictive models highlight the potential to advance our understanding of multigenic outcomes in plant immunity and can be further refined for applications in disease prediction. 

Computation graphs are Directed Acyclic Graphs (DAGs) where the nodes correspond to mathematical operations and are used widely as abstractions in optimizations of neural networks. The device placement problem aims to identify optimal allocations of those nodes to a set of (potentially heterogeneous) devices. Existing approaches rely on two types of architectures known as grouper-placer and encoder-placer, respectively. In this work, we bridge the gap between encoder-placer and grouper-placer techniques and propose a novel framework for the task of device placement, relying on smaller computation graphs extracted from the OpenVINO toolkit. The framework consists of five steps, including graph coarsening, node representation learning and policy optimization. It facilitates end-to-end training and takes into account the DAG nature of the computation graphs. We also propose a model variant, inspired by graph parsing networks and complex network analysis, enabling graph representation learning and jointed, personalized graph partitioning, using an unspecified number of groups. To train the entire framework, we use reinforcement learning using the execution time of the placement as a reward. We demonstrate the flexibility and effectiveness of our approach through multiple experiments with three benchmark models, namely Inception-V3, ResNet, and BERT. The robustness of the proposed framework is also highlighted through an ablation study. The suggested placements improve the inference speed for the benchmark models by up to over CPU execution and by up to compared to other commonly used baselines. 

Malware represents a significant security concern in today’s digital landscape, as it can destroy or disable operating systems, steal sensitive user information, and occupy valuable disk space. However, current malware detection methods, such as static-based and dynamic-based approaches, struggle to identify newly developed ("zero-day") malware and are limited by customized virtual machine (VM) environments. To overcome these limitations, we propose a novel malware detection approach that leverages deep learning, mathematical techniques, and network science. Our approach focuses on static and dynamic analysis and utilizes the Low-Level Virtual Machine (LLVM) to profile applications within a complex network. The generated network topologies are input into the GraphSAGE architecture to efficiently distinguish between benign and malicious software applications, with the operation names denoted as node features. Importantly, the GraphSAGE models analyze the network’s topological geometry to make predictions, enabling them to detect state-of-the-art malware and prevent potential damage during execution in a VM. To evaluate our approach, we conduct a study on a dataset comprising source code from 24,376 applications, specifically written in C/C++, sourced directly from widely-recognized malware and various types of benign software. The results show a high detection performance with an Area Under the Receiver Operating Characteristic Curve (AUROC) of 99.85%. Our approach marks a substantial improvement in malware detection, providing a notably more accurate and efficient solution when compared to current state-of-the-art malware detection methods. The code is released at https://github.com/HantangZhang/MGN. 

Integrating and processing information from various sources or modalities are critical for obtaining a comprehensive and accurate perception of the real world in autonomous systems and cyber-physical systems. Drawing inspiration from neuroscience, we develop the Information-Theoretic Hierarchical Perception (ITHP) model, which utilizes the concept of information bottleneck. Different from most traditional fusion models that incorporate all modalities identically in neural networks, our model designates a prime modality and regards the remaining modalities as detectors in the information pathway, serving to distill the flow of information. Our proposed perception model focuses on constructing an effective and compact information flow by achieving a balance between the minimization of mutual information between the latent state and the input modal state, and the maximization of mutual information between the latent states and the remaining modal states. This approach leads to compact latent state representations that retain relevant information while minimizing redundancy, thereby substantially enhancing the performance of multimodal representation learning. Experimental evaluations on the MUStARD, CMU-MOSI, and CMU-MOSEI datasets demonstrate that our model consistently distills crucial information in multimodal learning scenarios, outperforming state-of-the-art benchmarks. Remarkably, on the CMU-MOSI dataset, ITHP surpasses human-level performance in the multimodal sentiment binary classification task across all evaluation metrics (i.e., Binary Accuracy, F1 Score, Mean Absolute Error, and Pearson Correlation). 

Backpropagation (BP) has been a successful optimization technique for deep learning models. However, its limitations, such as backward- and update-locking, and its biological implausibility, hinder the concurrent updating of layers and do not mimic the local learning processes observed in the human brain. To address these issues, recent research has suggested using local error signals to asynchronously train network blocks. However, this approach often involves extensive trial-and-error iterations to determine the best configuration for local training. This includes decisions on how to decouple network blocks and which auxiliary networks to use for each block. In our work, we introduce a novel BP-free approach: a block-wise BP-free (BWBPF) neural network that leverages local error signals to optimize distinct sub-neural networks separately, where the global loss is only responsible for updating the output layer. The local error signals used in the BP-free model can be computed in parallel, enabling a potential speed-up in the weight update process through parallel implementation. Our experimental results consistently show that this approach can identify transferable decoupled architectures for VGG and ResNet variations, outperforming models trained with end-to-end backpropagation and other state-of-the-art block-wise learning techniques on datasets such as CIFAR-10 and Tiny-ImageNet. The code is released at https://github.com/Belis0811/BWBPF. 

Abstract Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network’s state and detect a phase transition between different states, to infer the TVCN’s dynamics. A phase of a TVCN is determined by its Forman–Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.