Mengjia Xu

Luca Candelori, Alexander G. Abanov, Jeffrey Berger et al.

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically to the estimation of intrinsic dimension of data sets. The idea is to learn a representation of each data point as a quantum state, encoding both local properties of the point as well as its relation with the entire data. Inspired by ideas from quantum geometry, we then construct from the quantum states a point cloud equipped with a quantum metric. The metric exhibits a spectral gap whose location corresponds to the intrinsic dimension of the data. The proposed estimator is based on the detection of this spectral gap. When tested on synthetic manifold benchmarks, our estimates are shown to be robust with respect to the introduction of point-wise Gaussian noise. This is in contrast to current state-of-the-art estimators, which tend to attribute artificial ``shadow dimensions'' to noise artifacts, leading to overestimates. This is a significant advantage when dealing with real data sets, which are inevitably affected by unknown levels of noise. We show the applicability and robustness of our method on real data, by testing it on the ISOMAP face database, MNIST, and the Wisconsin Breast Cancer Dataset.

Mengjia Xu

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and heterogeneous characteristics of industrial size networks. Graph embedding techniques can be effective in converting high-dimensional sparse graphs into low-dimensional, dense and continuous vector spaces, preserving maximally the graph structure properties. Another type of emerging graph embedding employs Gaussian distribution-based graph embedding with important uncertainty estimation. The main goal of graph embedding methods is to pack every node's properties into a vector with a smaller dimension, hence, node similarity in the original complex irregular spaces can be easily quantified in the embedded vector spaces using standard metrics. The generated nonlinear and highly informative graph embeddings in the latent space can be conveniently used to address different downstream graph analytics tasks (e.g., node classification, link prediction, community detection, visualization, etc.). In this Review, we present some fundamental concepts in graph analytics and graph embedding methods, focusing in particular on random walk-based and neural network-based methods. We also discuss the emerging deep learning-based dynamic graph embedding methods. We highlight the distinct advantages of graph embedding methods in four diverse applications, and present implementation details and references to open-source software as well as available databases in the Appendix for the interested readers to start their exploration into graph analytics.

Giuseppe Di Caro, Vahagn Kirakosyan, Alexander G. Abanov et al.

The accurate prediction of chromosomal instability from the morphology of circulating tumor cells (CTCs) enables real-time detection of CTCs with high metastatic potential in the context of liquid biopsy diagnostics. However, it presents a significant challenge due to the high dimensionality and complexity of single-cell digital pathology data. Here, we introduce the application of Quantum Cognition Machine Learning (QCML), a quantum-inspired computational framework, to estimate morphology-predicted chromosomal instability in CTCs from patients with metastatic breast cancer. QCML leverages quantum mechanical principles to represent data as state vectors in a Hilbert space, enabling context-aware feature modeling, dimensionality reduction, and enhanced generalization without requiring curated feature selection. QCML outperforms conventional machine learning methods when tested on out of sample verification CTCs, achieving higher accuracy in identifying predicted large-scale state transitions (pLST) status from CTC-derived morphology features. These preliminary findings support the application of QCML as a novel machine learning tool with superior performance in high-dimensional, low-sample-size biomedical contexts. QCML enables the simulation of cognition-like learning for the identification of biologically meaningful prediction of chromosomal instability from CTC morphology, offering a novel tool for CTC classification in liquid biopsy.

Jitesh Chavan, Rohit Lal, Anand Kamat et al.

State-space models (SSMs), Mamba in particular, are increasingly adopted for long-context sequence modeling, providing linear-time aggregation via an input-dependent, causal selective-scan operation. Along this line, recent "Mamba-for-vision" variants largely explore multiple scan orders to relax strict causality for non-sequential signals (e.g., images). Rather than preserving cross-block memory, the conventional formulation of the selective-scan operation in Mamba reinitializes each block's state-space dynamics from zero, discarding the terminal state-space representation (SSR) from the previous block. Arcee, a cross-block recurrent state chain, reuses each block's terminal state-space representation as the initial condition for the next block. Handoff across blocks is constructed as a differentiable boundary map whose Jacobian enables end-to-end gradient flow across terminal boundaries. Key to practicality, Arcee is compatible with all prior "vision-mamba" variants, parameter-free, and incurs constant, negligible cost. As a modeling perspective, we view terminal SSR as a mild directional prior induced by a causal pass over the input, rather than an estimator of the non-sequential signal itself. To quantify the impact, for unconditional generation on CelebA-HQ (256$\times$256) with Flow Matching, Arcee reduces FID$\downarrow$ from $82.81$ to $15.33$ ($5.4\times$ lower) on a single scan-order Zigzag Mamba baseline. Efficient CUDA kernels and training code will be released to support rigorous and reproducible research.

Yiran Huang, Amirhossein Nouranizadeh, Christine Ahrends et al.

Functional Magnetic Resonance Imaging (fMRI) is an imaging technique widely used to study human brain activity. fMRI signals in areas across the brain transiently synchronise and desynchronise their activity in a highly structured manner, even when an individual is at rest. These functional connectivity dynamics may be related to behaviour and neuropsychiatric disease. To model these dynamics, temporal brain connectivity representations are essential, as they reflect evolving interactions between brain regions and provide insight into transient neural states and network reconfigurations. However, conventional graph neural networks (GNNs) often struggle to capture long-range temporal dependencies in dynamic fMRI data. To address this challenge, we propose BrainATCL, an unsupervised, nonparametric framework for adaptive temporal brain connectivity learning, enabling functional link prediction and age estimation. Our method dynamically adjusts the lookback window for each snapshot based on the rate of newly added edges. Graph sequences are subsequently encoded using a GINE-Mamba2 backbone to learn spatial-temporal representations of dynamic functional connectivity in resting-state fMRI data of 1,000 participants from the Human Connectome Project. To further improve spatial modeling, we incorporate brain structure and function-informed edge attributes, i.e., the left/right hemispheric identity and subnetwork membership of brain regions, enabling the model to capture biologically meaningful topological patterns. We evaluate our BrainATCL on two tasks: functional link prediction and age estimation. The experimental results demonstrate superior performance and strong generalization, including in cross-session prediction scenarios.

Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis

Dynamic graph embedding has gained great attention recently due to its capability of learning low dimensional graph representations for complex temporal graphs with high accuracy. However, recent advances mostly focus on learning node embeddings as deterministic "vectors" for static graphs yet disregarding the key graph temporal dynamics and the evolving uncertainties associated with node embedding in the latent space. In this work, we propose an efficient stochastic dynamic graph embedding method (DynG2G) that applies an inductive feed-forward encoder trained with node triplet-based contrastive loss. Every node per timestamp is encoded as a time-dependent probabilistic multivariate Gaussian distribution in the latent space, hence we can quantify the node embedding uncertainty on-the-fly. We adopted eight different benchmarks that represent diversity in size (from 96 nodes to 87,626 and from 13,398 edges to 4,870,863) and diversity in dynamics. We demonstrate via extensive experiments on these eight dynamic graph benchmarks that DynG2G achieves new state-of-the-art performance in capturing the underlying temporal node embeddings. We also demonstrate that DynG2G can predict the evolving node embedding uncertainty, which plays a crucial role in quantifying the intrinsic dimensionality of the dynamical system over time. We obtain a universal relation of the optimal embedding dimension, $L_o$, versus the effective dimensionality of uncertainty, $D_u$, and we infer that $L_o=D_u$ for all cases. This implies that the uncertainty quantification approach we employ in the DynG2G correctly captures the intrinsic dimensionality of the dynamics of such evolving graphs despite the diverse nature and composition of the graphs at each timestamp. Moreover, this $L_0 - D_u$ correlation provides a clear path to select adaptively the optimum embedding size at each timestamp by setting $L \ge D_u$.

Qian Zhang, Konstantina Sampani, Mengjia Xu et al.

Microaneurysms (MAs) are one of the earliest signs of diabetic retinopathy (DR), a frequent complication of diabetes that can lead to visual impairment and blindness. Adaptive optics scanning laser ophthalmoscopy (AOSLO) provides real-time retinal images with resolution down to 2 $μm$ and thus allows detection of the morphologies of individual MAs, a potential marker that might dictate MA pathology and affect the progression of DR. In contrast to the numerous automatic models developed for assessing the number of MAs on fundus photographs, currently there is no high throughput image protocol available for automatic analysis of AOSLO photographs. To address this urgency, we introduce AOSLO-net, a deep neural network framework with customized training policies to automatically segment MAs from AOSLO images. We evaluate the performance of AOSLO-net using 87 DR AOSLO images and our results demonstrate that the proposed model outperforms the state-of-the-art segmentation model both in accuracy and cost and enables correct MA morphological classification.

Mengjia Xu, David Lopez Sanz, Pilar Garces et al.

Characterizing the subtle changes of functional brain networks associated with the pathological cascade of Alzheimer's disease (AD) is important for early diagnosis and prediction of disease progression prior to clinical symptoms. We developed a new deep learning method, termed multiple graph Gaussian embedding model (MG2G), which can learn highly informative network features by mapping high-dimensional resting-state brain networks into a low-dimensional latent space. These latent distribution-based embeddings enable a quantitative characterization of subtle and heterogeneous brain connectivity patterns at different regions and can be used as input to traditional classifiers for various downstream graph analytic tasks, such as AD early stage prediction, and statistical evaluation of between-group significant alterations across brain regions. We used MG2G to detect the intrinsic latent dimensionality of MEG brain networks, predict the progression of patients with mild cognitive impairment (MCI) to AD, and identify brain regions with network alterations related to MCI.

Wei Qiu, Jiaming Guo, Xiang Li et al.

Cell detection and cell type classification from biomedical images play an important role for high-throughput imaging and various clinical application. While classification of single cell sample can be performed with standard computer vision and machine learning methods, analysis of multi-label samples (region containing congregating cells) is more challenging, as separation of individual cells can be difficult (e.g. touching cells) or even impossible (e.g. overlapping cells). As multi-instance images are common in analyzing Red Blood Cell (RBC) for Sickle Cell Disease (SCD) diagnosis, we develop and implement a multi-instance cell detection and classification framework to address this challenge. The framework firstly trains a region proposal model based on Region-based Convolutional Network (RCNN) to obtain bounding-boxes of regions potentially containing single or multiple cells from input microscopic images, which are extracted as image patches. High-level image features are then calculated from image patches through a pre-trained Convolutional Neural Network (CNN) with ResNet-50 structure. Using these image features inputs, six networks are then trained to make multi-label prediction of whether a given patch contains cells belonging to a specific cell type. As the six networks are trained with image patches consisting of both individual cells and touching/overlapping cells, they can effectively recognize cell types that are presented in multi-instance image samples. Finally, for the purpose of SCD testing, we train another machine learning classifier to predict whether the given image patch contains abnormal cell type based on outputs from the six networks. Testing result of the proposed framework shows that it can achieve good performance in automatic cell detection and classification.

Mo Zhang, Xiang Li, Mengjia Xu et al.

Reliable cell segmentation and classification from biomedical images is a crucial step for both scientific research and clinical practice. A major challenge for more robust segmentation and classification methods is the large variations in the size, shape and viewpoint of the cells, combining with the low image quality caused by noise and artifacts. To address this issue, in this work we propose a learning-based, simultaneous cell segmentation and classification method based on the deep U-Net structure with deformable convolution layers. The U-Net architecture for deep learning has been shown to offer a precise localization for image semantic segmentation. Moreover, deformable convolution layer enables the free form deformation of the feature learning process, thus makes the whole network more robust to various cell morphologies and image settings. The proposed method is tested on microscopic red blood cell images from patients with sickle cell disease. The results show that U-Net with deformable convolution achieves the highest accuracy for segmentation and classification, comparing with original U-Net structure.