Magnitude pruning of recurrent neural networks (RNNs) ignores how information flows between neurons. An earlier version proposed to model RNN dependencies as a partially ordered set (poset) and to retain the meet-irreducible elements of its dependency lattice. By Birkhoff's representation theorem, the meet-irreducible ideals of a finite poset are in bijection with its elements, so retaining them retains everything; the critical-set criterion used earlier selects precisely the elements comparable to all others, of which a dense recurrent layer has none. Condensing a thresholded dependency graph into strongly connected components yields a well-defined dependency order, a graded order score and an acyclic pruning rule; for Cohen-Grossberg networks and LSTMs, acyclic pruning makes local stability decompose over modules. For a 128-unit LSTM pruned at matched sparsity on row-wise and chunked sequential MNIST (three seeds, equal training budgets), the original rules remove every recurrent weight or equal random column pruning; the order score is no better than degree, PageRank or norm; trained weights show little directional bias; and imposing acyclicity from initialisation costs 2.1 and 10.5 percentage points at 50% and 90% sparsity. In the networks studied, order structure must be imposed rather than discovered.
Brain function emerges from coordinated activity across anatomically connected regions, where structural connectivity (SC) -- the network of white matter pathways - provides the physical substrate for functional connectivity (FC) -- the correlated neural activity between brain areas. While these structural and functional networks exhibit substantial overlap, their relationship involves complex, indirect mechanisms, including the dynamic interplay of direct and indirect pathways, recurrent network interactions, and neuromodulatory influences. To systematically untangle how structural architecture shapes functional patterns, this work aims to establish a set of rules that decode how direct and indirect structural connections and motifs give rise to FC between brain regions. Specifically, using a generative linear model, we derive explicit rules that predict an individual's resting-state fMRI FC from diffusion-weighted imaging (DWI)-derived SC, validated against topological null models. Examining the rules reveals distinct classes of brain regions, with integrator hubs acting as structural linchpins promoting synchronization and mediator hubs serving as structural fulcrums orchestrating competing dynamics. Through virtual lesion experiments, we demonstrate how different cortical and subcortical systems distinctively contribute to global functional organization. Together, this framework disentangles the mechanisms by which structural architecture drives functional dynamics, enabling the prediction of how pathological or surgical disruptions to brain connectivity cascade through functional networks, potentially leading to cognitive and behavioral impairments.
The hypothalamus plays an important role in the regulation of the bodys metabolic state and behaviors related to survival. Despite its importance however, many questions exist regarding the intrinsic and extrinsic connections of the hypothalamus in humans, especially its relationship with the cortex. As a heterogeneous structure, it is possible that the hypothalamus is composed of different subregions, which have their own distinct relationships with the cortex. Previous work on functional connectivity in the human hypothalamus have either treated it as a unitary structure or relied on methodological approaches that are limited in modeling its intrinsic functional architecture. Here, we used resting state data from ultrahigh field 7 Tesla fMRI and a data driven analytical approach to identify functional subregions of the human hypothalamus. Our approach identified four functional hypothalamic subregions based on intrinsic functional connectivity, which in turn showed distinct patterns of functional connectivity with cortex. Overall, all hypothalamic subregions showed stronger connectivity with a cortical network, Cortical Network 1 composed primarily of frontal, midline, and limbic cortical areas and weaker connectivity with a second cortical network composed largely of posterior sensorimotor regions, Cortical Network 2. Of the hypothalamic subregions, the anterior hypothalamus showed the strongest connection to Cortical Network 1, while a more ventral subregion containing the anterior hypothalamus extending to the tuberal region showed the weakest connectivity. The findings support the use of ultrahigh field, high resolution imaging in providing a more incisive investigation of the human hypothalamus that respects its complex internal structure and extrinsic functional architecture.
Diverse human cognitive abilities are rooted in brain structural connectivity which has weights spanning several orders of magnitude. However, due to false-positive challenges in tractography, weak connectivity has been often treated as noise and ignored - despite its prevalence across mammalian brains. Here we show that weak connectivity significantly predicts human cognitive abilities and supports brain functions through amplification of its small weight in a nonlinear manner. Using the Human Connectome Project dataset (n=999) and multiple tractography algorithms, we constructed the whole-brain structural connectivity with heterogeneous weights of streamline numbers. We found that weak connectivity involves high individual variability and significantly predicts general cognitive ability and memory in individuals, and it is also critical for whole-brain dynamic simulation and structure-function coupling. Importantly, fusing two post-tractography filtering methods of streamlines potentially results in more reliable connectivity that preserves weak links and outperforms conventional thresholding in predicting cognitive abilities and functional connectivity. At the network level, weak connectivity expands the operational capacity of brain networks to enhance both global integration and fine-grained segregation, thereby supporting a functional balance essential for cognitive abilities. Finally, we identified a specific type of weak connectivity mainly linking visual/motor to limbic areas with negative gene co-expression, which has a disproportionately large impact on cognitive predictions and network dynamics.
Probing large language models (LLMs) has yielded valuable insights into their internal mechanisms by linking neural representations to interpretable semantics. However, how neurons functionally co-activate with each other to give rise to emergent capabilities remains largely unknown, hindering a deeper understanding and safer development of LLMs. In this work, we introduce graph probing, a method for uncovering the functional connectivity topology of LLM neurons and relating it to language generation performance. By analyzing internal neural graphs across diverse LLM families and scales, we discover a universal predictability of next-token prediction performance using only neural topology. This predictability is robust even when retaining just 1% of neuron connections or probing models after only 8 pretraining steps, highlighting the sparsity and early emergence of topological patterns. Further graph matching analysis suggests that, despite significant distinctions in architectures, parameters, and training data, different LLMs develop intricate and consistent neural topological structures that may form the foundation for their language generation abilities. Codes and data for the graph probing toolbox are released at https://github.com/DavyMorgan/llm-graph-probing.
Accurately localizing the brain regions that triggers seizures and predicting whether a patient will be seizure-free after surgery are vital for surgical planning and patient management in drug-resistant epilepsy. Stereo-electroencephalography (sEEG) delivers high-fidelity intracranial recordings that enable clinicians to precisely locate epileptogenic networks. However, the clinical identification is subjective and dependent on the expertise of the clinical team. Data driven approaches in this domain are sparse, despite the fact that sEEG offers high temporal-fidelity related to seizure dynamics that can be leveraged using graph structures ideal for imitating brain networks. In this study, we introduce a dual-task graph-neural network (GNN) framework that operates on windowed sEEG recordings to jointly predict seizure-freedom outcomes and identify seizure-onset-zone (SOZ) channels. We assemble non-overlapping 10 second windows from 51 clinical seizures spread across 20 pediatric patients, with sEEG data annotated by clinical experts. For each temporal window we construct a functional connectivity graph via thresholded Pearson correlations and extract rich node features (spectral, statistical, wavelet, Hjorth and local graph features), alongside six global graph descriptors. We optimize a combined cross-entropy loss with a tunable task-weight, and select model hyper-parameters via Optuna. Under window-level 10-fold cross-validation, the model achieves a mean graph-level accuracy of $89.31 \pm 0.0976 \%$ for seizure-freedom prediction and a node-level SOZ localization accuracy of $94.72. \pm 0.0041 \%$. For the best performing model, we ran additive and leave-one-out ablation studies to explore feature importance for graph and node-level accuracy.
Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in constrained spaces--such as the set of symmetric positive definite or correlation matrices--that can be modeled as Riemannian manifolds. However, using Riemannian tools typically requires redefining core operations (geodesics, norms, integration), making generative modeling computationally inefficient. In this work, we propose DiffeoCFM, an approach that enables conditional flow matching (CFM) on matrix manifolds by exploiting pullback metrics induced by global diffeomorphisms on Euclidean spaces. We show that Riemannian CFM with such metrics is equivalent to applying standard CFM after data transformation. This equivalence allows efficient vector field learning, and fast sampling with standard ODE solvers. We instantiate DiffeoCFM with two different settings: the matrix logarithm for covariance matrices and the normalized Cholesky decomposition for correlation matrices. We evaluate DiffeoCFM on three large-scale fMRI datasets with more than 4600 scans from 2800 subjects (ADNI, ABIDE, OASIS-3) and two EEG motor imagery datasets with over 30000 trials from 26 subjects (BNCI2014-002 and BNCI2015-001). It enables fast training and achieves state-of-the-art performance, all while preserving manifold constraints.
Data-driven approaches for depression diagnosis have emerged as a significant research focus in neuromedicine, driven by the development of relevant datasets. Recently, graph neural network (GNN)-based models have gained widespread adoption due to their ability to capture brain channel functional connectivity from both spatial and temporal perspectives. However, their effectiveness is hindered by the absence of a robust temporal biomarker. In this paper, we introduce a novel and effective biomarker for depression diagnosis by leveraging the discrete Fourier transform (DFT) and propose a customized graph network architecture based on Temporal Graph Convolutional Network (TGCN). Our model was trained on a dataset comprising 1,086 subjects, which is over 10 times larger than previous datasets in the field of depression diagnosis. Furthermore, to align with medical requirements, we performed propensity score matching (PSM) to create a refined subset, referred to as the PSM dataset. Experimental results demonstrate that incorporating our newly designed biomarker enhances the representation of temporal characteristics in brain channels, leading to improved F1 scores in both the real-world dataset and the PSM dataset. This advancement has the potential to contribute to the development of more effective depression diagnostic tools. In addition, we used SHapley Additive exPlaination (SHAP) to validate the interpretability of our model, ensuring its practical applicability in medical settings.
Clinical studies reveal disruptions in brain structural connectivity (SC) and functional connectivity (FC) in neuropsychiatric disorders such as schizophrenia (SZ). Traditional approaches might rely solely on SC due to limited functional data availability, hindering comprehension of cognitive and behavioral impairments in individuals with SZ by neglecting the intricate SC-FC interrelationship. To tackle the challenge, we propose a novel physics-guided deep learning framework that leverages a neural oscillation model to describe the dynamics of a collection of interconnected neural oscillators, which operate via nerve fibers dispersed across the brain's structure. Our proposed framework utilizes SC to simultaneously generate FC by learning SC-FC coupling from a system dynamics perspective. Additionally, it employs a novel multi-view graph neural network (GNN) with a joint loss to perform correlation-based SC-FC fusion and classification of individuals with SZ. Experiments conducted on a clinical dataset exhibited improved performance, demonstrating the robustness of our proposed approach.
Traditional functional connectivity based on functional magnetic resonance imaging (fMRI) can only capture pairwise interactions between brain regions. Hypergraphs, which reveal high-order relationships among multiple brain regions, have been widely used for disease analysis. However, existing methods often rely on predefined hypergraph structures, limiting their ability to model complex patterns. Moreover, temporal information, an essential component of brain high-order relationships, is frequently overlooked. To address these limitations, we propose a novel framework that jointly learns informative and sparse high-order brain structures along with their temporal dynamics. Inspired by the information bottleneck principle, we introduce an objective that maximizes information and minimizes redundancy, aiming to retain disease-relevant high-order features while suppressing irrelevant signals. Our model comprises a multi-hyperedge binary mask module for hypergraph structure learning, a hypergraph self-attention aggregation module that captures spatial features through adaptive attention across nodes and hyperedges, and a spatio-temporal low-dimensional network for extracting discriminative spatio-temporal representations for disease classification. Experiments on benchmark fMRI datasets demonstrate that our method outperforms the state-of-the-art approaches and successfully identifies meaningful high-order brain interactions. These findings provide new insights into brain network modeling and the study of neuropsychiatric disorders.
Brain network analysis using functional MRI has advanced our understanding of cortical activity and its changes in neurodegenerative disorders that cause dementia. Recently, research in brain connectivity has focused on dynamic (time-varying) brain networks that capture both spatial and temporal information on cortical, regional co-activity patterns. However, this approach has been largely unexplored within the Alzheimer's spectrum. We analysed age- and sex-matched static and dynamic fMRI brain networks from 315 individuals with Alzheimer's Disease (AD), Mild Cognitive Impairment (MCI), and cognitively-normal Healthy Elderly (HE), using data from the ADNI-3 protocol. We examined both similarities and differences between these groups, employing the Juelich brain atlas for network nodes, sliding-window correlations for time-varying network links, and non-parametric statistics to assess between-group differences at the link or the node centrality level. While the HE and MCI groups show similar static and dynamic networks at the link level, significant differences emerge compared to AD participants. We found stable (stationary) differences in patterns of functional connections between the white matter regions and the parietal lobe's, and somatosensory cortices, while metastable (temporal) networks' differences were consistently found between the amygdala and hippocampal formation. In addition, our node centrality analysis showed that the white matter connectivity patterns are local in nature. Our results highlight shared and unique functional connectivity patterns in both stationary and dynamic functional networks, emphasising the need to include dynamic information in brain network analysis in studies of Alzheimer's spectrum.
Predicting disease states from functional brain connectivity is critical for the early diagnosis of severe neurodegenerative diseases such as Alzheimer's Disease and Parkinson's Disease. Existing studies commonly employ Graph Neural Networks (GNNs) to infer clinical diagnoses from node-based brain connectivity matrices generated through node-to-node similarities of regionally averaged fMRI signals. However, recent neuroscience studies found that such node-based connectivity does not accurately capture ``functional connections" within the brain. This paper proposes a novel approach to brain network analysis that emphasizes edge functional connectivity (eFC), shifting the focus to inter-edge relationships. Additionally, we introduce a co-embedding technique to integrate edge functional connections effectively. Experimental results on the ADNI and PPMI datasets demonstrate that our method significantly outperforms state-of-the-art GNN methods in classifying functional brain networks.
Prolonged alcohol use results in neuroadaptations that mark more severe and treatment-resistant alcohol use. The goal of this study was to identify functional connectivity brain patterns underlying Alcohol Use Disorder (AUD)-related characteristics in fifty-five adults (31 female) who endorsed heavy alcohol use. We hypothesized that resting-state functional connectivity (rsFC) of the Salience (SN), Frontoparietal (FPN), and Default Mode (DMN) networks would reflect self reported recent and lifetime alcohol use, laboratory-based alcohol seeking, urgency, and sociodemographic characteristics related to AUD. To test our hypothesis, we combined the triple network model (TNM) of psychopathology with a multivariate data-driven approach, regularized partial least squares (rPLS), to unfold concurrent functional connectivity (FC) patterns and their association with AUD characteristics. We observed three concurrent associations of interest: i) drinking and age-related cross communication between the SN and both the FPN and DMN; ii) family history density of AUD and urgency anticorrelations between the SN and FPN; and iii) alcohol seeking and sex-associated SN and DMN interactions. These findings demonstrate the utility of combining theory- and data-driven approaches to uncover associations between resting-state functional substrates and AUD-related characteristics that could aid in the identification, development, and testing of novel treatment targets across preclinical and clinical models.
Our goal in this paper is to leverage the potential of the topological signal processing (TSP) framework for analyzing brain networks. Representing brain data as signals over simplicial complexes allows us to capture higher-order relationships within brain regions of interest (ROIs). Here, we focus on learning the underlying brain topology from observed neural signals using two distinct inference strategies. The first method relies on higher-order statistical metrics to infer multiway relationships among ROIs. The second method jointly learns the brain topology and sparse signal representations, of both the solenoidal and harmonic components of the signals, by minimizing the total variation along triangles and the data-fitting errors. Leveraging the properties of solenoidal and irrotational signals, and their physical interpretations, we extract functional connectivity features from brain topologies and uncover new insights into functional organization patterns. This allows us to associate brain functional connectivity (FC) patterns of conservative signals with well-known functional segregation and integration properties. Our findings align with recent neuroscience research, suggesting that our approach may offer a promising pathway for characterizing the higher-order brain functional connectivities.
This study investigated age-related changes in functional connectivity using resting-state fMRI and explored the efficacy of traditional deep learning for classifying brain developmental stages (BDS). Functional connectivity was assessed using Seed-Based Phase Synchronization (SBPS) and Pearson correlation across 160 ROIs. Clustering was performed using t-SNE, and network topology was analyzed through graph-theoretic metrics. Adaptive learning was implemented to classify the age group by extracting bottleneck features through mobileNetV2. These deep features were embedded and classified using Random Forest and PCA. Results showed a shift in phase synchronization patterns from sensory-driven networks in youth to more distributed networks with aging. t-SNE revealed that SBPS provided the most distinct clustering of BDS. Global efficiency and participation coefficient followed an inverted U-shaped trajectory, while clustering coefficient and modularity exhibited a U-shaped pattern. MobileNet outperformed other models, achieving the highest classification accuracy for BDS. Aging was associated with reduced global integration and increased local connectivity, indicating functional network reorganization. While this study focused solely on functional connectivity from resting-state fMRI and a limited set of connectivity features, deep learning demonstrated superior classification performance, highlighting its potential for characterizing age-related brain changes.
Understanding the organization of human brain networks has become a central focus in neuroscience, particularly in the study of functional connectivity, which plays a crucial role in diagnosing neurological disorders. Advances in functional magnetic resonance imaging and machine learning techniques have significantly improved brain network analysis. However, traditional machine learning approaches struggle to capture the complex relationships between brain regions, while deep learning methods, particularly Transformer-based models, face computational challenges due to their quadratic complexity in long-sequence modeling. To address these limitations, we propose a Core-Periphery State-Space Model (CP-SSM), an innovative framework for functional connectome classification. Specifically, we introduce Mamba, a selective state-space model with linear complexity, to effectively capture long-range dependencies in functional brain networks. Furthermore, inspired by the core-periphery (CP) organization, a fundamental characteristic of brain networks that enhances efficient information transmission, we design CP-MoE, a CP-guided Mixture-of-Experts that improves the representation learning of brain connectivity patterns. We evaluate CP-SSM on two benchmark fMRI datasets: ABIDE and ADNI. Experimental results demonstrate that CP-SSM surpasses Transformer-based models in classification performance while significantly reducing computational complexity. These findings highlight the effectiveness and efficiency of CP-SSM in modeling brain functional connectivity, offering a promising direction for neuroimaging-based neurological disease diagnosis.
3D neuroimages provide a comprehensive view of brain structure and function, aiding in precise localization and functional connectivity analysis. Segmentation of white matter (WM) tracts using 3D neuroimages is vital for understanding the brain's structural connectivity in both healthy and diseased states. One-shot Class Incremental Semantic Segmentation (OCIS) refers to effectively segmenting new (novel) classes using only a single sample while retaining knowledge of old (base) classes without forgetting. Voxel-contrastive OCIS methods adjust the feature space to alleviate the feature overlap problem between the base and novel classes. However, since WM tract segmentation is a multi-label segmentation task, existing single-label voxel contrastive-based methods may cause inherent contradictions. To address this, we propose a new multi-label voxel contrast framework called MultiCo3D for one-shot class incremental tract segmentation. Our method utilizes uncertainty distillation to preserve base tract segmentation knowledge while adjusting the feature space with multi-label voxel contrast to alleviate feature overlap when learning novel tracts and dynamically weighting multi losses to balance overall loss. We compare our method against several state-of-the-art (SOTA) approaches. The experimental results show that our method significantly enhances one-shot class incremental tract segmentation accuracy across five different experimental setups on HCP and Preto datasets.
Precise parcellation of functional networks (FNs) of early developing human brain is the fundamental basis for identifying biomarker of developmental disorders and understanding functional development. Resting-state fMRI (rs-fMRI) enables in vivo exploration of functional changes, but adult FN parcellations cannot be directly applied to the neonates due to incomplete network maturation. No standardized neonatal functional atlas is currently available. To solve this fundamental issue, we propose TReND, a novel and fully automated self-supervised transformer-autoencoder framework that integrates regularized nonnegative matrix factorization (RNMF) to unveil the FNs in neonates. TReND effectively disentangles spatiotemporal features in voxel-wise rs-fMRI data. The framework integrates confidence-adaptive masks into transformer self-attention layers to mitigate noise influence. A self supervised decoder acts as a regulator to refine the encoder's latent embeddings, which serve as reliable temporal features. For spatial coherence, we incorporate brain surface-based geodesic distances as spatial encodings along with functional connectivity from temporal features. The TReND clustering approach processes these features under sparsity and smoothness constraints, producing robust and biologically plausible parcellations. We extensively validated our TReND framework on three different rs-fMRI datasets: simulated, dHCP and HCP-YA against comparable traditional feature extraction and clustering techniques. Our results demonstrated the superiority of the TReND framework in the delineation of neonate FNs with significantly better spatial contiguity and functional homogeneity. Collectively, we established TReND, a novel and robust framework, for neonatal FN delineation. TReND-derived neonatal FNs could serve as a neonatal functional atlas for perinatal populations in health and disease.
Neuropathic pain, affecting up to 10% of adults, remains difficult to treat due to limited therapeutic efficacy and tolerability. Although resting-state functional MRI (rs-fMRI) is a promising non-invasive measurement of brain biomarkers to predict drug response in therapeutic development, the complexity of fMRI demands machine learning models with substantial capacity. However, extreme data scarcity in neuropathic pain research limits the application of high-capacity models. To address the challenge of data scarcity, we propose FMM$_{TC}$, a Foundation-Model-boosted Multimodal learning framework for fMRI-based neuropathic pain drug response prediction, which leverages both internal multimodal information in pain-specific data and external knowledge from large pain-agnostic data. Specifically, to maximize the value of limited pain-specific data, FMM$_{TC}$ integrates complementary information from two rs-fMRI modalities: Time series and functional Connectivity. FMM$_{TC}$ is further boosted by an fMRI foundation model with its external knowledge from extensive pain-agnostic fMRI datasets enriching limited pain-specific information. Evaluations with an in-house dataset and a public dataset from OpenNeuro demonstrate FMM$_{TC}$'s superior representation ability, generalizability, and cross-dataset adaptability over existing unimodal fMRI models that only consider one of the rs-fMRI modalities. The ablation study validates the effectiveness of multimodal learning and foundation-model-powered external knowledge transfer in FMM$_{TC}$. An integrated gradient-based interpretation study explains how FMM$_{TC}$'s cross-dataset dynamic behaviors enhance its adaptability. In conclusion, FMM$_{TC}$ boosts clinical trials in neuropathic pain therapeutic development by accurately predicting drug responses to improve the participant stratification efficiency.
Mental disorders are among the most widespread diseases globally. Analyzing functional brain networks through functional magnetic resonance imaging (fMRI) is crucial for understanding mental disorder behaviors. Although existing fMRI-based graph neural networks (GNNs) have demonstrated significant potential in brain network feature extraction, they often fail to characterize complex relationships between brain regions and demographic information in mental disorders. To overcome these limitations, we propose a learnable NeuroTree framework that integrates a k-hop AGE-GCN with neural ordinary differential equations (ODEs) and contrastive masked functional connectivity (CMFC) to enhance similarities and dissimilarities of brain region distance. Furthermore, NeuroTree effectively decodes fMRI network features into tree structures, which improves the capture of high-order brain regional pathway features and enables the identification of hierarchical neural behavioral patterns essential for understanding disease-related brain subnetworks. Our empirical evaluations demonstrate that NeuroTree achieves state-of-the-art performance across two distinct mental disorder datasets. It provides valuable insights into age-related deterioration patterns, elucidating their underlying neural mechanisms.