Robyn L. Miller

Eloy Geenjaar, Amrit Kashyap, Noah Lewis et al. · gatech

Functional magnetic resonance imaging (fMRI) data contain complex spatiotemporal dynamics, thus researchers have developed approaches that reduce the dimensionality of the signal while extracting relevant and interpretable dynamics. Models of fMRI data that can perform whole-brain discovery of dynamical latent factors are understudied. The benefits of approaches such as linear independent component analysis models have been widely appreciated, however, nonlinear extensions of these models present challenges in terms of identification. Deep learning methods provide a way forward, but new methods for efficient spatial weight-sharing are critical to deal with the high dimensionality of the data and the presence of noise. Our approach generalizes weight sharing to non-Euclidean neuroimaging data by first performing spectral clustering based on the structural and functional similarity between voxels. The spectral clusters and their assignments can then be used as patches in an adapted multi-layer perceptron (MLP)-mixer model to share parameters among input points. To encourage temporally independent latent factors, we use an additional total correlation term in the loss. Our approach is evaluated on data with multiple motor sub-tasks to assess whether the model captures disentangled latent factors that correspond to each sub-task. Then, to assess the latent factors we find further, we compare the spatial location of each latent factor to the motor homunculus. Finally, we show that our approach captures task effects better than the current gold standard of source signal separation, independent component analysis (ICA).

Eloy Geenjaar, Noah Lewis, Amrit Kashyap et al. · gatech

Communication within or between complex systems is commonplace in the natural sciences and fields such as graph neural networks. The brain is a perfect example of such a complex system, where communication between brain regions is constantly being orchestrated. To analyze communication, the brain is often split up into anatomical regions that each perform certain computations. These regions must interact and communicate with each other to perform tasks and support higher-level cognition. On a macroscale, these regions communicate through signal propagation along the cortex and along white matter tracts over longer distances. When and what types of signals are communicated over time is an unsolved problem and is often studied using either functional or structural data. In this paper, we propose a non-linear generative approach to communication from functional data. We address three issues with common connectivity approaches by explicitly modeling the directionality of communication, finding communication at each timestep, and encouraging sparsity. To evaluate our model, we simulate temporal data that has sparse communication between nodes embedded in it and show that our model can uncover the expected communication dynamics. Subsequently, we apply our model to temporal neural data from multiple tasks and show that our approach models communication that is more specific to each task. The specificity of our method means it can have an impact on the understanding of psychiatric disorders, which are believed to be related to highly specific communication between brain regions compared to controls. In sum, we propose a general model for dynamic communication learning on graphs, and show its applicability to a subfield of the natural sciences, with potential widespread scientific impact.

Bishal Thapaliya, Robyn Miller, Jiayu Chen et al.

Resting-state functional magnetic resonance imaging (rs-fMRI) is a noninvasive technique pivotal for understanding human neural mechanisms of intricate cognitive processes. Most rs-fMRI studies compute a single static functional connectivity matrix across brain regions of interest, or dynamic functional connectivity matrices with a sliding window approach. These approaches are at risk of oversimplifying brain dynamics and lack proper consideration of the goal at hand. While deep learning has gained substantial popularity for modeling complex relational data, its application to uncovering the spatiotemporal dynamics of the brain is still limited. We propose a novel interpretable deep learning framework that learns goal-specific functional connectivity matrix directly from time series and employs a specialized graph neural network for the final classification. Our model, DSAM, leverages temporal causal convolutional networks to capture the temporal dynamics in both low- and high-level feature representations, a temporal attention unit to identify important time points, a self-attention unit to construct the goal-specific connectivity matrix, and a novel variant of graph neural network to capture the spatial dynamics for downstream classification. To validate our approach, we conducted experiments on the Human Connectome Project dataset with 1075 samples to build and interpret the model for the classification of sex group, and the Adolescent Brain Cognitive Development Dataset with 8520 samples for independent testing. Compared our proposed framework with other state-of-art models, results suggested this novel approach goes beyond the assumption of a fixed connectivity matrix and provides evidence of goal-specific brain connectivity patterns, which opens up the potential to gain deeper insights into how the human brain adapts its functional connectivity specific to the task at hand.

Bradley T. Baker, Barak A. Pearlmutter, Robyn Miller et al.

Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of "Neural Collapse", where linear classifiers within DNNs converge to specific geometrical structures during late-stage training. However, the role of geometric constraints in learning extends beyond this terminal phase. For instance, gradients in fully-connected layers naturally develop a low-rank structure due to the accumulation of rank-one outer products over a training batch. Despite the attention given to methods that exploit this structure for memory saving or regularization, the emergence of low-rank learning as an inherent aspect of certain DNN architectures has been under-explored. In this paper, we conduct a comprehensive study of gradient rank in DNNs, examining how architectural choices and structure of the data effect gradient rank bounds. Our theoretical analysis provides these bounds for training fully-connected, recurrent, and convolutional neural networks. We also demonstrate, both theoretically and empirically, how design choices like activation function linearity, bottleneck layer introduction, convolutional stride, and sequence truncation influence these bounds. Our findings not only contribute to the understanding of learning dynamics in DNNs, but also provide practical guidance for deep learning engineers to make informed design decisions.

Yutong Gao, Charles A. Ellis, Vince D. Calhoun et al.

The high dimensionality and complexity of neuroimaging data necessitate large datasets to develop robust and high-performing deep learning models. However, the neuroimaging field is notably hampered by the scarcity of such datasets. In this work, we proposed a data augmentation and validation framework that utilizes dynamic forecasting with Long Short-Term Memory (LSTM) networks to enrich datasets. We extended multivariate time series data by predicting the time courses of independent component networks (ICNs) in both one-step and recursive configurations. The effectiveness of these augmented datasets was then compared with the original data using various deep learning models designed for chronological age prediction tasks. The results suggest that our approach improves model performance, providing a robust solution to overcome the challenges presented by the limited size of neuroimaging datasets.

James Amarel, Nicolas Hengartner, Robyn Miller et al.

Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training regimes and efficiently adapt to downstream tasks despite a paucity of examples for fine-tuning. However, reliably achieving genuine generalization - a necessary capability for producing novel scientific insights and robustly performing during deployment - remains a critical challenge. Establishing whether or not these requirements are met demands evaluation metrics capable of clearly distinguishing genuine model generalization from mere memorization. We apply the influence function formalism to systematically characterize how autoregressive PDE surrogates assimilate and propagate information derived from diverse physical scenarios, revealing fundamental limitations of standard models and training routines in addition to providing actionable insights regarding the design of improved surrogates.

Yutong Gao, Vince D. Calhoun, Robyn L. Miller

Understanding the relationship between cognition and intrinsic brain activity through purely data-driven approaches remains a significant challenge in neuroscience. Resting-state functional magnetic resonance imaging (rs-fMRI) offers a non-invasive method to monitor regional neural activity, providing a rich and complex spatiotemporal data structure. Deep learning has shown promise in capturing these intricate representations. However, the limited availability of large datasets, especially for disease-specific groups such as Alzheimer's Disease (AD), constrains the generalizability of deep learning models. In this study, we focus on multivariate time series forecasting of independent component networks derived from rs-fMRI as a form of data augmentation, using both a conventional LSTM-based model and the novel Transformer-based BrainLM model. We assess their utility in AD classification, demonstrating how generative forecasting enhances classification performance. Post-hoc interpretation of BrainLM reveals class-specific brain network sensitivities associated with AD.

Charles A. Ellis, Mohammad S. E. Sendi, Eloy P. T. Geenjaar et al.

Supervised machine learning explainability has developed rapidly in recent years. However, clustering explainability has lagged behind. Here, we demonstrate the first adaptation of model-agnostic explainability methods to explain unsupervised clustering. We present two novel "algorithm-agnostic" explainability methods - global permutation percent change (G2PC) and local perturbation percent change (L2PC) - that identify feature importance globally to a clustering algorithm and locally to the clustering of individual samples. The methods are (1) easy to implement and (2) broadly applicable across clustering algorithms, which could make them highly impactful. We demonstrate the utility of the methods for explaining five popular clustering methods on low-dimensional synthetic datasets and on high-dimensional functional network connectivity data extracted from a resting-state functional magnetic resonance imaging dataset of 151 individuals with schizophrenia and 160 controls. Our results are consistent with existing literature while also shedding new light on how changes in brain connectivity may lead to schizophrenia symptoms. We further compare the explanations from our methods to an interpretable classifier and find them to be highly similar. Our proposed methods robustly explain multiple clustering algorithms and could facilitate new insights into many applications. We hope this study will greatly accelerate the development of the field of clustering explainability.

A. Hunter, B. A. Moore, M. K. Mudunuru et al.

In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.