Brief Description: With the ever increasing amount of data acquired in neuroscience applications there is an essential need to develop computationally effective, robust, and interpretable data processing algorithms. Recent advancements in graph inference, topology, information theory and deep learning have shown promising results in analyzing biological/physiological data, as well as datasets acquired by intelligent agents. Combining elements from different disciplines of information theory, mathematics, and machine learning is paramount for developing the next generation of methods that will facilitate big data analysis under the realm of better understanding brain dynamics, as well as neuroinspired system dynamics in general. The goal of the workshop is to bring researchers working in data science, neuroscience, mathematics, and machine learning together to discuss challenges posed by analyzing multimodal data sets in neuroscience along with potential solutions, exchange ideas and present their latest work in designing and analyzing effective data processing algorithms. This workshop will serve as a great opportunity to discuss innovative future directions for neuroinspired processing of large amounts of data, while considering novel mathematical data models and computationally efficient learning algorithms.
Schedule:
9:00 - 9:40: Kathryn Hess, EPFL, Topological perspectives on the connectome
Abstract: Over the past decade or so, tools from algebraic topology have been shown to be very useful for the analysis and characterization of networks, in particular for exploring the relation of structure to function. I will describe some of these tools and illustrate their utility in neuroscience, primarily in the framework of a collaboration with the Blue Brain Project.
9:45 - 10:25: Moo Kyung Chung, University of Wisconsin, Topological Embedding of Dynamically Changing Brain Networks
Abstract: We introduce a novel topological framework for embedding time-varying brain networks into a low-dimensional space. Our Topological Embedding captures the evolving structure of functional connectivity by mapping dynamic birth and death values of topological features (connected components and cycles) into a 2D plane. Unlike traditional analyses that rely on synchronized time-points or direct comparisons of network matrices, our method aligns the dynamic behavior of brain networks through their underlying topological features, thus offering invariance to temporal misalignments and inter-subject variability. Using resting-state functional magnetic resonance images (rs-fMRI), we demonstrate that the topological embedding reveals stable 0D homological structures and fluctuating 1D cycles across time, which are further analyzed in the frequency domain through the Fourier Transform. The resulting topological spectrograms exhibit strong associations with age and cognitive traits, including fluid intelligence. This study establishes a robust and interpretable topological representation for the analysis of dynamically changing brain networks, with broad applicability in neuroscience and neuroimaging-based biomarker discovery. The talk is based on arXiv:2502.05814
10:30 - 11:00: Coffee Break
11:00 - 11:40: Anna Korzeniewska, Johns Hopkins University, From causal interactions among neural networks to significance in imaging brain tumor metabolism.
Abstract: Neural activity propagates swiftly across brain networks, often not providing enough data-points to model its dynamics. This limitation can be overcome by using multiple realizations, or repetitions, of the same process. However, once repetitions have been consumed for modeling, or only one is available, the significance of the neural dynamics cannot be assessed using traditional statistical methods. We propose a new method for assessing statistical confidence using the variance of a smooth estimator and a criterion for the choice of a smooth ratio. We show their applications to event-related neural propagations among eloquent and epileptogenic networks, and to metabolite kinetics in hyperpolarized 13C MRI (hpMRI) of brain tumor. The event-related causality (ERC) method - a multichannel extension of the Granger causality concept – was applied to multi-channel EEG recordings to estimate the direction, intensity, and spectral content of direct causal interactions among brain networks. A two-dimensional (2D) moving average, with a rectangular smooth window, sliding over points in the time-frequency plane, provided the smooth estimator and its error for statistical testing. The smooth size of the 2D moving average was determined by the W-criterion, which combines the difference between the smooth estimator and the real values with the confidence interval. The same approach was applied to 2D images of hpMRI of pyruvate metabolism of malignant glioma. A newly developed bivariate smoothing model ensured precise embedding of ERC’s statistical significance in time-frequency space, revealing complex frequency-dependent dynamics of causal interactions. The strength and pattern of neural propagations among eloquent networks reflected stimulus modality, lexical status, and syllable position in a sequence, uncovering mechanisms of speech control and modulation. The strength and pattern of high-frequency interactions among epileptogenic networks identified seizure onset zones and unveiled propagations preceding seizure onset. Statistical confidence of the difference between metabolic responses of tumor and normal tissue, obtained through hpMRI, allowed tumor delineation. Moving average provides an efficient smooth estimator and its error (optimal for reducing random noise while retaining sharp step response) and ensures precise embedding of statistical significance in two-dimensional space. The new approach overcomes several limitations of previously used 2D spline interpolation (restraint to a mesh of knots introducing artifactual distributions of variance and significance, and failure to converge in some cases), while W-criterion provides efficient choice of smooth size. The new technique has broad applicability to neuroscientific research and clinical applications, including planning for epilepsy surgery, localizing anatomical targets for responsive neuromodulation, and gauging tumor treatment response.
11:45 - 12:25: Vasileios Maroulas, University of Tennessee Knoxville, The Shape of Uncertainty.
Abstract: How does the brain know where it is and where it is going? Deep within our neural circuits, specialized cells—like head direction and grid cells—fire in intricate patterns to guide spatial awareness and navigation. But decoding these patterns requires tools that can keep up with the brain’s complexity. In this talk, I will share how we wre using topological deep learning to do just that. Our new models tap into higher-dimensional structures to predict direction and position—without relying on hand-crafted similarity measures. But that is just the beginning. I will also introduce a Bayesian framework for learning on graphs using sheaf theory, where uncertainty is not a bug but a feature. By placing probability distributions on the rotation group and learning them through the network, we gain robustness, flexibility, and accuracy—especially when data is scarce. Together, these advances point to a bold new direction: using geometry and topology to unlock the brain’s code and reshape how we learn from complex data.
