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Unraveling Temporal Dynamics of SPSD matrices via Riemmanian Multi-Scale Decomposition
Understanding the temporal dynamics of high-dimensional, time-varying systems remains a fundamental challenge across scientific disciplines. In many real-world systems, the interactions between sensors are also time-varying, which presents an additional level of complexity in extracting a meaningful representation and subsequent modeling. In this work, we introduce a novel multi-resolution framework for analyzing the temporal dynamics of Symmetric Positive Semi-Definite (SPSD) matrices, such as correlation matrices. A key innovation of our framework is a difference operator that respects the symmetry of the Riemannian manifold. We apply this operator recursively and extract a hierarchical representation of the temporal dynamics of SPSD matrices with a fine frequency resolution. We employ spectral analysis to select informative frequency components and extract key structural patterns. Specifically, our approach reveals which sensors of the original signal drive the correlational dynamics, thus enhancing both denoising and the interoperability of SPSD matrix evolution over time. We validate our method using synthetic data and real neural recordings from mice trained to perform a motor task. Our results demonstrate its ability to extract meaningful structures from complex temporal datasets and provide deeper insights into evolving network connectivity.
Yonatan Kleerekoper, Mohammad Kurtam, Yonatan Keselman, Amir Ghanayim, Jackie Sciller, Simon Musall, Yitzhak Schiller, and Hadas Benisty (Preprint)
VTA projections to M1 are essential for reorganization of layer 2-3 network dynamics underlying motor learning
The primary motor cortex (M1) is crucial for motor skill learning. Previous studies demonstrated that skill acquisition requires dopaminergic VTA (ventral-tegmental area) signaling in M1, however little is known regarding the effect of these inputs at the neuronal and network levels. We developed a novel geometric data analysis method for exploring the transformation of cellular dynamics induced by learning. Our findings demonstrate dopaminergic VTA-dependent formation of outcome signaling and new connectivity configuration of the layer 2-3 network, supporting reorganization of the M1 network for storing new motor skills.
Amir Ghanayim*, Hadas Benisty,*, Avigail Cohen-Rimon, Sivan Schwartz, Sally Dabdoob, Shira Lifshitz, Ronen Talmon and Jackie Schiller
Contextual Feature Selection with Conditional Stochastic Gates
We propose a novel architecture for learning the importance of each input variable for prediction of the target variable(s) as a function of a given context. Our extensive benchmark shows that c-STG improves feature selection, enhances prediction accuracy as well as model interpretability across multiple real-world domains.
Rapid fluctuations in functional connectivity of cortical networks encode spontaneous behavior
Experimental work across species has demonstrated that spontaneously generated behaviors are robustly coupled to variations in neural activity within the cerebral cortex. We used wide-field mesoscopic calcium imaging to monitor cortical dynamics in awake mice and developed an approach to quantify rapidly time-varying functional connectivity. Our approach generalizes the commonly used linear models linking behavior to neuronal activity: we formulate the modeling of behavior as a Taylor’s expansion where neuronal activity is the first order term and instantaneous correlations are the second order term. Using this model, we show that both terms are significant for modeling of spontaneous behaviors, meaning they are represented by fast changes in both the magnitude and correlational structure of cortical network activity. Moreover, the dynamic functional connectivity of mesoscale signals revealed subnetworks not predicted by traditional anatomical atlas-based parcellation of the cortex.
H. Benisty, A. Moberly, S. Lohani, D. Barson, R.R. Coifman, G. Mishne, J. Cardin, and M.J. Higley
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