Understanding how the brain generates cognition and intelligence is one of the most important scientific unknowns and provides crucial insights for developing novel artificial intelligence. The field of neuroscience has accumulated increasingly rich experimental findings that urgently call for a unified theoretical framework. Meanwhile, artificial intelligence and biological brain intelligence are showing divergent developmental trajectories. We aim to construct clear and in-depth mathematical theories, closely integrated with experiments, to provide unique theoretical perspectives for addressing these challenges.

Our research group focuses on a central question: How does the structure of neural networks shape their dynamics and functions? Neural dynamics is the substrate of cognition and behavior, while network connectivity forms the structural foundation for their emergence. Centered on this theme, we are committed to developing mathematical theories and analytical methods that combine neuroscience questions with various mathematical tools to provide new insights and approaches for analyzing increasingly complex neural data, and to jointly advance our understanding of biological learning mechanisms and fundamental principles of brain cognition.

I. Multidimensional Structure of Neural Population Activity and Covariance Spectrum Theory

Advances in multi-electrode and imaging techniques have revealed rich high-dimensional geometric features of neural population activity, such as dimensionality and communication subspaces. However, theoretical characterization of the generating mechanisms underlying these features and their roles in cognitive functions requires further exploration. We have systematically developed covariance spectrum theory for recurrent neural networks, establishing quantitative connections between the geometric features of population activity and the connection strengths of local circuits (PLOS Comput Biol 2022). This theory provides an analytical framework that is more robust and information-rich than widely used dimensionality analysis, and has revealed scale-invariance patterns in whole-brain neural activity (eLife 2025). Recent work has extended this theory to nonlinear and chaotic dynamical regimes, providing novel theoretical explanations for critical state phenomena in neural activity (arXiv 2025). We will continue exploring applications of this framework in analyzing multi-region interactions and dynamic changes in cognitive states.

II. Dynamics and Functional Roles of Connectivity Motifs in Non-local Networks

Connectivity motifs are structural features widely present in neural networks at multiple scales, existing not only in local circuits but also distributed extensively across brain regions, cortical layers, and mesoscale networks. Understanding how motifs at various scales influence overall network dynamics and computational functions is a key opportunity and challenge for extracting insights from connectomics data. Building on the PI's early work on motif cumulant theory (JSTAT 2013, PRE 2014, 2018), we are combining novel data such as mesoscale and brain-wide projectome data to explore the computational significance of these structural features in achieving cognitive functions and learning processes.

III. Dynamics-Network Structure Theory for Cognitive Functions and Biological Learning

How neural dynamics emerge through biological learning rules such as synaptic plasticity to realize cognitive functions is one of the field's central questions. Existing theoretical models often rely on simplified network structures or focus on single brain regions or local circuits, while increasing experimental evidence shows that advanced cognitive functions such as working memory and decision-making rely on collaborative computation across multiple brain regions. We aim to go beyond these limitations by investigating how neural networks form specific connectivity structures under biological learning rules, and how these structures support dynamics that implement complex cognitive functions.

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