A mechanism for the emergence of low-dimensional structures in brain dynamics

Recent neuroimaging advancements have led to datasets characterized by an overwhelming number of features. Different dimensionality reduction techniques have been employed to uncover low-dimensional manifold representations underlying cognitive functions, while maintaining the fundamental characteristics of the data. These range from linear algorithms to more intricate non-linear methods for manifold extraction. However, the mechanisms responsible for the emergence of these simplified architectures remain a topic of debate. Motivated by concepts from dynamical systems theory, such as averaging and time-scale separation, our study introduces a novel mechanism for the collapse of high dimension brain dynamics onto lower dimensional manifolds. In our framework, fast neuronal activity oscillations average out over time, leading to the resulting dynamics approximating task-related processes occurring at slower time scales. This leads to the emergence of low-dimensional solutions as complex dynamics collapse into slow invariant manifolds. We test this assumption via neural simulations using a simplified model and then enhance the complexity of our simulations by incorporating a large-scale brain network model to mimic realistic neuroimaging signals. We observe in the different cases the convergence of fast oscillatory fluctuations of neuronal activity across time scales that correspond to simulated behavioral configurations. Specifically, by employing various dimensionality reduction techniques and manifold extraction schemes, we observe the reduction of high-dimensional dynamics onto lower-dimensional spaces, revealing emergent low-dimensional solutions. Our findings shed light on the role of frequency and time-scale separation in neuronal activity, proposing and testing a novel theoretical framework for understanding the inner mechanisms governing low-dimensional pattern formation in brain dynamics.