Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons

Brain-computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.

The dynamics and geometry of choice in premotor cortex

The brain represents sensory variables in the coordinated activity of neural populations, in which tuning curves of single neurons define the geometry of the population code. Whether the same coding principle holds for dynamic cognitive variables remains unknown because internal cognitive processes unfold with a unique time course on single trials observed only in the irregular spiking of heterogeneous neural populations. Here we show the existence of such a population code for the dynamics of choice formation in the primate premotor cortex. We developed an approach to simultaneously infer population dynamics and tuning functions of single neurons to the population state. Applied to spike data recorded during decision-making, our model revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Our results reveal a common geometric principle for neural encoding of sensory and dynamic cognitive variables.

A unifying perspective on neural manifolds and circuits for cognition

Two different perspectives have informed efforts to explain the link between the brain and behaviour. One approach seeks to identify neural circuit elements that carry out specific functions, emphasizing connectivity between neurons as a substrate for neural computations. Another approach centres on neural manifolds - low-dimensional representations of behavioural signals in neural population activity - and suggests that neural computations are realized by emergent dynamics. Although manifolds reveal an interpretable structure in heterogeneous neuronal activity, finding the corresponding structure in connectivity remains a challenge. We highlight examples in which establishing the correspondence between low-dimensional activity and connectivity has been possible, unifying the neural manifold and circuit perspectives. This relationship is conspicuous in systems in which the geometry of neural responses mirrors their spatial layout in the brain, such as the fly navigational system. Furthermore, we describe evidence that, in systems in which neural responses are heterogeneous, the circuit comprises interactions between activity patterns on the manifold via low-rank connectivity. We suggest that unifying the manifold and circuit approaches is important if we are to be able to causally test theories about the neural computations that underlie behaviour.

Autonomous inference of complex network dynamics from incomplete and noisy data

The availability of empirical data that capture the structure and behaviour of complex networked systems has been greatly increased in recent years; however, a versatile computational toolbox for unveiling a complex system's nodal and interaction dynamics from data remains elusive. Here we develop a two-phase approach for the autonomous inference of complex network dynamics, and its effectiveness is demonstrated by the tests of inferring neuronal, genetic, social and coupled oscillator dynamics on various synthetic and real networks. Importantly, the approach is robust to incompleteness and noises, including low resolution, observational and dynamical noises, missing and spurious links, and dynamical heterogeneity. We apply the two-phase approach to infer the early spreading dynamics of influenza A flu on the worldwide airline network, and the inferred dynamical equation can also capture the spread of severe acute respiratory syndrome and coronavirus disease 2019. These findings together offer an avenue to discover the hidden microscopic mechanisms of a broad array of real networked systems.