Nonlinear manifolds underlie neural population activity during behaviour

Abstract

There is rich variety in the activity of single neurons recorded during behaviour. Yet, these diverse single neuron responses can be well described by relatively few patterns of neural co-modulation. The study of such low-dimensional structure of neural population activity has provided important insights into how the brain generates behaviour. Virtually all of these studies have used linear dimensionality reduction techniques to estimate these population-wide co-modulation patterns, constraining them to a flat "neural manifold". Here, we hypothesised that since neurons have nonlinear responses and make thousands of distributed and recurrent connections that likely amplify such nonlinearities, neural manifolds should be intrinsically nonlinear. Combining neural population recordings from monkey motor cortex, mouse motor cortex, mouse striatum, and human motor cortex, we show that: 1) neural manifolds are intrinsically nonlinear; 2) the degree of their nonlinearity varies across architecturally distinct brain regions; and 3) manifold nonlinearity becomes more evident during complex tasks that require more varied activity patterns. Simulations using recurrent neural network models confirmed the proposed relationship between circuit connectivity and manifold nonlinearity, including the differences across architecturally distinct regions. Thus, neural manifolds underlying the generation of behaviour are inherently nonlinear, and properly accounting for such nonlinearities will be critical as neuroscientists move towards studying numerous brain regions involved in increasingly complex and naturalistic behaviours.

MotorNet: a Python toolbox for controlling differentiable biomechanical effectors with artificial neural networks

“…Finally, most neurons showed a mixed preference for encoding time and reaching direction (neuron C8, A8). This heterogeneous set of responses matches empirical observations in non-human primate primary motor cortex recordings (Churchland & Shenoy, 2007; Michaels et al, 2016) and replicate similar visualizations from previously published work (Fortunato et al, 2023; Lillicrap & Scott, 2013; Safaie et al, 2023).…”

De novo motor learning creates structure in neural activity that shapes adaptation

“…In practice, these activity patterns can be examined by building a neural state space (from here, referred to as 'neural space') where each point denotes the state of the neural population. Numerous studies [11][12][13][14][15][16] have found that the activity of even hundreds of simultaneously recorded motor cortical neurons is well captured by relatively few population-wide activity patterns, an observation consistent with neural population activity being constrained to a lowdimensional surface-a 'neural manifold'-that can be estimated by applying a dimensionality reduction method [17][18][19][20][21] . Studies comparing neural population activity patterns evoked by sensory stimuli and optogenetic stimulation provide direct evidence of neural manifolds reflecting circuit connectivity constraints 22,23 .…”

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“…However, these time lags, on the order of a few tens of milliseconds, should be much shorter than the timescale of dynamics explored in this study. Third, the set of signals related to movement and/or cognitive processes may also be better described as occupying nonlinear manifolds rather than linear subspaces 92,93 . Subspaces (or manifolds) could also shift dynamically during behavior following changes in the activation of upstream or downstream brain regions 94,95 as a result of changes in context 16,48,96 .…”