Parametric control of flexible timing through low-dimensional neural manifolds

Beirán, Manuel; Meirhaeghe, Nicolas; Sohn, Hansem; Jazayeri, Mehrdad; Ostojic, Srdjan

doi:10.1101/2021.11.08.467806

Cited by 6 publications

(1 citation statement)

References 89 publications

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“…Although the anatomical substrate underlying this optimization process is beyond the scope of our study, the thalamo-basal ganglia-cortical loop is a natural candidate (Athalye et al, 2020; Kao et al, 2021). Low-dimensional inputs to the motor cortex (Dubreuil et al, 2022; Logiaco et al, 2021; Sauerbrei et al, 2020) could for instance serve to adjust the initial state within the optimal subspace dimensions (Beiran et al, 2021; Sohn et al, 2020). Further investigations will be needed to elucidate this circuit-level question.…”

Section: Discussionmentioning

confidence: 99%

Parallel planning through an optimal neural subspace in motor cortex

Meirhaeghe

Riehle

Brochier

2022

Preprint

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Preparatory activity in motor cortex may facilitate movement execution by representing movement parameters (representational theory) or by initializing movement-related dynamics to an optimal state (dynamical system theory). Here, we confronted these two theories using neural data from non-human primates. We analyzed the structure of preparatory activity in a task where animals needed to plan two movements simultaneously. Contrary to what the representational theory predicted, we did not find evidence for the concurrent representation of the two movements. Instead, our data revealed that parallel planning was achieved by adjusting preparatory activity to an intermediate state that served as an optimal initial condition to generate both movements. This optimization quantitatively explained fluctuations in the animals' behavior, and directly supported the dynamical system theory. Together, these results uncover a simple mechanism for planning multiple movements in parallel, and shed light on an enduring debate about the nature of preparatory activity in motor cortex.

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Section: Discussionmentioning

confidence: 99%

Parallel planning through an optimal neural subspace in motor cortex

Meirhaeghe

Riehle

Brochier

2022

Preprint

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The impact of sparsity in low-rank recurrent neural networks

Herbert

Ostojic

2022

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Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse. Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank. We first analyse the impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics. We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity matrices composed of a low-rank and a full-rank random component. This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters. Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.

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Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks

Shao

Ostojic

2022

Preprint

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How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary strategies to quantify the structure in connectivity, by specifying either the local statistics of connectivity motifs between small groups of neurons, or by defining network-wide low-rank patterns of connectivity that determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing, and in particular it remains to be clarified how local connectivity statistics are related to the global connectivity structure and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. This approach demonstrates that multi-population networks defined from local connectivity properties can in general be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks, and show that it leads to accurate predictions for both the low-dimensional dynamics, and for the activity of individual neurons. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.

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Parametric control of flexible timing through low-dimensional neural manifolds

Cited by 6 publications

References 89 publications

Parallel planning through an optimal neural subspace in motor cortex

Parallel planning through an optimal neural subspace in motor cortex

The impact of sparsity in low-rank recurrent neural networks

Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks

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