Parametric control of flexible timing through low-dimensional neural manifolds

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

doi:10.1016/j.neuron.2022.12.016

Cited by 34 publications

(36 citation statements)

References 65 publications

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“…Indeed, since invertible matrices form an open and dense subset in ℝ N × N , one could arbitrarily approximate any non-invertible connectivity array by a full-rank matrix, therefore obtaining some full-rank connectivity matrix with the same approximation power of the non-invertible one, thus discarding converse results. Nonetheless, the restriction of low-rank wirings could well have positive benefits for neural ensembles over other kinds of setups [25].…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, the number of degrees of freedom of the matrix depend linearly on N , instead of doing so quadratically, thus regularizing the connectivity in a way it can implement difficult tasks relying on a structured parsimonious connectivity of reduced complexity. Indeed, it’s been shown that low-rank structured networks generalize their behavior to novel stimulus better than their full dimensional counterpart [25].…”

Section: Resultsmentioning

confidence: 99%

“…In support of this proposal, many recent studies have focused on investigating the emergence of neural manifold phenomena in different types of neural networks, some of which having fully structured low-rank connectivity matrices [25], [28]- [30], while others possessing both a structured low-rank component and an unstructured random weight matrix [31]- [33].…”

Section: Introductionmentioning

confidence: 99%

“…These various types of networks describe the behavior of a neural circuit in terms of continuous population variables, primarily the passive somatic potential [14], synaptic conductance [15], [16], or an average of the firing rate of action potentials [17], [18], which is why they are commonly referred to as "firing rate models" in theoretical neuroscience [18]. Although they are crude approximations of neuronal dynamics that lack many nuances of the mechanisms of spike generation [16], their behavior exhibits many aspects of biological neuronal systems, such as recurrence, feedback, nonlinearity, and principal component activity [19], and thus they have appealed many neuroscientists who have found in them a way to simulate, interpret, and make sense of empirical data, showing that RNN setups are capable of replicating many experimental observations [10], [11], [19]- [25].…”

Section: Introductionmentioning

confidence: 99%

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Emergence of universal computations through neural manifold dynamics

Vicente

2023

Preprint

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There is growing evidence that many forms of neural computation may be implemented by low dimensional dynamics unfolding at the population scale. However, neither the connectivity structure nor the general capabilities of these embedded dynamical processes are currently understood. In this work, the two most common formalisms of firing-rate models are evaluated using tools from analysis, topology and nonlinear dynamics in order to provide plausible explanations for these problems. It is shown that low-rank structured connectivity predicts the formation of invariant and globally attracting manifolds in both formalisms, which generalizes existing theories to different neural models. Regarding the dynamics arising in these manifolds, it is proved they are topologically equivalent across the considered formalisms. It is also stated that under the low-rank hypothesis, dynamics emerging in neural models are universal. These include input-driven systems, which broadens previous findings. It is then explored how low-dimensional orbits can bear the production of continuous sets of muscular trajectories, the implementation of central pattern generators and the storage of memory states. It is also proved these dynamics can robustly simulate any Turing machine over arbitrary bounded memory strings, virtually endowing rate models with the power of universal computation. In addition, it is shown how the low-rank hypothesis predicts the parsimonious correlation structure observed in cortical activity. Finally, it is discussed how this theory could provide a useful tool from which to study neuropsychological phenomena using mathematical methods.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Emergence of universal computations through neural manifold dynamics

Vicente

2023

Preprint

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“…Another recent study [36] has investigated how a recurrent network could flexibly control its temporal dynamics using a different approach. They trained a low-rank recurrent network using back-propagation through time to produce specific dynamics with flexible timing, and showed that the resulting network can then be flexibly controlled by a one-dimensional input.…”

Section: Discussionmentioning

confidence: 99%

Dynamic control of sequential retrieval speed in networks with heterogeneous learning rules

Gillett

Brunel

2023

Preprint

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Temporal rescaling of sequential neural activity has been observed in multiple brain areas during behaviors involving time estimation and motor execution at variable speeds. Temporally asymmetric Hebbian rules have been used in network models to learn and retrieve sequential activity, with characteristics that are qualitatively consistent with experimental observations. However, in these models sequential activity is retrieved at a fixed speed. Here, we investigate the effects of a heterogeneity of plasticity rules on network dynamics. In a model in which neurons differ by the degree of temporal symmetry of their plasticity rule, we find that retrieval speed can be controlled by varying external inputs to the network. Neurons with temporally symmetric plasticity rules act as brakes and tend to slow down the dynamics, while neurons with temporally asymmetric rules act as accelerators of the dynamics. We also find that such networks can naturally generate separate 'preparatory' and 'execution' activity patterns with appropriate external inputs.

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