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Title: Disentangling the roles of dimensionality and cell classes in neural computations

Paper content:
The description of neural computations in the field of neuroscience relies on two competing views:
(i) a classical single-cell view that relates the activity of individual neurons to sensory or behavioural variables, and focuses on how different cell classes map onto computations;
(ii) a more recent population view that instead characterises computations in terms of collective neural trajectories, and focuses on the dimensionality of these trajectories as animals perform tasks.
How the two key concepts of cell classes and low-dimensional trajectories interact to shape neural computations is however currently not understood.
Here we address this question by combining machine-learning tools for training RNNs with reverse-engineering and theoretical analyses of network dynamics.
We introduce a novel class of theoretically tractable recurrent networks: low-rank, mixture of Gaussian RNNs.
In these networks, the rank of the connectivity controls the dimensionality of the dynamics, while the number of components in the Gaussian mixture corresponds to the number of cell classes.
Using back-propagation, we determine the minimum rank and number of cell classes needed to implement neuroscience tasks of increasing complexity.
We then exploit mean-field theory to reverse-engineer the obtained solutions and identify the respective roles of dimensionality and cell classes.
We show that the rank determines the phase-space available for dynamics that implement input-output mappings, while having multiple cell classes allows networks to flexibly switch between different types of dynamics in the available phase-space.
Our results have implications for the analysis of neuroscience experiments and the development of explainable AI.
With recent advances in deep-learning, the novel approach of training and reverse-engineering RNNs on neuroscience tasks has led to insights on the implementation of cognitive processes (see [1] for a review).
Reverse-engineering methods have however provided only partial understanding so far, by either focusing on the characterization of neural dynamics and leaving aside the description of learnt connectivity [2] , or the converse [3] .
Taking advantage of recent theoretical results on low-rank networks [4] , we present a reverse-engineering approach that leads to analytically tractable classes of RNNs performing various tasks.
Crucially, these classes of models exhibit well defined dimensionality and number of cell classes allowing us to identify the roles of these two properties on neural computation.
In this work we have provided an abstract description of computations performed in recurrent neural networks.
By focusing on simple tasks this has allowed us to identify the complementary roles of the two important aspects that are dimensionality (section 3.1) and cell classes (section 3.2).
Beyond these simple tasks, we have been able to use this understanding to build networks solving multiple tasks (section 3.3), and we expect these principles of neural computation to be important results for the development of procedures aiming at reverse-engineering networks trained on more complex, real-world tasks.

assistant: text: A theoretical analysis of a new class of RNNs, trained on neuroscience tasks, allows us to identify the role of dynamical dimensionality and cell classes in neural computations.