ANC Workshop - Arthur Pellegrino, Amos Storkey
Tuesday, 4th April 2023
The nonlinear manifolds of neural network dynamics - Arthur Pellegrino
Recent studies have proposed that the activity of both recurrent and biological neural networks is constrained to a task manifold. This manifold is often intrinsically lower dimensional than the full neural state space, and its geometry is directly related to task computation. However, means of using RNNs to explore the geometry of neural data manifolds are currently lacking.
In the present work, we develop a mathematical framework to analytically characterize the nonlinear manifolds which RNN activity is constrained to. Within this framework, we introduce a nonlinear dimensionality reduction method that consists of aligning and projecting neural data on RNN manifolds. Using this method, we show that comparing the manifolds of neural data to those RNNs trained to perform behavioural tasks enables generating and testing hypotheses regarding the origin of the geometry of neural data and its relationship to task computation. Furthermore, by noticing that the geometry of RNN manifolds is solely dependent on their weights, we illustrate how population-level learning can smoothly reshape manifolds to capture changes in neural activity occurring over slow timescales. Overall, we demonstrate that RNN manifolds can be used to probe the geometry of biological neural activity.
Event type: Workshop
Date: Tuesday, 4th April 2023
Speaker(s): Arthur Pellegrino, Amos Storkey
Chair/Host: Matthias Hennig