Mark Churchland will discuss how the dynamical systems approach developed and how to apply it. Shreya Saxena will follow, presenting "Network principles predict motor cortex population activity structure across movement speeds" (abstract below). 

Shreya Saxena: Network principles predict motor cortex population activity structure across movement speeds

We can often perform the same action at different speeds. Altering movement speed necessitates altering multiple aspects of muscle activity: frequency, amplitude, and overall pattern. How is neural activity structured to enable such changes? To predict the dominant structure of neural activity, we leveraged principles governing the dynamics of recurrent networks. Noise-robust network dynamics require neural trajectories to have ‘low trajectory tangling’; small changes in neural state should never be associated with large changes in its derivative. For a rhythmic trajectory, the lowest-tangled geometry is a circle. This yields the first prediction: regardless of the trajectory of muscle activity, the neural trajectory should – across all speeds – be dominated by two-dimensional circular structure. More complex signals should be present in other dimensions but should be small, to avoid increasing tangling. A second prediction arises from the observation that traversing the same trajectory at different speeds would increase tangling. Thus, the near-circular trajectories (one per speed) should be separated by a translation and/or tilt into new dimensions. To test these predictions, we recorded motor cortex population activity and muscle activity as monkeys performed a cycling task. Cycling speed was instructed by visual cues. We first analyzed the data for each speed separately. In the top two principal components, muscle trajectories varied greatly across speeds. Neural trajectories did not, but instead remained consistently circular. Analyzing all speeds together revealed that these circular trajectories were separated by a translation (orthogonal to the main plane of rotation) and tilted modestly into new dimensions. As a result, neural trajectory tangling remained low despite high muscle trajectory tangling. Simulations confirmed that this strategy naturally emerges during network optimization. These results demonstrate that the dominant features of motor cortex activity can be anticipated and explained by considering how network activity should be structured to remain noise-robust.