Thank you so much for the compliment! Indeed, we also think it aligns well with Gao&Ganguli's theory, while highlighting the role of state-feedback control in low-D dynamics. We have updated the preprint to include more comparisons with M1 recordings.

www.biorxiv.org/content/10.1...

Thanks a lot Josh! very encouraging to know the work is being well received!

Thank you for your comments :) Indeed the system has to be controllable. In fact, the formulation we use is MPC (receding horizon scheme). LQR was used to resolve the control gains at each step and repeating until task ends, ensuring that the controller is sensitive to sudden changes in task demands

Yes, it makes sense! Interconnections will reduce effective dimensions. what happens if a high D input is given, in general, is something i need to think about. You might find this article useful for when effective low ranks appear in random networks www.nature.com/articles/s41...

*correcting the username of my coauthor @fredcrevecoeur.bsky.social

...though a recent preprint from @runewberg.bsky.social group looks into distance depent connectivity and in the context of spinal cord dynamics

I didn't look into this aspect. But I'm curious to know the motivation behind it. In the current model, even if I present a high D input, the gains associated with task irrelevant info will be suppressed hence ending up with low D. But I didn't check distance dependent kernels...

I forgot to mention above...the last result (low-rank hypothesis) in fact suggests that low dimensionality must directly follow from the low dimensionality in task and limb dynamics. Hence, low D is expected in many networks including feedforward

Also, freezing the network gains while varying the task parameters (load level, force field, or target redundancy etc.,) did not inhibit flexibility. While gains of limb were necessary to tune motor output to task demands (2/2)

Thank you so much :) recurrent connectivity in the random networks can influence the shape of the trajectories, but low D dynamics appear even in feedforward case due to the gain-controlled feedback (1/2)

Thanks Kevin! your feedback on the manuscript has been super helpful :)