Prep: weekly mtg 20160127 (Byron, Steve, Matt, me) - mobeets/nullSpaceControl GitHub Wiki

First up, a bug in how I was selecting activity from B1 (incorrectly checking its thetas) led to habitual looking more like unconstrained. This is fixed now, and now habitual is way better than volitional!

Tiny things

  • We present activity in space spanned by Nul(B2). Choosing different rotations of Nul(B2) preserves norms, so one Nul(B2) seems as good as any other.
  • Can look at maximum variance axes of actual activity in Nul(B2)?

  • Vol = (zp in Nul(B2)) + (zv in Row(B1) to correct). We asked last week:
  • What if the zp we used to correct was 0? => similar, maybe slightly worse
  • What if it was the mean in of similar conditions? => identical, but with better variance, though inconsistent
  • What if instead of Row(B1) it was the first two or three factors from FA? => not there yet. will have to change code
  • Looked at actual activity in Nul(B2) as a function of various quartiles/deciles: trial_index, time, angular error, rs. time has biggest effect, but mostly noisy; others may change slightly

Explorations

  • Rotations of Hab: Suppose the monkey is trying to generate k1 during B2. Hab says he takes z from B1 during similar k1, but what if instead he takes some rotated z from k1? zp = (10 x 10)(10 x 1). Note that the null activity we predict is zh = Nul(B2)'(zp). But what if instead of solving for R = (10 x 10), we solve for an Rp = (8 x 8) matrix such that zh = Nul(B2)'(Rp)z, so that zp ≈ Rp*z? Can cross-validate at trial level, and R has predictive power, but not totally sure about the interpretation.

  • In another session, Vol and Hab are very close, and both as good.

  • Vol = Hab + Nul(B2)'(z in Row(B1))

So the Hab is a subset of the Vol. The Vol will add corrections in the Rowspace of B1. So you can think of this as the monkey trying the same kinematics as B1 (Hab), and then correcting by moving through B1.

  • plot with one panel per kinematics condition, null columns as x

You can see that Hab does a great job for all kinematics conds between about 90 and 270! Also, observed data for k=315 and k=0 is notably described by 1- or 2-d. Q: What are the errors like for these conditions?

Above, the x-axis is mean angular error (error = difference between monkey's goal velocity and actual velocity) on unfiltered data. The smaller this number, the more often the monkey meets his goal. (Note that normally we ignore all errors beyond 20 degs.)

So it looks like in general, the better the monkey is at controlling the cursor, the less his null space activity resembles what it was in the intuitive block. In k=315 and k=0, where he's best, his null space activity is minimal, and low-dimensional, and so it deviates from what's expected by the habitual hypothesis.