method

• decompose voxel-voxel covariance matrix
• evaluate spectrum on held-out data
• no shared variance = 0
• flexible

power-law spectra

• across trials in a person
• throughout visual cortex
• shared between people

"universal scale-free representations"

power-law spectra in V1

• both within humans and within mice
• both across humans and across mice

such difference, much wow

• individuals: varying neuroanatomy, visual experience
• species: mice don't see well, cortex organized differently
• neuroimaging methods: calcium imaging vs fMRI
• scales
  • units: 1 vs ~10^4 neurons
  • overall: 1 vs ~6,500 mm^3

How to understand the decomposition?

latent dimensions look suspiciously like a Fourier basis...

vs

covariance function for neuron i

if translationally invariant (i.e. spatially stationary for all i), latent dimensions will be the Fourier basis

empirically appears so

power-law covariance spectra at all scales​

coarse-graining analysis where we average the responses of neighboring neurons/voxels

all variance

basically no variance

How big should my Gaussian smoothing kernel be to reduce the variance by a factor f?

high-variance (low-rank) dimensions have bigger scales

low-variance dimensions have smaller scales

universal scaling properties of visual cortex representations across species, individuals, imaging methods, very different spatial scales

are basically all neurons being used?