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
||r_i - r_j||
How to understand the decomposition?
latent dimensions look suspiciously like a Fourier basis...
\operatorname{cov}\left(x_i, x_j\right)
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?
update_2024-10-23
By raj-magesh
