Extended Data Fig. 6: Empirical examination of the notion of a “manifold” in DeePSim and BigGAN latent spaces.
From: Neuronal tuning aligns dynamically with object and texture manifolds across the visual hierarchy
We analyzed the spectrum of the Jacobian inner product (that is, the pullback metric / Hessian) of BigGAN and DeePSim-FC6, considering both the full latent space and the top-500-eigenvector subspace, to assess the extent to which these generators satisfy the conditions of a Riemannian manifold. A, C, E. Eigenvalue spectra of the Jacobian inner product. The center line indicates the median eigenvalue across 1,000 randomly sampled latent points, and the shaded region denotes the 5th–95th percentile range. B, D. Histograms showing the number of near-zero eigenvalues at each sampled latent vector (1,000 total). Different colors correspond to different eigenvalue thresholds used to define near-zero modes. F. Illustration of violations of the non-intersection (injectivity) property in DeePSim and BigGAN: traversing one unit along a null vector in latent space produces negligible pixel space mean squared error (MSE) and effectively no perceptual change in the generated image.
