Fig. 3: Four possible mechanisms of VPL in neural populations.

a, To enhance sensory discriminability, the classical signal detection theory posits that signal enhancement predicts enlarged distances between two mean values while noise reduction predicts reduced variance of the two stimulus response distributions (stim1 and stim2). b, Stimulus orientation as a continuous stimulus variable can evoke high-dimensional population responses. c, If we continuously sweep the orientation value, the mean of population responses forms a closed-form ring in a high-dimensional neural space with dimensions equal to the number of units. The mean population responses to the two stimuli in a discrimination task are two points on the manifold. d,e, In realistic population responses, the trial-by-trial population responses to the two stimuli form two high-dimensional response distributions (that is, neural manifolds, d). The manifolds look elliptical rather than spherical due to pairwise noise correlations between units. In this high-dimensional neural space, the signal enhancement mechanism predicts an increased Euclidean distance (that is, signal separation, e) between two high-dimensional response distributions. f, However, no significant increase in signal separation is observed in any of the five layers (signal separation decreases in the first two layers; one-sided paired t-test, all t₍₃₎ > −1.27, all P > 0.146, all BF₁₀ <1.46; see full statistical results in Supplementary Table 3). g, The manifold shrinkage mechanism predicts reduced variance of the two neural manifolds. h, This is observed in all five layers (one-sided paired t-test, all t₍₃₎ > 8.39, all P < 0.002; see full statistical results in Supplementary Table 4). i, The signal rotation mechanism predicts that the positions of the centroid (that is, mean) of the two manifolds are changed by training. j, The rotation angle ranges from approximately 50° to 70° in all five layers. k, The manifold warping mechanism predicts that training changes the shape of noise correlations. l, Indeed, training mostly reduces the variance of the high-variance principal components of the population responses. The principal components (showing only components that account for >99% of the total variance) are ranked from high to low variance. m, The directions of the principal components rotate from pre- to post-test. Data are presented as mean ± s.e.m., with error bars and error shadings in f–m representing the s.e.m. across four (n = 4) reference orientations.