Fig. 5: Bipartite structure aligns with natural object boundaries formed by spatial frequency differences.
From: Functional bipartite invariance in mouse primary visual cortex receptive fields
a, We screened over 1 million crops from the Caltech-UCSD Birds-200-2011 (CUB) dataset using our predictive model to identify the 100 most highly activating (red) and 100 random (blue) crops for each neuron. For each crop, we computed a matching score by comparing its segmentation label (object = white, background = black) and the neuron’s ‘bipartite mask’ derived from its VEIspartial (variable subfield = white, fixed subfield = black). b, Highly activating natural crops with object boundaries yielded higher matching scores than random natural crops with object boundaries (two-sided Wilcoxon signed-rank test, W = 82,849, P = 6.5 × 10−118), with 51.4% of all neurons showing greater matching scores for highly activating crops than random natural crops (46.4% after BH correction) while only 4.9% showing lower matching scores to highly activating crops (4.1% after BH correction) (P < 0.05, two-sided Welch’s t-test with 76.2 average d.f.). One neuron (0.08%) was excluded from this analysis as it strictly preferred crops without object boundaries. c, Most V1 neurons preferred higher spatial frequency content in the variable subfield. The median frequency of texture crops exceeded that of VEIspartial (two-sided Wilcoxon signed-rank test, W = 34,381, P = 3.1 × 10−162), with 77.0% of neurons showing higher median spatial frequency in the variable subfield than the fixed (76.4% after BH correction), and only 4.8% showing the opposite (4.8% after BH correction) (P < 0.05, two-sided Welch’s t-test with 33.2 average d.f.). In contrast, simulated simple cells (blue cross) preferred higher median frequency in the fixed subfield (two-sided Wilcoxon signed-rank test, W = 302, P = 6.4 × 10−6) and simulated complex cells (red circle) preferred higher median frequency in the variable subfield (two-sided Wilcoxon signed-rank test, W = 14, P = 3.3 × 10−11), albeit both with very marginal effect. d, Model-predicted V1 neuronal responses correlate with spatial frequency within the variable and fixed subfield. For the majority of neurons (79.08%), the fixed subfield’s median frequency negatively correlated with the predicted response (median −0.14, one-tailed one-sample t-test against mean of 0, t = −33.38, P = 3.7 × 10−169, d.f. = 1,089). In contrast, for most neurons (64.75%), the variable subfield’s median frequency showed a positive correlation (median 0.09, one-tailed one-sample t-test against mean of 0, t = 16.23, P = 1.6 × 10−53, d.f. = 1,083). Four neurons were excluded from the fixed subfield analysis due to excessively small fixed subfield size. e, Parametric ‘CUB-grating’ dataset constructed from CUB segmentation masks, with object and background replaced by synthetic gratings. f, Using the CUB-grating dataset, we identified the most activating crop for each neuron. Simulated simple and complex cells predominantly preferred single grating images (83.3% and 75%, respectively). In contrast, V1 neurons exhibited a different pattern of preference (one-way chi-squared test, χ2 = 8,510, P < 10−308, and χ2 = 5,538, P < 10−308 for comparison against simulated simple and complex cells, respectively). While most simulated simple (83.3%) and complex (75%) cells preferred single grating images, V1 neurons almost exclusively preferred images with object boundaries (99.1%). V1 neurons showed preferences for boundaries defined by differences in spatial frequency alone (39.2%), orientation alone (21.6%), or a combination of both (38.3%). The marginal difference in preference was greater for spatial frequency than for orientation (P < 10−4, two-sided marginal difference bootstrapping). g, Top-100 activating crops from ‘high-frequency object’ images yielded higher mean matching scores than those from ‘low-frequency object’ images (two-sided Wilcoxon signed-rank test, W = 340,648, P = 2.0 × 10−52). Overall, 66.4% of neurons showed higher matching scores for ‘high-frequency object’ crops (same after BH correction), whereas 23.4% showed lower scores (23.3% after correction) (P < 0.05, two-sided Welch’s t-test, 170.2 average d.f.). a-g, Data were pooled from six mice, including 1,200 randomly selected neurons. Simulated simple and complex cells included 60 neurons each.
