Table of Contents

• Orientation domains and the proposed analysis
• Extra examples of continuity violations in the Topographic ICA literature
• Main Result: salt-and-pepper distribution of TICA oriented sensors
• Full set of statistical tests on randomness
• Extra results for images of bigger complexity and other settings of the algorithm

Supplementary Material: extra figures, data and code

1. Orientation domains and the proposed analysis:

This section describes the experimental orientation domains in the surface of the V1 cortex of a cat and a ferret. Using intrinsic optical imaging, different preferred orientations of the cells are represented with colors. The analysis shows that the Topographic ICA (TICA) topology fails to explain the smoothness found in the retina-cortex projection, contrary to what was proposed by Hyvärinen and Hoyer. The random scrambling of the oriented filters revealed in this study demonstrates that TICA does not account for the organization of orientation domains in primates.

2. Extra examples of continuity violations in the Topographic ICA literature:

Multiple examples of continuity violations in TICA are presented from various sources in the literature, including works by Hyvärinen et al. (2001, 2009) and Ma et al. (2008). In each case, there are clear violations of the expected local continuity of orientation domains in the image space. These results suggest that the functional explanation proposed by TICA is inconsistent with empirical observations in the retina-cortex projection.

3. Main Result: salt-and-pepper distribution of TICA oriented sensors:

The main finding of this analysis is that TICA produces a salt-and-pepper distribution of oriented filters in the image space, rather than continuous orientation domains. This inconsistency with the smooth retina-cortex projection is demonstrated across various visual angles and resolutions. New training sets were used for this analysis, and the results were consistent with the lack of continuity in the spatial distribution of TICA sensors.

4. Full set of statistical tests on randomness:

Statistical tests were conducted to determine whether TICA’s orientation domains are more similar to a Cartesian grid or a random sample. The tests show that TICA’s spatial distribution is random and does not form the distinct, continuous orientation domains observed in biological visual systems. These results are based on KL-divergence comparisons between the TICA distributions and uniform distributions.

5. Extra results for images of bigger complexity and other settings of the algorithm:

Further experiments were performed with more complex images and alternative algorithm settings, such as different nonlinearities and pooling neighborhoods. In every case, the results were consistent: the oriented filters produced by TICA remained scrambled and discontinuous. Even in cases with significantly higher complexity and larger PCA dimensions, TICA fails to produce locally continuous orientation domains in the image space.