Why Cats Have Orientation Columns and Mice Don't

Why are cat brains organized differently from mouse brains? Neurons in visual cortex are selective for edge orientation. In cats, neurons with similar preferences are spatially clustered, forming smooth gradients called orientation columns. In mice, orientation preferences are scattered randomly, a layout called "salt-and-pepper."

Earlier models like Swindale (1992) produce orientation maps through competitive development rules but require structured initial conditions. Najafian et al. (2022) needs no such initialization. The sorting is entirely local, driven by a single kernel whose width varies with afferent sampling density $V = I \times R$, the product of innervation density $I$ and receptive field radius $R$. A wide kernel (cat) lets afferents segregate into smooth domains. A narrow one (mouse) can't organize beyond nearest neighbors. One parameter, two species. The demonstration below walks through each stage of the model.

The Retinal Mosaic

The model begins with the retina. ON and OFF retinal ganglion cells (RGCs) are arranged on a jittered grid in visual space, each cell type forming a semi-regular mosaic. This mosaic is species-independent. What varies between cat and mouse is how densely the cortex samples it.

$$\text{ON}_x^{(i)} = x_\text{grid}^{(i)} + \text{Uniform}(-j_\text{on}, j_\text{on})$$ $$\text{OFF}_x^{(i)} = x_\text{grid}^{(i)} + \text{Uniform}(-j_\text{off}, j_\text{off})$$

ON cells (red) detect light increments; OFF cells (blue) detect decrements. The two mosaics are interleaved but independent, with slightly different jitter amplitudes. These afferents project to the cortex, where they must be sorted by eye input and contrast polarity.

Contralateral retinal mosaic: ON (red) and OFF (blue) RGCs.

The Sorting Filter

Afferent sorting is driven by a Difference-of-Gaussians (DoG) kernel, a Mexican hat that defines the spatial scale of attraction and repulsion:

$$K(x,y) = A \cdot \mathcal{N}(0, \sigma_c^2) - \mathcal{N}(0, \sigma_s^2)$$

where $A$ is the center-surround ratio. Same-type afferents within the central (positive) region are rewarded; different-type afferents in the center are penalized. The surround reverses these roles. For cats ($\sigma_c = 5$, $\sigma_s = 10$), the kernel spans many cells, enabling large-scale segregation. For mice ($\sigma_c = 0.5$, $\sigma_s = 1$), the kernel is narrow, so sorting happens only locally, if at all.

Cat

Mouse

DoG sorting filter. Red = excitatory center, blue = inhibitory surround.

Afferent Sorting

Cortical positions are initially assigned random eye (contra/ipsi) and polarity (ON/OFF) labels. The sorting algorithm iterates over every cell, computing an energy score based on the DoG kernel:

$$E = (S_\text{same}^\text{center} - S_\text{diff}^\text{center}) - (S_\text{same}^\text{surround} - S_\text{diff}^\text{surround})$$

For each cell, the 8 immediate neighbors are checked. If swapping with a different-type neighbor improves the energy, the swap is accepted. Sorting proceeds in two phases: first by ocular dominance (contra vs. ipsi, 3 iterations), then by ON/OFF polarity within each OD band (3 iterations).

With the cat kernel, clear OD columns and ON/OFF domains emerge. With the mouse kernel, the grid stays largely random.

Cat

Mouse

■ Contra-ON ■ Contra-OFF ■ Ipsi-ON ■ Ipsi-OFF

Orientation Maps

Primordial Orientation

After sorting, the spatial arrangement of ON and OFF afferents at each cortical location implicitly encodes an orientation preference. To extract it, we compute the centroid offset between local ON and OFF cells within a spread radius:

$$\vec{d} = \text{centroid}_\text{ON} - \text{centroid}_\text{OFF}$$

$$\theta = \text{atan2}(d_y, d_x) + 90°$$

The preferred orientation is perpendicular to the ON→OFF axis. This primordial map is noisy. It reflects the raw spatial statistics of afferent positions before any refinement.

Cat

Mouse

Primordial orientation map. Hue = preferred orientation.

Orientation Development

After birth, visual experience refines these primordial orientations through competitive development. Orientations are represented as complex numbers $z = e^{2i\theta}$, initialized with reduced selectivity and noise:

$$z \leftarrow \frac{z}{5} + z \cdot \mathcal{N}(0, 0.03)$$

Each iteration convolves the complex field with a DoG kernel (CSRatio = 1) and updates:

$$z \leftarrow z + \frac{K * z}{\max\vert K * z\vert} \cdot (1 - \vert z\vert)$$

For cat parameters, this amplifies local orientation coherence, sharpens selectivity, and produces pinwheel singularities, points where all orientations converge. For mouse parameters, the weak initial structure means development has little to work with, and the map remains salt-and-pepper.

Cat

Mouse

Developed orientation map. Watch for pinwheel singularities (cat) or salt-and-pepper noise (mouse).

Discussion

We initialize neural networks with random weights and treat every unit as interchangeable. Everything is learned from data, which means even simple computations need lots of examples. The cortex doesn't work this way. Neurons arrive with different time constants, plasticity rates, and receptive field properties, organized by local developmental rules before the animal ever opens its eyes. A zebra can walk within minutes of birth. It didn't learn locomotion from data. Evolution compressed millions of years of experience into developmental algorithms that wire the right circuits in advance.

References

Najafian, S., Koch, E., Bhatt, D.K. et al. A theory of cortical map formation in the visual brain. Nat Commun 13, 2303 (2022).