Hierarchy

Cortical cells respond to progressively more specific things the further you get from the retina, which is a claim about architecture rather than about any single cell. The same logic shows up inside a single neuron: a dendritic tree processes its inputs in stages before the soma ever sees them. The engineering versions follow other rules, and the overlap is narrower than the shared word suggests.

Selectivity, built in stages

Hubel and Wiesel proposed in 1962 that a complex cell pools simple cells sharing one orientation but staggered in position, so it responds to that orientation anywhere in a larger field — a scheme they called tentative. Felleman and Van Essen (1991) catalogued 305 connections among 32 visual and visual-association areas of the macaque and ranked the areas into ten levels by the layers each pathway leaves and lands in. A pathway terminating mainly in layer 4 counts as ascending, one avoiding layer 4 as descending, and one spread evenly across all layers as lateral.

Where an input lands matters inside one cell as well. Rall’s cable theory predicts that a distal synapse delivers a later, smaller and more smeared signal to the soma than a proximal one. Poirazi, Brannon and Mel (2003) could predict the firing rate of a detailed model of a hippocampal CA1 pyramidal cell in two stages: each thin terminal branch passes its own inputs through a sigmoid, and the trunk sums the results. Polsky, Mel and Schiller (2004) found evidence for the same subunits in rat neocortical neurons — nearby inputs on one thin branch summed sigmoidally, inputs on different branches linearly.

Levels of scale, levels of speed

Mallat’s 1989 pyramid algorithm, built on the multiresolution analysis he developed with Yves Meyer, splits a signal into a coarse approximation and the detail lost in halving the resolution, then repeats on the approximation with the same pair of filters. Nothing is thrown away: there are as many coefficients as samples, and the signal can be rebuilt exactly. Mallat read the result as independent frequency channels “as in Marr’s human vision model”.

Control engineering stacks feedback loops instead. In a current-mode converter an outer voltage loop sets the reference for an inner current loop, which is made much faster — a factor of about ten in bandwidth is a common choice for cascaded loops — so that the outer loop can treat it as ideal. Each level sets a goal and relies on a faster one to meet it.

Where the readings meet, and where they part

The filter bank meets cortex at its first stage: Olshausen and Field’s 1996 efficient-coding paper opens by describing simple-cell receptive fields as localised, oriented and bandpass, much like the basis functions of a wavelet transform. The control loops meet it in time: Murray and colleagues (2014) found the intrinsic timescale of spiking in monkey cortex lengthening from sensory to prefrontal areas.

They part in two ways. A wavelet pyramid is a hierarchy of scale that loses nothing; a complex cell is defined by what it gives up — exactly where the edge fell. And a control hierarchy is specified, with references flowing one way. The cortical one is inferred: most of its pathways run both ways, and Hilgetag, O’Neill and Young (1996) showed that the same laminar constraints fit a great many orderings equally well. The ranking is real, but it is not unique.