Efficient coding

Barlow’s suggestion, made a little over a decade after Shannon, was that the nervous system’s sensory front end should be understood as a code designed for its input statistics. Natural images are extremely redundant — neighbouring pixels are highly correlated — and transmitting that redundancy down a bandwidth-limited, metabolically expensive nerve is waste. So the early visual system should be doing something like decorrelation.

This is a rare thing in neuroscience: a normative theory. It does not describe what neurons do, it predicts what they ought to do, given the statistics of the world and a cost.

Why it earned its keep

Because the predictions came out.

Centre-surround receptive fields in retinal ganglion cells are approximately what you get if you whiten a signal with natural-image correlations. Olshausen and Field then made the sharper demonstration: train a model to represent natural image patches using as few simultaneously active units as possible, impose nothing else, and the units that emerge are localised, oriented, and bandpass — which is to say they look like the simple cells Hubel and Wiesel had recorded three decades earlier.

Nobody put edges into that model. Sparseness and natural image statistics were enough.

Where it goes on the engineering side

Straight into signal processing, and it is one of the cleanest cases of biology being ahead:

• Predictive and transform coding in image compression are the same redundancy argument.
• Sparse representation and compressed sensing are the same objective, formalised.
• Event cameras are the argument in silicon — do not transmit what has not changed.

The caution worth keeping is that “efficient” needs a specified cost. Efficient in bits, in spikes, in joules, or in decoding effort are different objectives that predict different codes, and it is easy to pick whichever one matches the data you already have.