  In neuroscience, population coding theory demonstrates that neural assemblies
can achieve fault-tolerant information processing. Mapped to nanoelectronics,
this strategy could allow for reliable computing with scaled-down, noisy,
imperfect devices. Doing so requires that the population components form a set
of basis functions in terms of their response functions to inputs, offering a
physical substrate for calculating. For this purpose, the responses of the
nanodevices should be non-linear, and each tuned to different values of the
input. These strong requirements have prevented a demonstration of population
coding with nanodevices. Here, we show that nanoscale magnetic tunnel junctions
can be assembled to meet these requirements. We demonstrate experimentally that
a population of nine junctions can implement a basis set of functions,
providing the data to achieve, for example, the generation of cursive letters.
We design hybrid magnetic-CMOS systems based on interlinked populations of
junctions and show that they can learn to realize non-linear
variability-resilient transformations with a low imprint area and low power.
