The scaling of winner-takes-all accuracy with population size

Empirical studies seem to support conflicting hypotheses with regard to the nature of the neural code. While some studies highlight the role of a distributed population code, others emphasize the possibility of a "single-best-cell" readout. One particularly interesting example of single-best-cell readout is provided by the winner-takes-all (WTA) approach. According to the WTA, every cell is characterized by one particular preferred stimulus, to which it responds maximally. The WTA estimate for the stimulus is defined as the preferred stimulus of the cell with the strongest response. From a theoretical point of view, not much is known about the efficiency of single-best-cell readout mechanisms, in contrast to the considerable existing theoretical knowledge on the efficiency of distributed population codes. In this work, we provide a basic theoretical framework for investigating single-best-cell readout mechanisms. We study the accuracy of the WTA readout. In particular, we are interested in how the WTA accuracy scales with the number of cells in the population. Using this framework, we show that for large neuronal populations, the WTA accuracy is dominated by the tail of the single-cell-response distribution. Furthermore, we find that although the WTA accuracy does improve when larger populations are considered, this improvement is extremely weak compared to other types of population codes. More precisely, we show that while the accuracy of a linear readout scales linearly with the population size, the accuracy of the WTA readout scales logarithmically with the number of cells in the population.