Spontaneous summation or numerosity-selective coding?

INTRODUCTION A key debate in numerical cognition concerns the neural code for number representation (e.g., Nieder and Merten, 2007; Roggeman et al., 2007; Viswanathan and Nieder, 2013). One idea is that individual neurons are tuned to individual numbers, with decreasing response to numbers with increasing distance (numerosity-selective coding or labeled-line coding). An alternative, more implicit way of representing number is by summation coding. Here, individual neurons fire either monotonically stronger or weaker to increasing number. The number can then be decoded from the pooled cell activity. The computational properties of both coding types have been studied. A summation code but not a numerosity-selective code was extracted without numberrelated training from a visual display in a recent modeling study (Stoianov and Zorzi, 2012). Also, the summation code serves as a precursor for a numerosityselective code in such models (Dehaene and Changeux, 1993; Verguts and Fias, 2004). Furthermore, each coding type has distinct advantages; summation coding is more suited for smaller-larger (i.e., magnitude) processing, numerosityselective coding is more efficient for same-different number discrimination (Verguts, 2007). In a number of papers, Nieder and colleagues demonstrated numerosityselective coding in macaque monkeys (e.g., Nieder et al., 2002; Nieder and Miller, 2004). However, number was always relevant for the task; in other words, animals were trained on number (e.g., Nieder et al., 2002). The computational modeling work jointly predicts that summation coding is primary and foundational to numerosity-selective coding, and that in the absence of number-relevant training, only summation coding would be observed. Consistently, Roitman et al. (2007) showed that only summation coding was observed in a single-unit recording study in which number was not relevant for solving the task. However, number was relevant for computing the reward at trial offset, so it may still be that numberrelevant learning took place during training. To determine the natural numerical coding system (i.e., without number learning), Viswanathan and Nieder (2013) recorded cells from ventral intraparietal area [VIP, in intraparietal sulcus (IPS)] and from prefrontal cortex (PFC) in two monkeys in a task without number relevance (and hence number learning). They found that neurons in both brain areas responded maximally to a given number (e.g., one neuron responded maximally to 1, another neuron maximally to 2, and so on). They interpret their data as suggesting numerosity-selective coding. They also found that the most frequently preferred numbers for these neurons were numbers 1 and 5, whereas a relatively small set of neurons were classified as tuned to intermediate numbers 2, 3, and 4. However, given the computational primacy of summation coding, we consider the possibility that the authors instead sampled summation coding neurons. Here, we show that the data are consistent with summation coding, and that summation coding can account for subtle and unexplained aspects of the data.