Symbol addition by monkeys provides evidence for normalized quantity coding

Abstract

Weber's law can be explained either by a compressive scaling of sensory response with stimulus magnitude or by a proportional scaling of response variability. These two mechanisms can be distinguished by asking how quantities are added or subtracted. We trained Rhesus monkeys to associate 26 distinct symbols with 0-25 drops of reward, and then tested how they combine, or add, symbolically represented reward magnitude. We found that they could combine symbolically represented magnitudes, and they transferred this ability to a novel symbol set, indicating that they were performing a calculation, not just memorizing the value of each combination. The way they combined pairs of symbols indicated neither a linear nor a compressed scale, but rather a dynamically shifting, relative scaling.macaque | normalization | number sense | value coding A nimals and humans can estimate the number of various items, and the precision of this approximate number sense decreases with magnitude. For example, although it is easy to recognize the difference between 2 and 4 items, it is more difficult to distinguish 22 from 24 items. This dependence of accuracy on magnitude is a property that the approximate number sense shares with more basic sensory processes. Weber (1) observed that in general, across many sensory modalities, the just noticeable difference between two stimuli is proportional to their magnitude. Fechner (2) proposed that Weber's observation could be explained if sensations were physiologically encoded as a logarithmic function of stimulus magnitude, but Stevens (3) argued instead that sensations obey a power law, with perceptual magnitude being proportional to a power function of the stimulus magnitude, with the power usually less than 1. Both a logarithmic and a power-less-than-one relationship between stimulus and internal coding are compressive, with the same physical difference between stimuli producing incrementally smaller internal differences between successively larger pairs of external stimuli. Any kind of compressive scaling would explain a decrease in discriminability with increasing magnitude if the noise in the internal representation is constant.However, an alternative possibility is that variability in encoding might increase with stimulus magnitude. In fact, the variability in the firing rates of cortical neurons tends to increase with firing rate (4-6). Therefore, to the extent that a stimulus parameter is encoded by the rate of neural firing, an increase in perceptual variability with stimulus magnitude may not require compressive scaling; it is also consistent with a linear neuronal representation with magnitude-dependent variability (7-10).Neurons that are tuned to numerosity have been recorded in monkey posterior parietal and lateral prefrontal cortex (11-13). The width and asymmetry of such tuning is consistent with a compressed scaling (14). However, neurons tuned to particular numerosities, or numerosity ranges, represent a labeled-line code and therefore are not, themselves, scaled to numerosity...

Perceptual learning in a non-human primate model of artificial vision

“…The animals reached 80% correct on the clear view symbols in an average of 30 days (logMAR 1.0–1.9). This learning rate is comparable to findings in Livingstone et al 35,. where animals also reached approximately 80% correct when associating reward magnitude with 26 symbols after 30 days of training.…”

“…The ability of monkeys to make visual discriminations between pairs of letters of the Roman alphabet has, to our knowledge, not previously been demonstrated. The capability of monkeys to perform this task is, however, not surprising given that monkeys have previously been trained to recognize arbitrary non-letter visually-presented objects3233, make tactile-visual associations using letters34, and associate visually presented letters or arbitrary symbols with reward magnitude35. Here, after learning to recognize letters in clear view and thus consolidate task rules, the monkeys learned to recognize the same set of letters using patterns of simulated phosphenes acting as sets of discrete visual elements, where each element mimicked activation of a small cluster of neurons in the lateral geniculate nucleus.…”

A rational analysis of the approximate number system

“… 1 Other work has criticized logarithmic scaling by arguing that it predicts nonlinear addition and subtraction (Stevens, 1960 ; Livingstone et al, 2014), since ψ ( x ) + ψ ( y ) = log x + log y ≠ x + y . This critique erroneously assumes that addition in numerical space of x + y must correspond to addition in the psychological space (e.g.…”

The Structural Effects of Modality on the Rise of Symbolic Language: A Rebuttal of Evolutionary Accounts and a Laboratory Demonstration

“…In other words, the individuals more easily acquired pairs where action symbols correctly matched signs for types of foods, which implies a processing of signs in terms of their conceptual relations (Deacon, 1997, p. 86). More recently, Livingstone et al (2014) trained rhesus monkeys on symbols representing distinct numbers of drops of liquid (implying a coding of magnitude). On tests involving combinations of these learned symbols, the individuals not only showed a capacity to process the relative values of signs within a context, but also transferred these subjective valuations to new symbols, suggesting a capacity to process combined signs in terms of novel relations.…”

“…On tests involving combinations of these learned symbols, the individuals not only showed a capacity to process the relative values of signs within a context, but also transferred these subjective valuations to new symbols, suggesting a capacity to process combined signs in terms of novel relations. Livingstone et al (2010, 2014) also outlined that value coding of signs involves similar neural processes in humans and monkeys implicating dopamine neurons and interactions between the midbrain, the orbitofrontal cortex, and nucleus accumbens (for a critical review of other findings of this type, see Núñez, 2017). …”