Seminar: University Seminary on Cognitive and Behavioral Neuroscience (#603)
Title: How the monkey cortex encodes numerical information
Speaker: Andreas Nieder, Ph.D., Massachusetts Institute of Technology
Attendees: Peter D Balsam (co-Chair), Psychology Department, Barnard College
Jacqui Rick, Psychology Department, Columbia University
Herbert S. Terrace (co-Chair), Psychology Department, Columbia University
Tomoko Inagaki, Psychology Department, Hunter College
Sheila Chase, Psychology Department, Hunter College
Jon Horvitz, Psychology Department, Columbia University
Jennifer Mangels, Psychology Department, Columbia University
Len Matin, Psychology Department, Columbia University
Dustin Merritt, Psychology Department, Columbia University
Robert L. Thompson, Psychology Department, Hunter College
Nate Kornell, Psychology Department, Columbia University
Lisa Son, Psychology Department, Barnard College
Bridget Finn, Psychology Department, Columbia University
Kate Lynch, Psychology Department, Columbia University
Emily Stern, Psychology Department, Columbia University
Chris Sommerfield, Psychology Department, Columbia University
Tammy Moscrip, Psychology Department, Columbia University
Douglas Candland, Psychology Department, Bucknell University
Herman Buschke, Department of Neurology, Albert Einstein College of Medicine
Lance Kriegsfeld, Department of Psychology, Columbia University
Ilia Karatsoreos, Department of Psychology, Columbia University
Rapporteur: Michael R. Drew
Summary:
Dr. Nieder’s talk focused on the neural correlates of numerosity in monkeys. Nieder began by hypothesizing that numerical abilities have biological precursors. Nieder argued that this claim is supported by both ontogenetic and phylogenetic evidence. Human infants can make numerical discriminations before acquiring language abilities. Animals can discriminate stimuli differing only in numerosity. For instance, Marc Hauser at Harvard has shown that untrained monkeys can add and subtract 1 from 2. Elizabeth Brannon and Herb Terrace at Columbia have shown that monkeys understand the ordinal relations among numerosities. Nieder was careful to avoid the term “counting” in describing animals performance. He explained that there multiple ways of representing quantity. Quantity may be encoded either numerically or non-numerically. Numerical encoding can be either verbal or non-verbal. Verbal representations are digital and exact, and seem only to be used by humans. Non-verbal numerical representations are approximate and language-independent. Non-numerical encoding strategies include subitizing and object-file representations. All non-numerical representations have a strict limit on the quantities that can be encoded. A distinguishing feature of non-verbal numerical representations is the set-size (or Weber fraction) signature. Non-verbal numerical representations conform to Weber’s law, meaning that when this type of representation is used, the size of a numerical just-noticeable difference is a constant proportion of the target quantity. Nieder explained that he will use the set-size signature to convince people that rhesus monkeys use non-verbal, numerical representations of quantity.
The remainder of the talk was divided into 3 sections: first Nieder presented behavioral data about numerical representations in rhesus monkeys, then he presented evidence of quantity-selective neurons in the monkey prefrontal cortex (PFC), and finally he described the behavioral relevance of these quantity-selective neurons.
The behavioral studies used a delayed-matching-to-quantity (DMTQ) task in which monkeys were trained to judge whether successive visual displays contained the same quantity of items. The task worked as follows. Monkeys were required to fixate a central stimulus on a computer display. Then between 1 and 7 dots appeared on the display for 800ms. This was the sample. The sample was followed by a delay of 1000ms and then by the target display, which lasted 1200ms and contained either the same number of items as the sample, one more item than the sample, or one less item than the sample. Monkeys were trained to release a lever if the sample and target contained the same number of items. Monkeys’ performance was significantly higher than chance for sample quantities 1 through 5. Performance (% correct) decreased as a function of the sample quantity, and for sample quantities 6 and 7 performance was at chance. To determine whether monkeys were discriminating based on quantity rather than some non-numerical characteristic, Nieder used seven sets of control stimuli in which the physical appearance of stimuli varied widely (across sets). For example, in one set, total item area was equated in each display; in another, total circumference was equated. Each stimulus display was used only once. Performance readily generalized across the different stimulus sets without additional training, suggesting that monkeys were discriminating based on quantity.
Nieder remarked that the fact that monkeys could only discriminate numerosities 1 through 4 or 5 may reflect that higher quantities require a complex numerical representation that cannot be used when subjects are given only a brief look at the display items. Nieder asserted that humans, too, are able to discriminate only the numbers 1 through 4 on sight. Higher numbers require more time to assess. Nieder argued that this explains why in many ancient number systems, the numbers 1 through 4 are represented by the actual quantities, and numbers beyond 4 are represented using complex symbols. Number systems may work this way because humans can assess the numbers 1-4 very quickly, in parallel. Numbers higher than 4 require serial processing. In humans, the time needed to assess numbers higher than 4 increases by about 200-300ms with each additional item. The monkeys in Nieder’s experiments seemed also to be assessing the numbers 1-4 in parallel. For each monkey there was only a small increase in response latency as a function of item quantity (approx. 50ms). Herb Terrace asked why the increase in latency as a function of item quantity was evidence of parallel processing. Dr. Nieder replied that the increase per item was much too small to be evidence of serial processing. Additional evidence for parallel processing comes from eye tracking data. When viewing displays with up to 5 items, monkeys made only one or two saccades (away from the fixation point) regardless of the number of items. Peter Balsam asked how long each saccade took. Nieder replied that he did not have that information handy, but that the important point is that the monkeys had plenty of time to make saccades during sample and target presentation. This means that small number of saccades observed by Nieder is not an artifact of the stimulus duration.
To understand the neural basis of numerosity, Nieder recorded from individual neurons in the PFC during performance of the DMTQ task. Of the 352 neurons recorded from, approximately 1/3 showed activity that varied significantly with the number of items in the display. Some quantity-selective neurons responded during presentation of the sample, some responded during the delay, and some responded during both the presentation and delay periods. The firing patterns were largely independent of the physical characteristics of the items (i.e., firing patterns were not affected by switches between the different sets of control stimuli). Nieder also recorded from the gyrus of the inferior parietal lobule (LIP), where only 7% of neurons were selective for quantity. The discussion that follows focuses on the PFC neurons.
Neurons selective for quantity showed a peak in firing rate in response to a particular quantity, and firing rate decreased as the numerical distance from the preferred quantity increased. Lance Kriegsfeld asked whether the quantity-selective neurons in the PFC are organized into a quantitative map, such that neurons with similar preferred quantities are grouped together spatially. Dr. Nieder replied that no such pattern was observed. To assess the behavioral correlates of quantity selectivity, monkeys were given additional DMTQ trials in which the numerical distance between sample and target displays varied widely. A numerical distance effect on performance was observed: the number of errors decreased as the numerical distance between sample and target increased. There was also a numerical magnitude effect: for any given numerical distance, discriminability decreased as target quantity increased. The relation was such that the performance bandwidth (the numerical distance between the target quantity and the sample quantity at which 60% of responses are correct) was directly related to the sample quantity. This is a manifestation of Weber’s law, which specifies that the size of a just-noticeable-difference is a constant proportion of the stimulus magnitude. Nieder suggested that, in light of his data, the famous law should be amended to use “cognitive magnitude” as the predictor variable.
The bandwidth for quantity-selective neurons was calculated by plotting tuning curves of individual neurons, then taking the numerical distance between the quantities (above and below the preferred quantity) at which a particular neuron responded at 60% of its own peak rate. Again, bandwidth was linearly related to the neuron’s preferred quantity. Moreover, the tuning curves were asymmetric when plotted on an absolute scale, but assumed a guassian shape when plotted on a logarithmic scale (i.e., x = log[quantity]). Thus, the neural data (as well as the behavioral data) conformed to Weber’s law, suggesting the neural filter properties underlie the numerical distance and magnitude effects on performance.
Nieder concluded by summarizing the major points of his talk:
Discussion:
Peter Balsam asked what Nieder would be willing to call counting. Nieder replied that counting is a verbal numerical ability; it is serial assessment of numerical information. Dr. Balsam: suppose the Weber fractions went down. How much would they have to go down for it to be evidence of counting? Nieder: Counting is a digital, exact representation and so increases in quantity would have no effect on accuracy. To be on the safe side I’m not calling this counting. But if humans are prevented from counting then even humans switch to analog representation and show Weber fractions. But when we have the chance we use a verbal system.
Herb Terrace remarked that the Weber fraction argument extends out to 11, but the neural selectivity seems to flatten out at 5. That is, no cells that respond to the quantities 6-10. Nieder replied that he did not test for quantities 6-10. Dr. Terrace: Would cells responding to quantities 6-10 be necessary for your hypothesis about the neural basis of the magnitude effect? Nieder: It would increase my confidence in the hypothesis. Dr. Terrace: Suppose you didn’t get neural selectivity out to 11? Then would you need another mechanism to explain performance? Dr. Nieder: I really do think I will find neurons that respond to numbers 6-11. It may be that some of the neurons that I classified as having a preferred quantity of 5 would have a higher preferred quantity had I tested higher quantities.
Peter Balsam asked whether anyone has found cells that respond on a dimension where there is categorical perception. Dr. Nieder: The strongest evidence I have seen comes from Friedman who trained monkeys to discriminate cats and dogs. The neurons reflect these categories. Dr. Balsam: Do the neurons respond in a continuous way? Nieder: The categories are artificially constructed so that the visual space is linear, but the monkey’s performance and the neural data show that category boundaries are as you would expect. Even though the stimuli were very similar, most of the monkeys had sharp category boundaries.
Len Matin: what do you think would happen if you required that the monkey to respond only to the subset of dots on the left side of the circular array and not the right. Presumably the same neurons ought to be doing the same responding to the total number. But the behavioral response is only based on one subset. In that case you might get some different results. Nieder: So you’re talking about the correlation between neural responses and behavior. I didn’t mention that on the error trials, the response rates of the units significantly dropped down. So the neural responses were really necessary for proper performance. Dr. Matin: What happens to the latencies on the error trials? Nieder: They stay constant. And the response latencies of the neurons were equal for all the numerosities, which may be an additional argument for parallel processing.
Herb Terrace: How does selectivity for number work? You have the visual information coming into the retina. Somehow between the retina and the PFC there’s selectivity for quantity. Do you have any ideas about how that works? Dr. Nieder: In theory, I think the visual system has to forget about all the sensory information except that there is an item or entity at the particular location. How that is done, I do not know.
Dr. Matin: Given the convergent hookup between PFC and sensory areas, do you expect to get integration across modalities? Neider: I would like to look into that. Are PFC cells extracting information independent of modality? This is not trivial in the behavioral literature. But this is one of the next really important steps – to be sure the neurons are really quantity selective, independent of modality. Dr. Matin: So if a given neuron responds to both somatosensory and visual stimuli, then you ought to be able to show some additive characteristics. Nieder: Yes, and the PFC is an ideal structure because even on the level of single neurons it is integrating across all these sensory inputs. Dr. Matin: Phenomenologically it is not obvious to expect additivity. That is, if I see a quantity over there and feel a quantity over here, it is not natural to add them. It will be difficult to do the experiment. Dr. Nieder: Yes, and that raises an important issue for my experiments. I only presented items simultaneously. What if I presented items sequentially? Only the future will tell what would happen. For some people it is not difficult to assume that there may be modality specific counting systems. Others assume that if we are really dealing with number, then somewhere in the brain there has to be numerical information that is is extracted regardless of stimulus modality or temporal relations.
Prepared by Michael R. Drew, October 23, 2002