On the origins of computationally complex behavior.

Grace, Randolph C.; Carvell, Georgina E.; Morton, Nicola J.; Grice, Matt; Wilson, A. J. C.; Kemp, Simon

doi:10.1037/xan0000227

Cited by 9 publications

(10 citation statements)

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“…Although our results cannot definitively reject the latter view, we believe that the speed of learning and accuracy of responding despite the noisy feedback is strong evidence of automaticity. If this is correct, magnitude comparison would be 'computationally complex' in Grace et al's (2019) definition, because it would have an action in the perceptual system that is functionally equivalent to algebraic computation as a proximate cause.…”

Section: Resultsmentioning

confidence: 99%

“…Algebraic fields generalize the intuitions underlying arithmetic over the real numbers, and highlight the structure necessary for arithmetic to work. Groups are associated with symmetriesthey effectively code the symmetries of an object that can be transformed in various ways while preserving its structureand it may be helpful to look for evidence of groups when considering the neural processes that might support computation by the perceptual system (see Grace et al, 2019).…”

Section: Ratios Differences and Noisy Feedback 22mentioning

confidence: 99%

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Nonsymbolic Estimation of Big and Small Ratios with Accurate and Noisy Feedback

Nj¹,

Wilson²,

Kemp³

et al. 2020

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Grace et al. (2018) showed that observers quickly learned to respond based on differences and ratios of stimulus magnitudes in a nonsymbolic task without explicit instruction. But were observers really responding based on differences and ratios, suggesting the perceptual system effectively computes these operations? As a stronger test of relational versus exemplar responding, we studied a version of this task with noisy feedback. In three experiments, observers viewed pairs of stimuli that varied in area, brightness, or length, and responded by clicking on a horizontal bar. For different groups, feedback was based on the ratio or difference of stimulus magnitudes, linearly scaled to the response bar, plus a Gaussian noise component that was constant for repetitions of each pair. Multiple regressions showed that for every observer across experiments, coefficients for the added noise were negative when entered in a model with trained values, and were statistically significant in 76% of individual cases. These results indicate that observers responded based on the differences or ratios of stimulus magnitudes, and effectively ignored or suppressed the added noise. Regressions also showed that differences and ratios described the data well, with the untrained relation accounting for significant variance in approximately half of individual cases, similar to Grace et al.’s (2018) results. Overall, these results suggest that the perceptual system automatically computes two operations, corresponding to differences and ratios, when comparing stimulus magnitudes.

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Section: Resultsmentioning

confidence: 99%

Section: Ratios Differences and Noisy Feedback 22mentioning

confidence: 99%

Nonsymbolic Estimation of Big and Small Ratios with Accurate and Noisy Feedback

Nj¹,

Wilson²,

Kemp³

et al. 2020

Preprint

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“…We have described navigation by path integration as 'computationally-complex behavior', as one-shot foraging journeys of individual organisms appear to require the equivalent of algebraic computation (Grace, Carvell, et al, 2020). Theoretical accounts of path integration include Gallistel's computational-representational theory, which assumes that organisms represent environmental variables such as angle with respect to the sun and distance travelled as vectors of real numbers stored in an engram, and proposes that the mechanism of molecular coding should be a prime focus of research (Gallistel, 2017(Gallistel, , 2018Langille & Gallistel, 2020).…”

Section: Computationally-complex Behaviormentioning

confidence: 99%

Implicit Computation and the Origins of Knowledge

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Morton²,

Grice³

et al. 2021

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Human infants have ‘core knowledge systems’ that support basic intuitions about the world including objects and their motion, space, number, and time. What is the origin of these systems, and what is their nature? Although often regarded as separate, domain-specific modules, evidence for similar abilities across many nonhuman species suggests that core systems might be integrated, consistent with views of modularity in evolutionary-developmental biology. Here we propose that core knowledge systems are based on an ability to form representations of the environment with algebraic structure – that is, on implicit computation. Algebraic groups encode symmetries, with computation inherent in the structure – a view that complements an understanding of computation as action or function. Our proposal is related to previous applications of group theory in perception and computational-representational accounts of learning (Gallistel, 1990), but suggests for the first time a common basis for core knowledge across humans and nonhumans. Implicit computation can be studied experimentally with an ‘artificial algebra’ task in which adults learn to respond based on arithmetic combinations of stimulus magnitudes, by feedback and without explicit instruction. Asking why organisms have a capacity for implicit computation suggests two possibilities: Either the geometric invariants of the world have been internalized in perceptual systems by natural selection (Shepard, 1994), or mathematical structure is intrinsic to the mind. Understood more broadly in a framework offered by Penrose (2004), implicit computation is a linchpin with potential to unlock some of the most fundamental questions about relationships between the mind, mathematics, and the world.

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“…Spatial navigation may be a more rewarding context in which to investigate the intelligence-related capacities animals display specifically with respect to “measuring numbers.” This could be especially interesting with respect to abstract intelligence because, when based on path integration, spatial navigation implies computationally complex behavior, by which we mean behavior that appears to require the equivalent of mathematical calculation by the animal ( Gallistel, 1990b ; Grace et al, 2020 ).…”

Section: Spatial Navigationmentioning

confidence: 99%

Arthropod Intelligence? The Case for Portia

et al. 2020

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Macphail’s “null hypothesis,” that there are no differences in intelligence, qualitative, or quantitative, between non-human vertebrates has been controversial. This controversy can be useful if it encourages interest in acquiring a detailed understanding of how non-human animals express flexible problem-solving capacity (“intelligence”), but limiting the discussion to vertebrates is too arbitrary. As an example, we focus here on Portia , a spider with an especially intricate predatory strategy and a preference for other spiders as prey. We review research on pre-planned detours, expectancy violation, and a capacity to solve confinement problems where, in each of these three contexts, there is experimental evidence of innate cognitive capacities and reliance on internal representation. These cognitive capacities are related to, but not identical to, intelligence. When discussing intelligence, as when discussing cognition, it is more useful to envisage a continuum instead of something that is simply present or not; in other words, a continuum pertaining to flexible problem-solving capacity for “intelligence” and a continuum pertaining to reliance on internal representation for “cognition.” When envisaging a continuum pertaining to intelligence, Daniel Dennett’s notion of four Creatures (Darwinian, Skinnerian, Popperian, and Gregorian) is of interest, with the distinction between Skinnerian and Popperian Creatures being especially relevant when considering Portia . When we consider these distinctions, a case can be made for Portia being a Popperian Creature. Like Skinnerian Creatures, Popperian Creatures express flexible problem solving capacity, but the manner in which this capacity is expressed by Popperian Creatures is more distinctively cognitive.

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On the origins of computationally complex behavior.

Cited by 9 publications

References 68 publications

Nonsymbolic Estimation of Big and Small Ratios with Accurate and Noisy Feedback

Nonsymbolic Estimation of Big and Small Ratios with Accurate and Noisy Feedback

Implicit Computation and the Origins of Knowledge

Arthropod Intelligence? The Case for Portia

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