scholarly journals Neural state space alignment for magnitude generalisation in humans and recurrent networks

2020 ◽  
Author(s):  
Hannah Sheahan ◽  
Fabrice Luyckx ◽  
Stephanie Nelli ◽  
Clemens Teupe ◽  
Christopher Summerfield
Keyword(s):  
Model Systems ◽  
Recurrent Networks ◽  
Comparison Task ◽  
State Spaces ◽  
Magnitude Comparison ◽  
Relational Patterns ◽  
Relational Knowledge ◽  
Neural Representations ◽  
Brain Signals ◽  
Relational Concepts

AbstractA prerequisite for intelligent behaviour is to understand how stimuli are related and to generalise this knowledge across contexts. Generalisation can be challenging when relational patterns are shared across contexts but exist on different physical scales. Here, we studied neural representations in humans and recurrent neural networks performing a magnitude comparison task, for which it was advantageous to generalise concepts of “more” or “less” between contexts. Using multivariate analysis of human brain signals and of neural network hidden unit activity, we observed that both systems developed parallel neural “number lines” for each context. In both model systems, these number state spaces were aligned in a way that explicitly facilitated generalisation of relational concepts (more and less). These findings suggest a previously overlooked role for neural normalisation in supporting transfer of a simple form of abstract relational knowledge (magnitude) in humans and machine learning systems.

scholarly journals Magnitude integration in the Archerfish

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tali Leibovich-Raveh ◽  
Ashael Raveh ◽  
Dana Vilker ◽  
Shai Gabay
Keyword(s):  
Animal Model ◽  
Grocery Store ◽  
The Body ◽  
Water Tank ◽  
Comparison Task ◽  
Magnitude Comparison ◽  
Mathematical Abilities ◽  
In The Wild ◽  
Numerical Magnitudes ◽  
Shortest Queue

AbstractWe make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals’ magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.

scholarly journals Neural representations of honesty predict future trust behavior

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Gabriele Bellucci ◽  
Felix Molter ◽  
Soyoung Q. Park
Keyword(s):  
Prefrontal Cortex ◽  
Dorsolateral Prefrontal Cortex ◽  
Multivariate Analyses ◽  
Posterior Cingulate Cortex ◽  
Ventromedial Prefrontal Cortex ◽  
Intraparietal Sulcus ◽  
Temporoparietal Junction ◽  
Neural Representations ◽  
Brain Signals ◽  
Dorsolateral Prefrontal

AbstractTheoretical accounts propose honesty as a central determinant of trustworthiness impressions and trusting behavior. However, behavioral and neural evidence on the relationships between honesty and trust is missing. Here, combining a novel paradigm that successfully induces trustworthiness impressions with functional MRI and multivariate analyses, we demonstrate that honesty-based trustworthiness is represented in the posterior cingulate cortex, dorsolateral prefrontal cortex and intraparietal sulcus. Crucially, brain signals in these regions predict individual trust in a subsequent social interaction with the same partner. Honesty recruited the ventromedial prefrontal cortex (VMPFC), and stronger functional connectivity between the VMPFC and temporoparietal junction during honesty encoding was associated with higher trust in the subsequent interaction. These results suggest that honesty signals in the VMPFC are integrated into trustworthiness beliefs to inform present and future social behaviors. These findings improve our understanding of the neural representations of an individual’s social character that guide behaviors during interpersonal interactions.

The Functional Neuroanatomy of Thematic Role and Locative Relational Knowledge

2007 ◽  
Vol 19 (9) ◽  
pp. 1542-1555 ◽  
Author(s):  
Denise H. Wu ◽  
Sara Waller ◽  
Anjan Chatterjee
Keyword(s):  
Conceptual Knowledge ◽  
Visual Motion ◽  
Critical Role ◽  
Temporal Cortex ◽  
Functional Neuroanatomy ◽  
Thematic Role ◽  
Point Of Entry ◽  
Relational Knowledge ◽  
Relational Concepts ◽  
The Relationship

Lexical-semantic investigations in cognitive neuroscience have focused on conceptual knowledge of concrete objects. By contrast, relational concepts have been largely ignored. We examined thematic role and locative knowledge in 14 left-hemisphere-damage patients. Relational concepts shift cognitive focus away from the object to the relationship between objects, calling into question the relevance of traditional sensory-functional accounts of semantics. If extraction of a relational structure is the critical cognitive process common to both thematic and locative knowledge, then damage to neural structures involved in such an extraction would impair both kinds of knowledge. If the nature of the relationship itself is critical, then functional neuroanatomical dissociations should occur. Using a new lesion analysis method, we found that damage to the lateral temporal cortex produced deficits in thematic role knowledge and damage to inferior fronto-parietal regions produced deficits in locative knowledge. In addition, we found that conceptual knowledge of thematic roles dissociates from its mapping onto language. These relational knowledge deficits were not accounted for by deficits in processing nouns or verbs or by a general deficit in making inferences. Our results are consistent with the hypothesis that manners of visual motion serve as a point of entry for thematic role knowledge and networks dedicated to eye gaze, whereas reaching and grasping serve as a point of entry for locative knowledge. Intermediary convergence zones that are topographically guided by these sensory-motor points of entry play a critical role in the semantics of relational concepts.

Un approccio attuale alla psicoterapia di coppia nell'ottica della psicologia del sé e della teoria dell'intersoggettivitŕ

INTERAZIONI ◽  
2009 ◽  
pp. 78-103
Author(s):  
Carla Leone
Keyword(s):  
Couples Therapy ◽  
Treatment Approach ◽  
Relational Patterns ◽  
Relational Experiences ◽  
Relational Knowledge ◽  
Therapeutic Dialogue ◽  
Key Points ◽  
Reliable Source ◽  
Selfobject Needs ◽  
Organizing Principles

- This paper applies central tenets of self psychology and intersubjective systems theory (e.g., Stolorow and Atwood, 1992) to couples therapy. The concepts of selfobject needs, unconscious organizing principles, and implicit relational knowledge are used to understand and conceptualize common couples' difficulties. A treatment approach is outlined, focused on improving partners' abilities to function as a reliable source of selfobject experience for each other. Major components include listening from within each partner's subjective perspective, attuned responsiveness to each partner's selfobject needs, close attention to narcissistic vulnerability, and the establishment of a joint therapeutic dialogue through which each partner's selfobject needs, organizing principles and implicit relational patterns can be illuminated and gradually transformed. The functions of defensiveness, resistance and aggression are discussed from this perspective, along with suggested responses to help reduce them. Overall, change is thought to occur through both partners' increased understanding of each other and their relationship, and through the facilitation of new relational experiences (between each partner and the couples therapist, and eventually between the partners) which eventually lead to new implicit relational knowledge for both partners. A case example is used throughout the paper to illustrate key points.

Further Evidence for a Spatial-Numerical Association in Children Before Formal Schooling

2014 ◽  
Vol 61 (4) ◽  
pp. 323-329 ◽  
Author(s):  
Mirjam Ebersbach ◽  
Koen Luwel ◽  
Lieven Verschaffel
Keyword(s):  
Snarc Effect ◽  
Formal Schooling ◽  
Comparison Task ◽  
Magnitude Comparison ◽  
Reading And Writing ◽  
Left Hand ◽  
Alternative Culture ◽  
Potential Alternative ◽  
The Right

Given the robust finding that number and space are associated systematically at least in school children and adults, it has been concluded that this association might be based on the frequent practice of reading or writing skills, which are usually consolidated by formal schooling. However, first studies contradict this assumption demonstrating that associations of “small” magnitudes with left space and of “large” magnitudes with right space exist already in preschoolers. The present study used a non-symbolic magnitude comparison task to examine whether kindergartners who have not yet been formally instructed in reading and writing show a SNARC effect, that is, whether they would respond more rapidly with the right hand to larger numbers and with the left hand to smaller numbers. This assumption was confirmed by the data. In view of further evidence for an association between number and space that evolves before children are proficient in reading and writing, the role of potential alternative culture-specific, individual, and universal foundations of this association is emphasized and discussed.

Relational Categories are More Mutable than Entity Categories

2017 ◽  
Vol 70 (10) ◽  
pp. 2007-2025 ◽  
Author(s):  
Jennifer Asmuth ◽  
Dedre Gentner
Keyword(s):  
Recognition Accuracy ◽  
Conceptual Structure ◽  
Intrinsic Properties ◽  
Relational Patterns ◽  
The Core ◽  
Relational Categories ◽  
Relational Concepts ◽  
Highly Correlated ◽  
Referential Function ◽  
Relational Nouns

Across three experiments, we explore differences between relational categories—whose members share common relational patterns—and entity categories, whose members share common intrinsic properties. Specifically, we test the claim that relational concepts are more semantically mutable in context, and therefore less stable in memory, than entity concepts. We compared memory for entity nouns and relational nouns, tested either in the same context as at encoding or in a different context. We found that (a) participants show better recognition accuracy for entity nouns than for relational nouns, and (b) recognition of relational nouns is more impaired by a change in context than is recognition of entity nouns. We replicated these findings even when controlling for factors highly correlated with relationality, such as abstractness–concreteness. This suggests that the contextual mutability of relational concepts is due to the core semantic property of conveying relational structure and not simply to accompanying characteristics such as abstractness. We note parallels with the distinction between nouns and verbs and suggest implications for lexical and conceptual structure. Finally, we relate these patterns to proposals that a deep distinction exists between words with an essentially referential function and those with a predicate function.

scholarly journals CARTESIAN PRODUCT PARTITIONING OF MULTI-DIMENSIONAL REACHABLE STATE SPACES

2016 ◽  
Vol 30 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Tuǧrul Dayar ◽  
M. Can Orhan
Keyword(s):  
State Space ◽  
Cartesian Product ◽  
Model Systems ◽  
Dimensional System ◽  
Reachable State ◽  
State Spaces ◽  
Cartesian Products ◽  
Higher Dimensional ◽  
The Matrix ◽  
Minimum Number

Markov chains (MCs) are widely used to model systems which evolve by visiting the states in their state spaces following the available transitions. When such systems are composed of interacting subsystems, they can be mapped to a multi-dimensional MC in which each subsystem normally corresponds to a different dimension. Usually the reachable state space of the multi-dimensional MC is a proper subset of its product state space, that is, Cartesian product of its subsystem state spaces. Compact storage of the matrix underlying such a MC and efficient implementation of analysis methods using Kronecker operations require the set of reachable states to be represented as a union of Cartesian products of subsets of subsystem state spaces. The problem of partitioning the reachable state space of a three or higher dimensional system with a minimum number of partitions into Cartesian products of subsets of subsystem state spaces is shown to be NP-complete. Two algorithms, one merge based the other refinement based, that yield possibly non-optimal partitionings are presented. Results of experiments on a set of problems from the literature and those that are randomly generated indicate that, although it may be more time and memory consuming, the refinement based algorithm almost always computes partitionings with a smaller number of partitions than the merge-based algorithm. The refinement based algorithm is insensitive to the order in which the states in the reachable state space are processed, and in many cases it computes partitionings that are optimal.

Preschoolers' Magnitude Comparisons are Mediated by a Preverbal Analog Mechanism

2000 ◽  
Vol 11 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Gavin Huntley-Fenner ◽  
Erin Cannon
Keyword(s):  
Discrimination Task ◽  
Age Groups ◽  
Comparison Task ◽  
Magnitude Representation ◽  
Magnitude Comparison ◽  
Error Patterns ◽  
Numerical Discrimination ◽  
Adults And Children ◽  
Analog Models

We report a study of 3- to 5-year-olds who performed a magnitude-comparison task. Stimuli were a series of pairs of arrays that sometimes differed in numerosity, and the children were asked to point to the more numerous array in each pair. The proportion of accurate responses was above chance for all age groups. However, error patterns were consistent with analog models of magnitude representation. Errors varied systematically with the ratio of stimulus pairs. Items with a 2:3 ratio were harder than items with a 1:2 ratio. Performance on posttests of verbal counting ability was variable, but did not predict performance on the numerical discrimination task. We argue that neither verbal counting nor nonnumerical perceptual strategies can explain these results. This study supports the hypothesis that adults and children share preverbal, analog representations of magnitude.

The Organization of Brain Activations in Number Comparison: Event-Related Potentials and the Additive-Factors Method

1996 ◽  
Vol 8 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Stanislas Dehaene
Keyword(s):  
Cognitive Task ◽  
Reaction Times ◽  
Event Related Potentials ◽  
Normal Subjects ◽  
Imaging Data ◽  
Comparison Task ◽  
Cerebral Lateralization ◽  
Magnitude Comparison ◽  
Number Comparison ◽  
Related Potentials

Measuring reaction times (RTs) using the additive-factors method provides information about the sequence of processing stages in a cognitive task. Here, I describe how the simultaneous recording of event-related potentials (ERPs) in the same task can provide complementary information that cannot be obtained using RTs alone. Most notably, ERP data can reveal the absolute activation time and the coarse brain localization of processing stages. RTs and ERPs can also be used to cross-validate a serial-stage model. These notions were applied to a study of the temporal unfolding of brain activations in a number comparison task. ERPs were recorded from 64 scalp electrodes while normal subjects classified numbers as larger or smaller than 5. Specific scalp signatures and timing data were obtained for stages of word and digit identification, magnitude comparison, response programming, and error capture and correction. The observed localizations were compatible with previous neuropsychological and brain imaging data and provided new insights into the cerebral lateralization and timing of number processing.

scholarly journals Storage and retrieval of addition facts: The role of number comparison

2001 ◽  
Vol 54 (4) ◽  
pp. 1005-1029 ◽  
Author(s):  
Brian Butterworth ◽  
Marco Zorzi ◽  
Luisa Girelli ◽  
A.R. Jonckheere
Keyword(s):  
Reaction Times ◽  
Naming Task ◽  
Comparison Task ◽  
Single Digit ◽  
Magnitude Comparison ◽  
Comparison Stage ◽  
Storage And Retrieval ◽  
Addition Task ◽  
Three Stages ◽  
Fact Retrieval

It is proposed that arithmetical facts are organized in memory in terms of a principle that is unique to numbers—the cardinal magnitudes of the addends. This implies that sums such as 4 + 2 and 2 + 4 are represented, and searched for, in terms of the maximum and minimum addends. This in turn implies that a critical stage in solving an addition problem is deciding which addend is the larger. The COMP model of addition fact retrieval incorporates a comparison stage, as well as a retrieval stage and a pronunciation stage. Three tasks, using the same subjects, were designed to assess the contribution of these three stages to retrieving the answers to single-digit addition problems. Task 3 was the addition task, which examined whether reaction times (RTs) were explained by the model; Task 1 was a number naming task to assess the contribution of the pronunciation stage; Task 2 was a magnitude comparison task to assess the contribution, if any, of the comparison stage. A regression equation that included just expressions of these three stages was found to account for 71% of the variance. It is argued that the COMP model fits not only the adult RT data better than do alternatives, but also the evidence from development of additional skills.

Sign in / Sign up

Export Citation Format

Share Document