Skip to main content
Top
Gepubliceerd in:

01-11-2020 | Original Article

A robot that counts like a child: a developmental model of counting and pointing

Auteurs: Leszek Pecyna, Angelo Cangelosi, Alessandro Di Nuovo

Gepubliceerd in: Psychological Research | Uitgave 8/2022

Log in om toegang te krijgen
share
DELEN

Deel dit onderdeel of sectie (kopieer de link)

  • Optie A:
    Klik op de rechtermuisknop op de link en selecteer de optie “linkadres kopiëren”
  • Optie B:
    Deel de link per e-mail

Abstract

In this paper, a novel neuro-robotics model capable of counting real items is introduced. The model allows us to investigate the interaction between embodiment and numerical cognition. This is composed of a deep neural network capable of image processing and sequential tasks performance, and a robotic platform providing the embodiment—the iCub humanoid robot. The network is trained using images from the robot’s cameras and proprioceptive signals from its joints. The trained model is able to count a set of items and at the same time points to them. We investigate the influence of pointing on the counting process and compare our results with those from studies with children. Several training approaches are presented in this paper, all of them use pre-training routine allowing the network to gain the ability of pointing and number recitation (from 1 to 10) prior to counting training. The impact of the counted set size and distance to the objects are investigated. The obtained results on counting performance show similarities with those from human studies.
Voetnoten
1
We also tested the model without that feature (when gestures are produced but the hand is not visible). That case is similar to what was presented by Pecyna and Cangelosi (2018). We found better performance with hand visible but these analyses are not in the scope of this paper.
 
2
Having this information in the visual input is useful for the model because the Convolutional Part (image processing part) can learn to react differently whenever the image has to be processed or not. We did not include other trigger data in the visual input because of the pre-training method we initially (and as a subsidiary study) used, where only part of the network was trained and it was not necessarily containing the visual processing units.
 
3
These seven angles composing the gesture output are: shoulder pitch, shoulder roll, shoulder yaw, elbow, wrist pronation/supination (roll), wrist pitch and wrist yaw.
 
4
Also a few subsidiary tests were performed using the presented model and they showed that the gesture pre-training increases the final training speed significantly (where the recitation pre-training had positive influence only if used together with the gesture pre-training).
 
5
At the beginning of our research, we were training the model to recite in a similar manner as in the case of gesture pre-training—only part of the network was trained. We found, however, that such a pre-trained network when trained to count, immediately loses the ability to recite (even if it is included in the final training set of simulated skills). This is likely because the model was never trained to produce any type of gesture output (in the case of recitation in the final training and current recitation pre-training the network is producing gestures—base position) and through backpropagation, gesture output error modifies the weights responsible for number recitation.
 
6
Those values represent the situation when children were counting objects from a smaller set: 7-10 (as it is closer to the one we use). We considered only pointing conditions and not the touch one which is analysed later. The values were expressed as the percentage of correct answers
 
7
We only considered the results of small sets from Alibali and DiRusso (1999) and we used the mean value and standard deviation presented in the article for the t test (2 conditions were compared: touch and point, conducted by 20 participants). Alibali and DiRusso (1999), however, found a statistical difference as they considered both ranges (small and large sets) together (having a larger number of samples). They also used a different test—repeated measures ANOVA.
 
8
In the case of the experiment with children, the small sets were covering 7 to 10 objects and big ones 13–17.
 
Literatuur
go back to reference Alibali, M. W., & DiRusso, A. A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14(1), 37–56.CrossRef Alibali, M. W., & DiRusso, A. A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14(1), 37–56.CrossRef
go back to reference Amit, D. J. (1988). Neural networks counting chimes. Proceedings of the National Academy of Sciences, 85(7), 2141–2145.CrossRef Amit, D. J. (1988). Neural networks counting chimes. Proceedings of the National Academy of Sciences, 85(7), 2141–2145.CrossRef
go back to reference Andres, M., Di Luca, S., & Pesenti, M. (2008). Finger counting: The missing tool? Behavioral and Brain Sciences, 31(6), 642–643.CrossRef Andres, M., Di Luca, S., & Pesenti, M. (2008). Finger counting: The missing tool? Behavioral and Brain Sciences, 31(6), 642–643.CrossRef
go back to reference Bertenthal, B., & Von Hofsten, C. (1998). Eye, head and trunk control: The foundation for manual development1. Neuroscience and Biobehavioral Reviews, 22(4), 515–520.CrossRefPubMed Bertenthal, B., & Von Hofsten, C. (1998). Eye, head and trunk control: The foundation for manual development1. Neuroscience and Biobehavioral Reviews, 22(4), 515–520.CrossRefPubMed
go back to reference De La Cruz, V. M., Di Nuovo, A., Di Nuovo, S., & Cangelosi, A. (2014). Making fingers and words count in a cognitive robot. Frontiers in Behavioral Neuroscience, 8, 13. De La Cruz, V. M., Di Nuovo, A., Di Nuovo, S., & Cangelosi, A. (2014). Making fingers and words count in a cognitive robot. Frontiers in Behavioral Neuroscience, 8, 13.
go back to reference Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1–2), 1–42.PubMed Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1–2), 1–42.PubMed
go back to reference Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626.PubMed Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626.PubMed
go back to reference Di Nuovo, A. (2017). An embodied model for handwritten digits recognition in a cognitive robot. In 2017 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1–6). IEEE. Di Nuovo, A. (2017). An embodied model for handwritten digits recognition in a cognitive robot. In 2017 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1–6). IEEE.
go back to reference Di Nuovo, A. (2018). Long-short term memory networks for modelling embodied mathematical cognition in robots. In 2018 International Joint Conference on Neural Networks (IJCNN) (pp. 1–7). IEEE. Di Nuovo, A. (2018). Long-short term memory networks for modelling embodied mathematical cognition in robots. In 2018 International Joint Conference on Neural Networks (IJCNN) (pp. 1–7). IEEE.
go back to reference Di Nuovo, A. (2020). A developmental neuro-robotics approach for boosting the recognition of handwritten digits. In 2020 International Joint Conference on Neural Networks (IJCNN) (pp. 1–8). IEEE. Di Nuovo, A. (2020). A developmental neuro-robotics approach for boosting the recognition of handwritten digits. In 2020 International Joint Conference on Neural Networks (IJCNN) (pp. 1–8). IEEE.
go back to reference Di Nuovo, A., De La Cruz, V. M., & Cangelosi, A. (2014a). Grounding fingers, words and numbers in a cognitive developmental robot. In 2014 IEEE Symposium on Computational Intelligence, Cognitive Algorithms, Mind, and Brain (CCMB) (pp. 9–15). IEEE. Di Nuovo, A., De La Cruz, V. M., & Cangelosi, A. (2014a). Grounding fingers, words and numbers in a cognitive developmental robot. In 2014 IEEE Symposium on Computational Intelligence, Cognitive Algorithms, Mind, and Brain (CCMB) (pp. 9–15). IEEE.
go back to reference Di Nuovo, A., De La Cruz, V. M., & Cangelosi, A. (2015). A deep learning neural network for number cognition: A bi-cultural study with the iCub. In 2015 Joint IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL-EpiRob) (pp. 320–325). IEEE. Di Nuovo, A., De La Cruz, V. M., & Cangelosi, A. (2015). A deep learning neural network for number cognition: A bi-cultural study with the iCub. In 2015 Joint IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL-EpiRob) (pp. 320–325). IEEE.
go back to reference Di Nuovo, A., De La Cruz, V. M., Cangelosi, A., & Di Nuovo, S. (2014b). The iCub learns numbers: An embodied cognition study. In 2014 International Joint Conference on Neural Networks (IJCNN) (pp. 692–699). IEEE. Di Nuovo, A., De La Cruz, V. M., Cangelosi, A., & Di Nuovo, S. (2014b). The iCub learns numbers: An embodied cognition study. In 2014 International Joint Conference on Neural Networks (IJCNN) (pp. 692–699). IEEE.
go back to reference Di Nuovo, A., & Jay, T. (2019). The development of numerical cognition in children and artificial systems: A review of the current knowledge and proposals for multi-disciplinary research. Cognitive Computation and Systems. Di Nuovo, A., & Jay, T. (2019). The development of numerical cognition in children and artificial systems: A review of the current knowledge and proposals for multi-disciplinary research. Cognitive Computation and Systems.
go back to reference Di Nuovo, A., & McClelland, J. L. (2019). Developing the knowledge of number digits in a child-like robot. Nature Machine Intelligence, 1(12), 594–605.CrossRef Di Nuovo, A., & McClelland, J. L. (2019). Developing the knowledge of number digits in a child-like robot. Nature Machine Intelligence, 1(12), 594–605.CrossRef
go back to reference Elman, J. L. (1990). Finding structure in time. Cognitive Science, 14(2), 179–211.CrossRef Elman, J. L. (1990). Finding structure in time. Cognitive Science, 14(2), 179–211.CrossRef
go back to reference Fischer, M. H., Kaufmann, L., & Domahs, F. (2012). Finger counting and numerical cognition. In F. Domahs, L. Kaufmann, & M. H. Fischer (Eds.), Handy numbers: Finger counting and numerical cognition (p. 6). Frontiers E-books. Fischer, M. H., Kaufmann, L., & Domahs, F. (2012). Finger counting and numerical cognition. In F. Domahs, L. Kaufmann, & M. H. Fischer (Eds.), Handy numbers: Finger counting and numerical cognition (p. 6). Frontiers E-books.
go back to reference Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.CrossRef Fuson, K. C. (1988). Children’s counting and concepts of number. New York: Springer.CrossRef
go back to reference Fuson, K. C., Richards, J., & Briars, D. J. (1982). The acquisition and elaboration of the number word sequence. In C. J. Brainerd (Ed.), Children’s logical and mathematical cognition (pp. 33–92). New York: Springer.CrossRef Fuson, K. C., Richards, J., & Briars, D. J. (1982). The acquisition and elaboration of the number word sequence. In C. J. Brainerd (Ed.), Children’s logical and mathematical cognition (pp. 33–92). New York: Springer.CrossRef
go back to reference Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1–2), 43–74.CrossRefPubMed Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1–2), 43–74.CrossRefPubMed
go back to reference Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.CrossRefPubMed Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.CrossRefPubMed
go back to reference Gelman, R. (1980). What young children know about numbers. Educational Psychologist, 15(1), 54–68.CrossRef Gelman, R. (1980). What young children know about numbers. Educational Psychologist, 15(1), 54–68.CrossRef
go back to reference Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge: Harvard University Press. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge: Harvard University Press.
go back to reference Gigliotta, O., Ponticorvo, M., Doricchi, F., & Miglino, O. (2019). Midpoint: A tool to build artificial models of numerical cognition. In International Work-Conference on the Interplay Between Natural and Artificial Computation (pp. 88–96). Springer. Gigliotta, O., Ponticorvo, M., Doricchi, F., & Miglino, O. (2019). Midpoint: A tool to build artificial models of numerical cognition. In International Work-Conference on the Interplay Between Natural and Artificial Computation (pp. 88–96). Springer.
go back to reference Goldin-Meadow, S., Levin, S. C., & Jacobs, S. (2014). Gestures role in learning arithmetic. In L. D. Edwards, D. Moore-Russo, & F. Ferrara (Eds.), Emerging perspectives on gesture and embodiment in mathematics (pp. 51–72). Charlotte: IAP. Goldin-Meadow, S., Levin, S. C., & Jacobs, S. (2014). Gestures role in learning arithmetic. In L. D. Edwards, D. Moore-Russo, & F. Ferrara (Eds.), Emerging perspectives on gesture and embodiment in mathematics (pp. 51–72). Charlotte: IAP.
go back to reference Graham, T. A. (1999). The role of gesture in children’s learning to count. Journal of Experimental Child Psychology, 74(4), 333–355.CrossRefPubMed Graham, T. A. (1999). The role of gesture in children’s learning to count. Journal of Experimental Child Psychology, 74(4), 333–355.CrossRefPubMed
go back to reference Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.CrossRefPubMed Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.CrossRefPubMed
go back to reference Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.CrossRefPubMed Le Corre, M., & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), 395–438.CrossRefPubMed
go back to reference Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52(2), 130–169.CrossRefPubMed Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52(2), 130–169.CrossRefPubMed
go back to reference Metta, G., Natale, L., Nori, F., Sandini, G., Vernon, D., Fadiga, L., et al. (2010). The iCub humanoid robot: An open-systems platform for research in cognitive development. Neural Networks, 23(8), 1125–1134.CrossRefPubMed Metta, G., Natale, L., Nori, F., Sandini, G., Vernon, D., Fadiga, L., et al. (2010). The iCub humanoid robot: An open-systems platform for research in cognitive development. Neural Networks, 23(8), 1125–1134.CrossRefPubMed
go back to reference Pecyna, L., & Cangelosi, A. (2018). Influence of pointing on learning to count: A neuro-robotics model. In 2018 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 358–365). IEEE. Pecyna, L., & Cangelosi, A. (2018). Influence of pointing on learning to count: A neuro-robotics model. In 2018 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 358–365). IEEE.
go back to reference Pecyna, L., Cangelosi, A., & Di Nuovo, A. (2019). A deep neural network for finger counting and numerosity estimation. In 2019 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 358–365). IEEE. Pecyna, L., Cangelosi, A., & Di Nuovo, A. (2019). A deep neural network for finger counting and numerosity estimation. In 2019 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 358–365). IEEE.
go back to reference Rodriguez, P., Wiles, J., & Elman, J. L. (1999). A recurrent neural network that learns to count. Connection Science, 11(1), 5–40.CrossRef Rodriguez, P., Wiles, J., & Elman, J. L. (1999). A recurrent neural network that learns to count. Connection Science, 11(1), 5–40.CrossRef
go back to reference Rotondaro, F., Ponticorvo, M., Gigliotta, O., Pinto, M., Pellegrino, M., Gazzellini, S., et al. (2019). The Number Interval Position Effect (NIPE) in the mental bisection of numerical intervals might reflect the influence of the decimal-number system on the gaussian representations of numerosities: A combined developmental and computational-modeling study. Cortex, 114, 164–175.CrossRefPubMed Rotondaro, F., Ponticorvo, M., Gigliotta, O., Pinto, M., Pellegrino, M., Gazzellini, S., et al. (2019). The Number Interval Position Effect (NIPE) in the mental bisection of numerical intervals might reflect the influence of the decimal-number system on the gaussian representations of numerosities: A combined developmental and computational-modeling study. Cortex, 114, 164–175.CrossRefPubMed
go back to reference Ruciński, M., Cangelosi, A., & Belpaeme, T. (2012). Robotic model of the contribution of gesture to learning to count. In 2012 IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL) (pp. 1–6). IEEE. Ruciński, M., Cangelosi, A., & Belpaeme, T. (2012). Robotic model of the contribution of gesture to learning to count. In 2012 IEEE International Conference on Development and Learning and Epigenetic Robotics (ICDL) (pp. 1–6). IEEE.
go back to reference Saxe, G. B., & Kaplan, R. (1981). Gesture in early counting: A developmental analysis. Perceptual and Motor skills, 53(3), 851–854.CrossRef Saxe, G. B., & Kaplan, R. (1981). Gesture in early counting: A developmental analysis. Perceptual and Motor skills, 53(3), 851–854.CrossRef
go back to reference Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6(3), 357–379.CrossRef Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6(3), 357–379.CrossRef
go back to reference Scherer, D., Müller, A., & Behnke, S. (2010). Evaluation of pooling operations in convolutional architectures for object recognition. In International conference on artificial neural networks (pp. 92–101). Springer. Scherer, D., Müller, A., & Behnke, S. (2010). Evaluation of pooling operations in convolutional architectures for object recognition. In International conference on artificial neural networks (pp. 92–101). Springer.
go back to reference Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220–251.CrossRef Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220–251.CrossRef
Metagegevens
Titel
A robot that counts like a child: a developmental model of counting and pointing
Auteurs
Leszek Pecyna
Angelo Cangelosi
Alessandro Di Nuovo
Publicatiedatum
01-11-2020
Uitgeverij
Springer Berlin Heidelberg
Gepubliceerd in
Psychological Research / Uitgave 8/2022
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI
https://doi.org/10.1007/s00426-020-01428-8

Andere artikelen Uitgave 8/2022

Psychological Research 8/2022 Naar de uitgave