A predictive coding model of gaze shifts and the underlying neurophysiology

References

• Adams, R., Shipp, S., & Friston, K. (2013). Predictions not commands: Active inference in the motor system. Brain Structure and Function, 218, 611–643. doi: 10.1007/s00429-012-0475-5
   PubMed Web of Science ®Google Scholar
• Albano, J. E., & Wurtz, R. H. (1982). Deficits in eye position following ablation of monkey superior colliculus, pretectum, and posterior-medial thalamus. Journal of Neurophysiology, 48, 318–337. doi: 10.1152/jn.1982.48.2.318
   PubMed Web of Science ®Google Scholar
• Andersen, R. A., Bracewell, R. M., Barash, S., Gnadt, J. W., & Fogassi, L. (1990). Eye position effects on visual, memory, and saccade-related activity in areas LIP and 7a of macaque. The Journal of Neuroscience, 10, 1176–1196.
   PubMed Web of Science ®Google Scholar
• Andersen, R. A., Essick, G. K., & Siegel, R. M. (1985). Encoding of spatial location by posterior parietal neurons. Science, 230(4724), 456–458. doi: 10.1126/science.4048942
   PubMed Web of Science ®Google Scholar
• Andersen, R. A., & Mountcastle, V. B. (1983). The influence of the angle of gaze upon the excitability of the light-sensitive neurons of the posterior parietal cortex. The Journal of Neuroscience, 3, 532–548.
   PubMed Web of Science ®Google Scholar
• Barlow, H. B. (1994). What is the computational goal of the neocortex? In C. Koch & J. L. Davis (Eds.), Large-scale neuronal theories of the brain (chapter 1, pp. 1–22). Cambridge, MA: MIT Press.
   Google Scholar
• Battaglia-Mayer, A., Caminiti, R., Lacquaniti, F., & Zago, M. (2003). Multiple levels of representation of reaching in the parieto-frontal network. Cerebral Cortex, 13, 1009–1022. doi: 10.1093/cercor/13.10.1009
   PubMed Web of Science ®Google Scholar
• Bays, P. M., & Husain, M. (2007). Spatial remapping of the visual world across saccades. NeuroReport, 18, 1207–1213. doi: 10.1097/WNR.0b013e328244e6c3
   PubMed Web of Science ®Google Scholar
• Becker, W., & Jürgens, R. (1979). An analysis of the saccadic system by means of double step stimuli. Vision Research, 19, 967–983. doi: 10.1016/0042-6989(79)90222-0
   PubMed Web of Science ®Google Scholar
• Blangero, A. (2008). The sensorimotor functions of the posterior parietal cortex: Evidence from patients with optic ataxia (PhD thesis). L'Universite De Lyon, France.
   Google Scholar
• Boussaoud, D., Jouffrais, C., & Bremmer, F. (1998). Eye position effects on the neuronal activity of dorsal premotor cortex in the macaque monkey. Journal of Neurophysiology, 80, 1132–1150. doi: 10.1152/jn.1998.80.3.1132
   PubMed Web of Science ®Google Scholar
• Bremmer, F. (2000). Eye position effects in macaque area V4. NeuroReport, 11, 1277–1283. doi: 10.1097/00001756-200004270-00027
   PubMed Web of Science ®Google Scholar
• Bremmer, F., Distler, C., & Hoffmann, K. P. (1997). Eye position effects in monkey cortex. II. pursuit- and fixation-related activity in posterior parietal areas LIP and 7a. Journal of Neurophysiology, 77, 962–977. doi: 10.1152/jn.1997.77.2.962
   PubMed Web of Science ®Google Scholar
• Broomhead, D. S., & Lowe, D. (1988). Multivariable functional interpolation and adaptive networks. Complex Systems, 2, 321–355.
   Google Scholar
• Brotchie, P. R., Andersen, R. A., Snyder, L. H., & Goodman, S. J. (1995). Head position signals used by parietal neurons to encode locations of visual stimuli. Nature, 375, 232–235. doi: 10.1038/375232a0
   PubMed Web of Science ®Google Scholar
• Bubic, A., von Cramon, D. Y., & Schubotz, R. I. (2010). Prediction, cognition and the brain. Frontiers in Human Neuroscience, 4, 1–15.
   PubMed Web of Science ®Google Scholar
• Cassanello, C. R., & Ferrera, V. P. (2007). Computing vector differences using a gain field-like mechanism in monkey frontal eye field. Journal of Physiology, 582, 647–664. doi: 10.1113/jphysiol.2007.128801
   PubMed Web of Science ®Google Scholar
• Cavanaugh, J., Berman, R. A., Joiner, W. M., & Wurtz, R. H. (2016). Saccadic corollary discharge underlies stable visual perception. The Journal of Neuroscience, 36, 31–42. doi: 10.1523/JNEUROSCI.2054-15.2016
   PubMed Web of Science ®Google Scholar
• Chinellato, E., Antonelli, M., Grzyb, B., & del Pobil, A. P. (2011). Implicit sensorimotor mapping of the peripersonal space by gazing and reaching. IEEE Transactions on Autonomous Mental Development, 3, 43–52. doi: 10.1109/TAMD.2011.2106781
   Google Scholar
• Clark, A. (2013). Whatever next? Predictive brains, situated agents, and the future of cognitive science. Behavioral and Brain Sciences, 36, 181–204. doi: 10.1017/S0140525X12000477
   PubMed Web of Science ®Google Scholar
• Cohen, M. E., & Ross, L. E. (1978). Latency and accuracy characteristics of saccades and corrective saccades in children and adults. Journal of Experimental Child Psychology, 26, 517–527. doi: 10.1016/0022-0965(78)90130-3
   PubMed Web of Science ®Google Scholar
• Colby, C. L. (1998). Action-oriented spatial reference frames in cortex. Neuron, 20, 15–24. doi: 10.1016/S0896-6273(00)80429-8
   PubMed Web of Science ®Google Scholar
• Colby, C. L., & Goldberg, M. E. (1999). Space and attention in parietal cortex. Annual Review of Neuroscience, 22, 319–349. doi: 10.1146/annurev.neuro.22.1.319
   PubMed Web of Science ®Google Scholar
• Crick, F., & Asanuma, C. (1986). Certain aspects of the anatomy and physiology of the cerebral cortex. In D. E. Rumelhart, J. L. McClelland, & The PDP Research Group (Eds.), Parallel distributed processing: Explorations in the microstructures of cognition. Volume 2: Psychological and biological models (pp. 333–371). Cambridge, MA: MIT Press.
   Google Scholar
• De Meyer, K., & Spratling, M. W. (2011). Multiplicative gain modulation arises through unsupervised learning in a predictive coding model of cortical function. Neural Computation, 23, 1536–1567. doi: 10.1162/NECO_a_00130
   PubMed Web of Science ®Google Scholar
• De Meyer, K., & Spratling, M. W. (2013). A model of partial reference frame transforms through pooling of gain-modulated responses. Cerebral Cortex, 23, 1230–1239. doi: 10.1093/cercor/bhs117
   PubMed Web of Science ®Google Scholar
• Deneve, S., Latham, P. E., & Pouget, A. (2001). Efficient computation and cue integration with noisy population codes. Nature Neuroscience, 4, 826–831. doi: 10.1038/90541
   PubMed Web of Science ®Google Scholar
• Deneve, S., & Pouget, A. (2003). Basis functions for object-centered representations. Neuron, 37, 347–359. doi: 10.1016/S0896-6273(02)01184-4
   PubMed Web of Science ®Google Scholar
• Dominey, P. F., & Arbib, M. A. (1992). A cortico-subcortical model for generation of spatially accurate sequential saccades. Cerebral Cortex, 2, 153–175. doi: 10.1093/cercor/2.2.153
   PubMed Web of Science ®Google Scholar
• Douglas, R. J., Martin, K. A. C., & Whitteridge, D. (1989). A canonical microcircuit for neocortex. Neural Computation, 1, 480–488. doi: 10.1162/neco.1989.1.4.480
   Web of Science ®Google Scholar
• Droulez, J., & Berthoz, A. (1991). A neural network model of sensoritopic maps with predictive short-term memory properties. Proceedings of the National Academy of Sciences USA, 88, 9653–9657. doi: 10.1073/pnas.88.21.9653
   PubMed Web of Science ®Google Scholar
• Duhamel, J., Colby, C., & Goldberg, M. (1992). The updating of the representation of visual space in parietal cortex by intended eye movements. Science, 255, 90–92. doi: 10.1126/science.1553535
   PubMed Web of Science ®Google Scholar
• Duhamel, J.-R., Bremmer, F., Ben Hamed, S., & Graf, W. (1997). Spatial invariance of visual receptive fields in parietal cortex neurons. Nature, 389, 845–848. doi: 10.1038/39865
   PubMed Web of Science ®Google Scholar
• Ebdon, M. (1992). The uniformity of cerebral neocortex and its implications for cognitive science (Technical Report CSRP-228). School of Cognitive and Computing Sciences, University of Sussex.
   Google Scholar
• Ebdon, M. (1996). Towards a general theory of cerebral neocortex (PhD thesis). University of Sussex, UK.
   Google Scholar
• Findlay, J., & Walker, R. (2012). Human saccadic eye movements. Scholarpedia, 7, 5095. revision 122018. doi: 10.4249/scholarpedia.5095
   Google Scholar
• Flash, T., & Sejnowski, T. J. (2001). Computational approaches to motor control. Current Opinion in Neurobiology, 11, 655–662. doi: 10.1016/S0959-4388(01)00265-3
   PubMed Web of Science ®Google Scholar
• Földiák, P. (1991). Learning invariance from transformation sequences. Neural Computation, 3, 194–200. doi: 10.1162/neco.1991.3.2.194
   PubMed Web of Science ®Google Scholar
• Freedman, E. G., & Sparks, D. L. (1997). Eye-head coordination during head-unrestrained gaze shifts in rhesus monkeys. Journal of Neurophysiology, 77, 2328–2348. doi: 10.1152/jn.1997.77.5.2328
   PubMed Web of Science ®Google Scholar
• Friston, K., Adams, R. A., Perrinet, L., & Breakspear, M. (2012). Perceptions as hypotheses: Saccades as experiments. Frontiers in Psychology, 3, 151.
   PubMed Web of Science ®Google Scholar
• Friston, K., & Kiebel, S. (2009). Predictive coding under the free-energy principle. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 364, 1211–1221. doi: 10.1098/rstb.2008.0300
   PubMed Web of Science ®Google Scholar
• Friston, K., Mattout, J., & Kilner, J. (2011). Action understanding and active inference. Biological Cybernetics, 104, 137–160. doi: 10.1007/s00422-011-0424-z
   PubMed Web of Science ®Google Scholar
• Friston, K. J., Daunizeau, J., Kilner, J., & Kiebel, S. J. (2010). Action and behavior: A free-energy formulation. Biological Cybernetics, 102, 227–260. doi: 10.1007/s00422-010-0364-z
   PubMed Web of Science ®Google Scholar
• Galletti, C., & Battaglini, P. P. (1989). Gaze-dependent visual neurons in area V3A of monkey prestriate cortex. The Journal of Neuroscience, 9, 1112–1125.
   PubMed Web of Science ®Google Scholar
• Galletti, C., Battaglini, P. P., & Fattori, P. (1993). Parietal neurons encoding spatial locations in craniotopic coordinates. Experimental Brain Research, 96, 221–229. doi: 10.1007/BF00227102
   PubMed Web of Science ®Google Scholar
• Galletti, C., Battaglini, P. P., & Fattori, P. (1995). Eye position influence on the parieto-occipital area PO (V6) of the macaque monkey. European Journal of Neuroscience, 7, 2486–2501. doi: 10.1111/j.1460-9568.1995.tb01047.x
   PubMed Web of Science ®Google Scholar
• Georgopoulos, A. P., Schwartz, A. B., & Kettner, R. E. (1986). Neuronal population coding of movement direction. Science, 233, 1416–1419. doi: 10.1126/science.3749885
   PubMed Web of Science ®Google Scholar
• Goldberg, M. E., & Bruce, C. J. (1990). Primate frontal eye fields. III. maintenance of a spatially accurate saccade signal. Journal of Neurophysiology, 64, 489–508. doi: 10.1152/jn.1990.64.2.489
   PubMed Web of Science ®Google Scholar
• Guitton, D., & Volle, M. (1987). Gaze control in humans: Eye-head coordination during orienting movements to targets within and beyond the oculomotor range. Journal of Neurophysiology, 58, 427–459. doi: 10.1152/jn.1987.58.3.427
   PubMed Web of Science ®Google Scholar
• Guo, K., & Li, C.-Y. (1997). Eye position-dependent activation of neurones in striate cortex of macaque. Neuro Report, 8, 1405–1409.
   PubMed Web of Science ®Google Scholar
• Hadjidimitrakis, K., Bertozzi, F., Breveglieri, R., Fattori, P., & Galletti, C. (2013). Body-centered, mixed, but not hand-centered coding of visual targets in the medial posterior parietal cortex during reaches in 3D space. Cerebral Cortex, 24, 3209–3220. doi: 10.1093/cercor/bht181
   PubMed Web of Science ®Google Scholar
• Hallett, P. E., & Lightstone, A. (1976). Saccadic eye movements to flashed targets. Vision Research, 16, 107–114. doi: 10.1016/0042-6989(76)90084-5
   PubMed Web of Science ®Google Scholar
• Hamker, F. H., Zirnsak, M., Calow, D., & Lappe, M. (2008). The peri-saccadic perception of objects and space. PLoS Computational Biology, 4, e31. doi: 10.1371/journal.pcbi.0040031
   PubMed Web of Science ®Google Scholar
• Hamker, F. H., Zirnsak, M., Ziesche, A., & Lappe, M. (2011). Computational models of spatial updating in peri-saccadic perception. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 366(1564), 554–571. doi: 10.1098/rstb.2010.0229
   PubMed Web of Science ®Google Scholar
• Harris, C. M., & Wolpert, D. M. (1998). Signal-dependent noise determines motor planning. Nature, 394, 780–784. doi: 10.1038/29528
   PubMed Web of Science ®Google Scholar
• Harris, C. M., & Wolpert, D. M. (2006). The main sequence of saccades optimizes speed-accuracy trade-off. Biological Cybernetics, 95, 21–29. doi: 10.1007/s00422-006-0064-x
   PubMed Web of Science ®Google Scholar
• Harris, K. D., & Shepherd, G. M. (2015). The neocortical circuit: Themes and variations. Nature Neuroscience, 18, 170–181. doi: 10.1038/nn.3917
   PubMed Web of Science ®Google Scholar
• Hartmann, T. S., Bremmer, F., Albright, T. D., & Krekelberg, B. (2011). Receptive field positions in area MT during slow eye movements. The Journal of Neuroscience, 31, 10437–10444. doi: 10.1523/JNEUROSCI.5590-10.2011
   PubMed Web of Science ®Google Scholar
• Heide, W., Blankenburg, M., Zimmermann, E., & Kömpf, D. (1995). Cortical control of double-step saccades: Implications for spatial orientation. Annals of Neurology, 38, 739–748. doi: 10.1002/ana.410380508
   PubMed Web of Science ®Google Scholar
• Henderson, J. M. (2017). Gaze control as prediction. Trends in Cognitive Sciences, 21, 15–23. doi: 10.1016/j.tics.2016.11.003
   PubMed Web of Science ®Google Scholar
• Henson, D. B. (1978). Corrective saccades: Effects of altering visual feedback. Vision Research, 18, 63–67. doi: 10.1016/0042-6989(78)90078-0
   PubMed Web of Science ®Google Scholar
• Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18, 1527–1554. doi: 10.1162/neco.2006.18.7.1527
   PubMed Web of Science ®Google Scholar
• Honda, H. (1991). The time courses of visual mislocalization and of extra-retinal eye position signals at the time of vertical saccades. Vision Research, 31, 1915–1921. doi: 10.1016/0042-6989(91)90186-9
   PubMed Web of Science ®Google Scholar
• Houk, J. C., Buckingham, J. T., & Barto, A. G. (1996). Models of the cerebellum and motor learning. Behavioral and Brain Sciences, 19, 368–383. doi: 10.1017/S0140525X00081474
   Web of Science ®Google Scholar
• Huang, Y., & Rao, R. P. N. (2011). Predictive coding. WIREs Cognitive Science, 2, 580–593. doi: 10.1002/wcs.142
   Web of Science ®Google Scholar
• Kaiser, M., & Lappe, M. (2004). Perisaccadic mislocalization orthogonal to saccade direction. Neuron, 41, 293–300. doi: 10.1016/S0896-6273(03)00849-3
   PubMed Web of Science ®Google Scholar
• Kapoula, Z., & Robinson, D. A. (1986). Saccadic undershoot is not inevitable: Saccades can be accurate. Vision Research, 26, 735–743. doi: 10.1016/0042-6989(86)90087-8
   PubMed Web of Science ®Google Scholar
• Kardamakis, A. A., & Moschovakis, A. K. (2009). Optimal control of gaze shifts. The Journal of Neuroscience, 29, 7723–7730. doi: 10.1523/JNEUROSCI.5518-08.2009
   PubMed Web of Science ®Google Scholar
• Kawato, M. (1995). Cerebellum and motor control. In M. A. Arbib (Ed.), The handbook of brain theory and neural networks (pp. 172–177). Cambridge, MA: MIT Press.
   Google Scholar
• Kim, D., Huh, S.-H., Seo, S.-J., & Park, G.-T. (2005). Self-organizing radial basis function network modeling for robot manipulator. In M. Ali & F. Esposito (Eds.), Innovations in applied artificial intelligence, volume 3533 of Lecture Notes in Computer Science (pp. 579–587). Berlin; Heidelberg: Springer.
   Google Scholar
• Komoda, M. K., Festinger, L., Philips, L. J., Duckman, R. H., & Young, R. A. (1973). Some observations concerning saccadic eye movements. Vision Research, 13, 1009–1020. doi: 10.1016/0042-6989(73)90140-5
   PubMed Web of Science ®Google Scholar
• Krommenhoek, K., Opstal, A. V., Gielen, C., & Gisbergen, J. V. (1993). Remapping of neural activity in the motor colliculus: A neural network study. Vision Research, 33, 1287–1298. doi: 10.1016/0042-6989(93)90215-I
   PubMed Web of Science ®Google Scholar
• Kusunoki, M., & Goldberg, M. E. (2003). The time course of perisaccadic receptive field shifts in the lateral intraparietal area of the monkey. Journal of Neurophysiology, 89, 1519–1527. doi: 10.1152/jn.00519.2002
   PubMed Web of Science ®Google Scholar
• Lappe, M., Awater, H., & Krekelberg, B. (2000). Postsaccadic visual references generate presaccadic compression of space. Nature, 403, 892–895. doi: 10.1038/35002588
   PubMed Web of Science ®Google Scholar
• Larochelle, H., Bengio, Y., Louradour, J., & Lamblin, P. (2009). Exploring strategies for training deep neural networks. Journal of Machine Learning Research, 1, 1–40.
   Google Scholar
• Latham, P. E., Deneve, S., & Pouget, A. (2003). Optimal computation with attractor networks. Journal of Physiology – Paris, 97, 683–694. doi: 10.1016/j.jphysparis.2004.01.022
   PubMedGoogle Scholar
• Law, J., Shaw, P., & Lee, M. (2013). A biologically constrained architecture for developmental learning of eye–head gaze control on a humanoid robot. Autonomous Robots, 35, 77–92. doi: 10.1007/s10514-013-9335-2
   Web of Science ®Google Scholar
• Lehky, S. R., Peng, X., McAdams, C. J., & Sereno, A. B. (2008). Spatial modulation of primate inferotemporal responses by eye position. PLoS ONE, 3, e3492. doi: 10.1371/journal.pone.0003492
   PubMed Web of Science ®Google Scholar
• Leigh, R. J., & Kennard, C. (2004). Using saccades as a research tool in the clinical neurosciences. Brain, 127, 460–477. doi: 10.1093/brain/awh035
   PubMed Web of Science ®Google Scholar
• Marjanović, M., Scassellati, B., & Williamson, M. (1996). Self-taught visually guided pointing for a humanoid robot. In P. Maes, M. Mataric, J.-A. Meyer, J. Pollack, & S. W. Wilson (Eds.), From animals to animats: Proceedings of the international conference on Simulation of Adaptive Behaviour (pp. 35–44). Cambridge, MA: MIT Press.
   Google Scholar
• Marzocchi, N., Breveglieri, R., Galletti, C., & Fattori, P. (2008). Reaching activity in parietal area V6A of macaque: Eye influence on arm activity or retinocentric coding of reaching movements? European Journal of Neuroscience, 27, 775–789. doi: 10.1111/j.1460-9568.2008.06021.x
   PubMed Web of Science ®Google Scholar
• Matin, L., & Pearce, D. G. (1965). Visual perception of direction for stimuli flashed during voluntary saccadic eye movmements. Science, 148, 1485–1487. doi: 10.1126/science.148.3676.1485
   PubMed Web of Science ®Google Scholar
• Mays, L. E., & Sparks, D. L. (1980). Dissociation of visual and saccade-related responses in superior colliculus neurons. Journal of Neurophysiology, 43, 207–232. doi: 10.1152/jn.1980.43.1.207
   PubMed Web of Science ®Google Scholar
• McCluskey, M. K., & Cullen, K. E. (2007). Eye, head, and body coordination during large gaze shifts in rhesus monkeys: Movement kinematics and the influence of posture. Journal of Neurophysiology, 97, 2976–2991. doi: 10.1152/jn.00822.2006
   PubMed Web of Science ®Google Scholar
• McGuire, L. M. M., & Sabes, P. N. (2009). Sensory transformations and the use of multiple reference frames for reach planning. Nature Neuroscience, 12, 1056–1061. doi: 10.1038/nn.2357
   PubMed Web of Science ®Google Scholar
• Melcher, D., & Colby, C. L. (2008). Trans-saccadic perception. Trends in Cognitive Sciences, 12, 466–473. doi: 10.1016/j.tics.2008.09.003
   PubMed Web of Science ®Google Scholar
• Mender, B. M. W. (2014). Models of primate supraretinal visual representations (PhD thesis). University of Oxford.
   Google Scholar
• Mender, B. M. W., & Stringer, S. M. (2015). A self-organizing model of perisaccadic visual receptive field dynamics in primate visual and oculomotor system. Frontiers in Computational Neuroscience, 9, 17. doi: 10.3389/fncom.2015.00017
   PubMed Web of Science ®Google Scholar
• Meng, Q., & Lee, M. H. (2007). Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks. Connection Science, 19, 25–52. doi: 10.1080/09540090600971302
   Web of Science ®Google Scholar
• Meng, Q., & Lee, M. H. (2008). Error-driven active learning in growing radial basis function networks for early robot learning. Neurocomputing, 71, 1449–1461. doi: 10.1016/j.neucom.2007.05.012
   Web of Science ®Google Scholar
• Michels, L., & Lappe, M. (2004). Contrast dependency of saccadic compression and suppression. Vision Research, 44, 2327–2336. doi: 10.1016/j.visres.2004.05.008
   PubMed Web of Science ®Google Scholar
• Mohsenzadeh, Y., Dash, S., & Crawford, J. D. (2016). A state space model for spatial updating of remembered visual targets during eye movements. Frontiers in Systems Neuroscience, 10, 39. doi: 10.3389/fnsys.2016.00039
   PubMed Web of Science ®Google Scholar
• Molina-Vilaplana, J., Pedreño-Molina, J. L., & López-Coronado, J. (2004). Hyper RBF model for accurate reaching in redundant robotic systems. Neurocomputing, 61, 495–501. doi: 10.1016/j.neucom.2004.06.006
   Web of Science ®Google Scholar
• Morrone, M. C., Ross, J., & Burr, D. C. (1997). Apparent position of visual targets during real and simulated saccadic eye movements. The Journal of Neuroscience, 17, 7941–7953.
   PubMed Web of Science ®Google Scholar
• Mountcastle, V. B. (1998). Perceptual neuroscience: The cerebral cortex. Cambridge, MA: Harvard University Press.
   Google Scholar
• Muhammad, W., & Spratling, M. W. (2015). A neural model of binocular saccade planning and vergence control. Adaptive Behavior, 23, 265–282. doi: 10.1177/1059712315607363
   Web of Science ®Google Scholar
• Muhammad, W., & Spratling, M. W. (2017a). A neural model for eye-head-arm coordination. Advanced Robotics, 31(12), 650–663. doi: 10.1080/01691864.2017.1315319
   Web of Science ®Google Scholar
• Muhammad, W., & Spratling, M. W. (2017b). A neural model of coordinated head and eye movement control. Journal of Intelligent and Robotic Systems, 85, 107–126. doi: 10.1007/s10846-016-0410-8
   Web of Science ®Google Scholar
• Mumford, D. (1992). On the computational architecture of the neocortex II: The role of cortico-cortical loops. Biological Cybernetics, 66, 241–251. doi: 10.1007/BF00198477
   PubMed Web of Science ®Google Scholar
• Mumford, D. (1994). Neuronal architectures for pattern-theoretic problems. In C. Koch & J. L. Davis (Eds.), Large-scale neuronal theories of the brain (pp. 125–152). Cambridge, MA: MIT Press.
   Google Scholar
• Nakamura, K., & Colby, C. L. (2002). Updating of the visual representation in monkey striate and extrastriate cortex during saccades. Proceedings of the National Academy of Sciences USA, 99, 4026–4031. doi: 10.1073/pnas.052379899
   PubMed Web of Science ®Google Scholar
• Niemeier, M., Crawford, J. D., & Tweed, D. B. (2003). Optimal transsaccadic integration explains distorted spatial perception. Nature, 422(6927), 76–80. doi: 10.1038/nature01439
   PubMed Web of Science ®Google Scholar
• O'Reilly, R. C., & McClelland, J. L. (1992). The self-organization of spatially invariant representations (Technical Report PDP.CNS.92.5). Department of Psychology, Carnegie Mellon University.
   Google Scholar
• Park, J., & Sandberg, I. W. (1991). Universal approximation using radial-basis-function networks. Neural Computation, 3, 246–257. doi: 10.1162/neco.1991.3.2.246
   PubMed Web of Science ®Google Scholar
• Perrinet, L. U., Adams, R. A., & Friston, K. J. (2014). Active inference, eye movements and oculomotor delays. Biological Cybernetics, 108, 777–801. doi: 10.1007/s00422-014-0620-8
   PubMed Web of Science ®Google Scholar
• Pertzov, Y., Avidan, G., & Zohary, E. (2011). Multiple reference frames for saccadic planning in the human parietal cortex. The Journal of Neuroscience, 31, 1059–1068. doi: 10.1523/JNEUROSCI.3721-10.2011
   PubMed Web of Science ®Google Scholar
• Phillips, W. A., & Singer, W. (1997). In search of common foundations for cortical computation. Behavioral and Brain Sciences, 20, 657–722. doi: 10.1017/S0140525X9700160X
   PubMed Web of Science ®Google Scholar
• Pola, J. (2011). An explanation of perisaccadic compression of visual space. Vision Research, 51, 424–434. doi: 10.1016/j.visres.2010.12.010
   PubMed Web of Science ®Google Scholar
• Pouget, A., Dayan, P., & Zemel, R. S. (2003). Inference and computation with population codes. Annual Review of Neuroscience, 26, 381–410. doi: 10.1146/annurev.neuro.26.041002.131112
   PubMed Web of Science ®Google Scholar
• Pouget, A., Deneve, S., & Duhamel, J. R. (2002). A computational perspective on the neural basis of multisensory spatial representations. Nature Reviews Neuroscience, 3, 741–747. doi: 10.1038/nrn914
   PubMed Web of Science ®Google Scholar
• Pouget, A., & Sejnowski, T. J. (1994). A neural model of the cortical representation of egocentric distance. Cerebral Cortex, 4, 314–329. doi: 10.1093/cercor/4.3.314
   PubMed Web of Science ®Google Scholar
• Pouget, A., & Sejnowski, T. J. (1997). Spatial transformations in the parietal cortex using basis functions. Journal of Cognitive Neuroscience, 9, 222–237. doi: 10.1162/jocn.1997.9.2.222
   PubMed Web of Science ®Google Scholar
• Pouget, A., & Snyder, L. (2000). Computational approaches to sensorimotor transformations. Nature Neuroscience, 3(supplement), 1192–1198. doi: 10.1038/81469
   PubMedGoogle Scholar
• Quaia, C., Optican, L. M., & Goldberg, M. E. (1998). The maintenance of spatial accuracy by the perisaccadic remapping of visual receptive fields. Neural Networks, 11, 1229–1240. doi: 10.1016/S0893-6080(98)00069-0
   PubMed Web of Science ®Google Scholar
• Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2, 79–87. doi: 10.1038/4580
   PubMed Web of Science ®Google Scholar
• Robinson, D. (1975). Oculomotor control signals. In G. Lennerstrand & P. Bach-Y-Rita (Eds.), Basic mechanisms of ocular motility and their clinical implications (pp. 337–378). Oxford, UK: Pergamon Press.
   Google Scholar
• Saeb, S., Weber, C., & Triesch, J. (2011). Learning the optimal control of coordinated eye and head movements. PLoS Computational Biology, 7(11), e1002253. doi: 10.1371/journal.pcbi.1002253
   PubMed Web of Science ®Google Scholar
• Salinas, E., & Abbott, L. F. (1995). Transfer of coded information from sensory to motor networks. The Journal of Neuroscience, 15, 6461–6474.
   PubMed Web of Science ®Google Scholar
• Salinas, E., & Abbott, L. F. (1996). A model of multiplicative neural responses in parietal cortex. Proceedings of the National Academy of Sciences USA, 93, 11956–11961. doi: 10.1073/pnas.93.21.11956
   PubMed Web of Science ®Google Scholar
• Salinas, E., & Sejnowski, T. J. (2001). Gain modulation in the central nervous system: Where behavior, neurophysiology and computation meet. The Neuroscientist, 7, 430–440. doi: 10.1177/107385840100700512
   PubMed Web of Science ®Google Scholar
• Schilling, R. J., Carroll, J. J., & Al-Ajlouni, A. F. (2001). Approximation of nonlinear systems with radial basis function neural networks. IEEE Transactions on Neural Networks, 12, 1–15. doi: 10.1109/72.896792
   PubMed Web of Science ®Google Scholar
• Schlag, J., Schlag-Rey, M., & Pigarev, I. (1992). Supplementary eye field: Influence of eye position on neural signals of fixation. Experimental Brain Research, 90, 302–306. doi: 10.1007/BF00227242
   PubMed Web of Science ®Google Scholar
• Schneegans, S., & Schöner, G. (2012). A neural mechanism for coordinate transformation predicts pre-saccadic remapping. Biological Cybernetics, 106, 89–109. doi: 10.1007/s00422-012-0484-8
   PubMed Web of Science ®Google Scholar
• Siegel, R. M., Raffi, M., Phinney, R. E., Turner, J. A., & Jando, G. (2003). Functional architecture of eye position gain fields in visual association cortex of behaving monkey. Journal of Neurophysiology, 90, 1279–1294. doi: 10.1152/jn.01179.2002
   PubMed Web of Science ®Google Scholar
• Smith, M., & Crawford, J. (2001). Self-organizing task modules and explicit coordinate systems in a neural network model for 3-D saccades. Journal of Computational Neuroscience, 10, 127–150. doi: 10.1023/A:1011264913465
   PubMed Web of Science ®Google Scholar
• Smith, M., & Crawford, J. (2005). Distributed population mechanism for the 3-D oculomotor reference frame transformation. Journal of Neurophysiology, 93, 1742–1761. doi: 10.1152/jn.00306.2004
   PubMed Web of Science ®Google Scholar
• Snyder, L. H., Grieve, K. L., Brotchie, P., & Andersen, R. A. (1998). Separate body- and world-referenced representations of visual space in parietal cortex. Nature, 394, 887–891. doi: 10.1038/29777
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2005). Learning viewpoint invariant perceptual representations from cluttered images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 753–761. doi: 10.1109/TPAMI.2005.105
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2008a). Predictive coding as a model of biased competition in visual selective attention. Vision Research, 48, 1391–1408. doi: 10.1016/j.visres.2008.03.009
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2008b). Reconciling predictive coding and biased competition models of cortical function. Frontiers in Computational Neuroscience, 2, 1–8. doi: 10.3389/neuro.10.004.2008
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2009). Learning posture invariant spatial representations through temporal correlations. IEEE Transactions on Autonomous Mental Development, 1, 253–263. doi: 10.1109/TAMD.2009.2038494
   Google Scholar
• Spratling, M. W. (2010). Predictive coding as a model of response properties in cortical area V1. The Journal of Neuroscience, 30, 3531–3543. doi: 10.1523/JNEUROSCI.4911-09.2010
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2011). A single functional model accounts for the distinct properties of suppression in cortical area V1. Vision Research, 51, 563–576. doi: 10.1016/j.visres.2011.01.017
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2012a). Predictive coding accounts for V1 response properties recorded using reverse correlation. Biological Cybernetics, 106, 37–49. doi: 10.1007/s00422-012-0477-7
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2012b). Predictive coding as a model of the V1 saliency map hypothesis. Neural Networks, 26, 7–28. doi: 10.1016/j.neunet.2011.10.002
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2012c). Unsupervised learning of generative and discriminative weights encoding elementary image components in a predictive coding model of cortical function. Neural Computation, 24, 60–103. doi: 10.1162/NECO_a_00222
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2013). Image segmentation using a sparse coding model of cortical area V1. IEEE Transactions on Image Processing, 22, 1631–1643. doi: 10.1109/TIP.2012.2235850
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2014a). Classification using sparse representations: A biologically plausible approach. Biological Cybernetics, 108, 61–73. doi: 10.1007/s00422-013-0579-x
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2014b). A single functional model of drivers and modulators in cortex. Journal of Computational Neuroscience, 36, 97–118. doi: 10.1007/s10827-013-0471-7
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2016a). A neural implementation of Bayesian inference based on predictive coding. Connection Science, 28, 346–383. doi: 10.1080/09540091.2016.1243655
   Web of Science ®Google Scholar
• Spratling, M. W. (2016b). Predictive coding as a model of cognition. Cognitive Processing, 17, 279–305. doi: 10.1007/s10339-016-0765-6
   PubMed Web of Science ®Google Scholar
• Spratling, M. W. (2017). A review of predictive coding algorithms. Brain and Cognition, 112, 92–97. doi: 10.1016/j.bandc.2015.11.003
   PubMed Web of Science ®Google Scholar
• Spratling, M. W., De Meyer, K., & Kompass, R. (2009). Unsupervised learning of overlapping image components using divisive input modulation. Computational Intelligence and Neuroscience, 2009(381457), 1–19. doi: 10.1155/2009/381457
   Google Scholar
• Sun, G., & Scassellati, B. (2005). A fast and efficient model for learning to reach. International Journal of Humanoid Robotics, 2, 391–413. doi: 10.1142/S0219843605000569
   Google Scholar
• Templeman, J. N., & Loew, M. H. (1989). Staged assimilation: A system for detecting invariant features in temporally coherent visual stimuli. In Proceedings of the international joint conference on Neural Networks (IJCNN89) (vol. 1, pp. 731–738). New York, NY: IEEE Press.
   Google Scholar
• Todorov, E. (2004). Optimality principles in sensorimotor control. Nature Neuroscience, 7, 907–915. doi: 10.1038/nn1309
   PubMed Web of Science ®Google Scholar
• Tomlinson, R. D., & Bahra, P. S. (1986). Combined eye-head gaze shifts in the primate. I. Metrics. Journal of Neurophysiology, 56, 1542–1557. doi: 10.1152/jn.1986.56.6.1542
   PubMed Web of Science ®Google Scholar
• Tweed, D. (1997). Three-dimensional model of the human eye-head saccadic system. Journal of Neurophysiology, 77, 654–666. doi: 10.1152/jn.1997.77.2.654
   PubMed Web of Science ®Google Scholar
• Tweed, D., Glenn, B., & Vilis, T. (1995). Eye-head coordination during large gaze shifts. Journal of Neurophysiology, 73, 766–779. doi: 10.1152/jn.1995.73.2.766
   PubMed Web of Science ®Google Scholar
• Umeno, M. M., & Goldberg, M. E. (1997). Spatial processing in the monkey frontal eye field. I. Predictive visual responses. Journal of Neurophysiology, 78, 1373–1383. doi: 10.1152/jn.1997.78.3.1373
   PubMed Web of Science ®Google Scholar
• van Hemmen, J. L., & Schwartz, A. B. (2008). Population vector code: A geometric universal as actuator. Biological Cybernetics, 98, 509–518. doi: 10.1007/s00422-008-0215-3
   PubMed Web of Science ®Google Scholar
• van Rossum, M. C. W., & Renart, A. (2004). Computation with populations codes in layered networks of integrate-and-fire neurons. Neurocomputing, 58–60, 265–270. doi: 10.1016/j.neucom.2004.01.054
   Web of Science ®Google Scholar
• Wallis, G. (1996). Using spatio-temporal correlations to learn invariant object recognition. Neural Networks, 9, 1513–1519. doi: 10.1016/S0893-6080(96)00041-X
   PubMed Web of Science ®Google Scholar
• Weber, C., Elshaw, M., Triesch, J., & Wermter, S. (2007). Neural control of actions involving different coordinate systems. In M. Hackel (Ed.), Humanoid robots: Human-like machines. Vienna, Austria: I-Tech Education and Publishing.
   Google Scholar
• Weber, C., & Wermter, S. (2007). A self-organizing map of sigma-pi units. Neurocomputing, 70, 2552–2560. doi: 10.1016/j.neucom.2006.05.014
   Web of Science ®Google Scholar
• Westheimer, G. (1954). Eye movement responses to a horizontally moving visual stimulus. Archives of Ophthology, 52, 932–941. doi: 10.1001/archopht.1954.00920050938013
   PubMed Web of Science ®Google Scholar
• Wetter, S. M. C. I. V., & Opstal, A. J. V. (2008). Experimental test of visuomotor updating models that explain perisaccadic mislocalization. Journal of Vision, 8, 8. doi: 10.1167/8.14.8
   PubMed Web of Science ®Google Scholar
• Wolpert, D. M., & Kawato, M. (1998). Multiple paired forward and inverse models for motor control. Neural Networks, 11, 1317–1329. doi: 10.1016/S0893-6080(98)00066-5
   PubMed Web of Science ®Google Scholar
• Wolpert, D. M., Miall, R. C., & Kawato, M. (1998). Internal models in the cerebellum. Trends in Cognitive Sciences, 2, 338–347. doi: 10.1016/S1364-6613(98)01221-2
   PubMed Web of Science ®Google Scholar
• Wurtz, R. H. (2008). Neuronal mechanisms of visual stability. Vision Research, 48, 2070–2089. doi: 10.1016/j.visres.2008.03.021
   PubMed Web of Science ®Google Scholar
• Xing, J., & Andersen, R. A. (2000a). Memory activity of LIP neurons for sequential eye movements simulated with neural networks. Journal of Neurophysiology, 84, 651–665. doi: 10.1152/jn.2000.84.2.651
   PubMed Web of Science ®Google Scholar
• Xing, J., & Andersen, R. A. (2000b). Models of the posterior parietal cortex which perform multimodal integration and represent space in several coordinate frames. Journal of Cognitive Neuroscience, 12, 601–614. doi: 10.1162/089892900562363
   PubMed Web of Science ®Google Scholar
• Zhang, P.-Y., Lü, T.-S., & Song, L.-B. (2005). RBF networks-based inverse kinematics of 6R manipulator. The International Journal of Advanced Manufacturing Technology, 26, 144–147. doi: 10.1007/s00170-003-1988-0
   Web of Science ®Google Scholar
• Ziesche, A., & Hamker, F. H. (2011). A computational model for the influence of corollary discharge and proprioception on the peri-saccadic mislocalization of briefly presented stimuli in complete darkness. The Journal of Neuroscience, 31, 17392–17405. doi: 10.1523/JNEUROSCI.3407-11.2011
   PubMed Web of Science ®Google Scholar
• Ziesche, A., & Hamker, F. H. (2014). Brain circuits underlying visual stability across eye movements – converging evidence for a neuro-computational model of area LIP. Frontiers in Computational Neuroscience, 8, 25. doi: 10.3389/fncom.2014.00025
   PubMed Web of Science ®Google Scholar
• Zipser, D., & Andersen, R. A. (1988). A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons. Nature, 331(6158), 679–684. doi: 10.1038/331679a0
   PubMed Web of Science ®Google Scholar