Vector reconstruction from firing rates

  • Emilio Salinas
  • L. F. Abbott
Article

Abstract

In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons.

Keywords

Firing Rate Visual Motion Motion Perception Tuning Curve Place Cell 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altes R.A. (1989) Ubiquity of hyperacuity. J. Acoust. Soc. Am. 85:943–952.Google Scholar
  2. Bacon J.P. and Murphey R.K. (1984) Receptive fields of cricket (Acheta domesticus) interneurons are related to their dendritic structure. J. Physiol. (Lond.) 272:779–797.Google Scholar
  3. Baldi P., Heiligenberg W. (1988) How sensory maps could enhance resolution through ordered arrangements of broadly tuned receivers. Biol. Cybern. 59:313–318.Google Scholar
  4. Bialek W. (1989) Theoretical physics meets experimental neurobiology. In: Jen E, ed. Lectures in Complex Systems, SFI Studies in the Science of Complexity, Vol. 2. Addison-Wesley, Redwood City CA. pp. 413–595.Google Scholar
  5. Bialek W., Rieke F., de Ruyter van Steveninck R.R., Warland, D. (1991) Reading a neural code. Science 252:1854–1857.Google Scholar
  6. Burnod Y., Grandguillaume P., Otto, I., Ferraina S., Johnson P.B., Caminiti R. (1992) Visuomotor transformation underlying arm movements toward visual targets: A neural network model of cerebral cortical operations. J. Neurosci. 12:1435–1452.Google Scholar
  7. Camhi J.M., Levy A. (1989) The code for stimulus direction in a cell assembly in the cockroach. J. Comp. Physiol. A165:83–97.Google Scholar
  8. Camhi, J.M. and Tom, W. (1978) The escape behavior of the cockroach Periplaneta americana I. Tuning response to wind puffs. J. Comp. Physiol. A128:193–201.Google Scholar
  9. Caminiti R., Johnson P.B., Galli C., Ferraina S., Burnod Y. (1991) Making arm movements within different parts of space: The premotor and motor cortical representations of a coordinate system for reaching to visual targets. J. Neurosci. 11:1182–1197.Google Scholar
  10. Chen L.L., McNaughton B.L., Barnes C.A., Ortiz E.R. (1990) Head-directional and behavioral correlates of posterior cingulate and medial prestriate cortex neurons in freely-moving rats. Soc. Neurosci. Abst. 16:441.Google Scholar
  11. Churchland P.S., Sejnowski T.J. (1992) The Computational Brain. MIT Press, Cambridge MA.Google Scholar
  12. Eichenbaum H. (1993) Thinking about brain cell assemblies. Science 261:993–994.Google Scholar
  13. Foldiak P. (1993) The ideal homunculus: statistical inference from neural population responses. In: Eeckman F.H. and Bower J., eds. Computation and Neural Systems. Kluwer Academic Publishers, Norwell MA. pp. 55–60.Google Scholar
  14. Foldiak P. (1991) Models of Sensory Coding. Cambridge Univ. Ph.D. Thesis.Google Scholar
  15. Portier P.A., Kalaska J.F., Smith A.M. (1989) Cerebellar neuronal activity related to whole-arm reaching movements in the monkey. J. Neurophysiol. 62:198–211.Google Scholar
  16. Georgopoulos A.P., Kettner R.E., Schwartz A. (1988) Primate motor cortex and free arm movements to visual targets in three-dimensional space. II. Coding of the direction of movement by a neuronal population. Neurosci. 8:2928–2937.Google Scholar
  17. Georgopoulos A.P., Lurito J.T., Petrides M., Schwartz A., Massey J.T. (1989) Mental rotation of the neuronal population vector. Science 243:234–236.Google Scholar
  18. Georgopoulos A.P., Schwartz A. and Kettner R.E. (1986) Neuronal population coding of movement direction. Science 233:1416–1419.Google Scholar
  19. Georgopoulos A.P., Taira M, Lukashin A. (1993) Cognitive neurophysiology of the motor cortex. Science 260:47–52.Google Scholar
  20. Gilbert C.D., Wiesel T.N. (1990) The influence of contextual stimuli on the orientation selectivity of cells in primary visual cortex of the cat. Vision Res. 30:1689–1701.Google Scholar
  21. Gozani S.N., Miller J.P. (1993) Ensemble coding of information by eight primary sensory interneurons in the cricket cercal system (in preparation).Google Scholar
  22. Kalaska J.F., Caminiti R., Georgopoulos A.P. (1983) Cortical mechanisms related to the direction of two-dimensional arm movements: relations in parietal area 5 and comparison with motor cortex. Exp. Brain. Res. 51:247–260.Google Scholar
  23. Kiefer J.C. (1987) Introduction to Statistical Inference. Springer-Verlag, NY.Google Scholar
  24. Knudsen E.I., DuLac S., Esterly S.D. (1987) Computational maps in the brain. Annu. Rev. Neurosci. 10:41–65.Google Scholar
  25. Konishi M. (1987) Centrally synthesized maps of sensory space. Trends Neurosci. 9:163–168.Google Scholar
  26. Lee C, Rohrer W.H., Sparks D.L. (1988) Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332:357–360.Google Scholar
  27. Lehky S.R., Sejnowski T.J. (1990) Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity. J. Neurosci. 10:2281–2299.Google Scholar
  28. Linsker R. (1993) Local synaptic learning rules suffice to maximize mutual information in a linear network. Neural Comp. 4:691–702.Google Scholar
  29. Lukashin, A.V. (1990) A learned neural network that simulates properties of the neural population vector. Biol. Cybern. 63:377–382.Google Scholar
  30. Miller J.P., Jacobs G.A., Theunissen F. (1991) Representation of sensory information in the cricket cercal sensory system. I. Response properties of the primary interneurons. J. Neurophysiol. 66:1680–1689.Google Scholar
  31. O'Keefe J., Nadel L. (1978) The Hippocampus as a Cognitive Map. Clarendon, Oxford.Google Scholar
  32. Oneill W.E., Suga N. (1982) Encoding of target range information and its representation in the auditory cortex of the mustache bat. J. Neurosci. 2:17–31.Google Scholar
  33. Optican L.M., Richmond B.J. (1987) Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex III. Information theoretic analysis. J. Neurophysiol. 57:163–178.Google Scholar
  34. Paradiso M.A. (1988) A theory for the use of visual orientation information which exploits the columnar structure of striate cortex. Biol. Cybern. 58:35–49.Google Scholar
  35. Rieke F.M. (1991) Physical Principles Underlying Sensory Processing and Computation. Univ. of California Berkeley PhD Thesis.Google Scholar
  36. Schwartz A., Kettner R.E., Georgopoulos A.P. (1988) Primate motor cortex and free arm movements to visual targets in three-dimensional space. I. Relations between single cell discharge and direction of movement. J. Neurosci. 8:2913–2927.Google Scholar
  37. Sejnowski T.J. (1988) Neural populations revealed. Nature 332:308.Google Scholar
  38. Seung H.S., Sompolinsky H. (1993) Simple neural network models of psychophysical tasks. Proc. Natl. Acad. Sci. (USA) (in press).Google Scholar
  39. Shor R.H., Miller A.D., Tomko D.L. (1984) Responses to head tilt in cat central vestibular neurons. I. Direction of maximum sensitivity. J. Neurophysiol. 51:136–146.Google Scholar
  40. Snippe H.P., Koenderink J.J. (1992) Discrimination thresholds for channel-coded systems. Biol. Cybern. 66:543–551.Google Scholar
  41. Steinmetz M.A., Motter B.C., Duffy C.J., Mountcastle V.B. (1987) Functional properties of parietal visual neurons: Radial organization of directionalities with the visual field. J. Neurosci. 7:177–191.Google Scholar
  42. Suga N., Horikawa J. (1986) Multiple time axes for representation of echo delays in the auditory cortex of the mustached bat. J. Neurophysiol. 55:776–805.Google Scholar
  43. Suzuki I., Timerick J.B., Wilson V.J. (1985) Body position with respect to the head or body position in space is coded in lumbar interneurons. J. Neurophysiol. 54:123–133.Google Scholar
  44. Taube J.S., Muller R.I., Ranck J.B.J. (1990) Head direction cells recorded from the postsubicullum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10:420–435.Google Scholar
  45. Theunissen F. (1993) An Investigation of Sensory Coding Principles Using Advanced Statistical Techniques. Univ. of California Berkeley PhD Thesis.Google Scholar
  46. Theunissen F., Miller J.P. (1991) Representation of sensory information in the cricket cercal sensory system. II. Information theoretic calculation of system accuracy and optimal tuning-curve widths of four primary interneurons. J. Neurophysiol. 66:1690–1703.Google Scholar
  47. Touretzky D.S., Redish A.D., Wan H.S. (1993) Neural representation of space using sinusoidal arrays. Neural Comp. 5:869–884.Google Scholar
  48. Van Gisbergen J.A.M., Van Opstal A.J., Tax A.M.M. (1987) Collicular ensemble coding of saccades based on vector summation. Neuroscience 21:541–555.Google Scholar
  49. Van Opstal A.J., Kappen H. (1993) A two-dimensional ensemble coding model for spatial-temporal transformation of saccades in monkey superior colliculus. Network 4:19–38.Google Scholar
  50. Vogels R. (1990) Population coding of stimulus orientation by cortical cells. J. Neurosci 10:3543–3558.Google Scholar
  51. Warland D., Landolfa M.A., Miller J.P., Bialek W. (1991) Reading between the spikes in the cercal filiform hair receptors of the cricket. In: Eeckman F. and Bower J., eds. Analysis and Modeling of Neural Systems. Kluwer Academic Publishers, Norwell, MA.Google Scholar
  52. Wilson M.A., McNaughton B. (1993) Dynamics of the hippocampal ensemble code for space. Science 261:1055–1058.Google Scholar
  53. Young M.P., Yamane S. (1992) Sparse population coding of faces in the inferotemporal cortex. Science 256:1327–1331.Google Scholar
  54. Zhang J., Miller J.P. (1991) A mathematical model for resolution enhancement in layered sensory systems. Biol. Cybern. 64:357–364.Google Scholar
  55. Zohary E. (1992) Population coding of visual stimuli by cortical neurons tuned to more than one dimension. Biol. Cybern. 66:265–272.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Emilio Salinas
    • 1
  • L. F. Abbott
    • 1
  1. 1.Biology Department and Center for Complex SystemsBrandeis UniversityWaltham

Personalised recommendations